Dialogue about Systems

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Author: Shelia Guberman

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The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

Open Access Publications


Dialogue about Systems

Polimetrica


Shelia Guberman, Gianfranco Minati

International Scientific Publisher


2007 Polimetrica ® S.a.s. Corso Milano, 26 20052 Monza – Milano Phone ++39. 039.2301829 Web site: www.polimetrica.com Cover project by Arch. Diego Recalcati ISBN 978-88-7699-061-8 Printed Edition ISBN 978-88-7699-062-5 Electronic Edition The electronic edition of this book is not sold and is made available in free access. This book is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.


Dedication “To Evelyne who understands good science and good people”



Contents 1 Starting the Dialogue Msg.1 Two basic statements on systems Msg.2 Role of the observer . . . . . . . . Msg.3 The observer disappears! . . . . . Msg.4 A lot to learn . . . . . . . . . . . Msg.5 You are wrong! . . . . . . . . . . Attachment 1 . . . . . . . . . . . . . . .

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2 Partitioning the whole Msg.6 Symbolic vs. Sub-symbolic . . . . . . . . . . . . . . . . Msg.7 Do you agree the observer has to decide? . . . . . . . . Msg.8 Modelling and generalizing . . . . . . . . . . . . . . . . Msg.9 Observer and description are basic to my understanding of systems . . . . . . . . . . . . . . . . . . . . . . . . . Msg.10 Effective thinking . . . . . . . . . . . . . . . . . . . . Msg.11 Thank you for pointing out my mistake . . . . . . . . Msg.12 When elements are autonomous systems . . . . . . . Attachment 2 . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 Nine agreements Msg.13 Excellent! . . . . . . . . . . . . . . . . . . . . Msg.14 Forget about flocks . . . . . . . . . . . . . . Msg.15 How to measure the success of our model . . Msg.16 Managing system behavior . . . . . . . . . . Msg.17 Something bigger than science - life itself . . Msg.18 The effectiveness of modelling and simulating Msg.19 Prof. Wita Wojtkowski . . . . . . . . . . . . Msg.20 I’m glad . . . . . . . . . . . . . . . . . . . .

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Msg.21 Step 5: Reviewing and reconstructing the model . . . Msg.22 A meta-level approach . . . . . . . . . . . . . . . . . . Msg.23 Modifying the system: add the observer and/or expand the object . . . . . . . . . . . . . . . . . . . . . Msg.24 History of mathematics . . . . . . . . . . . . . . . . . Msg.25 Back to the salt mines . . . . . . . . . . . . . . . . . . Msg.26 Ergodic systems, fluctuations . . . and Damn the Details! Msg.27 From Galileo to Kepler . . . . . . . . . . . . . . . . . Msg.28 Knowing ”how” and knowing ”why” . . . . . . . . . . Msg.29 There is nothing better for practice than a good theory Msg.30 Sapir-Whorf hypothesis and explaining . . . . . . . . Msg.31 Levels of description . . . . . . . . . . . . . . . . . . . Attachment 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 A first balance Msg.32 Theory is not a theory about Nature Mind . . . . . . . . . . . . . . . . . . Msg.33 When Nature understands itself . . . Msg.34 Lack of a Theory of Emergence . . . . Msg.35 Sorry about my engineering mind . . Msg.36 Observer-oriented . . . . . . . . . . . Msg.37 Let’s summarize . . . . . . . . . . . . Msg.38 Adding practical examples . . . . . . Attachment 4 . . . . . . . . . . . . . . . . . .

52 53 55 57 58 59 63 65 68 71 72 74 81

but about the . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81 81 82 85 86 87 88 88

5 How they interact vs. what they are 97 Msg.39 Publishing our Dialogue . . . . . . . . . . . . . . . . . 97 Msg.40 The interpretation of the Parts depends upon the Whole 98 Msg.41 An Abductive way of thinking . . . . . . . . . . . . . 99 Msg.42 Measuring my scientific achievement on the Mozart Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Msg.43 Multiple belonging and emergence . . . . . . . . . . . 104 Msg.44 Reductionism - a terminology problem? . . . . . . . . 108 Msg.45 Is the term linear applicable to systems defined only by formulae? . . . . . . . . . . . . . . . . . . . . . . 109 Msg.46 When processes of emergence are reduced to linear combinations of properties . . . . . . . . . . . . . . . 111 Attachment 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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6 A concluding case 119 Msg.47 I have to fill these expressions with some particular content . . . . . . . . . . . . . . . . . . . . . . . . . 119 Msg.48 Logical rather than mathematical representation . . . 120 7 Concluding Remarks

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A ”GENERAL SYSTEM THEORY” AS ”THEORY OF EMERGENCE” 131 A.1 The paradox of a General System Theory without emergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 A.1.1 Reductionist usage of the concept of system . . . 134 A.1.2 Von Bertalanffy’s view . . . . . . . . . . . . . . . 135 A.1.3 Emergence: a non-reductionist usage of the concept of system . . . . . . . . . . . . . . . . . . . 136 A.1.4 Emergence and General System Theory . . . . . 138 A.1.5 Inter- and Trans-disciplinarity . . . . . . . . . . . 139 A.2 General System Theory and Emergence . . . . . . . . . 140 B Evolution of the ”good continuation” principle B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . B.2 Good continuation - what does it mean? . . . . . . . . . B.3 Wertheimer . . . . . . . . . . . . . . . . . . . . . . . . . B.4 Kohler . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.5 Arnheim . . . . . . . . . . . . . . . . . . . . . . . . . . . B.6 The Imitation Principle and the Spirit of Gestalt psychology . . . . . . . . . . . . . . . . . . . . . . . . . . . B.7 Art and technology . . . . . . . . . . . . . . . . . . . . . B.7.1 Handwriting . . . . . . . . . . . . . . . . . . . . B.7.2 Art . . . . . . . . . . . . . . . . . . . . . . . . . . B.8 Bad continuation . . . . . . . . . . . . . . . . . . . . . .

147 147 148 151 154 156

C Wholes and parts – analysis of concepts C.1 Wholeness . . . . . . . . . . . . . . . . . . . . C.2 What are parts of the whole? . . . . . . . . . C.3 Do the parts depend upon the whole? . . . . C.4 Is the whole more than the sum of its parts? C.5 Algorithmic approach to partition . . . . . . C.6 Conclusions . . . . . . . . . . . . . . . . . . . Addendum ”Damn the details” (DD) algorithm . .

175 176 177 179 181 184 186 186

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S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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Preface Dialogue comes from the Greek composite word Dialogos. Dia means through and logos stands for meaning. The contemporary meaning is closer to dia and legein meaning speak : the sense is then broadened to conversation. Confusion between the roots dia and di led to the mistaken understanding of Dialogue as a conversation between only two subjects. Instead of presenting conclusive results as in treatises, manuals and textbooks, here the form of the dialogue has been used to offer the reader knowledge in an open way, i.e., to accompany the authors along the path of argument, creation and discovery. The focus is on the process as well as on the results. That is why the word Dialogue was used. Plato‘s Dialogues is the founding work of this approach, while Galileo‘s Dialogo sui Massimi Sistemi is also the founding work of science. In one way it is always a good strategy to be inspired by giants, in another we really did establish a dialogue between us. In this sense, this dialogue is not a literary form in itself, but a good combination of a real process of interaction with an excellent and suitable literary form. In our view, the form of dialogue is appropriate for a cultural enterprise just as systemic thinking is. The process of the production of systemic thinking should still focus more on the process itself rather than on results. There is still an enormous amount of work necessary for the theoretical formulation of strategy and purpose as well as for defining the role of disciplinary knowledge for inter- and trans-disciplinarity. We have to set up a theoretically robust framework for generalizing, rather than making generic based on disciplinary knowledge as a necessary condition. We did not start with the idea of presenting to the reader the results of our dialogue. The dialogue presented here was a real dialogue not only producing cognitive results but, being a real dialogue, also the birth of a friendship, that is a continuous dialogue (based on thinking how the other could react to something even though not physically present) between us. The target audience are those who find themselves dissatisfied with the strategy of going deeper and deeper into single disciplinary knowledge and collecting different disciplinary knowledge. We invite these readers to join us.

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Chapter 1 Starting the Dialogue

Msg.1 Two basic statements on systems From: Shelia Subject: Your paper

Date: 09 Oct 2005

Dear Gianfranco, I was very impressed with our discussions that lovely evening we spent together at Evelyne‘s home. I returned to California and read your paper again. First of all, I would like to express my deep satisfaction with two basic statements you made in your presentation (see Appendix A): Statement 1: Emergence is a process that can only be considered as observer-dependent.

This was von Bertalanffy‘s biggest mistake when he decided to build the theory of systems as a regular physical science, which excludes the presence of a subject, a human mind. Statement 2: There is a crucial difference between man-made systems (such as the electrical power network of Europe, or a computer) and natural systems (such as the economy, or a living body).

The explanation of this latter fact derives from Statement 1. Because we are not dealing with systems in nature, but with the systems in our mind (i.e., with the description of the system, with the model of the system), the first problem is: how should the whole be divided into parts. In the case of artificial systems we know the design, we know 1

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from which parts it was assembled, we know the relationships between the parts. In the case of natural objects the representation of the whole system is not available, we have to choose an adequate partition between an infinite number of possible partitions. Here is the challenge, here is the battlefield for Systems Theory. In my opinion this is the first time in the history of Systems Science where a systems scientist has faced up to the real problems and recognized the main problems of Systems Theory. At the same time the paper has raised a number of questions, and some issues have to be clarified. Here are some quotes from your paper with my comments. [from Appx. A: . . . 2.1 Reductionist usage of the concept of system The concept of system is often used in a way that we may consider to be reductionist. On this subject let us recall, in short, that: 1) Set is intended as a group of elements having a rule of belonging, allowing one to decide whether an element belongs to it or not. 2) Structure is intended as given by relationships among components, such as order, ratio, and connection; . . . ]

Structure is always defined over a set of elements. So, it would be appropriate to say: Structure is given by relationships among a set’s elements. [from Appx A: . . . 3) Organisation is intended as given by behavioral rules for elements, such as prioritising, synchronising and selecting; 4) Interaction between elements takes place when the behavior of one influences that of another, . . . ]

Because you didn’t define the term ”behavior” it is difficult to apply the common meaning of the word ”interaction”. For example, the ”behavior” of planets (the elements) is described by 1) the position, and 2) the velocity. But these two parameters do not influence the other’s behavior. The two parameters, which do influence the other’s behavior are 1) relative position, and 2) mass. Moreover, when a heavy body is placed on support there is an interaction between them: the gravitational force of the body is applied to the support, and the reaction force is applied to the body, but nothing moves - no behavior. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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[from Appx A: . . . 2.2 Von Bertalanffy’s view Von Bertalanffy, introduced the concept of system as being constituted of interacting elements Pi (i = 1, 2, . . . , n). Let us briefly recall his approach. Consider a measure Qi for elements Pi . In a system S any variation of Qi is a function of all other variations Qi . In the same way variation of a measure Qi induces variations in all other Qi . . . . ]

This is not correct: the equation states that the variation in Qi dQi /dt is a function of all other Qi and is not a function of all other variations - dQi /dt [from Appx A: . . . Interdependence is general and not related to particular roles in organisations and structures. . . . ]

What does this mean? [from Appx A: . . . How do the interacting elements transform into a new reality (i.e., system) - different from a machine, structure or organisation (such as flocks, swarms, industrial districts and traffic)? . . . ]

This means that interacting elements do not constitute a system. Is that your point? [from Appx A: . . . 2.3 Emergence: a non-reductionist usage of the concept of system What is emergence and why is it so important in modern cultural and scientific approaches? A formal definition of emergent properties has been introduced by [Baas and Emmeche, 1997]: ”Let {Sj }j ∈ I be a family of general systems or ”agents”. . . . ” ]

We don’t have a definition of system, nor do we know what a ”general system” is. There is no definition of ”agent” and substitution of one undefined notion by another undefined notion gets us nowhere. [from Appx A: . . . ”Let Obs1 be ”observation” mechanisms and Int1 be interactions between agents. The observation mechanisms measure the properties of the agents to be used in the interactions. . . . ]

The property can be measured using different means (for example, the mass can be measured with scales, or dynamically, as a reaction on a known force - it follows from the equivalence of the inertial mass and the gravitational mass). But it will not change the behavior of the system. So Obs1 has to be the measure of the property. The interaction Int1 is defined as interactions between agents, i.e., between general systems, which are considered as ”wholes”, as objects. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Now I don’t see the difference between S2 = R (Si , Obs1 , Int1 ) and von Bertalanffy’s system mentioned above - it also has interacting objects Pi , measures of properties Qi , and an interaction function f . [from Appx A: . . . This could be a stable pattern or a dynamically interacting system. We call an emergent structure which may be subject to new observational mechanisms. This leads to the following definition: Property P of S2 is emergent if and only if it is observable on S2 but not at a lower level, i.e., at the S1 level.” For instance, while observing the behavior of a group of people or cars, the flight patterns of a group of birds, one might conclude that they respectively form a crowd, traffic jam and flock (property P ). The property P , not observable by looking at individual behavior, is said to be an emergent property of the group. . . . ]

I would be completely satisfied with the last sentence without the word emergent. What new meaning does it add? Of course, P - the predicate, which describes the relation between two elements - could not be observed or measured on one element of the set. Best wishes, Shelia Guberman

Msg.2 Role of the observer From: Gianfranco Subject: Re: Your Paper

Date: 10 Oct 2005

Dear Shelia, Thank you very much for your interesting comments and appreciation. I was very pleased to have the opportunity to meet you and spend some time together for discussion. Following your presentation at the Conference in Paris [see Appendix B for Shelia’s full paper presented at the 2005 UES conference in Paris], I was very interested to check out my ideas with you. The approach based on the constructive, cognitive and creative role of S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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the observer, initiated by Uncertainty Principles in physics, has been introduced in contexts other than classical Systems Science, such as Gestalt, cognitive science and cognitive psychology. I appreciated very much, amongst all your other comments, those you made on Michelangelo’s Creation of Man (see Appendix B). The issue has been dealt with by scientists interested in emergence rather than Systems Science; see, for instance, [Baas and Emmeche, 1997], and [Bonabeau and Dessalles, 1997]. The point is that the role of the observer has been considered for emergence as being distinct from Systemics. Please find my responses to your comments below. From my paper [Appendix A]; [From Appx A: . . . 2.1 Reductionist usage of the concept of system The concept of system is often used in a way that we may consider to be reductionist. On this subject let us recall, in short, that: - Set is intended as a group of elements having a rule of belonging, allowing one to decide whether an element belongs to it or not. - Structure is intended as given by relationships among components, such as order, ratio, and connection . . . ]

Your comment: S. [ Msg.1 . . . Structure is always defined over a set of elements. So, it would be appropriate to say: Structure is given by relationships among a set’s elements. . . . ]

Yes. We may also consider structures of relationships and structures of structures. [from Appx A: . . . - Organisation is intended as given by behavioral rules for elements, such as prioritising, synchronising and selecting; - Interaction between elements takes place when the behavior of one influences that of another, . . . ] S. [Msg.1 . . . Because you didn’t define the term ”behavior” it is difficult to apply the common meaning of the word ”interaction”. For example, the ”behavior” of planets (the elements) is described by 1) the position, and 2) the velocity. But these two S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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parameters do not influence the other’s behavior. The two parameters, which do influence the other’s behavior are 1) relative position, and 2) mass. Moreover, when a heavy body is placed on support there is an interaction between them: the gravitational force of the body is applied to the support, and the reaction force is applied to the body, but nothing moves - no behavior. . . . ]

Behavior in general may be intended as a way of changing. Behavior of an entity (e.g., element, set, structure, system) in an environment may be intended as the changing of some variables describing its state. The observer is required during (e.g., changes in atmospheric conditions) or after (e.g., geological changes) for the process of detecting the changes. It is also possible to have an expected behavior. Behavior depends upon: • How the entity processes the input whether from itself and/or from the environment. For example, a glass processes the impact with a bullet by breaking, a living being may process fear. • What is considered as input by the cognitive model of the observer - e.g., an increase in temperature, caused the breakdown of a device, in an abductive way of thinking. More specifically: a) In the case of entities not equipped with a cognitive system, even simulated, we have reactions to an environment. Behaviorism, as introduced by Skinner, assumed this conceptual framework as being sufficient to explain human behavior (stimulus-response). b) In the case of elements equipped with a cognitive system, even simulated, the processing of the input is described not only by using the specific disciplinary level of description of physics, biology, chemistry, engineering, etc., but also by the cognitive system, as introduced by cognitive science (the novelty is that the element provided with a cognitive system processes not only external input, but internal input too by using cognitive models). In the computationalist approach cognitive systems and cognitive models are coincident with different hierarchical levels of software (for instance, operating systems and applications). In Systemics we are interested in behavior and interaction when interaction affects behavior. We may have interactions which do not affect behavior (your example related to gravity) and behavior not established by interactions (e.g., changes induced by time). S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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[from Appx A: . . . 2.2 Von Bertalanffy’s view Von Bertalanffy, introduced the concept of system as being constituted of interacting elements Pi (i = 1, 2, . . . , n). Let us briefly recall his approach. Consider a measure Q for elements Pi . In a system S any variation of Qi is a function of all other variations Qi . In the same way variation of a measure Qi induces variations in all other Qi . . . . ] S. [Msg.1 . . . This is not correct: the equation states that the variation in Qi dQi /dt is a function of all other Qi and is not a function of all other variations dQi /dt . . . ]

For some reason the symbol of system beside the equations disappeared in the version of the paper on the CD.  dQ1 /dt = f1 (Q1 , Q2 , ..., Qn )     dQ2 /dt = f2 (Q1 , Q2 , ..., Qn ) ..  .    dQn /dt = fn (Q1 , Q2 , ..., Qn ) [ from Appx A: . . . Interdependence is general and not related to particular roles in organisations and structures. . . . ] S. [Msg.1 . . . What does this mean? . . . ]

It means that systems may be established in at least in two ways: (a) In an organized way, i.e., in a network of pre-established relations or organizations, such as electronic circuits, mechanical devices and assembly-lines where components have specific functional roles, and (b) Through processes of self-organization identified with so-called order-disorder transitions, establishing, within suitable boundary conditions, ordered frameworks as systems, such as ferromagnetism, superconductivity and cognitive processing in collective behavior. The two cases are not rigidly separated: autonomous - equipped with cognitive system - agents may also interact as non-autonomous agents (e.g., military and civilian professional roles); in organizations it is also possible to have effects of self-organization (e.g., firms and teams) and in self-organized systems it is also possible to have organizational components (e.g., roles in ant-hills and beehives). S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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[from Appx A: . . . How do the interacting elements transform into a new reality (i.e., system) - different from a machine, structure or organisation (such as flocks, swarms, industrial districts and traffic)? . . . ] S. [Msg.1 . . . This means that interacting elements do not constitute a system. Is that your point? . . . ]

I mean that interacting seems to be a necessary but not sufficient condition for the emergence of systems. The Theory of Emergence is expected to clarify this point. I’m in the process of writing a paper with a colleague on this subject. [From Appx A: . . . 2.3 Emergence: a non-reductionist usage of the concept of system What is emergence and why is it so important in modern cultural and scientific approaches? A formal definition of emergent properties has been introduced by [Baas and Emmeche, 1997]: Let {Sj }j ∈ I be a family of general systems or ”agents”. . . . ] S. [Msg.1 . . . We don’t have a definition of system, nor do we know what a ”general system” is. There is no definition of ”agent” and substitution of one undefined notion by another undefined notion gets us nowhere. . . . ]

Structures (given by relationships among a set’s elements, as we said above) have properties different from those of its components (e.g., properties of materials, such as hardness, rigidity, and impermeability). A system is established when interacting elements make emergent (role of the observer) an entity having properties different and not deducible from those of its components. Examples of systemic properties, disappearing when interaction is stopped, are for instance: adaptive, anticipatory, autonomous, autopoietic, chaotic, complex, connectionist, deterministic, dissipative, equifinal, goal-seeking, homeostatic, openclosed, living, and self-organized. Examples of non-systemic properties, by assuming a suitable level of description, may be: weight and speed in physics or numerical properties in mathematics. Organization is a particular kind of explicitly designed structure within which elements interact for specific functional purposes (i.e., electronic and mechanical devices).



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A General System is obtained when considering systemic properties only, with no reference to specific disciplinary implementations, for instance anticipatory, autonomous, autopoietic, living, etc., systems are general systems. A family of General Systems is constituted by any kind of system having some common systemic property, for instance, being open and deterministic or a living being. An agent may be intended as a causal factor. It may be a system or not. I think that Baas and Emmeche intended General Systems to be such a conceptual framework to act even as causal factor such as agents having effects on behavior. The idea, I think, is that a system may be established by: 1. Interacting agents (e.g., devices established by components interacting when powered on); 2. Systems (e.g., flocks established by interacting systems, such as birds); 3. General systems, (i.e., systems having general systemic common properties, e.g., living beings, establishing a higher level of general system, such as social systems from living beings). [From Appx A: . . . ”Let {Si }i ∈ I be a family of general systems or ”agents”. Let Obs1 be ”observation” mechanisms and Int1 be interactions between agents. The observation mechanisms measure the properties of the agents to be used in the interactions” ...] S. [Msg.1 . . . The property can be measured using different means (for example, the mass can be measured with scales, or dynamically, as a reaction on a known force - it follows from the equivalence of the inertial mass and the gravitational mass). But it will not change the behavior of the system. So Obs1 has to be the measure of the property . . . ]

The interactions then generate a new kind of structure 1 S2 = R (Si , Obs1 , Int1 ) which is the result of the interactions.

S. [Msg.1 . . . The interaction Int1 is defined as interactions between agents, i.e., between general systems, which are considered as ”wholes”, as objects. Now I don’t see the difference between S2 = R (S1i , Obs1 , Int1 ) and von Bertalanffy’s system mentioned above - it also has interacting objects Pi , measures of properties Qi , and an interaction function f . . . . ]


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Differences from von Bertalanffy’s view are: The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

1) Functions f may not be explicitly known; 2) There is an explicitly, necessary reference to the observer; 3) From same interacting elements different systems may emerge (e.g., families, audience and markets from the same people), depending upon the cognitive model of the interacting elements and of the observer. S. [Msg.1 . . . First of all, I would like to express my deep satisfaction with two basic statements in your paper (see Appendix A): Statement 1: Emergence is a process that can only be considered as observer-dependent. This was von Bertalanffy‘s biggest mistake when he decided to build the theory of systems as a regular physical science, which excludes the presence of a subject, a human mind. Statement 2: There is a crucial difference between man-made systems (such as the electrical power network of Europe, or a computer) and natural systems (such as the economy, or a living body). The explanation of this latter fact derives from Statement 1. Because we are not dealing with systems in nature, but with the systems in our mind (i.e., with the description of the system, with the model of the system), the first problem is: how should the whole be divided into parts. In the case of artificial systems we know the design, we know from which parts it was assembled, we know the relationships between the parts. In the case of natural objects the representation of the whole system is not available, we have to choose an adequate partition between an infinite number of possible partitions. Here is the challenge, here is the battlefield for Systems Theory. . . . ]

Yes, the systemic view relates to cognitive approaches: we do not discover in an objectivist way only, but think that something does, in a way, depend upon how effective it is to think in this way. S. [Msg.1 . . . In my opinion this is the first time in the history of System Science where a system scientist has faced up to the real problems and recognized the main problems of Systems Theory. ...] S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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I’m very pleased with your appreciation. With a co-author, we recently introduced some related issues, such as the Dynamical Usage of Models (DYSAM) and the concept of ”Collective Beings” (when the same elements simultaneously give rise to different systems, by interacting in different ways and through simultaneous usage of different cognitive models) [Minati and Pessa, 2006]. I’ll send you a copy. I think we should now speak of a Theory of Emergence rather than of General System Theory 1 . In my opinion we will not reach a comprehensive Theory of Emergence until we are able to solve the following problem which, if I understood your presentation, you mentioned in your talk in Paris, which I appreciated very much: In order to model processes of emergence researchers use computational tools, such as Neural Networks, Cellular Automata, Genetic Algorithms and agent-based models. These are very useful tools to artificially reproduce, in a conceptually analogical way, processes of emergence. In any case, this approach is completely dependent upon computers: instead of theoretical considerations, there are computational steps (What if Simplicio had had computers available?2 ). [From Appx A: . . . For instance, while observing the behavior of a group of people or cars, the flight patterns of a group of birds, one might conclude that they respectively form a crowd, traffic jam and flock (property P ). The property P , not observable by looking at individual behavior, is said to be an emergent property of the group. . . . ] S. [ Msg.1 . . . I would be completely satisfied with the last sentence without the word emergent. What new meaning does it add? Of course, P - the predicate, which describes the relation between two elements - could not be observed or measured on one element of the set. . . . ]

I had in mind the three points listed above regarding the differences from von Bertalanffy’s view (Msg.2). Best wishes, Gianfranco 1 I titled the proceedings of the third conference of the Italian Systems Society having this topic in mind: Minati, G., Pessa, E., and Abram, M. (eds.), Systemics of Emergence: Research and Development, Springer, 2006. See: http://www.springeronline.com/sgw/cda/frontpage/0,11855,4-40109-2272684205-0,00.html 2 A colleague made this point during a discussion of the same issues.



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Msg.3 The observer disappears! The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

From: Shelia Date: 12 Oct 2005 Subject: Re: Your paper

Dear Gianfranco, Thanks for your reply. There are a lot of things to discuss, and I would like to learn a lot from you. I suggest we go ahead taking small steps. This is what I suggest for our discussion today. If I understand you correctly, behavior requires an observer, i.e., behavior consists of changes described by the observer. I like that definition very much. It is in agreement with the term expected behavior, because the observer may already have ideas about the behavior of that kind of object from his/her past experience. But to me such an understanding of behavior contradicts some of your statements: G. [From Msg.2: . . . 1. behavior in general may be intended as a way of changing . . . ]

Here the observer disappears! G. [From Msg.2: . . . 2. ”behavior may be intended as the changing of some variables”. . . . ]

Once more - the observer disappears! Sincerely, Shelia

Msg.4 A lot to learn From: Gianfranco Date: 13 Oct 2005 Subject: Your comments and more

Dear Shelia, Yes, we have a lot to discuss. I think I have a lot to learn from you. I like to think that the more I learn from you, the more you learn from me and viceversa. With reference to your comments: S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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S. [Msg.2: . . . But to me such an understanding of behavior contradicts some of your statements: 1. behavior in general may be intended as a way of changing. Here the observer disappears! . . . ]

When we speak of a ”way of changing” and not only of ”changing” we need an observer modelling the ”way” and not just to detect the changing. In my view ”modeling way of changing” is an abductive process. S. [Msg.2 . . . behavior may be intended as the changing of some variables. . . . Once more - the observer disappears! . . . ]

The observer creates/selects which variables and models the process of measurement of some variables. I would like very much to have your comments on my final statements of Msg.2: G. [Msg.2 . . . In order to model processes of emergence researchers use computational tools, such as Neural Networks, Cellular Automata, Genetic Algorithms and agent-based models. These are very useful tools to artificially reproduce, in a conceptually analogical way, processes of emergence. In any case, this approach is completely dependent upon computers: instead of theoretical considerations, there are computational steps (What if Simplicio had had computers available?). . . . ]

Sincerely, Gianfranco

Msg.5 You are wrong! From: Shelia Subject: Your paper

Date: 17 Oct 2005

Dear Gianfranco, 1. I accept your explanation of points 1. and 2. as a definition of behavior: the description of the ”way of changing” has to be made by an observer, and the set of variables has to be chosen by an observer. Now, would you agree that before the variables are chosen, before the way of changing is described, before the relations between the elements are defined - the elements of the system (or the parts of the whole) S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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have to be defined? The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

In general, there are many ways in which a system can be divided into parts. Some of the partitions are adequate for the problem in hand, and some of them are not. If the observer starts with the wrong partition, there is no chance of the analysis of the system being fruitful. I agree with you 100% that there is a crucial difference between an artificial (man-made) system and natural systems. For the former, we know the goal of the system, from which parts it was constructed, the relations between the parts, and the parameters that reflect the interaction. For the latter (natural systems) all these questions have to be answered by the observer. Trying to investigate such complex systems as the economy, culture, ecological systems, the Santa Fe guys took as granted the existing partitions of these systems, and the relations between them. But that is wrong. So, applying nonlinear equations and supercomputers to incorrect representations of a system could not help. From my 40-year-long experience, I have learnt that solutions to difficult problems (oil exploration, handwriting recognition, earthquake forecasting) came only after the representation of the complex object had been changed. 2. I would be glad to receive your basic papers. If you have some of your papers in the computer - send them to me and I will print them here. I will certainly send you some of my papers. Please find attached (Attachment 1: A Complex look at Sports) my review on a recent report from the SFI panel on sports problems. Best wishes, Shelia



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Attachment 1 The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

A Complex look at Sports3 The question on the table was: ”Can Game Theory, complexity science, or even neuropsychology provide useful insights into how to: 1) Build better teams, 2) Rank teams, 3) Value players, 4) Predict tournament outcomes?” The first goal means: build teams, which will stay high in tournament. One can create a theory but how can one prove it? There would have to be 10 teams following these instructions for 5 years and 10 control teams, which would not know the tested theory. It would never happen no coach would use a theory that doesn’t guarantee a result. The results for the second point can be tested only by comparing the ranking list with the results of a tournament (or a number of tournaments). Thus, to be testable the problem has to be formulated as the goal in point 4) - predict tournament outcomes. That is precisely what happened in the conference. When Prof. Ken Massey wanted to estimate his ranking program, he said that at best his maximum likelihood model is able to predict roughly 75 percent of games in baseball and about 66 percent in the NFL. The goal of ranking teams was soon dismissed. ”It is a messy exercise”, said Ken Massey, a visiting professor of mathematics at Hollins University, ” . . . the very idea of creating a one-dimensional list of teams in order of merit, not to mention the notion of singling out the team that is ”best,” is inherently artificial”. The goal in point 3) means that each player has to be assigned a value (a number), i.e., they will be ranked. It has no sense because different players have different values for different teams. So, only one problem could be scientifically discussed and tested - prediction of tournament outcomes. 3 This attachment was written by Shelia reviewing an article which appeared in the SFI Bulletin, A Complex look at Sports, Spring 2005, p. 30. http://www.santafe.edu/research/publications/bulletin/spring2005v20n1.pdf


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The first hope (Game Theory) was dismissed by everybody on the panel. ”Game Theory involves the formal analysis of situations where completely rational individuals strive to maximize their own gains by competing or cooperating with others according to an established set of rules. The theory captures certain aspects of economics and strategy extremely well”, Colin Camerer, a Caltech economist said, ”but is deafeningly silent on all sorts of other factors-things like pride, herd mentality, and emotional attachment- that influence economic and strategic decisions in real life.” USC’s Chow touched on this issue earlier in the day. ”One word has been left out in all of this so far,” he said: ”Emotion. Football is a game of emotions, no question. The human element is so important”. It was known from the time Game Theory was formulated that human games and Game Theory have little in common. The second panacea (complexity science) was never mentioned in the discussion. It seems like complexity science is unknown to the participants of the panel or, maybe, it doesn’t exist?! The third medicine (neuropsychology) shared the fate of ”complexity science” - it was never mentioned. ”Scott E. Page, SFI External Faculty member and a complex systems professor at the University of Michigan, agreed that linear models can never capture the complexity of interactions”. That statement is written on the holy banner of the Santa Fe Institute (SFI). The second statement on the banner is ”non-linear models can capture the complexity of interactions”. Both statements are wrong. If the system (the whole) is misrepresented, i.e., sub-divided into parts in an incorrect manner, then neither linear nor non-linear models will solve the problem. There are examples of complex problems that can not be resolved using nonlinear descriptions of interactions. One of them is the geological prognosis of large oilfields. After changing the description of the system, success was achieved based on linear decision rules with no interactions [Guberman and Izvekova, 1972]. Prof. Page also showed the way for improvement. ”Instead of simply summing up a player’s vector of attributes,” he said, ”look for interactions between them.” The idea is really great but a bit late. Forty years ago pattern recognition was applied for the first time to a complex practical problem for precisely that purpose: to extract more information from the model by using the relations between parameters [Guberman et al., 1964]. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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David Romer, a professor of political economy at U.C. Berkeley ”has programmed a complex model that analyzes the vast, chess-like tree of contingencies sprawling before the future of any decision.” Use of a chess-like tree is a very popular tool for game modeling. But it is completely inadequate because it is anti-intellectual: it does not envisage the existence of any plan. The full tree-search tests all possible paths. The existence of a plan means testing a limited set of paths. If the plan does not lead to a good solution it will be rejected and a new plan will be tested. ”Dean Oliver, author of the book Basketball on Paper, is the creator of RoboScout, a software program that watches basketball games and analyzes them . . . RoboScout looks for - and apparently finds - factors that can better predict the outcome of basketball match-ups”. That is the single positive result mentioned in the review. It was achieved not by using non-linear dependencies between a priori given factors but by finding new factors, i.e., by changing the description of the system. The impression of the review is as follows. A number of scientists came together to discuss their attempts to build useful models of real games. They reported on different approaches (statistical, graph theory, pattern recognition) and recognized that many problems have no sense and the rest can not be solved because the phenomena are too complicated and involve a lot of soft parameters (emotions, interpersonal relations, influence of environment, and so on). After the review was finished two words were added on the top - ”complexity science” as a tribute to the institution, which organized the meeting. It is quite similar to the rules, which existed in Soviet science: to every scientific paper on applications has to be added on the top: ”All the following was done in accordance with the plans of the Communist Party”.




Chapter 2 Partitioning the whole

Msg.6 Symbolic vs. Sub-symbolic From: Gianfranco Date: 18 Oct 2005 Subject: Defining variables

Dear Shelia, I like your emphasis on the preliminary analytical approach to model a system. The observer has to process in an abductive, inductive, deductive way (depending on the effectiveness) the collected data. In any case, agent-based approaches, self-organization processes and processes of emergence are centred on the way in which interactions take place, using sub-symbolic tools such as Neural Networks and Cellular Automata. If I understood your point, we may simulate them, but it doesn’t mean that we understand them until we have a complete symbolic description by using new, suitable, invented variables with corresponding relationships and interactions. This doesn’t mean finding the ”right” one, but the one suitable for managing in general the phenomenon being considered: we may have multiple, simultaneous, representations at different levels of description. One of the papers sent via regular mail relates to the Dynamic Usage of Models: the subject is discussed in more detail in the book Collective Beings [Minati and Pessa, 2006]. Did I understand your point? Best wishes, Gianfranco 19


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Msg.7 Do you agree the observer has to decide? From: Shelia Date: 21 Oct 2005 Subject: Re: Defining variables

Dear Gianfranco, It seems that you got my point and that you moved further on arranging and enriching the main theme. In principle, my thinking is that of an engineer. I always start with a practical problem and if I find a good solution I can sometimes generalize it. But on the metascientific level I move very slowly. So, to move forward I would like your answer to a simple question: Do you agree that before exploring a system the observer has to decide of which elements the system consists, i.e., how the whole has to be divided into parts? Only after this can one define the relations between the parts. As you emphasized, in different tasks the partition of the whole can be different, and consequently the relations between the parts will also be different. Best wishes, Shelia

Msg.8 Modelling and generalizing From: Gianfranco Date: 22 Oct 2005 Subject: Did I get your point?

Dear Shelia, Starting from your question: S. [Msg.7 . . . Do you agree that before exploring a system the observer has to decide of which elements the system consists, i.e., how the whole has to be divided into parts? Only after this can one define the relations between the parts. As you emphasized, in different tasks the partition of the whole can be different, and consequently the relations between the parts will also be different. . . . ] S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Yes. The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

When dealing with systems (and not only) I think we always use the strategy of modelling. To model a system means to have a description of it at a level of description suitable for the interests of the observer. We may consider two cases: 1) The modelling of a device (e.g., mechanical or electrical) is related to a level of description of interest to the observer: usually this level of description relates to functionalities. At this level of description the problem is to manage and use the system and its properties. This level is the macroscopic level related to emergent properties rather than the microscopic level related to interacting components. When the device is not working properly or we have to design systems having different functionalities, then there is a need to explain how the system works and to deal not only with emergent properties. An effective strategy is to select or invent a suitable configuration of components assumed to interact: this micro-model may be effective in explaining how the system works and then can act on the system itself (e.g., repairing, improving, reproducing). 2) Another approach is used when this strategy (i.e., to select or invent a suitable configuration of components assumed to interact) is not sufficient to explain how the system works. This is the case of ”collective phenomena” for which the main focus is on the architecture, reaction time, information exchange, noise, phase transitions, symmetry breaking, and so on. They relate both to: - Collective phenomena established by autonomous agents (e.g., flocks, ant-hills, industrial districts, car traffic), and - Collective phenomena established by non-autonomous agents (e.g., superconductivity and superfluidity). I agree that in both cases the observer must, as a necessary condition for dealing with the system, select or invent a suitable configuration of components assumed to be interacting. But in the first case this is necessary and sufficient (the whole is divided into parts), whereas in the second case it is not. When dealing, for instance, with a neural network we need to know, of course, about neurons and synapses. But this is not S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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sufficient: we need to know, for instance, its architecture, about its layers and their respective weights. The same elements interacting within a different architecture may make emergent a system having different behavior (such as neural networks possessing a different architecture). This relates to dealing with complex systems by considering only emergent properties, such as the ability to learn for living beings or neural networks. We may simulate the process, learning in this case, (for instance by modelling with neural networks), but this does not explain the phenomenon. I understand your point that we always need to have elements interacting (in the first case by assuming a division of the whole into parts; in the second by inventing interacting components able to simulate the process). This may explain the behavior of the system (case 1) or may not (case 2). In general we may have different modelling producing different nonequivalent generalizations. For instance: a) Structures, such as buildings, ships and airplanes, modelled through structural engineering or through neural networks and cellular automata looking for dynamic, emergent equilibria. b) Firms modelled as organizations or as collective phenomena. c) Illness modelled as a physico-chemical or psychological problem. d) Markets modelled as economic or political processes. I like your emphasis on the selection or invention of interacting components as a necessary condition. The generalization of a system has this choice within it, and this is a limit to the process of generalization! This strategy may be hidden by the fact that modelling using the same selection of interacting components is done by adjusting parameters and adding variables as for agents in agent-based modelling. Usually the same selection of components is not used, but the same kind of selection of interacting components. This takes place by using effectively working models and superimposing them onto practical problems by adapting variables and equations, without a new, suitable modelling of the system. An example of this lies in the principles of maximum satisfaction in economics, as introduced S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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by Alfred Marshall: they are completely unrealistic, but still used because it becomes easy to model economic systems. The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

By assuming that, for instance, markets and insects have the same behavior simulated by the same models, is a strategy having implicit the assumption that the behavior of the systems are based on the same selection of interacting components. Thank you so much, Shelia! I think your point is becoming clearer to me. This is the intrinsic limitation of generalizing. We may introduce different levels of reductionism and correspondingly different levels of generalization. Please let me know if I got your point. Maybe we could collaborate in writing something about this for the Systems community. Best wishes, Gianfranco

Msg.9 Observer and description are basic to my understanding of systems From: Shelia Date: 23 Oct 2005 Subject: Re: Did I get your point?

Dear Gianfranco, I was happy to get your ”Yes” on my question. I am happy as well to share your statement: S. [ . . . When dealing with systems (and not only) I think we always use the strategy of modelling. To model a system means to have a description of it at a level of description suitable for the interests of the observer. . . . Msg.8]

The notions of ”observer” and ”description” are basic in my understanding of systems.



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Before going further I would like to summarize my understanding of your position. On the same set of objects (your example - society of people) the observer can define different systems: a) economic system (buyers and sellers), b) social system (according to Karl Marx - workers, farmers, bourgeoisie, intelligentsia, clerics), political system, reproductive system and so on. In each case the observer has to: 1) define a subset of population, which will be the elements of the system (for example, adults or working people or women); 2) define the relations between the elements, which are characteristic of that particular system. In all these cases we could not be sure that there is such a system as the ”economy” or ”society” - these notions are our inventions, they are very soft, we don’t know where their borders are. Even if we are lucky and the system exists, we are not sure that our model is correct, that we have represented the system using the correct elements and their meaningful relations (for example, the element of society could be not an individual but a family). In most cases the systems will exist only in our mind. So, how can we recognize when we succeed, that such a system really does exist in nature, and that our model is correct? As always in science, we have to compare the predictions of our model of the system with reality. To continue the comparison of our positions I suggest defining an example of a system (or two examples) to illustrate our general concepts. I will suggest some, which I know as a practician: 1. The solar system, 2. The system of handwriting, 3. The Earth as a geological system, 4. The phonological system of speech. What would be your suggestions? It would be great to write a paper. Maybe it would be interesting to publish our exchange in letters, our Dialogue, like those of Plato or Galileo’s Dialogue Concerning the Two Chief World Systems.

Best wishes, Shelia S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Msg.10 Effective thinking The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

From: Gianfranco Date: 24 Oct 2005 Subject: Dealing with systems

Dear Shelia, I feel uncomfortable with the words ”reality” and ”existent”. I think that knowing is based on the following strategy: ”trying to find out how it is more effective to think how something is” rather than ”trying to find out how something really is”. This relates to Pierce’s abduction. In the first case, multiple, non-equivalent modelling and theories coexist because they relate to different levels of description used by the observer (e.g., classical mechanics and quantum mechanics); knowing is possible through levels of description only. In the second case, multiple, non-equivalent modelling and theories are intended as different steps towards the truth. By the way, the second strategy is a particular case of the first one: they are not in contradiction (e.g., it may be, in some cases and depending upon the observer, more effective to be objectivist than constructivist). Knowing is a process having some embedded limitations such as Uncertainty Principles in Science, as introduced by Heisenberg. We can call reality the object of this process, but as soon as we speak of reality, we move into the knowledge of reality. As soon as we know reality, it is not reality anymore. Systems may then be considered as our inventions only: they are effective when they work, i.e., when through this tool (this description) we may be effective (e.g., designing, changing, implementing, interacting, and so on). Speaking of reality there are usually two intrinsic contradictory positions. On the one hand, we can say that systems really exist when their usage is effective. For instance, when we have some artificially designed systems effectively working (i.e., doing what we want) and, vice versa, when we understand how a natural system works (i.e., as if we had designed it), then we may apply effective, modifying actions to it (we test the system, i.e., we check correspondence between the designed S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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behavior and the detected behavior of the system). On the other hand, when we experience effects of abductively unmodelled input, they are usually called reality. The two points of view are coincident when considering what is not real: we may speak of something that does not exist (i.e., the model that we have of it doesn’t work ) and we may model the source of an input in a wrong way (i.e., the model doesn’t work ). The truthfulness of a theory is a different subject. This relates to the results of the process of testing. The truthfulness of a theory is its effectiveness for the observer. On this point, I always like to say that to be very effective we must be very abstract, otherwise we become only empiricist. I like your proposal to compare our ideas through the definition of a couple of systems. By the way, I noticed that in the list of your proposals there are only non-autonomous systems. We may also consider autonomous systems, that is, systems equipped with cognitive systems. These may be, for instance, autonomous agents (e.g., robots) or living beings (e.g., animals and human beings). This difference is very important because in the latter case the process of interaction between the component parts takes place as information processing, whereas in the former, the process of interaction can be fully described through physical interactions. With reference to non-autonomous systems we may consider the system of handwriting. This may be considered having different levels of description in mind. For instance, for: a) Reproducing the same text in different formats (e.g., transposing from handwritten text to standard encoded text, such as ASCII, through Optical Character Recognition and Tablet PC). The system must be trained. b) Understanding the meaning of the text, that is, making decisions based upon the text; (such as recognizing a signature to authorize an action). S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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c) Making a user-profile by using the text as a source for psychological information, or so-called handwriting analysis or graphology. The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

We will then have three different descriptions of the system. I think that (but you are the expert) we must first of all distinguish between alphabetical languages and languages based on ideograms. In the first case we will focus upon alphabets, as complete standardized sets of letters. Through them it is possible to constitute morphemes. A morpheme is a meaningful linguistic unit consisting of a word that cannot be divided into smaller meaningful parts. This is useful when it is necessary to: a) Use a level of description which is suitable, in short, for extracting (i.e., recognizing) numbers and elements of the alphabets. Issues involved include the one you mentioned in your paper presented at the UES in Paris and related to Gestalt and training processes. Elements are lines, angles, and circles. Relations are given by their position and dimension, while interaction may be represented by considering the letters coming before and after and the correspondence of the complete word with a dictionary. Words coming before and after may help in the interpretation of a letter. b) Use a level of description suitable for validating, for example, testing correspondence between one signature and another. Elements of the system are not letters, but rather graphical elements, pressure, dynamics in writing, geometrical aspects (such as up and down extremes, length, holes, angles). Relations are given by the order of elements, while interaction is given by the presumed process of writing (posture, right- or left-hand writing), the writing implement (pen, ballpoint pen, fountain pen, pencil), the support (soft/hard, stable/unstable and in which way), the writer (age, male/female, physical temporary, permanent or changing illness, nationality). c) Use a level of description suitable for recognizing standards. One may or may not already have some information about the writer (age, sex, illness, nationality). Elements are those listed in the socalled Green Sheet containing 119 traits, which can be evaluated from basic traits. Relations and interactions are given by the fact that traits are scored by the frequency and intensity of various strokes. Pressure is also an important element. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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All these cases are passive systems because the observer invents and establishes them when used. The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

Similar observations are valid for non-passive (but still non-autonomous) systems. With reference to autonomous systems we may consider systems able to make some complex environment-based tasks, such as to adapt, find, and possessing strategies. This applies to sufficiently complex living beings but also to collective phenomena when considering the behavior of ant-hills, flocks, and industrial districts. Consider the example of flocks, interesting, for instance, because of the H5N1, highly pathogenic strain of avian influenza (bird flu). Elements of flocks are birds. By the way the min/max number of birds in a flock are not defined. We should define precisely when a bird begins to be an element of a flock and when it is no longer. Relations may be given by the dynamics of the distance between birds. Interaction may be given by the processing carried out by each bird of the information regarding neighbours and the contexts (e.g., prey, atmospheric conditions, and light). The behavior of a flock may be influenced in several ways, such as artificially introducing noise during their interchange of information or disturbing their cognitive processing. Another level of description could be that related to what birds carry. For example, they may transport seeds or viruses. In this case the interest may be focussed upon where, when and how many they land. The interest may be on how they leave what they transported (e.g., by excreting, becoming prey, diffusing matter in the air or in water). The observer then designs different systems. In any case, they are systems because the observer models and detects them, but also because the agents themselves detect the system by actively processing the information and maintaining the system for their interests, from their level of description. Because agents are autonomous, the observer models their behavior taking into account the information processing by them: this kind of system evolves and does not just move within a space of predefined states. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Turning now to the difference between reality and nature it is clear that nature is part of what we call reality: reality may be a situation (e.g., someone has money, is the boss, and so on) whereas nature is interactive, i.e., it may be interrogated. Reality can only answer questions, and so it is not reality anymore. An experiment is like posing a question to nature. Nature answers by making something happen. If we don’t ask a question, nature doesn’t tell us anything. Reality is silent until we interrogate it: then we need to use knowledge, and reality as such disappears. I like your idea: ”it would be interesting to publish our exchange in letters, our Dialogue, like those of Plato or Galileo’s Dialogue Concerning the Two Chief World Systems.” I like it because we can present a process involving more than just results, and also because the idea is inspired by something that great people did. Best wishes, Gianfranco

Msg.11 Thank you for pointing out my mistake From: Shelia Date: 26 Oct 2005 Subject: Re: Dealing with systems

Dear Gianfranco, I am enjoying our conversation more and more. I completely agree with your interpretation of the words ”reality” and ”existent”. I was wrong using them in my context. My point was only to emphasize that for assessing the quality of our models we have to compare the results of our predictions with our measurements of nature. So, thank you for pointing out my mistake.


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Your understanding of the handwriting recognition problem is the best I have ever met in the ”professional” community. What is interesting to me in that example is the following. All previous attempts to resolve the problem of recognition dealt with the script as a series of geometrical objects. Accordingly, the characters were represented as different sets of geometrical elements: for example, dots, or arcs and straight strokes, or holes and ends, and so on. But the problem had not been solved even after 20 years of work (the 1960s-70s). The solution was found when handwriting was treated not as an image but as a trajectory of the pen’s movement and the elements of writing were defined as elementary movements (I referred to them in my talk in Paris). The long and difficult tests were successful. So, as you put it, ”the truthfulness of the model is its effectiveness for the observer”. So far, it seems to me that we agree on the following. The observer decides: 1. What is the object of his interest (the system). 2. What are the parts of the object (the elements of the system). 3. What kind of relations between the parts are significant for the existence and functioning of the system. In systems with elements possessing cognitive systems we have to define the interaction by means of information. 4. How good is the model of the system. The business of systemic science is to develop effective methods and tools for resolving these four types of problems independently from the nature of the particular system. As an example of a scientific approach to problem 2 (dividing the whole into parts) I have to mention Gestalt psychology (which was acknowledged by von Bertalanffy as the precursor of General System Theory). The basic principles of Gestalt psychology (proximity, similarity, good continuation) explain how we describe a complex image, i.e., how we divide it into parts. On the sheet of paper we see clusters of dots according to the proximity principle. Another example of some theory of partition is handwriting. The idea that the writing has to be treated as a track of movement of the writer’s S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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pen came as an application of Bongard’s imitation principle: ”The adequate language of describing systems is the language that could describe the process of creating the object”. The script is produced by the movement of a pen. So, describe the writing with the elements of pen movement. And that is precisely what I did - find the seven basic elements of pen movement. The imitation principle gives an adequate solution in speech recognition. You can learn more about that in the paper I have sent you [Guberman and Andreewsky, 1996]. Now I will turn to your example. 1. The object (the system) is the flock. 2. The elements are birds. 3. As you write ”relations may be given by the dynamics of the distance between birds.” If the relations between the elements are defined as distances, the flock is a cluster of birds. You write ”We should precisely define when a bird begins to be an element of a flock and when it is no longer.” There are rules of belonging of the element to the cluster - see my paper I have sent you on clustering analysis. 4. But I missed the last step: what is our problem and how we will test the quality of our model? Best wishes, Shelia

Msg.12 When elements are autonomous systems From: Gianfranco Date: 28 Oct 2005 Subject: More comments and proposals

Attachment 2: Gianfranco, A proposal for lines of research on emergence, May 21, 2005. Dear Shelia, I’m very pleased that we are both enjoying our conversation. Yes, I S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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think it is very productive and interesting. I agree with all your observations and comments. The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

1) I would like to complete my point of view about reality with a couple of comments. Reality can only answer questions, and so it is not reality anymore. An experiment is like posing a question to nature. Nature answers by making something happen. If we don’t ask a question, nature doesn’t tell us anything. Reality is silent until we interrogate it: then we need to use knowledge, and reality as such disappears. 2) By the way when I said: ”We should define precisely when a bird begins to be an element of a flock and when it is no longer”, I meant that we need to have a rule for deciding. It may be not at all a precise belonging: on the contrary I have in mind a rule of fuzzy belonging. 3) With reference to my example, I would like to ask you to change it with an easier one, by considering human, social systems. Elements are autonomous systems performing information processing. We may consider a social system described, for instance, as a market, audience or team. We will have three levels of description with specific elements, relationships and interactions: a) Market: elements are human beings as buyers (no children, no people who are non-autonomous for any reason, no homeless people, no soldiers on a mission). Relationships are given, for instance, by their mobility (e.g., working shifts, living areas, transportation systems). Interactions are given when they constitute the collective phenomena of markets: for instance, through the process of selecting (e.g., advertising, creation of artificial needs, inducing life styles) and buying (e.g., process of purchasing: kind of stores, their location, parking facilities, financial instruments). Markets of goods and services are measurable in different ways: by using financial parameters, quantities of people involved, quantities of goods, over any kind of timespan. b) Audience: elements are human beings accepting rules (e.g., paying for attendance, suitable behavior while attending) S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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and intending to consume a virtual product (e.g., music, movies, theatre, and sporting events). In this way, an audience is a special market having some specific rules, whereas for markets, rules are the same for any product (most of them are even sold in the same stores, because the rules are the same). Relationships are given, for instance, by adopting and respecting a configuration, staying in a queue, arrival times. Interactions are given, for instance, when they collectively process information and then make emergent a collective reaction (e.g., clapping). c) Team: elements are human beings having some common physical characteristics (e.g., age, sex, physical fitness, specific abilities) and respecting specific rules. Examples are sport teams and orchestras. Relationships are given, for instance, by having roles and respecting a configuration when playing. Interactions are given, for instance, when playing, that is, processing mutual behavior and position. The interest of the observer in modelling these systems is based on their ability to show a behavior: they need input and produce output. Through effective modelling it is possible to use their autonomous behavior. This is, we may say, a reductive usage of their autonomy. My interest in introducing this kind of example lies in the fact that elements are autonomous systems and when acting as elements of a specific system they remember their belonging to other systems. This is very important because whatever happens during their belonging to one system influences what happens during their belonging to another one. It is possible to influence the processing of information of elements in one system when acting as elements of another. This is not true for autonomous elements having simple cognitive systems. For instance, there are no multiple swarms or multiple flocks (we may have birds eating, drinking, hunting, reproducing, fighting, even producing collective behaviors, but different than flocking or swarming). The model is considered for obtaining effectiveness in managing complex systems established by autonomous elements, usually social systems. Unfortunately, sometimes, it may be effective for manipulating systems. By the way, the same model is useful S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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for detecting processes of managing/manipulating [Minati, 2004] [Minati, 2006a]. This relates to the concept of Collective Beings, multiple systems consisting of the same elements simultaneously or dynamically showing different kinds of interactions (see Attachment 2 below). 4) The problem of modelling and managing this kind of system requires a more complete and sophisticated approach to emergence, going beyond the classical x-level systems (where x-level stands for an index of complexity of description of the system) where, modelled by the observer, there are only elements and interactions. I think that the classical problems so well summarised by you [Msg.11]: [ . . . The observer decides: 1. What is the object of his/her interest (the system). 2. What are the parts of the object (the elements of the system). 3. What kind of relations between the parts are significant for the existence and functioning of the system. In systems with elements possessing cognitive systems we have to define the interaction by means of information. 4. How good is the model of the system. The business of systemic science is to develop effective methods and tools for resolving these four types of problems independently from the nature of the particular system. . . . ]

should be considered for x-level systems. We have x-level systems when considering autonomous elements, emerging elements, emergent effects affecting in their turn the elements, passage between emergence, de-emergence, multiple systems, Collective Beings and so on, as mentioned in Attachment 2 below. I would just like to mention that System Dynamics (SD), introduced by Forrester, is, in my view, for 0-level systems (the lowest level of complexity) because there is no active role of the observer, only elements and reactions. The general idea is to have a hierarchy of systemic descriptions of increasing complexity. For me this is an introductory problem to a General Theory of Emergence (At the moment I’m working on this with an Italian S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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colleague, my co-author of several publications) as mentioned in Attachment 2 below. We need to sophisticate the concept of emergence by considering multiple-emergence, de-emergence and the role of what is emergent affecting the elements themselves (i.e., the system affecting its elements). On this issue, I attach an introductory, draft document which I wrote some months ago which I’m very pleased to share with you (Attachment 2 below). It is not easy to find scientists interested in these new issues (particularly in Italy)! I know that it may be very controversial, but I think it is good for us not to agree on everything. I prefer to say something interesting, controversial, and activate processes rather than to be just right. Please find below the draft of some ideas related to lines of research on emergence that I wrote some months ago (Attachment 2). With my very best wishes, Gianfranco



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A proposal for lines of research on emergence1 1. Emergence, emergent effects, substitution of elements 2. Emergence from emergences 3. Reproduction and retention of emergence 4. Organization of emergent effects 5. Emergent effects controlling the process of emergence 6. De-emergence 7. Passage between different emergences 8. Life and emergent properties from living matter Introduction Within the framework of the intense activity, in both specific disciplinary and inter-disciplinary research on emergence, this note does not focus upon issues dealing with problems of definition, nor with searches for coherence and applicational approaches, but on the introduction of some novel issues, requiring reformulation, reorganization, updates and completion of the approaches usually adopted. In the very description of such issues there are profound and implicit references to questions of a different nature, hidden in abstract formulations. Abstract formulations are, on the one hand, a guarantee of generalization and disciplinary independence and, on the other, a promise of trans-disciplinary validity. Lines of research introduced more recently are converging: the name of the convergent point is the Theory of Emergence. How can we conceive this? New operators, new representations, new formalizations, new approaches. What are the relationships with Quantum Field Theory? I personally think that the main aspect will be the ability to go beyond sub-symbolic knowledge, supported today by an enormous computational power to model and simulate (what if the various Simplicios of science had had computers?). Should 1 This attachment is based upon a paper presented by Gianfranco at a meeting of the Italian Systems Society (Associazione Italiana per la Ricerca sui Sistemi (AIRS), www.airs.it), Rome, May 21st, 2005.



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sub-symbolic knowledge be intended as an aspect of our lack of knowledge, able to model and simulate without producing any new explicit knowledge? Spectacularly and threateningly, with a Theory of Emergence we will probably have a Theory of Life. 1. Emergence, emergent effects, substitution of elements A distinction has been introduced between (a) processes of emergence - detection by the observer of coherence in the interaction of elements (e.g., collective behaviors) - and (b) effects sustained by a continuous process of emergence - even after detection of the establishment of a process of emergence, the observer can detect different and also successive properties sustained by the process of emergence (e.g., different physical properties, such as the speed and shape of a flock or computational properties, such as the ability to classify and optimise). Consider now the case in which effects are not only supported by a continuous process of emergence, but that a variation (i.e., substitution, addition, subtraction, or mutation) of interacting elements takes place during the process itself. In this context, we will not consider the possible influences on the emergent effect. We will instead consider the possible role of the emergent effect on the process of variation of the interacting elements. In one case the variation may take place without, at certain levels of description, the effects produced by the process of emergence having any active role in the variation of interacting elements (e.g., an emergent superconduction has no effect on the process of variations in the matter from which it emerges). In another case an effect produced by the continuous process of emergence may play an active role in the process of variation of the interacting elements. Consider, for instance, cognitive activities emerging from neurological processes which are, in their turn, supported by (but also managing ) vital processes emerging from interacting elements (in this case living matter). In the process of cellular regeneration and substitution, keeping alive organisms, the psychological-cognitive effects of the emerging mind - play an active role. In this case the supported effects may play an active role not only by S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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producing variations in the interacting matter, but even in searching for new interacting elements to sustain the process of emergence from which they emerge or, on the contrary, how to stop it (”suicide”). A further example is the case of emergent computation, when current computational processes, supported, for instance, by a neural network, may autonomously decide to be supported by another neural network having a different architecture. In this case the interacting matter is in fact computation, obviously supported by hardware. Substitution of interacting matter may be gradual (with reference to parameters and levels of description used by the observer detecting emergence) leading, in some cases, to a complete substitution over time (e.g., the periodical complete cellular substitution in human beings, except for the brain and gonads). Complete and instantaneous substitutions (always with reference to parameters and levels of description used by the observer detecting emergence), completely changing the interacting matter, may take place as in the above example related to emergent computation. By allowing an external action, one may consider the example of a score being played by another orchestra, certainly not deriving from a decision or effect of the emergent music. Obviously, the same orchestra repeating a performance may be intended as a change of matter or not, depending on the level of description. 2. Emergence from emergences Processes of emergence may be established by elements being in their turn the effects of other processes of emergence. Consider, for instance, collective behaviors of living elements. This is a case of multiple and dynamic processes of emergence. 3. Reproduction and retention of emergence Systems may be established by explicit organization or self-organization (emergence), as briefly illustrated in Table 2.1. The difference between the two is not only usually fuzzy, but they may even be both simultaneously present (e.g., ant-hills and industrial districts). S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy



Systems from organization, as sets of structured elements: Devices, machines, assembly lines, teams, procedures

39 Systems from emergence (self-organization): Flocks, swarms, fish schools, in physics superconductivity and ferromagnetism, life (artificial life)

Table 2.1: The two ways by which systems are established In organized systems the process of reproduction and retention of effects produced by organization may be considered discretized, i.e., performed by specific roles. In this case the problem is perpetuating the organization (e.g., replacing workers, components, transplants) rather than the process of emergence from new interacting matter. Emergent effects, such as collective behaviors, are not organized per se, and what can at least be perpetuated is the supporting process of emergence, by acting on the interaction and the interacting matter. In fact there are combinations between the two extremes and at different levels. 4. Organization of emergent effects It is also interesting to note how emergent effects may take place not as isolated or as sequential processes of emergence, but also as combined processes. Emergent effects may be combined in such a way to establish new systemic properties. For instance, neural computations, typically emergent, may be combined, even using symbolic computations. Moreover, living beings equipped with cognitive systems at different levels of complexity, emerging from living matter, may establish collective behaviors and organizations. 5. Emergent effects controlling the process of emergence The concept of meta-consciousness introduced by Edelman (see, for instance, [Edelman, 1990]) as consciousness (self-processing) of being conscious (processing the self-processing), may be extended by considering an upper level of consciousness as processing the supporting process of emergence. This upper level theoS.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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retically allows the mind to look for other systems from which to continue to emerge (see Table 2.2). The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

1. Consciousness as knowledge and processing of the supporting process of emergence; 2. Consciousness as processing of first-level consciousness (as in human beings); 3. Consciousness as self-processing (e.g., animals with sophisticated cognitive systems, such as dogs and dolphins). Table 2.2: The three levels of consciousness The same comments and proposals can not be considered sic et simpliciter for collective behaviors, because it would be necessary to act simultaneously at the three different levels of description. As a matter of fact, in the cases considered above there is an identity to maintain: the problem is, for instance, to keep emergent this specific mind. In the case of collective behaviors, the level of description assumed does not refer to specificities, but to maintain emergent an effect in general (e.g., superconductivity, swarms, and flocks). This reasoning could be extended to collective behaviors in general if the subjects were observing themselves: as if a flock became conscious of itself, becoming observer of itself.

6. De-emergence Besides processes of emergence it is important to study processes of de-emergence: processes by which the emergent system loses coherence, stability, it can no longer be recognized as such by the observer. How can one describe and manage processes of deemergence? With reference to what has been discussed above, the question relates, for instance, to the process of changing from matter in the living state to the non-living state. Applications include the possibility of deactivating dangerous processes of emergence and manipulating processes of emergence, such as consensus in



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social systems. We must consider possible relationships with processes of de-coherence in Quantum Mechanics. The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

7. Passage between different emergences We refer to the need to study not only the establishment of emergence and de-emergence. It is necessary also to study the passage between different processes of emergence. What does this mean? The problem may relate, for instance, to (a) The process by which the same interacting matter supports different processes of emergence; (b) The interaction between emergent effects; (c) The passage of an emergent effect to being an effect of other process(es) of emergence. Let us now consider the concept of Collective Beings, introduced by the author, as multiple systems constituted of the same elements simultaneously or dynamically having different kinds of interactions, that is, making emergent different systems. In Collective Beings the three kinds of processes listed above take place because of the very nature of the system. 8. Life and emergent properties from living matter There is consensus in considering that matter may be definable as living when it regenerates, reproduces and is able to evolve. In this context we are interested in emergent properties of living matter, with particular reference to cognitive properties, necessarily supported by organization and emergence in the brain. Also in this case it is possible to distinguish between supporting in general emergent life (problem solved by reproduction and evolution) and supporting the emergence of specific effects (e.g., specific mental and cognitive functions). The peculiar purpose of evolution in producing matter able to understand itself (i.e., able to have the three levels of consciousness mentioned above, in point 5.) involves the production of specific emergent effects maintainable and sustainable not only by matter variable over time (e.g., cellular regeneration), but even by different matter or devices, even of a completely different nature (as in the case of emergent computation). In short, a higher level of definition of life can relate S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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to the ability to render emergent from other supporting processes, the same cognitive processes. In this case living matter may be intended as matter rendering emergent cognitive functions able to sustain themselves, independently from the matter itself. Which is the presumable evolutionary advantage for matter to understand itself ? The reason why evolution produced matter able to understand itself (corresponding to the mission of cognitive science, when understanding studies itself ), may be precisely to allow the establishment of emergent properties independently from the specific interacting matter supporting the process of emergence. Conclusions We have outlined some possible lines of research related to emergence and the possibility of formulating a complete theory. To summarize, the lines of research mentioned are: a) Study of the difference between processes of emergence and effects supported by continuous processes of emergence; b) Variation (partial or total, gradual or complete) of interacting matter, supporting the process of emergence, during the process itself; c) Effects of variation of interacting matter on emergent effects; d) Influence of emergent effects on variations in the interacting matter from which they emerge; e) Processes of emergence from the interaction of effects, in their turn, supported by emergent processes; f) Reproduction and retention of emergence; g) Organization of emergent effects and processes; h) Influence of emergent effects on processes of emergence; i) De-emergence; j) Passage between different processes of emergence; k) Life as the ability to make emergent from other supporting processes the same cognitive processes. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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These lines of research are not only based on inter-disciplinarity leading to issues related to emergence being considered by using common approaches for modelling and simulating, but even on trans-disciplinarity by dealing with problems and processes (e.g., openness/closedness, phase transitions, symmetry breaking, growth/development, goal-seeking) to be formulated, represented and considered independently from specific disciplinary aspects. This last aspect indicates how the search for a General Theory of Emergence has now become the search for a more complete generalization and representation of General System Theory itself.




Chapter 3 Nine agreements

Msg.13 Excellent! From: Shelia Date: 30 Oct 2005 Subject: Re: More comments and proposals

Dear Gianfranco, 1. I got your papers [Minati et al., 1998] [Minati, 2006b] [Minati, 2002]. Thank you. I have started to read them. It takes time for me to go through theoretical constructs. In my work, I always start with a practical problem. If I find a good solution, sometimes I see that there is something more general. So, I started with the paper that contains a number of examples (including handwriting). Now I am trying to gain an understanding of your ideas in the case of simple examples. I chose two: 1) flock of birds, and 2) handwriting. In the case of a flock I would like to understand the fourth step (see my list of 4 steps in system analysis): S. [Msg.7 . . . 4. What is our problem and how will we test the quality of our model? . . . ]

After we finish that example I would like to discuss the handwriting system. 2. Here are my quick comments on two of your points.

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G. [Msg.12 . . . 1) I would like to complete my point of view about reality with a couple of comments. Reality can only answer questions, and so it is not reality anymore as intended by objectivistic thinkers. An experiment is like posing a question to nature. Nature answers by making something happen. If we don’t ask, nature doesn’t tell us anything. Reality is silent until we interrogate it: then we need knowledge, and reality as such disappears . . . ]

Excellent! G. [Msg.12 . . . By the way when I said: ”We should define precisely when a bird begins to be an element of a flock and when it is no longer”, I meant that we need to have a rule for deciding. It may be not at all a precise belonging: on the contrary I have in mind a rule of fuzzy belonging . . . ]

Excellent! Best wishes, Shelia Attachment 3: Shelia, Yes, Nov. 11, 2005

Msg.14 Forget about flocks From: Gianfranco Subject: Flocking

Date: 30 Oct 2005

Dear Shelia, S. [Msg.13 . . . In the case of a flock I would like to understand the fourth step (see my list of 4 steps in system analysis) 4. What is our problem and how will we test the quality of our model? After we finish that example I would like to discuss the handwriting system. . . . ]

You can find my comments in Msg.12. I asked if I could change the example and I introduced a new one: I realized flocking was not so easy for introducing the ideas I had in mind. Sorry about this change.



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Best wishes, Gianfranco The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

Msg.15 How to measure the success of our model From: Shelia Date: 30 Oct 2005 Subject: Re: More comments and proposals

Dear Gianfranco, As you suggested I tried to analyze another example - your example a) S. [Msg.12 . . . a) Market: elements are human beings as buyers (no children, no people who are non-autonomous for any reason, no homeless people, no soldiers on a mission). Relationships are given, for instance, by their mobility (e.g., working shifts, living areas, transportation systems). Interactions are given when they constitute the collective phenomena of markets: for instance, through the process of selecting (e.g., advertising, creation of artificial needs, inducing life styles) and buying (e.g., process of purchasing: kind of stores, their location, parking facilities, financial instruments). Markets of goods and services are measurable in different ways: by using financial parameters, quantities of people involved, quantities of goods, over any kind of timespan ...]

This description contains a set of systems. Let us pick one. Following the four steps I mentioned earlier. 1. The system is a market of goods. 2. The elements are persons (subset of people). 3. The relations between the elements (persons) are defined as mobility. The interactions are 1) selecting, 2) buying. I could not find an answer to the last question: 4. What is the goal of investigating that system and how will we measure the success of our model?



48 My two questions are: The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

i) What is the answer to point 4? ii) What is wrong with flocks? Are they not a system? I continue to read your paper and work on the handwriting example. I hope that after analysing these two examples I will be better prepared to go ahead with more complex notions. Sorry for my slowness. Best wishes, Shelia

Msg.16 Managing system behavior From: Gianfranco Subject: Answers

Date: 31 Oct 2005

Dear Shelia, You asked me: S. [Msg.15 . . . 1) What is the answer to point 4? . . . ]

The goal is to have the possibility of manipulating the system (the market in this case) and foreseeing its behavior: - To manipulate means that the observer is able to make agents buy specific products (for instance, new products, products having certain prices, products inducing the need to buy other products, products requiring additional services, i.e., able to induce the establishment of new markets); - To foresee means that the observer is able to regulate the input and other systems depending upon the expected behavior (for instance, regulate the input of products to be sold and the number of simultaneous buyers). The other systems which must show a suitable behavior are, for instance, the transportation system, the parking system and the warehouses. A way to measure the success of the model may be, for instance, to measure the quantity, the speed and the financial value of goods processed by the system over a certain period of time. The measurement should consider changes over time and the total amount over specific periods. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Please also refer to the discussion in Msg. 12 - after point c). The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

S. [Msg.15 . . . What is wrong with flocks? Are they not a system? ...]

I asked to change the example related to flocks because birds have a simple cognitive system and it was not as easy for me to find examples of multiple systems established by changing the cognitive model adopted. S. [Msg.15 . . . I continue to read your paper and work on the handwriting example. I hope that after analysing these two examples I will be better prepared to go ahead with more complex notions. Sorry for my slowness. . . . ]

Thank you for giving me your attention. I’m proud of it. Best wishes, Gianfranco

Msg.17 Something bigger than science - life itself From: Shelia Subject: Re: Answers

Date: 01 Nov 2005

Dear Gianfranco, Let me describe how I understand your market model. Then you can show me what is wrong in my understanding of it and we can then proceed. 1. We create the market model as it was described in previous messages under steps 1, 2 and 3. 2. Now we define our goal. Quote: ”The goal is to have the possibility of manipulating the system (the market in this case) and foreseeing its behavior”. In my words ”you have the ability to change some of the parameters of the system and you are able to forecast what will be the values of the output parameters”. In your example the input you can change is the number of agents S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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that are buying a specific product. The output parameter, which you measure, is ”the quantity of goods that change ownership as a function of time (from these numbers one can calculate the total amount over specific periods)”. When we are dealing with the model of a system we can use a computer. We can change the input parameters at will to find out how the model reacts to our manipulation and measure the output parameters. The model itself is the machine for forecasting. I still await the final step: to answer the question - did my model tell me something useful about the real market? Because that was the real goal - to get some knowledge about the real market, to learn what have I to do to manipulate the real market and be able to foresee the results. I admire your attitude to science - firstly, to have fun, to come up with crazy ideas, because there is something bigger than science (which both of us love) - life itself. Thank you for the fun I am having from our exchange. Shelia

Msg.18 The effectiveness of modelling and simulating From: Gianfranco Subject: Something useful

Date: 02 Nov 2005

Dear Shelia, The model, when it performs well with respect to the behavior of the real system (i.e., measurement of variables and parameters related to the behavior of the model correspond to variables and parameters related to the behavior of the real system), is expected to be useful for at least two reasons: - Structural architectural aspects of the model can be taken as valid for the real system. We can detect, for instance, that there are some bifurcation points after which the system adopts a different S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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structure (phase transitions), such as: after reaching some geographical extensions the market takes on a different structure and behavior; after reaching certain financial dimensions the market structure and behavior change. This is a very well-known effect for corporations changing structure and behavior when changing dimensions (e.g., workers, financial variables, production, and so on). - Thanks to simulation we are able to decide, for instance, whether it is more profitable to invest money in advertising or in reducing prices or changing the packaging of a product. The possibility of simulating is, in my view, the most important result. I appreciate very much your final comment: ”I admire your attitude to science - firstly, to have fun, to come up with crazy ideas, because there is something bigger than science (which both of us love) - life itself.” I was lucky to meet you (I really must thank Evelyne). Best wishes, Gianfranco

Msg.19 Prof. Wita Wojtkowski From: Shelia Date: 02 Nov 2005 Subject: Prof. Wojtkowski

Dear Gianfranco, I have recieved an e-mail from Prof. Wita Wojtkowski. She has heard about our discussions from you and is willing to participate. I welcome this possibility and she also told me that you have no objections. Please, confirm that this is OK with you, that you agree to send her our correspondence. Best wishes. Shelia S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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Msg.20 I’m glad The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

From: Gianfranco Subject: Prof. Wojtkowski

Date: 02 Nov 2005

Dear Shelia, I am very pleased that my dear, old friend Wita is interested in our discussion. I have also noticed that you have written some papers together. I’ll send her copies of our correspondence so far, so she will be up to date. I’m glad to have her on board with us. Best wishes, Gianfranco

Msg.21 Step 5: Reviewing and reconstructing the model From: Shelia Date: 03 Nov 2005 Subject: Re: Something useful

Dear Gianfranco, I would like to note with satisfaction that we are moving ahead step by step and still are in mutual agreement. I agree with your last statement. I will try to put it into my own words. If the predictions of some parameters of our model closely agree with the behavior of the real market’s corresponding parameters, we conclude that our model is good and we can use it to our benefit - we could intentionally change some input parameters (such as redistributing our investments) to reap more profit, or predict future critical points in market development (e.g., a bifurcation point). Next step. History teaches us that most system models, which have been developed during our civilization were wrong. Particularly market models, S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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handwriting models, and oil exploration models (an area, in which I am very much involved). So, how do we proceed? Now comes step 5. 5. Reviewing (reconstructing) the model, which means reviewing one of the following parts of the model (or all of them together): a) Reviewing the whole object of our interest (the simple case - from your example - excluding children or seniors, or in more complex cases - as we both find crucial - including the observer), b) Reviewing the partition of the whole (dividing the system into parts), i.e., changing the elements (for example, the element of the TV-set market may be not a person but a family), c) Reviewing the relations or interactions (as, for example, Santa Fe did: substitute the linear relations with nonlinear ones). It is obvious that everybody can pass steps 1 - 4 but the comparison of the model with the real system has nearly always failed and to proceed one has to review the model. On this crucial point the Theory of Systems has to be the guide. Do you agree with step 5? Best wishes, Shelia

Msg.22 A meta-level approach From: Gianfranco Date: 03 Nov 2005 Subject: Absolutely yes, but ..

Dear Shelia, You asked me: S. [Msg.21 . . . Do you agree with step 5? . . . ] S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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Yes. Absolutely. The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

This is the history of science, i.e., changing approach, description, models, tools used to represent, variables, relations, considering the observer, and so on. I like to say that we need to create (thanks to logical inferences such as induction, deduction and abduction) a new description of the problem, in our case, of the system. Science began with a new description of the system of planets: from geocentric to heliocentric. I suggest avoiding use of the word ”wrong”. Rightness or wrongness depend upon what the observer expects. One description may be very suitable, for instance, for religious purposes but very poor for scientific purposes. This relates to the problem which occurs when one level of description offers something valid for another level of description. For instance, when religion offers something valid for science or science offers something valid for religion. We may argue about the validity and the effectiveness of a given level of description, but not about what takes place within it. We have first of all to decide whether we have the same purposes. Then we can discuss the effectiveness of the levels of description adopted and related elaborations. I feel uncomfortable imagining myself going to a population having a very different culture and telling them what is ”wrong” and what is ”right”. I feel uncomfortable designing a system (i.e., social, religious, political, economic or scientific) for somebody else. What, as a system scientist, I am required to do is to represent other approaches within my approach, not having the purpose of correcting them, but of understanding them. I may correct them only in the case where we both have the same purposes. Only in this case would I be able to manage without imposing something only because it is ”right” at my level of description. Yes, Systems Thinking is, in my view, a meta-level approach having validity precisely because of its solid roots at a scientific level. What do you think? Best wishes, Gianfranco S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Msg.23 Modifying the system: add the observer and/or expand the object From: Shelia Date: 04 Nov 2005 Subject: Re: Absolutely yes, but ..

Dear Gianfranco, Absolutely yes. Before taking the next step I would like to apologize for two things: 1) I am moving slowly: I will try to reformulate the same statement 2 or 3 times to be sure I have understood it correctly (taking into consideration my poor English), and 2) I am not very fluent at the philosophical level, I need to create a solid base on the first level of systems analysis. This is why I am so interested in markets, handwriting, and oil exploration systems. Now, back to step 5. What kind of science can we suggest for solving the three basic problems: a) Reviewing the whole object of our interest (the simple case - from your example - excluding children or seniors, or in more complex cases - as we both find crucial - including the observer), b) Reviewing the partition of the whole (dividing the system into parts), i.e., changing the elements (for example, the element of the TV-set market may be not a person but a family), c) Reviewing the relations or interactions (as, for example, Santa Fe did: substitute the linear relations with nonlinear ones) . As you stated in your last e-mail ”Science began with a new description of the system”. Changes in description mean 1) to change what we want to describe (point a above), and 2) to change how we describe it (points b and c). From my own experience, I have learnt S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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that there are some general rules (principles, methods, approaches, . . . ), which can be applied to systems that belong to different branches of science and technology. I would like to start with point a) - how to change the object which we are analyzing - the system - in a reasonable manner. I know two methods. 1. To add the observer to the object. According to your approach, this is a fundamental feature of a system (a system exists only as an observer’s model). But for many researchers that is not what they start with. And when they fail to resolve a complex problem and look around for new approaches - this is what the systems approach will recommend first of all. Let me give you an example of how this works in a real application: Handwriting Recognition. Traditionally, handwritten script was described as a line drawing, which consisted of holes, crossings, loops, arcs, etc. Many algorithms had been presented over a period of 40 years but none had succeeded. Then I came up with a different approach, following observations on a patient with brain trauma (demonstrated by Prof. Luria in Moscow Brain Surgery Hospital). I understood that the object I had to investigate was not the script, the image on the paper, but a system consisting of the writer, the script, and the reader. The reader (the observer) doesn’t look at the script as at a dead image, but as a track of the writer’s pen. The essence of the written character is not the geometrical pattern but a kinematic pattern. That approach was a break-through. It improved not only character recognition but also the division of words into characters, eliminating the need for normalization, skeletonization and so on. That technology was licensed 20 years later by two major software houses: Apple Corporation and Microsoft. You can learn more from my paper with Evelyne [Guberman and Andreewsky, 1996], which I have sent you. 2. To expand the object. I know three different examples of that kind of change: 1) the surrounding environment of the initial object could serve as a good reference point for parameters in which we are interested. I have a medical example - interpretation of ECGs. 2) The surrounding objects are the same kind of objects S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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and they compete for the limited resources (for example, space). I have an example from oil-field exploration. 3) Dual description of objects (for example, the space of abstract parameters and the real geometrical (Euclidian) space. I have an example from interpretation of the results of geophysical surveys of oil wells. Each example shows that such a transformation of the initial object leads to success. It is now very late. I will continue tomorrow. Good morning! Shelia

Msg.24 History of mathematics From: Gianfranco Subject: Worlds

Date: 04 Nov 2005

Dear Shelia, Yes, the two ways: 1. To add the observer to the object and 2. To expand the object, are very effective. I know how successful you were on applying the first. I would also like to mention another approach, from the history of mathematics, which is more congenial to me. Completely new mathematical worlds were created. I have in mind, for instance, geometry, differential equations and cardinality for dealing with the infinite. A very interesting (systemic) point is to enquire about the homogeneity or non-homogeneity of a culture from a disciplinary point of view, that the harmonic development of, for instance, mathematics, philosophy, linguistic, physics, architecture, music and so on: one discipline is spurred on by the others. Thank you for spending your time (even late at night) on our discussions. Good morning! Gianfranco S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Msg.25 Back to the salt mines The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

From: Shelia Subject: Re: Worlds

Date: 04 Nov 2005

Dear Gianfranco, Both of us spend time on such an exchange of ideas, both are equally interested, both of us enjoy it. So, we are happy! It is an interesting point about harmony of development of sciences and free sciences. And this raises another problem - why in some countries at some times there are deviations from that rule. For example, Russia in the 20th century was very good in mathematics and the arts but poor in biology, philosophy, physics. My understanding is that the cause is the Russian education system. On the contrary, here in the US people hold the opposite view - that a Russian education is superior to an American one. They are wrong. Oops! Sorry, I promised not to use that word - I have to say ”they don’t match my cultural pattern”. I found support for my point of view in the brilliant book by Richard Feynman - American physicist, Nobel prize winner and joker - ”Surely You’re Joking, Mr. Feynman”. I learned a lot from this book about science and life and I re-read it every couple of years. OK. Now back to salt mines. Step 5, point b: reviewing the partition of the whole (dividing the system into parts). How can System Science help on this problem? 1. This is the main goal of Gestalt psychology, which is a part (in fact, the first part) of Systems Theory. The main rules of grouping (proximity, similarity, common fate, good continuation, closeness) explain how our mind organizes our visual perception. There is a generalization of Gestalt principles (which are applicable to the real 3-dimensional world) to abstract N-dimensional spaces. Please look at the paper on clustering I sent you, by Prof.Wojtkowski and myself [Guberman and Wojtkowski, 2002]. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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2. Michael Bongard’s Imitation Principle 1 This principle states that the best language for describing objects is the language which describes the creation of the object. In the cases of handwriting and speech recognition it was the key to the solution (see my paper with Evelyne [Guberman and Andreewsky, 1996]). I also applied it successfully to the problem of recognizing polyhedrons in drawings. The tricky question was: who produces polyhedrons? I published a paper on that matter. The principle is applicable to perception of art in general (not only visual art) - dancing, instrumental music. When you listen to a singer, you perceive not only the sequence of notes, but the depth of singer’s breath, the tension of his chest, the inclination of his body. One has to take into consideration all of this when investigating the perception of vocal art. 3. Not long ago I found that one of the basic principles of Gestalt psychology is really a particular case of the ”imitation principle”. Whilst looking at a drawing the observer recreates the plan which was in the mind of the creator of that drawing: which were the parts of his plan and in which sequence they were generated. This approach eliminates one of the basic Gestalt principles (closeness) as it becomes extraneous. Best wishes, Shelia

Msg.26 Ergodic systems, fluctuations . . . and Damn the Details! From: Gianfranco Date: 06 Nov 2005 Subject: Partition of the whole

Dear Shelia, You wrote: S. [Msg.25 . . . Both of us spend time on such an exchange of ideas, both are equally interested, both of us enjoy it. So, we are 1 M.

Bongard - brilliant Russian scientist, died at the age of 45, see his book on recognition problems [Bongard, 1970] S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


60 happy! The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

It is an interesting point about harmony of development of sciences and free sciences. And this raises another problem - why in some countries at some times there are deviations from that rule. For example, Russia in the 20th century was very good in mathematics and the arts but poor in biology, philosophy, physics. My understanding is that the cause is the Russian education system. On the contrary, here in the US people hold the opposite view - that a Russian education is superior to an American one. They are wrong. Oops! Sorry, I promised not to use that word - I have to say ”they don’t match my cultural pattern”. I found support for my point of view in the brilliant book by Richard Feynman - American physicist, Nobel prize winner and joker ”Surely You’re Joking, Mr. Feynman”. I learned a lot from this book about science and life and I re-read it every couple of years. ...]

I think this point about harmony of development of sciences and free sciences can not be a rule. This is what we expect to take place under normal conditions, that is, for instance, without fluctuations. Normal systems can also be considered ergodic systems, to which it is possible to apply the traditional methods of statistical mechanics, in order to connect in a clear way the microscopic features with the macroscopic phenomenology. By the way the property of ergodicity is completely lost during a structural change or a phase transition. I think that we may enquire about the effects of structural changes on all aspects of a system and not only on those related to the structural aspects directly involved in the process of change. So the rule is not the assumption of harmonic, linear change in all aspects of the system, but modelling the system of complex processes of change. Yes, you are right (Oops! this is becoming contagious!) I also love Feynman’s book.

S. [Msg.25 . . . OK. Now back to salt mines. Step 5, point b: reviewing the partition of the whole (dividing the system into parts). How can System Science help on this problem? S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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1. This is the main goal of Gestalt psychology, which is a part (in fact, the first part) of Systems Theory. The main rules of grouping (proximity, similarity, common fate, good continuation, closeness) explain how our mind organizes our visual perception. There is a generalization of Gestalt principles (which are applicable to the real 3-dimensional world) to abstract N-dimensional spaces. Please look at the paper on clustering I sent you, by Prof. Wojtkowski and myself [Guberman and Wojtkowski, 1996]. 2. Michael Bongard’s Imitation Principle. This principle states that the best language for describing objects is the language which describes the creation of the object. In the cases of handwriting and speech recognition it was the key to the solution (see my paper with Evelyne [Guberman and Andreewsky, 1996]). I also applied it successfully to the problem of recognizing polyhedrons in drawings. The tricky question was: who produces polyhedrons? I published a paper on that matter. The principle is applicable to perception of art in general (not only visual art) - dancing, instrumental music. When you listen to a singer, you perceive not only the sequence of notes, but the depth of singer’s breath, the tension of his chest, the inclination of his body. One has to take into consideration all of this when investigating the perception of vocal art. 3. Not long ago I found that one of the basic principles of Gestalt psychology is really a particular case of the ”imitation principle”. Whilst looking at a drawing the observer recreates the plan which was in the mind of the creator of that drawing: which were the parts of his plan and in which sequence they were generated. This approach eliminates one of the basic Gestalt principles (closeness) as it becomes extraneous. . . . ...]

Back to salt mines (well, I’m disabled and I cannot work in this underground business) . . . 1) I read the paper by Prof. Wojtkowski and yourself about clustering and the DD algorithm [Guberman and Wojtkowski, 2002]. Excellent. Excellent also as a basis for establishing the working framework for the fundamental problem of systems science, i.e., the opposite of clustering. I mean the strategy for the selection of S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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variables, relations, interactions and modelling the macro versus the micro. The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

2) Now we can discuss the most suitable strategy for the selection of variables, relations, interactions and modelling the macro versus the micro. I read your paper which was translated into French by Evelyne [Guberman, 1984]. I was, of course, very interested in the last part, that related to ADLD and systems theory. At the beginning of the paper there is something not clear to me (I translate from French into English): We may carry out a set without being able to define it (by grouping, for instance, the sun, thinking and an orange), but we cannot carry out a set of nondefined objects (p. 168). In mathematics a set is defined by any rule of belonging (given, for instance, by a list of elements or by a property which elements must have). The idea is that anytime I consider an element I am able to decide whether or not it belongs to the set. Having a set is equal to defining it. You note that, for systems, the situation is the opposite: the whole comes before its elements. Trying to translate into your words, I may have a system without being clear about its elements (do you agree?). The issue related to reconstruction is now, for instance, the way by which memory, intended as a process, is assumed, by cognitive science, to work (we do not find something we remember in a warehouse, but actively rebuild it from available details). This is part of the so-called constructivist approach. I understand your point by considering the fundamental role of the observer in deciding the level of description. The question, I think, is: are we looking for rules telling us how to decompose a system into elements, relations, interactions and observer? The rule for reductionism is to consider the microlevel. I think that we should look not for rules, but for non-rule-based strategies and approaches. The only judge is effectiveness. One example for all: Quantum Physics. The principle: the best language for describing objects is the language in which the creation of the object could be described works very well for man-made systems, but what about natural systems? We may assume that there were some ghost creators such as evolution and systemic principles taken as constant in nature, e.g., adaptive, allopoietic, anticipatory, autopoietic, bifurS.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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cating, chaotic, dissipative, equifinal, ergodic, goal-seeking, openclosed, self-organized, and symmetry breaking. This is what transdisciplinarity is about. You mentioned music. On one hand, listening to music may be assumed to be coupled with the representation of what is assumed to produce it (what about blind people who excel in music?). On the other, is the music itself able to induce in the listener what it intended to represent. I am not referring to simple onomatopoeic music. But to music representing logical thought as in Bach (see the Art of Fugue for harpsichord) and situations such as the dying breath of Jesus on the cross in his Saint John Passion. 3) This is the process of abduction. We reconstruct a possible configuration such that it may explain what we are considering. This may be assumed as the strategy by which our cognitive system works and it fits well with the previous point 2. Is the entire Gestalt approach understandable as an abductive approach? The point with General System Theory is that we do not look for any representation which is locally effective, but for representations being generally effective. This is true for the old objectivist view. Best wishes, Gianfranco

Msg.27 From Galileo to Kepler From: Shelia Date: 07 Nov 2005 Subject: Re: Partition of the whole

Dear Gianfranco, The miners force their way through the rocks. We are forcing our way through scientists’ minds - which are much harder (see the paper from Galileo to Kepler in Concluding Remarks). 1. Maybe it was a mistake - to send you the French translation of my paper: a) I don’t know French and I could not be sure that all was OK, and b) the Russian version was written 20 years ago. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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So, let me explain my point of view. Your explanation of a set in mathematics is absolutely correct: you have the elements, you have the rule of belonging - you have the set. There are people in Systems Science who claim that the system (the whole) comes first, the elements are secondary. To me this is nonsense. So, I don’t agree that ”the whole comes before its elements” - in the Russian version it was a quote from somebody’s paper. My point is as follows. The whole can be divided into parts so that each part has a meaning, and the whole has a meaning. This result can be achieved in a recursive process of partition: we generate a hypothesis of a particular partition and if some of the parts (or the whole) don’t have a meaning, we move on to the next partition. The trick is to find a way of decreasing the number of hypotheses. By the way, the algorithm ”Damn the details” in the French paper solves the latter problem (but is not universal) see also the addendum in Appendix C. You will find more in Prof. Wojtkowski’s and my paper in the proceedings of Third Congress on Systems Science in Rome [Guberman and Wojtkowski, 1996]. Here is my answer to your question: ”I may have a system without being clear about its elements” (do you agree?). Yes, if we choose the ”market” as a system, it is not clear to us whether we know all the elements of the market or that we have chosen the right elements (individuals versus families). Only in the end of the recursive process of testing the model (comparing with real data) and improving the model - if we finally succeed - only then we will know what the market is, what are its parts. I agree with you that ”The only judge is effectiveness.” 2.

S. [Msg.26 . . . The principle: ”the best language for describing objects is the language in which the creation of the object could be described” works very well for man-made systems, but what about natural systems? . . . ]

I would like to differentiate between man-made systems: 1) systems whose construction we know about - parts, relations, interactions (the electrical power network of Europe, or a supercomputer), and 2) systems, which also are man-made but we don’t have details of their construction (handwriting, big cities, marS.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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kets). For the former we know the right partition and relations, so they are not of interest to Systems Theory. I understand that the ”imitation principle” is good for the latter case. I agree with you that it doesn’t work for natural systems (life, ecosystems) and I have no solution for that. 3. I don’t understand the meaning of ”abductive approach ” in your question: G. [Msg.26 . . . Is the entire Gestalt approach understandable as an abductive approach? . . . ]

Please, explain. 4. We have done a great job. We have described 5 basic steps in the systems approach. We have formulated some procedures which can help us in improving our models, which means improving the understanding of particular systems. We have also formulated several goals for systems science. Would you like to proceed? What could be the next steps? What particular system would we like to discuss? Best wishes, Shelia PS. I forgot to mention in my previous e-mail that you can find more details about the application of Bongard’s ”imitation principle” to the basic rules of Gestalt psychology in my paper at the last Congress in Paris [Guberman, 2005].

Msg.28 Knowing ”how” and knowing ”why” From: Gianfranco Date: 07 Nov 2005 Subject: Details and sub-symbolic

Dear Shelia, You wrote:



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S. [Msg.27 . . . The miners force their way through the rocks. We are forcing our way through scientists’ minds - which are much harder . . . ]

Yes, you are right. I think we should consider the difference between a) knowing ”how” and b) knowing ”why”. The first question relates to considering analogies and models suitable for various usages. People usually have no idea how, for instance, an electronic watch, or a TV set, or a computer work. They model systems at a level of description suitable for their usage. At this level inquiring about components, relations and interactions is very superficial, i.e., suitable just for their usage. The observer divides the whole into functional components. The second question, ”why?”, relates to more sophisticated models in order to be able, for instance, to fix, design, change and simulate. The observer divides the whole into structural components. Here it would be suitable to apply your intelligent recursive process ”Damn the details”. That way we have a strategy for dealing with details. I have introduced this distinction because I think the strategy doesn’t work with collective behaviors when we use the ”how” approach in a sophisticated way. I will explain. At the moment we model collective behaviors by using tools having the same level of description as the phenomena to be modeled and which are unable to explicitly (that is, symbolically) represent them (is this correct?), i.e., sub-symbolic computation such as neural networks and cellular automata. We may say that in this case we adopt the same strategy as in point a) but having the possibility to simulate and using suitable models. So we have to decide between two possibilities: - We accept that representation will be of a different nature for collective phenomena; - Or we use sub-symbolic representation while waiting for a more general symbolic representation where possible, for instance, by applying your approach. I’m sorry to say that this reminds me of the fundamental difference between quantistic and non-quantistic physics. Are the two problems of the same nature?



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What do you think? The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

Re. the second question: S. [Msg.26 . . . The principle: ”the best language for describing objects is the language in which the creation of the object could be described” works very well for man-made systems, but what about natural systems? . . . ] S. [Msg.27 . . . I would like to differentiate between man-made systems: 1) systems whose construction we know about - parts, relations, interactions (the electrical power network of Europe, or a supercomputer), and 2) systems, which also are man-made but we don’t know have details of their construction (handwriting, big cities, markets). For the former we know the right partition and relations, so they are not of interest to Systems Theory. I understand that the ”imitation principle” is good for the latter case. I agree with you that it doesn’t work for natural systems (life, ecosystems) and I have no solution for that. . . . ]

You are right to make this distinction. Why not apply your strategy when possible? In all other cases, I think we have to face the problem mentioned above about sub-symbolic versus symbolic. S. [Msg.27 . . . 3. I don’t understand the meaning of ”abductive approach” in your question ”Is the entire Gestalt approach understandable as an abductive approach?” Please, explain. . . . ]

I refer to the Gestalt approach, in short, for ideas more than perceptions. We may try to use the strategy to reconstruct the way in which an idea has been generated. Abduction relates to inventing hypotheses able to support models which fit with data. My question is: can the Gestalt approach for ideas be considered as being a process of abduction? S. [Msg.27 . . . 4. We have done a great job. We have described 5 basic steps in the systems approach. We have formulated some procedures which can help us in improving our models, which means improving the understanding of particular systems. We have also formulated several goals for systems science. Would you like to proceed? What could be the next steps? What particular system would we like to discuss? . . . ]

I’m very pleased. My proposals are: First of all, we should organise our correspondence and formulate some conclusions. Could you do that? Of course, I’ll help. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Second, I would like to discuss with you the two main issues of this message: symbolic/sub-symbolic, Gestalt/abduction. Thirdly, I would like to discuss issues and systems related to emergence. I very much appreciate the fact that we have different experiences and approaches to science, but we are both looking for the same kind of result: effectiveness. It may be practical and very abstract (well, to be practical we need to be very abstract, otherwise we are just empiricist). Please let me have your suggestions. Best wishes, Gianfranco

Msg.29 There is nothing better for practice than a good theory From: Shelia Date: 09 Nov 2005 Subject: Re: Details and sub-symbolic

Dear Gianfranco, I received your book yesterday [Minati et al., 2006]. Thank you very much. It looks nice. I suppose it is Bach on the cover. As always I will start with applications because, as you mentioned, effectiveness is the crucial point. I want to learn how systems theory works. From the very beginning, I found some themes familiar to me: cellular automata (I was involved in the early 1960s), lava flow, fingerprints. I hope to find more. I will start with point 3 in your last e-mail. G. [Msg.28 . . . I refer to the Gestalt approach, in short, for ideas more than perceptions. We may try to use the strategy to reconstruct the way in which an idea has been generated. Abduction relates to inventing hypotheses able to support models which fit with data. My question is: can the Gestalt approach for ideas be considered as being a process of abduction? . . . ]

I respect Gestalt psychology very much as a guide to human perception. But I have found nothing reasonable at all in the attempts made to apply it to other areas - social sciences, biology, economics, etc. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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empty words only and nothing behind them. I have attached the full version of my paper [see Appendix B] in Paris - in the second part you will find some examples. But your question still makes sense to me in two ways: 1) Can we use the imitation principle and ”reconstruct the way in which an idea has been generated”? Before answering that question let us recall the usefulness of imitation in the perception of drawings. That way we can construct a brief description of an image, which describes not only the particular image but a family of similar images with the same gestalt (see Appendix B). When one writes the character ”a” the message to the reader is not ”look at that: how big it is, how thick the line is and so on”. The message is: ”Look at that: it is a symbol of ”a””. That is the power of the imitation principle, the power of Gestalt. But in the case of ideas, I can’t find a way to use the history of construction. Any ideas? 2) Is there any way to create new ideas, hypotheses, models? I know two: linguistic and structural. An example of the linguistic way is the use of metaphor. When electricity, in the 18th century, was considered as a fluid, and the flow of electricity through wires was described as a current of fluid through pipes, it gave rise to the ideas behind Ohm’s and Kirchoff’s laws. The essence of the structural way is given in the following examples: i) A car can not be described at the molecular level (i.e., one can’t predict the behavior of the car from its description at the molecular level). To understand the car one needs a small number of big parts - an intermediate level of description (engine, tyres, brakes, fuel tank, . . . ); ii) One can’t deal with a script as a collection of points. One needs an intermediate level of description (the seven elements); iii) One can’t predict the psychological behavior of the brain at the level of neurons. One needs an intermediate level of representation. That is why neurophysiology is in a big crisis. Many other examples could be listed. I would like to bring your attention to the fact that I have used some words, which are keywords in your writings: symbol, description, level of representation. It shows that our vision of the problem is similar. I am very satisfied about this. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Concerning point 2. The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

G. [Msg.28 . . . Why not apply your strategy when possible? In all other cases, I think we have to face the problem mentioned above about sub-symbolic versus symbolic. . . . ]

I agree. Concerning point 1: G. [Msg.28 . . . So we have to decide between two possibilities: - We accept that representation will be of a different nature for collective phenomena; - Or we use sub-symbolic representation while waiting for a more general symbolic representation where possible, for instance, by applying your approach. I’m sorry to say that this reminds me of the fundamental difference between quantistic and non-quantistic physics. Are the two problems of the same nature? . . . ]

I need more explanations and, particularly, examples: 1) symbolic and sub-symbolic; 2) ”we model collective behaviors using tools having the same level of description as the phenomena to be modeled”; 3) what is the analogy with quantum and non-quantum physics? Concerning your proposals 1) I will start to work on a summary of our correspondence. 2) I am ready to discuss all three topics: symbolic/sub-symbolic, Gestalt/abduction, emergence. Please, lead the discussion and please use examples whenever possible. 3) Concerning relations between theory and practice I recall that when I worked on nuclear physics applications I had a slogan on the wall of my lab: ”There is nothing better for practice than a good theory”. Best wishes, Shelia S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Msg.30 Sapir-Whorf hypothesis and explaining From: Gianfranco Date: 10 Nov 2005 Subject: Language, subsymbolic, quantum

Dear Shelia, S. [Msg.29 . . . I received your book yesterday. Thank you very much. It looks nice. I suppose it is Bach on the cover. . . . ]

Yes, you may read some details on the back cover. S. [Msg.29 . . . Can we use the imitation principle and ”reconstruct the way in which an idea has been generated”? Before answering that question let us recall the usefulness of imitation in the perception of drawings. That way we can construct a brief description of an image, which describes not only the particular image but a family of similar images with the same gestalt (see Appendix B). When one writes the character ”a” the message to the reader is not ”look at that: how big it is, how thick the line is and so on”. The message is: ”Look at that: it is a symbol of ”a””. That is the power of the imitation principle, the power of Gestalt. But in the case of ideas, I can’t find a way to use the history of construction. Any ideas?” . . . ]

I think we should consider the tools used to produce ideas and, first of all, language. I’m thinking of constructivism, the Sapir-Whorf hypothesis, the relationship between thought and word is not a thing but a process, a continual movement back and forth from thought to word and from word to thought: .... thought is not merely expressed in words; it comes into existence through them. [Vygotsky, 1962]. I have a research paper in progress with a colleague in the US about that. S. [Msg.29 . . . I would like to bring your attention to the fact that I have used some words, which are keywords in your writings: symbol, description, level of representation. It shows that our vision of the problem is similar. I am very satisfied about this. ...]

Oh, yes. We are in perfect harmony. I would like to concentrate on language. S. [Msg.29 . . . Concerning point 1 I need more explanations and, particularly, examples: 1) symbolic and sub-symbolic . . . ] S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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For instance, when we are able to formalize a process and we write equations, such as the Lotka-Volterra equations, we consider that we have understood. We were able to represent the process and use our representation. When using the sub-symbolic approach, that is, when we use CA or NN we are very effective in using that representation, i.e., simulating, but what about the explanation? S. [Msg.29 . . . 2) we model collective behaviors by using tools having the same level of description of the phenomena to be modelled - what does this mean? . . . ]

This is very close to point 1) above. I mean that we reproduce in an analogue way the collective behavior of elements by using formal agents, but I’m afraid we do not explain it. S. [Msg.29 . . . 3) what is the analogy with quantum and nonquantum physics. . . . ]

I have in mind that in QFT we may have non-equivalent models to explain the same phenomena. Are we doing the same with collective phenomena and emergence? I’m glad you like the book. Best wishes, Gianfranco

Msg.31 Levels of description From: Shelia Date: 12 Nov 2005 Subject: Re: Language, sub-symbolic, quantum

Attachment 3: Shelia, Yes, Nov. 11, 2005 Dear Gianfranco, G. [Msg.30 . . . When we are able to formalize a process and we write equations, such as the Lotka-Volterra equations, we consider that we have understood. We were able to represent the process and use our representation. When using the subsymbolic approach, that is, when we use CA or NN we are very effective in using that representation, i.e., simulating, but what about the explanation? . . . ] S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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I have problems with this difference - I do not see the difference. Let me explain. I have never worked with the Volterra equations. I have worked with the Generic scalar transport equation. It is a very general equation, which describes the flow of any fluid: water, gas, plasma, neutron gas. It describes the balance of matter in each elementary volume, all the transfer processes expressing a certain conservation principle. The physical model is described by that equation. How is the equation used? You can predict the distribution of matter in the given volume by defining 1) the given geometry, 2) the boundary conditions, and 3) parameters of the matter. If you have a computer model that works well, it means that you can make the same predictions by changing the same parameters (the given geometry, the border conditions, and parameters of the matter) and get the same distribution of matter. Did I miss something? S. [Msg.29 . . . 2) we model collective behaviors by using tools having the same level of description of the phenomena to be modelled . . . ] G. [Msg.30 . . . This is very close to point 1) above. I mean that we reproduce in an analogue way the collective behavior of elements by using formal agents, but I’m afraid we do not explain it. . . . ]

1. What are ”levels of description”? In my understanding it is ”descriptions of different levels of the system”. But from the context of your writings it seems that you use it as ”different descriptions of the system”. Which is correct? 2. It is time to discuss ”collective behavior”. Please, describe an example of a system and its model (in CA, NN or any other) S. [Msg.29 . . . 3) what is the analogy with quantum and nonquantum physics? . . . ] G. [Msg.30 . . . I have in mind that in QFT we may have nonequivalent models to explain the same phenomena. Are we doing the same with collective phenomena and emergence? . . . ]

Because at this point ”collective phenomena” arise, I will postpone the discussion (until after we have discussed the previous point).



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Best wishes, Shelia


I have started to summarize our dialogue. First, I have collected all the various points, upon which we explicitly agree. It is funny that each of us has expressed his acceptance of the other’s ideas an equal number of times: 9 versus 9! Take a look at the attached file (Attachment 3). I will continue.



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Written by Shelia on November 11th as a summary of the Dialogue so far. 1) S. [Msg.1 . . . Structure is given by relationships among a set’s elements . . . ] G. [Msg.2 . . . Yes. We may also consider structures of relationships and structures of structures. . . . ]

2) G. [Msg.1 . . . There is a crucial difference between man-made systems (such as the electrical power network of Europe, or a computer) and natural systems (such as the economy, or a living body) . . . ]

. S. [Msg.1 . . . The explanation of this latter fact derives from Statement 1. Because we are not dealing with systems in nature, but with the systems in our mind (i.e., with the description of the system, with the model of the system), the first problem is: how should the whole be divided into parts. In the case of artificial systems we know the design, we know from which parts it was assembled, we know the relationships between the parts. In the case of natural objects the representation of the whole system is not available, we have to choose an adequate partition between an infinite number of possible partitions. Here is the challenge, here is the battlefield for Systems Theory. . . . ] G. [Msg.2 . . . Yes, the systemic view relates to cognitive approaches: we do not discover in an objectivist way only, but think that something does, in a way, depend upon how effective it is to think in this way. . . . ] S. [Msg.5 . . . I agree with you 100% that there is a crucial difference between an artificial (man-made) system and natural systems. For the former, we know the goal of the system, from which parts it was constructed, the relations between the parts, and the parameters that reflect the interaction. For the latter (natural systems) all these questions have to be answered by the observer. . . . ] S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


76 3) The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

S. [Msg.9 . . . I was happy to get your ”Yes” on my question. I am happy as well to share your statement: . . . ] G. [Msg.8 . . . When dealing with systems (and not only) I think we always use the strategy of modelling. To model a system means to have a description of it at a level of description suitable for the interests of the observer. . . . ]

4) S. [Msg.7 . . . Do you agree that before exploring a system the observer has to decide of which elements the system consists, i.e., how the whole has to be divided into parts? Only after this can one define the relations between the parts. As you emphasized, in different tasks the partition of the whole can be different, and consequently the relations between the parts will also be different. . . . ] G. [Msg.8 . . . Yes. . . . ] G. [Msg.8 . . . . . . I agree that in both cases the observer must, as a necessary condition for dealing with the system, select or invent a suitable configuration of components assumed to be interacting. But in the first case ( . . . The modelling of a device (e.g., mechanical or electrical) is related to a level of description of interest to the observer: usually this level of description relates to functionalities . . . ) this is necessary and sufficient (the whole is divided into parts), whereas in the second case it is not . . . ]

5) S. [Msg.11 . . . So, as you put it, ”the truthfulness of the model is its effectiveness for the observer”. So far, it seems to me that we agree on the following. The observer decides: 1. What is the object of his interest (the system). 2. What are the parts of the object (the elements of the system). S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy



3. What kind of relations between the parts are significant for the existence and functioning of the system. In systems with elements possessing cognitive systems we have to define the interaction by means of information. 4. How good is the model of the system. ...]

6) S. [Msg.21 . . . I agree with your last statement. I will try to put it into my own words. If the predictions of some parameters of our model closely agree with the behavior of the real market’s corresponding parameters, we conclude that our model is good and we can use it to our benefit - we could intentionally change some input parameters (such as redistributing our investments) to reap more profit, or predict future critical points in market development (e.g., a bifurcation point). . . . ] S. [Msg.21 . . . History teaches us that most system models, which have been developed during our civilization were wrong. Particularly market models, handwriting models, and oil exploration models (an area, in which I am very much involved). So, how do we proceed? Now comes step 5. 5. Reviewing (reconstructing) the model, which means reviewing one of the following parts of the model (or all of them together): a) Reviewing the whole object of our interest (the simple case - from your example - excluding children or seniors, or in more complex cases - as we both find crucial - including the observer), b) Reviewing the partition of the whole (dividing the system into parts), i.e., changing the elements (for example, the element of the TV-set market may be not a person but a family), c) Reviewing the relations or interactions (as, for example, Santa Fe did: substitute the linear relations with nonlinear ones). It is obvious that everybody can pass steps 1 - 4 but the comparison of the model with the real system has nearly always failed and to proceed one has to review the model. On this crucial S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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point the Theory of Systems has to be the guide. . . . The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

Do you agree with step 5? . . . ] G. [Msg.22 . . . Yes. Absolutely. . . . ]

7) G. [Msg.22 . . . I suggest avoiding use of the word ”wrong”. Rightness or wrongness depend upon what the observer expects. . . . ] S. [Msg.23 . . . Absolutely yes. . . . ]

. 8) S. [Msg.23 . . . 1. To add the observer to the object. According to your approach - that is a fundamental feature of a system (a system exists only as an observer’s model). But for many researchers that is not what they start with. And when they fail to resolve a complex problem and look around for new approaches - this is what the systems approach will recommend first of all. . . . Let me give you an example of how this works in a real application: Handwriting Recognition. Traditionally, handwritten script was described as a line drawing, which consisted of holes, crossings, loops, arcs, etc. Many algorithms had been presented over a period of 40 years but none had succeeded. Then I came up with a different approach, following observations on a patient with brain trauma (demonstrated by Prof. Luria in Moscow Brain Surgery Hospital). I understood that the object I had to investigate was not the script, the image on the paper, but a system consisting of the writer, the script, and the reader. The reader (the observer) doesn’t look at the script as at a dead image, but as a track of the writer’s pen. The essence of the written character is not the geometrical pattern but a kinematic pattern. That approach was a break-through. It improved not only character recognition but also the division of words into characters, eliminating the need for normalization, skeletonization and so on. That technology was licensed 20 years later by two major software houses: Apple Corporation and Microsoft. You can learn more from my paper with Evelyne [Guberman and Andreewsky, 1996], which I have sent you. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy



2. To expand the object. I know three different examples of that kind of change: 1) the surrounding environment of the initial object could serve as a good reference point for parameters in which we are interested. I have a medical example - interpretation of ECGs. 2) The surrounding objects are the same kind of objects and they compete for the limited resources (for example, space). I have an example from oil-field exploration. 3) Dual description of objects (for example, the space of abstract parameters and the real geometrical (Euclidian) space. I have an example from interpretation of the results of geophysical surveys of oil wells. Each example shows that such a transformation of the initial object leads to success. . . . ] G. [Msg.24 . . . Yes, the two ways: 1. To add the observer to the object and 2. To expand the object, are very effective. ...]

9) G. [Msg.26 . . . I may have a system without being clear about its elements . . . ] S. [Msg.27 . . . Here is my answer to your question: ”I may have a system without being clear about its elements” (do you agree?). Yes, if we choose the ”market” as a system, it is not clear to us whether we know all the elements of the market or that we have chosen the right elements (individuals versus families). Only in the end of the recursive process of testing the model (comparing with real data) and improving the model - if we finally succeed - only then we will know what the market is, what are its parts. I agree with you that ”The only judge is effectiveness.” . . . ] G. [Msg.26 . . . The principle: ”the best language for describing objects is the language in which the creation of the object could be described” works very well for man-made systems, but what about natural systems? . . . ] S. [Msg.27 . . . I would like to differentiate between man-made systems: 1) systems whose construction we know about - parts, relations, interactions (the electrical power network of Europe, or a supercomputer), and 2) systems, which also are man-made but we don’t have details of their construction (handwriting, big cities, markets). For the former we know the right partition and relations, so they are not of interest to Systems Theory. I understand that the ”imitation principle” is good for the latter S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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case. I agree with you that it doesn’t work for natural systems (life, ecosystems) and I have no solution for that. . . . ]

G. [Msg.28 . . . Why not apply your strategy when possible? In all other cases, I think we have to face the problem mentioned above about sub-symbolic versus symbolic. . . . ] S. [Msg.29 . . . I agree . . . ]

The score: Gianfranco : Shelia = 9:9


G. [Msg.28 . . . You are right to make this distinction . . . ]


A first balance

Msg.32 Systems Theory is not a theory about Nature but about the Mind

Date: 12 Nov 2005 From: Gianfranco Subject: Re: Note

Date: 12 Nov 2005 From: Gianfranco Subject: Note

Dear Gianfranco,

Whilst compiling the summary it crossed my mind that Systems Theory is not a theory about Nature but about the mind: how the mind (the observer) has to explore nature. It is some kind of meta science. So, by its very nature, it is interdisciplinary. Does this make any sense? Shelia

Msg.33 When Nature understands itself


Chapter 4

Dear Shelia,

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Absolutely, yes. We may enlarge upon this point by considering the inquiring activity of the mind as being not external to Nature, but as an integral part of it: understanding may be recursively (e.g., understanding understanding understanding) considered as an emergent process through which Nature understands itself. In this way Systems Theory as meta-science is the science of Nature, whereas disciplines are simplifications, approximations and reductions based upon considering the mind and Nature as being separated. Congratulations, you have made a very important and crucial point! Thank you. Gianfranco

Msg.34 Lack of a Theory of Emergence From: Gianfranco Date: 12 Nov 2005 Subject: Models, level of representation and more

Dear Shelia, G. [Msg.30 . . . When we are able to formalize a process and we write equations, such as the Lotka-Volterra equations, we consider that we have understood. We were able to represent the process and use our representation. When using the sub-symbolic approach, that is, when we use CA or NN we are very effective in using that representation, i.e., simulating, but what about the explanation? . . . ] S. [Msg.31 . . . I have problems with this difference - I do not see the difference. Let me explain. I have never worked with the Volterra equation. I have worked with the Generic scalar transport equation. It is a very general equation, which describes the flow of any fluid: water, gas, plasma, neutron gas. It describes the balance of matter in each elementary volume, all the transfer processes expressing a certain conservation principle. The physical model is described by that equation. How is the equation used? You can predict the distribution of matter in the S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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given volume by defining 1) the given geometry, 2) the boundary conditions, and 3) parameters of the matter. If you have a computer model that works well, it means that you can make the same predictions by changing the same parameters (the given geometry, the border conditions, and parameters of the matter) and get the same distribution of matter. Did I miss something? . . . ]

I will try to explain my point of view. I’m trying to say something I’m not really sure about, just my point of view to be discussed. When we use a symbolic model we do not only have a tool that works for predicting, but also a tool for designing, controlling and managing. This is because, within the model, we represent our understanding of the phenomenon, the knowledge used to deal with it. When we use a sub-symbolic model, I’m afraid we have a tool which is only good for predicting and simulating. That is, we have a tool designed based on analogy. I mean that we make virtual agents, or cells of CA or neurons and weights of NN, to behave on computers in the same way as real agents do, but we do not have an effective model of them. The theoretical name of this problem is the ”lack of a theory of emergence”. In the former case, when we have a model, we have a higher level of description, whereas in the latter case, we use the same level of description by making virtual agents behave in the same way as real agents do. But this is not a model and there is no understanding in it. In my view models are not just tools but representations of our understanding. What do you think? S. [Msg.29 . . . 2) we model collective behaviors by using tools having the same level of description of the phenomena to be modelled . . . ] G. [Msg.30 . . . This is very close to point 1) above. I mean that we reproduce in an analogue way the collective behavior of elements by using formal agents, but I’m afraid we do not explain it. . . . ] S. [Msg.31 . . . 1. What are ”levels of description”? In my understanding it is ”descriptions of different levels of the system”. But from the context of your writings it seems that you use it as ”different descriptions of the system”. Which is correct? . . . ]

In my view the concept of level of description relates to: a) The disciplinary knowledge adopted by the observer when dealing with a phenomenon. For instance, when considering a human S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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being crying through physics or chemistry or biology or psychology. In a systemic view, different disciplinary knowledge is not considered as an alternative; b) The cognitive model adopted by the observer. In short, a cognitive system may be assumed as being a system of models interacting within a cognitive architecture. For instance, when considering a system of emotions, beliefs, purposes, attitudes, memory, etc.; and c) The kind and quantity of variables, relations and interactions and the scaling used in general by the observer to model a system. S. [Msg.31 . . . 2. It is time to discuss ”collective behavior”. Please, describe an example of a system and its model (in CA, NN or any other) . . . ]

Examples of systems established by collective behavior between agents are: collective behavior of particles giving rise to ferromagnetism and superconductivity; collective behavior of agents, such as ants, wasps and birds, giving rise to ant-hills, swarms and flocks. There are different models in the literature based on sub-symbolic computation, such as NN and CA. S. [Msg.29 . . . 3) what is the analogy with quantum and nonquantum physics? . . . ] G. [Msg.30 . . . I have in mind that in QFT we may have nonequivalent models to explain the same phenomena. Are we doing the same with collective phenomena and emergence? . . . ] S. [Msg.31 . . . Because at this point ”collective phenomena” arise, I will postpone the discussion (until after we have discussed the previous point). . . . ]

OK S. [Msg.31 . . . I have started to summarize our dialogue. First, I have collected all the various points, upon which we explicitly agree. It is funny that each of us has expressed his acceptance of the other’s ideas an equal number of times: 9 versus 9! Take a look at the attached file (Attachment 3). I will continue . . . ]

I have read the attachment. Very impressive! Best wishes, Gianfranco S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Msg.35 Sorry about my engineering mind The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

From: Shelia Date: 13 Nov 2005 Subject: Re: Models, levels and more

Dear Gianfranco, G. [Msg.34 . . . I will try to explain my point of view. I’m trying to say something I’m not really sure about, just my point of view to be discussed. When we use a symbolic model we do not only have a tool that works for predicting, but also a tool for designing, controlling and managing. This is because, within the model, we represent our understanding of the phenomenon, the knowledge used to deal with it. When we use a sub-symbolic model, I’m afraid we have a tool which is only good for predicting and simulating. That is, we have a tool designed based on analogy. I mean that we make virtual agents, or cells of CA or neurons and weights of NN, to behave on computers in the same way as real agents do, but we do not have an effective model of them. The theoretical name of this problem is the ”lack of a theory of emergence”. In the former case, when we have a model, we have a higher level of description, whereas in the latter case, we use the same level of description by making virtual agents behave in the same way as real agents do. But this is not a model and there is no understanding in it. In my view models are not just tools but representations of our understanding. What do you think? . . . ]

It seems that I understand every sentence, but I still have difficulties in understanding the point. It seems that I can’t concretize the problem. Sorry, but I need examples: 1) An example of an existing symbolic model and your comments on how you can use it (in general, is the symbolic model only a mathematical construction, or could it be a computer model?), 2) An example of an existing sub-symbolic model and your comments on how you can use it and what you can’t get using that model. One more question. Consider a system of integral-differential equations, which describes the behavior of a system. Is it a symbolic system? Let S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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us say ”yes”. But if we can’t resolve the system it is of no use: we don’t know how the variables are connected. The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

About ”level of description”: In my lexicon the term ”level” is strongly connected to the structural hierarchy. For example, the body can be described as a system of organs (brain, heart, stomach) - that is the top level of description. Each organ can be described as a system of tissues. That is the first level of description. And so on. But your examples show that the descriptions (chemical, emotional) are parallel, not subordinate. So, maybe in your lexicon ”level” has a different meaning.

G. [Msg.34 . . . Examples of systems established by collective behavior between agents are: collective behavior of particles giving rise to ferromagnetism and superconductivity; collective behavior of agents, such as ants, wasps and birds, giving rise to ant-hills, swarms and flocks. There are different models in the literature based on sub-symbolic computation, such as NN and CA . . . ]

Would you, please, show me a paper on modeling ants, or wasps, or birds with NN or CA and explain to me what is missing in that model, and how the symbolic model should look. Sorry about my engineering mind. Best wishes, Shelia

Msg.36 Observer-oriented From: Gianfranco Subject: Converging

Date: 14 Nov 2005

Dear Shelia, As you know there is a vast literature, such as that produced by the Santa Fe Institute, using sub-symbolic modeling based, for instance, on CA and NN. But I think that, because of my personal problems and S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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point of view, we are going to spend too much time on subjects leading us far from the core of our discussion that we have in progress. We first have to make convergent the process we have started, and already we have some very good results. The subject related to symbolic and subsymbolic models may be discussed later, as an extension of our main discussion. Probably, after consolidating our results, we could move towards the subject of emergence. Levels of description: My view is not only based upon structuring and scaling, related to the system. My view tries to be more observeroriented because this is crucial for emergence and it is also fundamental for the inter- and trans-disciplinary approach for Systems Science. Otherwise, why should Systems Science be inter- and trans-disciplinary? Thank you for having an engineering mind. I have not and this is why we complement each other so well. Best wishes, Gianfranco

Msg.37 Let’s summarize From: Shelia Date: 14 Nov 2005 Subject: Re: Converging

Dear Gianfranco, I agree that we have to summarize our results before moving forward. I will finish the draft of our discussions as a regular text very soon. At the same time I still like the idea of publishing our Dialogue. I think that both versions could be useful. What do you think? If you also agree with this idea, could you prepare a draft? Best wishes, Shelia S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Msg.38 Adding practical examples

Attachment 4: Shelia, Intermediate summary - Final version, Nov. 14, 2005 Dear Gianfranco,

Here is the draft (Attachment 4). Please, take a look and decide what has to be deleted and what has to be added. We can expand the text by 1) explaining in detail our point of view, 2) by adding expanded descriptions for some practical examples. Best wishes, Shelia


From: Shelia Date: 14 Nov 2005 Subject: Re: Converging



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Written by Shelia on November 14th as an Intermediate summary of the Dialogue. Intermediate summary Final version Despite an infinite number of publications on Systems Theory, Systems Approach, Systems Philosophy, Systems Movement there is no widely accepted definition of ”system” or ”systems theory”. Almost every author gives a new definition. We prefer the initial definition given by von Bertalanffy: A set of elements standing in interrelations [von Bertalanffy, 1968, p55]. There is a crucial difference between man-made systems (such as the electrical power network of Europe, or a computer) and natural systems (such as the economy, or a living body). The explanation of that fact comes from statement 1 [Msg.1]. Because we deal not with the systems in nature, but with the systems in our mind (i.e., with the description of the system, with the model of the system), the first problem is: how does the whole have to be divided into parts. In the case of artificial systems we know the design, we know from which parts it was assembled, we know the relations between the parts. In the case of natural objects a representation of the whole system is not available, we have to choose an adequate partition between an infinite number of possible partitions. As soon as the parts are defined the appropriate relations and interactions have to be chosen. Moreover, one can not be sure that the set of objects called a system is complete (contains all parts necessary for normal functioning) or whether there are superfluous parts. The goal of exploring a particular system is to make predictions about that system’s behavior. Accordingly, the final judgment of how well we define the system and how well we describe the system (i.e., define the parts, the relations and the interactions between parts) is the effectiveness of our model (i.e., how well it makes predictions). All the procedures just described assume the existence of an observer. The observer has to define, which objects belong to the system, how the system has to be divided into parts, which kind of interactions will be taken into consideration. To model a system means to have a description suitable for the interests of the observer. In both cases the observer must, as a necessary condition for dealing with the system, select or invent a suitable configuration of components assumed to be interacting. But in the case of a man-made system (e.g., mechanical or electrical device) the observer chooses the S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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description which is interesting to the observer (usually it relates to functionalities). This is necessary and sufficient (the whole is already divided into parts). In the case of natural systems the observer has to invent the configuration. This is a crucial point in creating Systems Theory. The classical sciences will not tolerate the involvement of an observer - a human mind - in a theory. Many difficulties, which Systems Theory has met over the past 50 years, were caused by the intention of developing the theory within the framework of classical science - ignoring the observer. Despite the claim that Systems Theory has no limits, most of the examples mentioned, which need the systemic approach, were natural (non man-made) systems. In that case the observer describes the system. This establishes a close connection between Systems Theory and Gestalt Psychology. This is why von Bertalanffy called Gestalt Psychology ”the predecessor of Systems Theory”[von Bertalanffy, 1968]. In his book von Bertalanffy made a number of important and remarkable statements on the foundations of General System Theory (GST). 1. Von Bertalanffy explained one of the basic statements in system analysis - emergent characteristics: ”The constitutive characteristics are not explainable from the characteristics of isolated parts. The characteristic of the complex therefore, compared to those of the elements, appear as ”new” or ”emergent””. It is clear from that statement that: a) Three terms have the same meaning - constitutive characteristics, characteristic of the complex, and emergent characteristics (we will use the term emergent). b) Emergent characteristics are characteristic of the complex (the whole, the system) as opposed to those of the elements. c) If one examines the isolated parts, the characteristics of each part could be found. By examining the first part, a list of characteristics will be created. By examining the second part some new characteristics could be found, if that part is different (from the first one). When one turns to a new object - the set of parts mentioned above - new characteristics can be defined (like average distance between parts, total weight, S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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centre of mass). Some of them can be calculated from characteristics of isolated parts (for example, total weight, centre of mass), but some characteristics could not (such as average distance between parts). The former are called additive characteristics. If one introduces a new object - the system (which is the set of parts with a defined structure of relations between parts: the whole, the complex), new characteristics will be found (with respect to the parts’ characteristics and the set characteristics), because the object is different. These will be characteristics of the whole - the emergent characteristics. That is why von Bertalanffy describes their main feature as ”new”. They do not appear, they do not emerge (like Venus from the sea foam). They are carefully selected by the observer for resolving a particular problem. 2. Von Bertalanffy stated that systems exist only in the mind of the observer: ”A system as total of parts with its interrelations has to be conceived of as being composed instantly” [von Bertalanffy, 1968, p55]. First, he indicates that the system was composed according to the will of the observer, composed like a symphony or a poem. Secondly, an instant transformation is impossible in the physical world - it is possible only in our minds. 3. Despite the fact that during the last 40 years many definitions of ”system” have been proposed, von Bertalanffy still gave the best: ”A system is a total of parts with its interrelations”. In our intention to emphasize the crucial role of the observer we will interpret the term ”interrelations” in a broader sense as ”relations + interactions”. We define an interaction between parts when changes in one part cause changes in another part, which are described by the observer. Changes described by the observer we will call behavior of the parts. 4. Von Bertalanffy discussed one of the fundamental maxims of the system approach: ”The whole is more then the sum of its parts”. Von Bertalanffy wrote: ” If, however, we know the total of parts contained in a system and the relations between them, the behavior of the system may be derived from the behavior of the parts”[von Bertalanffy, 1968, p55]. That emphasizes the difference between cutting the whole into pieces, S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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which does not lead us to understanding the system, and dividing into parts, which leads us to creating an adequate model of the system and explaining (or forecasting) the system’s behavior. We would like to mention that our definition of the term ”behavior” (within the context of systems) shows that ”behavior of the parts” in von Bertalanffy’s statement reflects not only the parts themselves but the influence on them of the other parts as well, i.e., it takes into consideration the interrelations and interactions between parts. Overall, this statement claims the partition of the whole (in other words - finding an adequate language of description) as a fundamental problem of Systems Theory. To summarize the above we present 5 steps, which the observer has to take when exploring a system. 1. The observer decides what is the object of interest (the system). 2. The observer decides what are the parts of the object (the elements of the system). 3. The observer decides what kind of relations between the parts are necessary for the existence and functioning of the system. In systems with elements possessing cognitive systems we have to define the interaction by means of information. 4. The observer decides how good is the model of the system. 5. The observer reviews (reconstructs) the model, which means reviewing one of the following parts of the model (or all of them): a) Reviewing the whole object of interest, b) Reviewing the partition of the whole (dividing the system into parts), i.e., changing the elements, c) Reviewing the relations or interactions. Up to this point we have formulated a systemic approach, or a systemic philosophy, but not a systemic theory. A theory needs rules to be formulated, as a guide to exploring a system. What rules can we propose for defining or reviewing the object of interest - the system (Step 5, point b)? 1. Adding the observer to the object. This is a fundamental feature of a system - a system exists only as an observer’s model. But S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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for many researchers that is not where they started. And when they fail to resolve a complex problem and look around for new approaches, this is what systems theory will recommend first of all. Here is an example of how it works in an application. Handwriting recognition. Traditionally the handwritten script was described as a line drawing, which consists of holes, crossings, loops, arcs, etc. Many algorithms have been presented over the past 40 years but no one has succeeded. A quite different approach was initiated by observing a patient with brain trauma (as demonstrated by Prof. Luria in the Moscow Brain Surgery Hospital). It turns out that the object to investigate is not the script, the image on the paper, but a system that consists of the writer, the script, and the reader (the observer). The reader (the observer) does not look at the script as a dead image, but as a track of the writer’s pen. The essence of the written character is not the geometrical pattern but a kinematic pattern. The approach was a break-through. It improved not only the recognition of characters but also the division of words into characters, eliminating the need for any kind of normalization (in size, inclination, and thickness). Twenty years later this technology was licensed by two software giants - Apple Corporation and Microsoft. 2. To expand the object. I know three different examples of that kind of change: 1) The surrounding environment of the initial object could serve as a good reference point for parameters, in which we are interested. I have a medical example - interpretation of ECGs [Gel’shtein et al., 1971] 2) The surrounding objects are the same kind of objects and they compete for the limited resources (for example, space). For an example, see the paper in oil field exploration [Guberman et al., 1997]. 3) Dual description of objects (for example, the space of abstract parameters and the real geometrical (Euclidean) space. An example can be found in the interpretation of the results of a geophysical survey of oil wells [Guberman and Izvekova, 1972]. Each example shows that such a transformation of the initial object leads to success. What rules can we propose for Step 5, point b: reviewing the partition of the whole (dividing the system into parts)? S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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1. The Gestalt principles of grouping according to similarity, proximity, good continuation and common faith. Partition is the main goal of Gestalt psychology, which is a part (in fact, the first part) of Systems Theory. It explains how our mind organizes our visual perception. There is a generalization of Gestalt principles (which are applicable to the real 3-dimensional world) to abstract N-dimensional spaces [Guberman and Wojtkowski, 2002]. 2. Michael Bongard’s Imitation Principle.1 This principle states that the best language for describing objects is the language which describes the creation of the object. In the cases of handwriting and speech recognition it was the key to the solution. It was successfully applied to the problem of recognizing polyhedrons in drawings [Guberman, 1980]. The principle is applicable not only to the perception of visual art but to the perception of art in general - dancing, instrumental music. Not very long ago it was found that one of the basic principles of Gestalt psychology is really a particular case of the ”imitation principle”. Looking at the drawing the observer recreates the plan that was in the mind of the creator of the drawing: the various parts of his plan and the sequence in which they were generated. This approach allows one to eliminate one of the basic Gestalt principles (closeness) as extraneous [Guberman, 2005]. We have no general rules for executing step 5, point c) - reviewing the relations or interactions between the elements. But there are negative examples, which show that changing the relations between the given elements of the system does not improve the result, i.e., the usefulness of the model. The reason was that the particular partition of the whole used (the elements of the system) was wrong. As a result no ”improvements” in relations between these elements can bring success. The most prominent example is the Institute of Complexity in Santa Fe (USA). It was organized for dealing with complex natural systems economy, society, culture, environment and so on. The belief was that the solution (creating valid models of these systems) could be done if 1) the relations between the elements were described by non-linear equations, and 2) to resolve these equations using a supercomputer. It was clear from the very beginning that the partitions of these systems were never challenged and therefore there was no chance of success. 1 see

[Bongard, 1970]



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Note added: Abstract from Gel’shtein et al. [Gel’shtein et al., 1971]. Abstract The task was to develop a computer system for automatic interpretation of electrocardiograms (ECGs). The advanced set of ECGs consisted of 12 curves - the electrical signals from 12 points across the rib case. The signals are closely correlated but different. The ECG is a periodical signal. Each period contains the same number of extrema marked Q, R, S, P, T. There are manuals, which describe the typical interval of amplitudes (in mV) for each extremum in each measuring point on the chest for each heart disease. For each particular disease only some extrema in some of the curves are informative. These informative parameters were used for teaching the computer to simulate the diagnoses made by physicians. The results were not satisfactory. So, it was decided to check whether the information in the manuals is sufficient to perform correct diagnoses. For that purpose a set of 12 filtered ECG curves were drawn. In each curve only informative spikes were drawn. The rest of the curve was deleted. As a result on some curves only one spike remained, on some curves two spikes remained (for example, Q and S). When that set of filtered curves was presented to an experienced cardiologist he refused to make any decision. That was an indicator that the physician needs not only the informative spikes but the rest of the spikes - as a reference point. The real information is not in the amplitude of the important spike but in the amplitude ratio between this spike and its neighbours. So, it was decided to present the information to the computer not as numbers (amplitudes) but as typical patterns, like ”Q is higher than S”, or ”Q is equal to S” and so on. As a result, despite the fact that the information became more approximate the results improved dramatically.



How they interact vs. what they are

Msg.39 Publishing our Dialogue Date: 15 Nov 2005 From: Gianfranco Subject: Re: Converging

Dear Shelia,

Of course I agree with the idea of publishing what we have discussed. My first, general idea is to organize a publication articulated in this way: 1) Our Dialogue;

2) Summary (using the text you sent me)

3) Appendices relevant for a better understanding of our Dialogue.

4) References.

This will take care of the first draft of our Dialogue (Part 1). I’ll also propose titles.

With reference to the summary that you sent me, I like it, but I think we have to:


Chapter 5

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a) Expand it with more details and general examples, and The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

b) Add supporting references and examples when we use strong statements, such as: definition of system (”Almost every author gives a new definition”); the negative reference to the Santa Fe Institute. Could you take care of this for Part 1)? I have some unpublished material that can be inserted as appendices. I could propose the text for Part 3). I’m also thinking, for example, about the paper you presented in Paris. Do you have other unpublished material for the appendices? I would like you to prepare a new version, publishable in this context, of your paper ”Reflections on Ludwig von Bertalanffy’s GST . . . ”, published in ”Gestalt Theory” in 2004 [Guberman, 2004]. Then, depending on the quantity, we could decide to publish a paper or a small booklet. Do you have any ideas about that? We could start the references as well. I think we are going to produce a very good contribution for Systems. Best wishes, Gianfranco

Msg.40 The interpretation of the Parts depends upon the Whole From: Shelia Subject: Plan

Date: 16 Nov 2005

Dear Gianfranco, I like your plan and completely agree with it. In the attached file (see Attachment 4) there is an ’Intermediate summary’. I am looking at the proceedings of the Santa Fe Institute. I found a 2005 review of their work on Sport. It might be a good example because everybody knows the issue. I will re-edit the paper on S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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von Bertalanffy. And I also intend to prepare a text for the appendix on the analysis of Aristotle’s famous statements: ”The whole is more than the sum of its parts ”, and ”The part depends upon the whole”. Best wishes, Shelia

Msg.41 An Abductive way of thinking From: Gianfranco Date: 25 Nov 2005 Subject: ”Whole and parts” and our projects

Dear Shelia, Thank you for your appreciative words. I sent a message a couple of weeks ago to Evelyne, to express my gratitude for providing me with the opportunity of meeting you. I like very much the idea that von Bertalanffy’s book may be considered an artistic book able to induce scientific research activities. Sometimes, science, in order not to be self-referential, needs some external, non-homogeneous input (e.g., consciousness and philosophy of mind; the ”second” Wittgenstein). With reference to the ”whole and the parts” I have the following ideas. First of all we could make a distinction between - Elements considered by the observer as elementary, disjointed units (i.e., having no relationships, no interactions between them); - Components considered by the observer as elements, elementary units having relationships and interactions between them, sufficient to establish a system. In the first case the reductionist, that is, non-systemic, approach is based upon considering the properties of aggregations of elements given by the replication of properties of elements (they are additive). Examples: weight, physical dimensions, electrical conductivity, simple thermodynamic properties. In the second case we have to consider various possibilities. In my view, all cases are abductive ways of thinking (see Msg. 26, point 3). S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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1) The observer considers as components of a system that s/he has in mind, non-suitable elements as well as non-suitable relationships and interactions between them. The system doesn’t work (e.g., handwriting recognition as a geometrical problem or the meaning of a phrase as a collection of the meanings of single words). 2) The observer considers as components of a system that s/he has in mind, suitable elements as well as suitable relationships and interactions between them. The system works (e.g., as in the handwriting recognition algorithm and learning processes). 3) The reductionist approach is based upon the assumption that the macroscopic level may be explained by the microscopic level by avoiding any process of emergence (e.g., by reducing psychology to neurology, life to molecular biology and behavior to synapses). In all cases it is a matter of levels of description. I hope you had a good Thanksgiving day. Best wishes, Gianfranco

Msg.42 Measuring my scientific achievement on the Mozart Scale From: Shelia Date: 26 Nov 2005 Subject: Re: ”Whole and parts” and our projects

Dear Gianfranco, 1. Editing: a) Each of us will have to take care of his own part of the text (clarify, shorten, delete repetitions); b) if either of us finds that something can be improved (text or construction) - we will discuss it. 2. Publishing: I have no experience of publishing in the US. My comments on your last e-mail are as follows. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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G. [Msg.41 . . . I like very much the idea that von Bertalanffy’s book may be considered an artistic book able to induce scientific research activities. Sometimes, science, in order not to be selfreferential, needs some external, non-homogeneous input (e.g., consciousness and philosophy of mind; the ”second” Wittgenstein) . . . ]

I agree. Let me tell you my theory on this matter. When I am listening to Mozart, Vivaldi, Paganini, Verdi - my soul is flying very high and the feeling in my heart is so beautiful. Sometimes in my work I find a solution to a hard problem and my soul enjoys it. And I have a feeling of how big my achievement is. How do I measure it? I compare it to the feeling when I am listening to Mozart - that is the absolute scale of spiritual achievement - not the response of the scientific community, not the prizes, not the degrees. G. [Msg.41 . . . With reference to the ”whole and the parts” I have the following ideas. First of all we could make a distinction between - Elements considered by the observer as elementary, disjointed units (i.e., having no relationships, no interactions between them); - Components considered by the observer as elements, elementary units having relationships and interactions between them, sufficient to establish a system. . . . ]

To my understanding an element is always a part of something. According to ”Webster’s” - element is a ”constituent part”. On some occasions the observer decides to take some element out of the whole (of the system) and investigate it as an independent object. One can investigate the solar system, but one can also investigate the Earth - geology. What is wrong with that? Why does it have to be called with the bad word ”reductionism”? Let me explain my understanding of ”reductionism”. Thinking that life can be explained on the physical level (with the laws of physics) - is reductionism and it is a wrong idea, which will never succeed because it will be too complicated. Explain the car at the molecular level is impossible - it is too complicated - the number of elements will be about infinite. But nobody calls it ”reductionism” - it is simple stupidity. The right thing to do is describe the car at a higher level - as consisting of body, engine, brakes, electrical generator and so on. The number of parts (elements) will be reasonable, so our mind can catch S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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the relations between them, i.e., understand the design, the whole. Of course, this works because the parts were chosen, in an adequate manner, by the observer. The observer, however, does not do the partitioning him/herself - s/he gets it from the manual because the car is a man-made object. Is this reductionism? Yes, it is. Look at the definition of ”reductionism”: nature of complex things can always be reduced to (be explained by) simpler or more fundamental things (Wikipedia). So, ”reductionism” is not so bad. Moreover, it is impossible to understand any object (system) if it can not be represented in parts. We both agree that the ”whole” and the ”parts” are inseparable, one doesn’t exist without the other. The only way to understand a complex whole (a system) is by representing it in simpler parts together with their relationships. In my opinion we don’t have to avoid reduction (it is inevitable). The problem is to perform the reduction the right way - reduce the system to adequate parts, to the right description. In many cases we are talking about levels of description: the human body can be described at the levels of organs, the organs can be described at the tissue level, then at cell level, then at molecular level, and so on. Here we have a hierarchy of levels. But this is not always the case. Sometimes the descriptions can not be ordered. For example, the written word can be described as consisting of characters, characters - of strokes (parts of the line with constant curvature), strokes of points. But one can represent characters as consisting of movement elements (represented in my paper with Evelyne [Guberman and Andreewsky, 1996]). The strokes and the elements can not be ordered: they belong to the same level between the level of characters and the level of dots. That is why I prefer to use not the expression ”right level of description”, but ”right description”. The real line of reductionism is between those who claim life can be explained on the basis of the laws of nature vs. those who claim people have a soul or another quality that separates them from the material world. G. [Msg.41 . . . In the first case the reductionist, that is, nonsystemic, approach is based upon considering the properties of aggregations of elements given by the replication of properties of elements (they are additive). Examples: weight, physical dimenS.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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sions, electrical conductivity, simple thermodynamic properties. In the second case we have to consider various possibilities. The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

In my view, all cases are abductive ways of thinking: 1) The observer considers as components of a system that s/he has in mind, non-suitable elements as well as non-suitable relationships and interactions between them. The system doesn’t work. (e.g., handwriting recognition as a geometrical problem or the meaning of a phrase as a collection of the meanings of single words). . . . ]

Yes G. [Msg.41 . . . 2) The observer considers as components of a system that s/he has in mind, suitable elements as well as suitable relationships and interactions between them. The system works. (e.g., as in the handwriting recognition algorithm and learning processes). . . . ]

Yes G. [Msg.41 . . . 3) The reductionist approach is based upon the assumption that the macroscopic level may be explained by the microscopic level by avoiding any process of emergence . . . ]

In my understanding, the macroscopic level is the level of the whole. What is the microscopic level? For me, it is a level consisting of too many parts, so it is impossible to understand how the whole works. In that case assumption 3) is wrong. G. [Msg.41 . . . (e.g., by reducing psychology to neurology, life to molecular biology and behavior to synapses). In all cases it is a matter of levels of description. . . . ]

No, behavior can not be explained in terms of synapses, but the adequate level of describing behavior may not be the level of behavior. One can’t explain behavior in terms of behavior. A reduction has to be made, there have to be more simple units at the next (lower) level, from which the behavior can be constructed. Best wishes, Shelia



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Msg.43 Multiple belonging and emergence The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

From: Gianfranco Date: 26 Nov 2005 Subject: Projects and reductionism

Dear Shelia, S. [Msg.42 . . . 1. Editing: a) Each of us will have to take care of his own part of the text (clarify, shorten, delete repetitions); b) if either of us finds that something can be improved (text or construction) - we will discuss it. . . . ]

Yes, I agree S. [Msg.42 . . . 2. Publishing: I have no experience of publishing in the US. . . . ]

Wita do you have any proposals? Please find my other comments below. G. [Msg.41 . . . With reference to the ”whole and the parts” I have the following ideas. First of all we could make a distinction between - Elements considered by the observer as elementary, disjointed units (i.e., having no relationships, no interactions between them); - Components considered by the observer as elements, elementary units having relationships and interactions between them, sufficient to establish a system. ...] S. [Msg.42 . . . To my understanding an element is always a part of something. According to ”Webster’s” - element is a ”constituent part”. On some occasions the observer decides to take some element out of the whole (of the system) and investigate it as an independent object. One can investigate the solar system, but one can also investigate the Earth - geology. . . . ]

. First of all, there are an indefinite number of ways by which an element can be intended as a constituent of something else. We have to face the possibility of multiple belonging. For instance, a human being may be a component of a corporation (i.e., worker), a component of a family (i.e., a parent or son/daughter) and a component of a team (i.e., S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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a player). By using the word ”element”, I intended none of its possible belongings to be considered, i.e., its possible constitutive roles. When considering an element we abstract from it any of its possible belonging. For instance, we may consider a firm by itself, that is by considering the effectiveness of its production, processing, energy consumption and waste; a particle or a bird at certain levels of isolation. S. [Msg.42 . . . What is wrong with that? Why does it have to be called with the bad word ”reductionism”? Let me explain my understanding of ”reductionism”. Thinking that life can be explained on the physical level (with the laws of physics) - is reductionism and it is a wrong idea, which will never succeed because it will be too complicated. Explain the car at the molecular level is impossible - it is too complicated - the number of elements will be about infinite. But nobody calls it ”reductionism” - it is simple stupidity. The right thing to do is describe the car at a higher level - as consisting of body, engine, brakes, electrical generator and so on. The number of parts (elements) will be reasonable, so our mind can catch the relations between them, i.e., understand the design, the whole. Of course, this works because the parts were chosen, in an adequate manner, by the observer. The observer, however, does not do the partitioning him/herself - s/he gets it from the manual because the car is a man-made object. Is this reductionism? Yes, it is. Look at the definition of ”reductionism”: nature of complex things can always be reduced to (be explained by) simpler or more fundamental things (Wikipedia). So, ”reductionism” is not so bad. Moreover, it is impossible to understand any object (system) if it can not be represented in parts. We both agree that the ”whole” and the ”parts” are inseparable, one doesn’t exist without the other. The only way to understand a complex whole (a system) is by representing it in simpler parts together with their relationships. In my opinion we don’t have to avoid reduction (it is inevitable). The problem is to perform the reduction the right way - reduce the system to adequate parts, to the right description. In many cases we are talking about levels of description: the human body can be described at the levels of organs, the organs can be described at the tissue level, then at cell level, then at molecular level, and so on. Here we have a hierarchy of levels. But this is not always the case. Sometimes the descriptions can not be ordered. For example, the written word can be described as consisting of characters, characters - of strokes (parts of the line S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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with constant curvature), strokes of points. But one can represent characters as consisting of movement elements (represented in my paper with Evelyne [Guberman and Andreewsky, 1996]). The strokes and the elements can not be ordered: they belong to the same level between the level of characters and the level of dots. That is why I prefer to use not the expression ”right level of description”, but ”right description”. The real line of reductionism is between those who claim life can be explained on the basis of the laws of nature vs. those who claim people have a soul or another quality that separates them from the material world. . . . ] G. [Msg.41 . . . In the first case the reductionist, that is, nonsystemic, approach is based upon considering the properties of aggregations of elements given by the replication of properties of elements (they are additive). Examples: weight, physical dimensions, electrical conductivity, simple thermodynamic properties. ...]

In systemic words reductionism is the negation of any processes of emergence. For instance, the more and more detailed study and knowledge of single birds does not allow the observer to ”see” a flock. It is after having seen a flock (thanks to a suitable cognitive model) that the observer may study single birds from a different and more general perspective. Reductionism is to consider that any possible knowledge comes from getting more and more detailed knowledge of the elements. I respect Wikipedia, but this definition is very ineffective. It doesn’t work at all for complexity and chaotic behavior. Identification of components, that is, performing a suitable partitioning of the whole, is a first, necessary, step for defining a system. Then we need to consider emerging properties (e.g., openness, learning and autopoiesis) characterizing the system. Processes of emergence based on a suitable partitioning of the system, on suitable interactions and relationships between parts and on the active role of the observer (equipped with a cognitive system and using a suitable cognitive model) may then be described and managed. This is the whole story, as you well know, of collective behavior and self-organization studied, for instance, in physics by Synergetics and by the theory of Dissipative Structures. The writer of this definition in Wikipedia doesn’t know about it! G. [Msg.41 . . . In the second case we have to consider various possibilities. In my view, all cases are abductive ways of thinking (see Msg. 26, point 3). S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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1) The observer considers as components of a system that s/he has in mind, non-suitable elements as well as non-suitable relationships and interactions between them. The system doesn’t work. (e.g., handwriting recognition as a geometrical problem or the meaning of a phrase as a collection of the meanings of single words). . . . ] S. [Msg.42 . . . Yes. . . . ] G. [Msg.41 . . . 2) The observer considers as components of a system that s/he has in mind, suitable elements as well as suitable relationships and interactions between them. The system works. (e.g., as in the handwriting recognition algorithm and learning processes). . . . ] S. [Msg.42 . . . Yes. . . . ] G. [Msg.41 . . . 3) The reductionist approach is based upon the assumption that the macroscopic level may be explained by the microscopic level by avoiding any process of emergence . . . ] S. [Msg.42 . . . In my understanding, the macroscopic level is the level of the whole. What is the microscopic level? For me, it is a level consisting of too many parts, so it is impossible to understand how the whole works. In that case assumption 3) is wrong. . . . ]

Yes, this is what has been introduced with thermodynamics and statistical physics. The approach based on the assumption that the macroscopic level may be explained by the microscopic, is suitable only when relationships between components are linear, for instance, when properties are additive. Nevertheless this approach is still used even when relationships are non-linear, for instance, for dealing with collective phenomena in social systems (e.g., safety in a social system is not equal to the sum of personal individual safety). This is another devastating form of reductionism, i.e., reducing a system established by non-linear relationships to a system assumed to have been established by linear relationships. I think that this kind of distinction should be emphasized. G. [Msg.41 . . . (e.g., by reducing psychology to neurology, life to molecular biology and behavior to synapses). In all cases it is a matter of levels of description. . . . ] S. [Msg.42 . . . No, behavior can not be explained in terms of synapses, but the adequate level of describing behavior may not be the level of behavior. One can’t explain behavior in terms of S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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behavior - a reduction has to be made, there have to be more simple units at the next (lower) level, from which the behavior can be constructed. . . . ]

Emergent properties, as said above, can be explained not only by using a necessarily lower level of description, but also by considering interactions, relationships and observer, identifiable at the behavioral level. Best wishes, Gianfranco

Msg.44 Reductionism - a terminology problem? From: Shelia Date: 26 Nov 2005 Subject: Re: Projects and reductionism

Dear Gianfranco, Philosophical questions were always difficult for me. So I would like to divide them into small steps. I will answer in a number of e-mails one point at a time. The first one follows. Sorry for this inconvenience. S. [Msg.42 . . . No, behavior can not be explained in terms of synapses, but the adequate level of describing behavior may not be the level of behavior. One can’t explain behavior in terms of behavior - a reduction has to be made, there have to be more simple units at the next (lower) level, from which the behavior can be constructed. . . . ] G. [Msg.43 . . . Emergent properties, as said above, can be explained not only by using a necessarily lower level of description, but also by considering interactions, relationships and observer, identifiable at the behavioral level. . . . ]

Maybe it is a terminology problem. In my mind I have a tree that represents the phenomenon (see Fig. 5.1). At the top is the phenomenon itself (the whole). There is a bunch of arrows from the whole to the second level. At the second level there are (adequate) parts, which are connected by arrows to the whole and to other parts (relationships and interactions). Each part has a bunch of arrows to the second level (to S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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the parts of the parts). It seems that when you mentioned the top level - the level of the phenomenon - it is the first level in my picture. Then I agree that to explain the whole you have to investigate the parts and the relationships between them at the level of the phenomenon itself (which is my first level). If one tries to understand the phenomenon by investigating only the parts - without the relationships between the parts - that is reductionism.

Figure 5.1: Representation of the whole and lower levels of description If so, I have a question: do you know any examples of such an approach? Please, describe it. No such examples come to my mind. Best wishes, Shelia

Msg.45 Is the term linear applicable to systems defined only by formulae? From: Shelia Date: 27 Nov 2005 Subject: Re: Projects and reductionism

Here are more questions. G. [Msg.43 . . . microscopic, is suitable only when relationships between components are linear, for instance, when properties are additive. . . . ] S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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1. Is there an example of a system with linear relationships between components? The example has to contain: The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

a) The name of the system (the phenomenon); b) The list of parts; c) The list of relationships and interactions; d) Proof that the relationships are linear. 2. Is the term ”linear” applicable to systems defined only by formulae? What could this mean for all other cases? G. [Msg.43 . . . Nevertheless this approach is still used even when relationships are non-linear, for instance, for dealing with collective phenomena in social systems (e.g., safety in a social system is not equal to the sum of personal individual safety). . . . ]

3. We don’t have a good model of a social system, so, we don’t know what the adequate parts of that system are. How could we prejudge that the relationships between those parts would be non-linear? G. [ Msg.43 . . . This is another devastating form of reductionism, i.e., reducing a system established by non-linear relationships to a system assumed to have been established by linear relationships. . . . ]

4. When starting to investigate a system it is reasonable to assume that the relationships are linear, because in many, many cases (at least in physics) it works well and many useful results have been obtained. But in many cases it is not true - the relationships are nonlinear. We learn this from unsuccessful attempts to model the system using a linear model. There is no way to know this in advance. But according to the concept (see above), the attempt to build a linear model is reductionism, i.e., it is wrong to do so. In my opinion it is a normal step in scientific research. Best wishes, Shelia S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Msg.46 When processes of emergence are reduced to linear combinations of properties From: Gianfranco Date: 28 Nov 2005 Subject: Linearity, reductionism and more

Attachment 5: Gianfranco, How they interact rather than what they are. Dear Shelia, S. [Msg.42 . . . No, behavior can not be explained in terms of synapses, but the adequate level of describing behavior may not be the level of behavior. One can’t explain behavior in terms of behavior - a reduction has to be made, there have to be more simple units at the next (lower) level, from which the behavior can be constructed. . . . ] G. [Msg.43 . . . Emergent properties, as said above, can be explained not only by using a necessarily lower level of description, but also by considering interactions, relationships and observer, identifiable at the behavioral level. . . . ] S. [Msg.44 . . . Maybe it is a terminology problem. In my mind I have a tree that represents the phenomenon (see Fig. 5.1). At the top is the phenomenon itself (the whole). There is a bunch of arrows from the whole to the second level. At the second level there are (adequate) parts, which are connected by arrows to the whole and to other parts (relationships and interactions). Each part has a bunch of arrows to the second level (to the parts of the parts). It seems that when you mentioned the top level the level of the phenomenon - it is the first level in my picture. Then I agree that to explain the whole you have to investigate the parts and the relationships between them at the level of the phenomenon itself (which is my first level). If one tries to understand the phenomenon by investigating only the parts - without the relationships between the parts - that is reductionism. If so, I have a question: do you know any examples of such an approach? Please, describe it. No such examples come to my mind. . . . ]

In my view, this takes place when emergent properties are reduced to linear composition of properties of elements. For instance, good health for a person is reduced to summing up: having no heart problems, no digestive problems, good blood pressure, no intestinal problems . . . That’s the approach used in hospitals for ”screening” a S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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patient. Another example is given by considering the safety of a social system as being equal to the sum of personal individual safety ( . . . the more people have weapons available and the more they are safe). Dealing with emergent systemic properties means to use other emergent properties and properties of the elements. We may take the example of training a Neural Network. The learning phase is very closely related to the training set established by the observer. G. [Msg.43 . . . The approach based on the assumption that the macroscopic level may be explained by the microscopic, is suitable only when relationships between components are linear, for instance, when properties are additive. . . . ]

. S. [Msg.45 . . . 1. Is there an example of a system with linear relationships between components? The example has to contain: a) b) c) d)

The name of the system (the phenomenon); The list of parts; The list of relationships and interactions; Proof that the relationships are linear.

2. Is the term ”linear” applicable to systems defined only by formulae? What could this mean for all other cases? ...]

Point 1) In short, as you very well know, a linear function f (x) satisfies the following two properties: Additivity: f (x + y) = f (x) + f (y). Homogeneity: f (αx) = αf (x) for every α. Systems that satisfy both homogeneity and additivity properties are linear systems. These two rules, taken together, are often referred to as the principle of superposition.

I’m very grateful for your specific request because it helps to make explicit two important points. We define a structured set as a set in which components all hold relationships between them. Relationships may be linear or nonlinear. Any configuration having linear relationships between the elements may S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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give rise to a linear structured set, often inappropriately named linear system as we shall see below. In this case, the properties of the structured set are linear combinations of the properties of the components. Properties of structured sets are thus not emergent. Example: a) Any classical optical system, which does not include fluorescent parts b) Lenses, mirrors . . . c) List of relationships: they are topological (position and orientation of each optical component) d) Experimental evidence: quantity of light in output is equal to the quantity in input multiplied by (1-attenuation coefficient). The final behavior may be determined a priori. Other examples may relate to networks of amplifiers: the final amplifying power is equal to a multiplication of the properties of single amplifiers. Same for filters. We say that two components interact when one’s behavior influences another’s. More specifically, two components interact when one’s output sets the parameters for the other. We define as a system any structured set when its components also interact amongst themselves (relationships define conditions under which interactions take place). The properties of a system are all emergent, that is they cannot be computed as linear combinations of properties of the elements. It follows that the expression linear system is, in itself, contradictory. G. [Msg.43 . . . The approach based on the assumption that the macroscopic level may be explained by the microscopic, is suitable only when relationships between components are linear . . . ]

that is when dealing with a structured set having linear relationships between components. S. [Msg.45 . . . 2. Is the term ”linear” applicable to systems defined only by formulae? What could this mean for all other cases? ...]

For instance, a way of reasoning may be considered as being linear when considering specific input data only, without other aspects perturbing the linearity of the inference. For instance, a person is considered guilty of something because s/he did it. A nonlinear approach is based upon also considering other related issues. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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G. [Msg.43 . . . Nevertheless this approach is still used even when relationships are non-linear, for instance, for dealing with collective phenomena in social systems (e.g., safety in a social system is not equal to the sum of personal individual safety). . . . ] S. [Msg.45 . . . 3. We don’t have a good model of a social system, so, we don’t know what the adequate parts of that system are. How could we prejudge that the relationships between those parts would be non-linear? . . . ]

What we know at the moment is that by using a certain partitioning of the whole (the reference is to collective behaviors in general), the linear assumption is ineffective, whereas the nonlinear assumption is more effective. It is possible that we will find such a new partitioning suitable to be considered in a linear manner. The use of the linear approach in the first case is a reductionistic approach. G. [Msg.43 . . . This is another devastating form of reductionism, i.e., reducing a system established by non-linear relationships to a system assumed to have been established by linear relationships. . . . ] S. [Msg.45 . . . 4. When starting to investigate a system it is reasonable to assume that the relationships are linear, because in many, many cases (at least in physics) it works well and many useful results have been obtained. But in many cases it is not true - the relationships are nonlinear. We learn this from unsuccessful attempts to model the system using a linear model. There is no way to know this in advance. But according to the concept (see above), the attempt to build a linear model is reductionism, i.e., it is wrong to do so. In my opinion it is a normal step in scientific research . . . ]

I agree that it is suitable to start from the simplest hypothesis. But not always, this is not the case for classes of problems which are already known for some of their specific aspects. My statement relates to systems, i.e., to processes established by processes of emergence, non-linear per se. Generally speaking, it is always possible to hope to find a partitioning of the whole which will be able to establish what are now emergent properties as properties of a linear structured set. In this case, however, we will have to change the definition of system. For the moment the definition of system does not allow one to apply linearity to a nonlinear description of the whole.


Please also find more details in Attachment 5.


Best wishes, Gianfranco


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Attachment 5 Gianfranco Minati The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

When it is more interesting how they interact rather than what they are We refer to emergent properties, that is the properties of systems. We may list several systemic, emergent properties for which the study of the interacting components adds little or no useful information, such as coherency, learning, openness, autopoiesis and anticipation. 1) Reductionism considers that all possible knowledge comes from obtaining more and more detailed knowledge of components. In systemic terms reductionism is the negation of any processes of emergence. For instance, a more detailed study and knowledge of single birds does not allow the observer to see a flock. It is AFTER having seen a flock (thanks to a suitable cognitive model) that the observer may study single birds from a different and more general perspective. 2) Another kind of reductionistic approach is that based upon the assumption that the macroscopic level may be explained by the microscopic. This approach is suitable only when relationships between components are linear, for instance, when properties are additive, such as weight, physical dimensions, electrical conductivity, simple thermodynamic properties. Nevertheless this approach is still used even when relationships are non-linear, for instance when dealing with collective phenomena in social systems (e.g., the safety of a social system is not equal to the sum of personal individual safety). This is another devastating form of reductionism, i.e., the reduction of a system established through non-linear relationships to a system assumed to have been established through linear relationships. 3) Non-systemic approaches are not only based upon the explanation of a higher level of description through the use of a lower one (e.g., by reducing psychology to neurology, life to molecular biology and behavior to synapses), but also by the disjointed usage of the different levels of description and the related specific disciplinary knowledge (i.e., specializations). In this way a phenomenon is considered, for instance, as physical or chemical or S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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biological or psychological. In the systemic view the purpose is not to search for the more general level, but rather to establish the more suitable approach by simultaneously considering all the possible levels of description and the relationships between them. This corresponds to the focusing of the systemic view on inter- and trans-disciplinarity. In this way, a phenomenon is considered, for instance, as physical and chemical and biological and psychological, where the and means that the observer considers the relationships between them and the representations of one into another, as mentioned at several points in our dialogue. Within this framework the dynamical usage and mutual representation of the different levels is the systemic level. It is important to understand how sometimes the purpose of obtaining more generalizations requires more detailed knowledge (e.g., a genome) whereas, in other cases, different cognitive modeling (e.g., detection of collective behavior, such as flocks) is necessary. The effectiveness of focusing upon interactions rather than on the properties of components is shown, for instance, by the widespread usage of agent-based models. Agents do simulate the behavior of elements and their behavioral properties. The balance between the study of emergent properties and structural-functional properties is given by different aspects: 1) Emergent properties bring attention to behavioral properties of components; 2) Higher levels of theory lead to the consideration of structuralfunctional properties in different ways; 3) Experimental data and details, not yet conceived in theories or behaviors are instrumental in abducing the assumption of levels 1 and 2 by introducing generalizations. In any case, it is a question of levels of description and details are not considered in an absolute way, but depend upon the level of description adopted.




Chapter 6 A concluding case

Msg.47 I have to fill these expressions with some particular content From: Shelia Date: 29 Nov 2005 Subject: Re: Publishing and new, improved, draft

Dear Gianfranco, I feel very confused. There are too many words and expressions that I don’t understand. This is because I can’t fill these expressions with some particular content. So, I will try to go through your explanations with some examples in my mind. I would like to use one of your examples. G. [Msg.46 . . . good health for a person is reduced to summing up: having no heart problems, no digestive problems, good blood pressure, no intestinal problems . . . That’s the approach used in hospitals for ”screening” a patient. . . . ]

That is, according to your definition: G. [ Msg.46 . . . a linear composition of properties of elements. ...]

Now I will go through your comments and 1) interpret your statement for the particular case of the abovementioned ”health problem”, 2) ask you to interpret it if I am not able to do so myself. G. [ . . . Point 1) In short, as you very well know, a linear function f (x) satisfies

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the following two properties: Additivity: f (x + y) = f (x) + f (y). Homogeneity: f (αx) = αf (x) for every α. Systems that satisfy both homogeneity and additivity properties are linear systems . . . ]

1. ”Health” is the system, the parts are: heart problems, digestive problems, blood pressure, intestinal problems and so on. Do you agree? 2. Now I want to check whether the additivity property f (x + y) = f (x) + f (y) is true. I suppose that x = heart problems, and y = digestive problems. 3. Now what I don’t understand: a) What is f ()? b) Is f (x) the same in f (x) and f (y)? c) What does ”+” mean? In the definition of linearity ”+” is an arithmetic addition. All is OK with the right ”+” if f (x) and f (y) are arithmetic functions. But what does ”+” mean in (x + y)? The arithmetic addition works between numbers only, but x and y are not numbers, they are states of the body’s sub-systems (heart problems and digestive problems). We can’t use another definition of the ”+” for the left part of the equation because it is essential for the definition of linearity that the ”+” is the same both on the left and on the right.

Or is all my interpretation wrong? Best wishes, Shelia

Msg.48 Logical rather than mathematical representation From: Gianfranco Date: 30 Nov 2005 Subject: Linearity for the example of health S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Dear Shelia, The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

S. [ . . . I feel very confused. There are too many words and expressions that I don’t understand . This is because I can’t fill these expressions with some particular content. So, I will try to go through your explanations with some examples in my mind. I would like to use one of your examples. . . . Msg.47]

Thank you so much. As you will see, I had to reformulate the representation (logical rather than mathematical). At this point, I propose we stop the discussion and concentrate on formatting our exchanges so far.

We may consider the human body as a structured set or as a system. In the first case no processes of emergence are possible. A measurement of its final, global performance is given by a linear combination of measurements of components, as for an electronic amplifier. All measurements relate to input and output, from the source of power to the first component, then from component to component and, finally, from the last component to the overall output. This is the output of the system. In an electronic structured set all measurements relate to signals processed by single components. In this way, the process of measuring relates to physically homogeneous properties. By reducing a complex system (a system is complex when processes of emergence take place within it ) to a structured set we have to reduce: interactions to relations; non-homogeneity amongst the various outputs to a single kind of output.

We may model this reduction (i.e., the human body considered as a structured set rather than a complex system) by considering the general performance of a human body as a linear combination of the performances of its individual organs. Thus, the measurement of good performance for organs is the same as that used for the human body generally. A linear function f (x) satisfies the following two properties: S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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- Additivity : f (x + y) = f (x) + f (y). The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

- Homogeneity : f (αx) = αf (x) for every α. Systems that satisfy both homogeneity and additivity properties are linear systems, i.e., structured sets. We may consider variables such as: GH (Good Health) HP (Heart Problems) DP (Digestive Problems) BP (Blood Pressure) IP (Intestinal Problems) Unfortunately a definition of GH in mathematical terms of HP, DP, BP, IP is not possible because there is no homogeneous way of measuring them.

For modeling this approach (i.e., the human body considered as a structured set rather than a complex system) it may be suitable to consider qualitative issues represented by the values TRUE/FALSE of propositions and binary logical operators such as OR, AND. We may consider logical linearity as being given by the - Associative law (a∗ b)∗ c = a∗ (b ∗ c), where the asterisk represents a binary operator. - Commutative law (a ∗ b) = (b ∗ a), where the asterisk represents a binary operator. Notes: 1) Associativity In propositional logic, conjunction and disjunction are associative; implication is not. Let p and q be propositions: p → q, ’p materially implies q’, means that the conjunction of p and ¬ q is false. If (a*b) → q it doesn’t mean that a → q and b → q. In mathematics, addition and multiplication are associative, subtraction and multiplication are not. For instance: (a + b) + c = a + (b + c) (a − b) − c = a − (b − c)



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2) Commutativity In propositional logic, a proposition that the arguments of a certain function or operator can change place with no effect on the result. Examples are addition, since for any two numbers a, b, a + b = b + a. Disjunction, since for any two propositions p and q, p ν q has the same truth-value of q ν p. Examples of non-commutative operations are subtraction (a − b), division (a/b), exponentiation (ab ), function composition (f or g), and conditional operators since if p then q is not equivalent to if q then p. Consider now the following logical variables: GH (Good Health), assuming values TRUE or FALSE HP (Heart Problems), assuming values TRUE or FALSE DP (Digestive Problems), assuming values TRUE or FALSE BP (Blood Pressure), assuming values TRUE or FALSE IP (Intestinal Problems), assuming values TRUE or FALSE The reductionistic modeling of human health may be illustrated by considering the validity of: (HP and DP and BP and IP ) → GH and GH → (HP and DP and BP and IP ) Where GH = TRUE if and only if HP = TRUE DP = TRUE BP = TRUE IP = TRUE; GH = FALSE if and only if any of the other variables are FALSE. In such a model the activity of the organs are considered as being linearly connected (not sequential). Organs are autonomous units considered sequentially and processing in parallel each other’s output. This is represented by the validity of the commutative law. Parallel processing allows one to model a non-sequential interdependence, but not interactions, avoiding in this way any process of emergence. Interaction is based on the processing of different simultaneous S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Thank you, Shelia. Gianfranco


inputs (with feedback effects), crucial for processes of emergence such as collective behaviors. In this linearly reduced model the process of interaction is not considered. In this model we have only series of problems but not their emergence.



Chapter 7 Concluding Remarks

Galileo to Kepler1 Comrades In the Pursuit of Truth Padua, August 4, 1597 I received your book, most learned sir, which you sent me by Paulus Amberger, not some days since, but only a few hours ago. And as this Paulus has notified me of his return to Germany, I would consider myself ungrateful if I did not now send you my thanks in the present letter. I thank you, therefore, and most especially because you have judged me worthy of such a token of your friendship. So far I have read only the introduction of your work, but I have to some extent gathered your plan for it, and I congratulate myself on the exceptional good fortune of having such a man as a comrade in the pursuit of truth. For it is too bad that there are so few who seek the truth and so few who do not follow a mistaken method of philosophy. This is not, however, the place to lament the misery of our century, but to rejoice with you over such beautiful ideas for proving the truth. So I add only, and I promise, that I shall read your book at leisure; for I am certain that I shall find the noblest things in it. And this I shall do the more gladly, because I accepted the view of Copernicus many years ago, and from this standpoint I have discovered from their origins many natural phenomena, which doubtless cannot be explained on the basis of the more commonly accepted hypothesis. I have written many direct and indirect arguments for the Copernican view, but until now I have not 1 Galileo,

G., 1597, Comrades In the Pursuit of Truth, in: The Portable Renaissance Reader, (Ross, J.B., 1953), 597 (11), Penguin, New York.

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dared to publish them, alarmed by the fate of Copernicus himself, our master. He has won for himself undying fame in the eyes of the few, but he has been mocked and hooted at by an infinite multitude (for so large is the number of fools). I would dare to come forward publicly with my ideas if there were more people of your way of thinking. As this is not the case, I shall refrain. The shortness of time and my eager desire to read your book compel me to close, but I assure you of my sympathy, and I shall always gladly be at your service. Farewell and do not neglect to send me further good news of yourself.

Shelia’s concluding remarks: After three months of intensive work we are midway. To understand where we are, we have to look forward as well as backwards. When we started this dialogue in the fall of 2005, it seemed like two people trying to talk from the opposite banks of a wide river. We are products of different cultures - Italian and Russian; of different social systems - Gianfranco is a product of free society, and I am a product of a totalitarian regime. We have different relations with Systems Science - Gianfranco is a top level professional, and I am, at best, a top level amateur. Gianfranco is a born theoretician, and my background is that of a practical engineer. But despite all the differences there were two points in our understanding of Systems Science which sparked the dialogue. Both were convinced at that moment that something was ”rotten in the state of Denmark”, that significant changes have to be made to Systems Theory. Both were convinced that the crucial point of the theory is to accept the existence of the Observer. And, at last, we were ready for a dialogue because each of us was not afraid to be wrong and to admit it. During these three months we have argued about dozens of issues: meanings of words and expressions, definitions, numbers, formulae, views on Bertalanffy and Galileo in the pursuit of trust. We gave up our positions when we realized that they were no longer justified. We managed to draft a document emphasizing the primacy of the ObS.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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server which: The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

- Formulates the problem, - Defines the phenomena considered together as a system, - Chooses an adequate description of the system in hand, - Checks how well the problem is solved, and which provides the Observer with a number of guidelines and tools to do a better job. If a theory provides recommendations for solving practical problems, then it has to be tested. This allows one to qualify Systems Theory as a scientific theory in accordance with Karl Popper’s criterion - it has to be a means to disprove a theory. This has never been the case so far. Looking at the road ahead I can not see any ”End of the road” sign. But I can see a lot of holes, bumps, and even flooded stretches. Some of them could be mirages but not all of them. There are a number of theoretical notions which I have not completely understood and I will have to work with Gianfranco to clarify them. These are emergence, symbolic and sub-symbolic systems, linearity. There is a bad habit in publications on Systems Theory - some basic notions are defined through the use of other undefined words. Some clearing up has to be done there. As a physicist I find myself uncomfortable when, in non-physical publications, I come across references to some quantum effects. The most popular is Heisenberg’s uncertainty principle. Sometimes it is described as a psychological phenomenon, as an interference between the observer and matter, as a bridge between the living psychic world and the ”dead” world of nature. The point is that the uncertainty principle does not describe the interaction between the electron and the observer, but between the electron and the observation tool. And here I have to admit that I am guilty myself (Mea culpa! Confiteor!). I opened a book of mine published 20 years ago and found the following. ”The same data can be considered as numbers (deterministic model), as random variables (stochastic model), or as logical variables S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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(descriptive model), and one can choose the answer that would better meet the requirements of a specific problem. Such an approach is consistent with the complementary principle by Niels Bohr.” It is obvious that the coding problem described above has nothing to do with Bohr’s principle. But it is such a pleasure to show the high level of the author’s education. And it sounds so solid scientifically that few can resist.

Gianfranco’s concluding remarks: Our dialogue has helped us reach some significant results, such as the importance of selecting suitable partitioning of the whole as well as suitable relations and interactions, for inventing a systemic description of a phenomenon. The dialogue helped to set the cultural framework for describing and handling some crucial issues of systemics such as: reductionism; generalization; lines of research for emergence; reality and constructivism; steps for dealing with systems; Gestalt; the Good-continuation principle; Bougard’s ”imitation principles”; Bertalanffy’s approach; linearity; level of description. We both based our considerations on the theoretical, active, role of the observer (which is passive only when it is a generator of relativism) making abductive inferences about phenomena, as within the cultural framework of constructivism. We still have other issues to discuss, such as symbolic and subsymbolic modeling and some aspects of a future ”Theory of Emergence”. The reason for publishing this dialogue was not to teach something definitive but rather to express a fresh way of understanding the socalled systemic approach, by redefining approaches and ways of thinking too often stereotyped within the Systems community. The Systems community needs to know and use problems and solutions from various disciplines not only to interpret them from a generic (rather than a general ) systemic point of view, but to design fresh, innovating interdisciplinary operational and effective research strategies. The more general, i.e., more theoretical, the view is, the more effective it is, otherwise it becomes only generic or empiricist. This is why the systemic view is abductive, constructivist and, naturally, transdisciplinary, i.e., dealing with systemic properties per se, and interdisciS.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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plinary, i.e., dealing with systemic properties within various disciplines. The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

Our dialogue has been (and continues to be) so productive because, in my view, it is based on logical openness, i.e., a continuous abductive process of mutual modeling sustained by understanding science as an ideal and not as a profession. Shelia in the process of mutual modeling between us retains his rigour as a style and not as a rule. He really visits new places not to see new things in the old light, but to see old things in a new light.

A final reflection from the authors We decided to use the dialogue format inspired by the great scientific tradition culminating in the writings of Plato and Galileo. We also realize the important differences of purpose in that kind of classical publication and our modest attempt. The goal of the great scientists was to prove their ideas. They themselves construct the dialogue. They put in the mouths of their opponents very difficult questions to demonstrate the real power of the ideas they promote. The dialogue represents two points of view, which will not be changed during the conversation. Nevertheless from the very beginning we know who is right and who is wrong. The dialogue presented here is a dynamical process, a conversation of ”comrades in the pursuit of truth” (as Galileo put it). As you can see we started with a lot of differences in understanding terms, definitions, concepts and goals of System Science. During three months of everyday exchange from opposite parts of the globe we were able to work out a common platform on the basics in Systems Science. The essence of the problems we have discussed is ”How to make science?” How to make science before starting to write integro-differential equations? How to make science after it turns out that the model was wrong and the equations don’t work? Our dialogue itself is also a part of the project ”How to make science?” The open discussion of practices used in scientific work is part of a broader cultural trend. In literary studies, not only newly found manuscripts and portraits of Dante and Tolstoy, but also the very history of their discoveries, are of considerable interest. In the theS.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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atre, which had concealed its secrets behind the scenes for so many centuries, today stagehands and decorators, make-up artists and costumiers appear on the stage, - their work often takes place in front of the spectators. On television, microphones and cameras which formerly were carefully concealed now show up constantly on the screen. In architecture, buildings appear in which all engineering services are exposed (George Pompidou National Art and Cultural Centre in Paris). In Puppet Theatre the puppeteer comes out from behind the screen and performs his art in front of everybody. The walls of hairdresser shops are made of glass. We try to investigate the non-formal part of making science to discover which pieces of that part can be formalized and become regular science.



Appendix A

”GENERAL SYSTEM THEORY” AS ”THEORY OF EMERGENCE”1 Gianfranco Minati2 1. Introduction 2. The paradox of a General System Theory without Emergence 2.1 Reductionist usage of the concept of system 2.2 Von Bertalanffy’s view 2.3 Emergence: a non-reductionist usage of the concept of system 2.4 Emergence and General System Theory 2.5 Inter- and Trans-disciplinarity 3. General System Theory and Emergence 4. Conclusions

1 This Appendix is based on a paper published in the Proceedings of the 6th Systems Science European Congress, E.N.S.A.M., Paris, France, Sept. 19-22, 2005. 2 Author’s address: Italian Systems Society, http://www.airs.it Via Pellegrino Rossi, 42 20161 Milano, Italy. Email:[email protected] http://www.geocities.com/lminati/gminati/index.html References in this Appendix are included in the Bibliography Section

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Abstract The concept of system, due to the complexity of problems, is currently necessarily used in many disciplinary fields, but in a reductionist way, based on considering a system as a structured and organised set of interacting elements with focus on structure, organisation, and roles of elements rather than on interaction. This amounts to considering Systems Theory as First-order Cybernetics. Within such a framework only a limited number of systemic properties are considered and a wide range of collective phenomena are ignored. This reductionist approach is used for methodologies and representations, by considering systems established through organised behavior and structures (e.g., devices, corporations and networks) within an objectivistic framework rather than a constructivistic one, without using more general frameworks (as in General System Theory) such as the process of emergence. Emergence is the process of formation of new, self-organised collective entities from the coherent behavior of interacting components - a process that can only be considered as observer-dependent, depending upon the level of description (as for constructivism, not only relative to the observer). Moreover, the reductionist usage of the concept of system implies a lack of focus on trans-disciplinary effects, i.e., systemic properties considered per se, placing emphasis only upon inter-disciplinarity between adjacent disciplines (such as physics and engineering, biology and chemistry) having common models, approaches and languages. Emergence is the framework within which this kind of reductionist usage of the concept of system is not possible. Some problems from specific disciplines and results themselves call for a generalised approach which is not only possible but necessary within the theoretical framework of emergence. A short review of those problems, such as Collective Phenomena; Phase Transitions in Physics; Dynamic Usage of Models (DYSAM); Multiple systems, Uncertainty Principles; Physical and Logical Openness; Modelling Emergence; Systemic meaning of theorisations as in Quantum Field Theories (QFT) is introduced here. The purpose is to identify the systemic contents of disciplinary research having the potential to produce profound innovations in systems research devoted to transdisciplinarity. The change is expected to be so innovative as to name this process with particular reference to emergence: from General System Theory to Theory of Emergence.



133 Introduction


This contribution introduces how, within the framework of the distinction between Systems Theory, based on First-order Cybernetics, and General System Theory, the process of emergence is the general model of the establishment of systems, it is the core of general systems thinking, theoretically based on constructivism based on Second-order Cybernetics. The focus is on emergence, the real web of the theoretical problems of General System Theory. We mention some results from specific disciplines and fields of research having great relevance to General System Theory. We refer to some systemic content of disciplinary research with the potential for producing profound innovations in systems research devoted to trans-disciplinarity. Paradoxically, systemic issues are dealt with by disciplinary research such as Synergetics, Phase transitions, and Collective Phenomena in Physics; Neural Networks, Cellular Automata and Genetic Algorithms in Computer Science; Evolutionary Games Theory in Mathematics; Self-organisation in Biology, Physics and Chemistry; in Cognitive Sciences, Sociology, Economics, Education, and other disciplines [Mikhailov and Calenbuhr, 2002], more than by world-wide established systems societies officially devoted to trans-disciplinarity and expected to culturally support this purpose through conferences, workshops, research projects, by establishing networks, knowledge sources, research centres and networks, publications, and educational activities.

A.1

The paradox of a General System Theory without emergence

General System Theory [von Bertalanffy, 1968] had very important conceptual and cultural effects at least related, if not directly consequent, to its approach. The theoretical and scientific aspects of this approach have been applied in many disciplinary fields, especially in physics, biology, cognitive science and information science leading to the birth, for instance, of the science of complexity [Cowan et al., 1994]. By the way, the cultural impact of the usage of the concept of system, related to the acceptance of a non-mechanistic, non-deterministic view of reality, has been greatly diminished because of its reductionist usage. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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A.1.1


Reductionist usage of the concept of system


The concept of system is often used in a way that we may consider to be reductionist. On this subject let us recall, in short, that: - Set is intended as a group of elements having a rule of belonging, allowing one to decide whether an element belongs to it or not. - Structure is intended as given by relationships among components, such as order, ratio, and connection; - Organisation is intended as given by behavioral rules for elements, such as prioritising, synchronising and selecting; - Interaction between elements takes place when the behavior of one influences that of another, and that there is some overlap amongst the last three concepts. The reductionist usage of the concept of system is based upon the consideration of a system as a structured and organised set of interacting elements with focus on structure and organisation rather than on interaction. In this conceptual view interactions take place within the framework of structures and organisations. Such kinds of systems are artificially designed (e.g., electronic devices or networks) or, in the other cases, modelled by using this level of description (e.g., corporations or living bodies) focusing on roles. In this view systemic properties are related to structure and organisation. Examples of such properties relate to automation, availability, energy-consumption, robustness and reliability, concerning, for instance, electronic and mechanical devices or teams. This level of description in using the concept of system is related to Cybernetics, based on self-regulatory mechanisms as in the well-known Watt regulator. Theoretically, it relates to First-order Cybernetics concerning circular causal processes such as control, negative feedback, automatism, and computing optimisation. This approach gave rise to Control Theory and is used not only for devices and organisations, but has been generalised, that is, applied to different kinds of systems, by considering it coincident with General System Theory. As we shall see, this approach is only a minor part of General System Theory. This initial approach to systems is reductionist because it considers only interaction among elements in organisations and structures and because it is a subset of a larger class identified, as we shall see, by emergence. In this case systemic properties are reduced only to the effects S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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of structures and organisations. In this view each element has a role, a function, and may be substituted, if not functioning correctly, without acting upon all other elements (as for machines). This may be related to symbolic processing compared to sub-symbolic processing [Pessa, 1994]. Moreover, this approach is considered within the philosophical framework of objectivism. Such a reductionist usage of the concept of system is at the basis of Systems Theory rather than General System Theory. This approach is considered within several disciplines focussing upon problems such as self-control and self-regulation: they relate to Firstorder Cybernetics as introduced by [Wiener, 1948] [Wiener, 1961], and developed by [Ashby, 1956]. Generalisation of this approach is allowed by recognising the suitability of the same modelling approach in different contexts, such as when the eye is exposed to light and the pupillary reflex acts as a regulatory process or when in economics, financial actions (e.g., exchange and interest rates) regulate markets. In General System Theory, as introduced by [von Bertalanffy, 1968], generalisation relates to the usage of systemic properties in general, independently from conceptually adopting the same organisation and structure in modelling, see Sec. 2.3. General System Theory is reducible to Systems Theory and related methodologies when considering, for instance, design, control and self-regulation only: this is merely one, less general way of establishing systems. It has now been recognised that systems belong to a larger class established by Second-order Cybernetics and processes of emergence.

A.1.2

Von Bertalanffy’s view

Von Bertalanffy, introduced the concept of system as being constituted of interacting elements Pi (i = 1, 2, . . . , n). Let us briefly recall his approach. Consider a measure Qi for elements Pi . In a system S any variation of Qi is a function of all other variations Qi . In the same way variation of a measure Qi induces variations in all other Qi. This situation is well described by a system of ordinary differential equations:    dQ1 /dt = f1 (Q1 , Q2 , ..., Qn )   dQ2 /dt = f2 (Q1 , Q2 , ..., Qn ) ..  .    dQn /dt = fn (Q1 , Q2 , ..., Qn ) If elements are all of the same kind it is possible to consider the single S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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equation: The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

dQ/dt = f (Q) Interdependence is general and not related to particular roles in organisations and structures. In the case introduced by von Bertalanffy it is not possible to consider such kind of system as a machine where elements may be substituted without acting upon others. This approach to modelling systems is based upon variations of a measure Qi , variations that are a function fi of all other variations Qi . This interaction always takes place even in machines, but it is not relevant for certain levels of description. It is not relevant when focusing, for instance, upon certain levels of description regarding regulation, control and reliability. How do the interacting elements transform into a new reality (i.e., system) - different from a machine, structure or organisation (such as flocks, swarms, industrial districts and traffic)? The answer is through the process of emergence.

A.1.3

Emergence: a non-reductionist usage of the concept of system

What is emergence and why is it so important in modern cultural and scientific approaches? A formal definition of emergent properties has been introduced by [Baas and Emmeche, 1997]: ”Let {Si }i ∈ I be a family of general systems or ”agents”. Let Obs1 be ”observation” mechanisms and Int1 be interactions between agents. The observation mechanisms measure the properties of the agents to be used in the interactions. The interactions then generate a new kind 1 of structure S2 = R (Si , Obs1 , Int1 ) which is the result of the interactions. This could be a stable pattern or a dynamically interacting system. We call S2 an emergent structure which may be subject to new observational mechanisms Obs2 . This leads to the following definition: P is an emergent property P ∈ Obs2 (S2 ) and P ∈ / Obs2 (S1i ) Property P of S 2 is emergent if and only if it is observable on S 2 but not at a lower level, i.e., at the S 1 level.” For instance, while observing the behavior of a group of cars or people, the flight patterns of a group of bees, one might conclude that S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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they respectively form traffic jam, a crowd and swarms (property P). The property P, not observable by looking at individual behavior, is said to be an emergent property of the group. In short, emergence is: • A process of formation of new, self-organised, collective entities from the coherent behavior of interacting components (for instance flocks, automobile traffic, industrial districts, superconductivity, ferromagnetism and the laser effect). Emergence is identified with order-disorder transitions, when ordered frameworks occur within systems fulfilling suitable boundary conditions. Such processes have been denoted as self-organisation processes and this term has become synonymous with emergence. • A process that can only be considered as observer-dependent, that is by taking into account that: - Collective properties emerge at a level of description higher (i.e., by using a more general cognitive model) than the one used for component parts; - Collective properties are detected as new by the observer depending upon the cognitive model adopted, and which can detect the establishment of coherence. The role of the observer is related to the work of von Foerster in Secondorder Cybernetics [von Foerster, 1981] [von Foerster, 2003]. The concept of emergence allows one to avoid the classical objectivistic approach without adopting a merely relativistic one, whilst supporting and inducing a constructivist one based upon Cognitive Science. The previous Section considered suitable interactions, structures and organisations as conditions for the establishment of a system. Without considering structures and organisations, interaction is still a necessary, but not sufficient, condition for the emergence of a system: ways of interacting must be such as to establish self-organised collective entities from coherent behaviors, detected by an observer. In Systems Theory focus is placed upon organisation and structure (as for machines and corporations: the design is explicitly established or assumed by the agent-designer ). In emergent phenomena there is self-organisation detected by using the cognitive model of the S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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observer (such as flocks and industrial districts: comprehended as selforganised by the agent-observer) and may be detected at a lower level by considering the ergodic behavior of agents [Minati, 2002a] [Minati and Pessa, 2006]. At different levels of description and with reference to the cognitive model used by the observer: • Interacting elements may make emergent a system having emergent properties supported by continuous processes of interaction (e.g., swarming); • Interacting elements may generate stable or unstable results of processes of interaction (e.g., ferromagnetism); • Interacting elements may generate processes of emergence realised to be such only at a later moment in time by the observer, thanks to higher levels of knowledge, that is of modelling (e.g., social processes in history; physical processes); • Elements may interact without making emergent (i.e., not recognised as such by an observer) new properties, such as incoherent sounds, words or chemical elements without reacting.

A.1.4

Emergence and General System Theory

The general conceptual framework based upon interactions between elements used to describe the establishment (emergence) of systems having properties different and non deducible from those of their component parts is the basis of the systemic approach showing that the way to manage emergent processes is not to act upon explicit (symbolic models) rules nor upon single elements, but upon interaction (sub-symbolic models). This is possible by acting upon overall parameters (such as order parameters) identified, for instance, in Synergetics [Haken, 1983] [Haken, 1987] and in the study of Dissipative Structures [Prigogine, 1967] [Prigogine, 1980]. Moreover, it is possible to influence system behavior by acting upon their boundaries (i.e., by opening and closing) and upon the general context, that is on the availability of energy and space or by influencing ways of processing information (e.g., by changing weights and layers in Neural Networks and cognitive models for systems provided with cognitive systems). S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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The theoretical framework of emergence does not allow a reductionist, non-systemic usage (i.e., by using Systems Theory instead of General System Theory ) of systemic properties. That is because it relates to collective, self-organised processes in which the reduction of systems to structures and organisation is unsuitable for using and managing them. Within the framework of emergence a non-reductionist usage of the concept of system provides a greater variety of systemic properties related, for instance, to chaos, complexity, dissipation, ergodicity, growing vs. developing, learning, openness, symmetry breaking, etc. The process of emergence may be considered as the general model for the establishment of systems, as the core of general systems thinking, theoretically based on constructivism [Butts and Brown, 1989]. The reductionist usage of the concept of system, based upon designing organisation, structure and functionalities is a particular case of the more general framework of emergence.

A.1.5

Inter- and Trans-disciplinarity

When the conceptual schema of interaction is applied by considering disciplines instead of agents, the process of interacting is named interdisciplinarity. We have inter-disciplinarity when the interaction is intended to take place between approaches and disciplinary knowledge by using the same models, representations and simulations based upon systemic properties, such as adaptive, anticipatory, autonomous, autopoietic, balanced, chaotic, complex, connectionist, deterministic, dissipative, equifinal, ergodic, far from equilibrium, goal-seeking, growing vs. developing, heuristic, hierarchic, homeostatic, in equilibrium, open and closed, oscillating, self-organised, symmetry breaking, etc. In this way, the approaches, problems, and solutions adopted for systemic properties considered in a specific discipline are also used for systemic properties in other disciplines. In the reductionist usage of the concept of system only a few systemic properties are available for designing inter-disciplinarity and, as we shall see, for trans-disciplinary research. Trans-disciplinarity studies systemic properties per se. Transdisciplinarity deals with systemic properties and problems in general, with no reference to specific disciplinary contexts. This is its close connection with General System Theory. The tasks of trans-disciplinarity are to identify systemic properties and study them in general. For instance, the study of openness or complexity as a systemic property per S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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se. Research at trans-disciplinary level uses a higher level of generalisation and abstraction than disciplinary and inter-disciplinary research, but is not independent. If it is considered independent we do not look into the telescope as Galileo’s adversaries did when culture was based upon the assumption of being autonomous, independent from any other level of knowledge. The telescope of trans-disciplinarity is disciplinary and inter-disciplinary research. The study of emergence is a trans-disciplinary issue. Trans-disciplinarity asks questions such as: How may systemic properties be induced? How may systemic properties be managed? How are systemic properties related? How may systemic properties be measured? How may systemic properties be represented? All these questions refer to a single, specific, crucial theoretical issue: modelling emergence, that is the establishment of systemic properties. It is important to clarify that the trans-disciplinary approach relates to the establishment of robust theoretical generalisations (that is, to knowledge based upon systemic properties, applicable to different disciplinary fields) and not to a metaphorical, generic usage of disciplinary knowledge. Generalising requires a crucial theoretical effort, while making generic, metaphoric allows one to extend the usage of the concept by trading with less rigour, less specificity, and lower theoretical levels. This relates to the role of popularising - very different, in systemic terms, from generalising.

A.2

General System Theory and Emergence

General System Theory has often been identified with scientific disciplinary theories, approaches and methodologies based upon a limited, reductionist usage of the concept of system as introduced above. We are now facing the process by which General System Theory is becoming more and more a Theory of Emergence looking for suitable, general models and formalisations of its fundamental bases. Emergence [Minati and Pessa, 2002] refers to the core theoretical problems of the processes from which systems are established. By considering Systemics as a cultural extension of General System Theory (i.e., Corpus of concepts, principles, applications and methodology based on using concepts of interaction, system, emergence, interS.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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and trans- disciplinarity) we correspondingly need to look for, and to be ready for, the establishment of a Second Systemics, a Systemics of Emergence relating to new crucial disciplinary and general issues, such as: 1. Collective Phenomena Examples of Collective Phenomena in physics are, for instance, superconductivity, ferromagnetism, and the laser effect, which are manifestations of collective effects and cannot be described by using traditional models of physics [Minati, 2001] [Minati and Pessa, 2006]. Collective Behavior emerges in social systems leading to, for instance, the emergence of traffic, markets, ethics [Minati, 2002b] [Minati, 2004] and industrial districts [Pyke and Sengenberger, 1992]. In biology, Collective Behavior leads to the emergence of swarms, anthills, herds, biological growth, and societies [Mikhailov and Calenbuhr, 2002]. 2. Phase Transitions, as in physics and in learning processes. In physics a phase relates to the state of matter. In short, a phase is a set of states of a physical system having uniform properties such as density, electrical conductivity and index of refraction. The expression phase transitions relates to processes of changing from one phase of matter to another. First-order phase transitions occur over a finite time and the two phases may coexist. They take place with changes in one or more physical properties when small changes occur, for instance, in a thermodynamic variable, such as temperature [Goldenfeld, 1992]. Examples are transitions between solid, liquid and gaseous phases (boiling, melting and sublimation). Second-order phase transitions occur without continuity and simultaneously over the whole system involved in the process and there is no coexistence of the two phases. This kind of phase transition consists of an internal, global and simultaneous process of restructuring [Minati and Pessa, 2006]. Examples are transitions involving the occurrence of superconductivity and superfluidity, and the transition from the paramagnetic to the ferromagnetic state. The theoretical schema of the phase transition process has been considered in other domains as well, including learning (such as in neural networks) where learning is considered as a phase transition process [Penna and Pessa, 1995]. 3. Dynamic Usage of Models (DYSAM). S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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On the basis of research in different fields such as: The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

- Evolutionary Game Theory [Maynard-Smith, 1982] [Weibull, 1995]; - Evolutionary Stable Strategies (ESS) applied to model ecosystems [Huberman and Hogg, 1988] [Huberman and Hogg, 1993], biological systems [Hines, 1987] [Schuster, 1998], and markets [Gintis, 2000]; - Iterated prisoner dilemma game of great interest for game theorists [Pessa et al., 1998]; it has been well established how, in games with incomplete information and having a high enough level of complexity (such as the iterated prisoner dilemma) one can not have a single equilibrium point, but only a multiplicity of different equilibrium points [Nash, 1950a] [Nash, 1950b] [Nash, 1951]. On this basis, the socalled Dynamic Usage of Models (DYSAM) was introduced, relating to the fact that when dealing with processes of emergence and multiple systems, so-called Collective Beings [Minati, 2001] [Minati and Pessa, 2006], see point 4, the strategy based upon looking for the most effective model is largely ineffective. The strategy introduced with DYSAM is based upon the simultaneous usage of multiple models allowing usage of errors and redundancy (as in models of cognitive science) instead of having the only strategy of avoiding them or of optimising. 4. Multiple systems, emerging from the same components, but simultaneously having different interactions amongst them. The concept of multiple-systems was introduced several years ago in various fields, such as in psychology with multiple-memory-systems [Tulving, 1985]. The concept also relates to the multiple belonging of elements. Multiple systems are considered to emerge from the same elements when simultaneously some of them are undergoing different kinds of interactions [Minati, 2001] [Minati and Brahms, 2001] [Minati and Brahms, 2002] [Minati and Pessa, 2006] naming them Collective Beings. The concept was introduced especially when considering agents equipped with cognitive models and capable of simultaneously handling different kinds of interactions. Examples of Collective Beings are families, workers, buyers, and students: components simultaneously belong to different systems, that is, they handle different interactions. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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5. Uncertainty principles A principle of Uncertainty was introduced, although not intended as such, within the domain of Fourier Analysis. When analysing signals, Fourier Analysis allows one to find the predominant frequency components, but not when a specific frequency component enters into play. In general Uncertainty Principles arise in situations where the phenomenon under study is modelled using fluctuations, fuzziness, probability and noise. The Heisenberg Uncertainty Principle, introduced in 1927 by the German physicist Werner Heisenberg, states that, with reference to atomic or subatomic particles, ”The more precisely the position is determined, the less precisely the momentum (mass times velocity) is known in this instant, and vice versa.” [Heisenberg, 1971]. So far Uncertainty Principles have been considered as relating to the representations used to model a phenomenon. Another way of introducing such a principle is to consider the role of the observer in situations where the process itself of observing interferes with the system under study, as well as in more general contexts with reference to problems of cognitive science, when science studies itself as in the fundamental contributions of von Foerster relating to constructivistic principles [von Foerster, 1981] [von Foerster, 2003]. 6. Physical and logical openness A distinction between thermodynamic and logical openness has been made [Minati et al., 1998]. In logical openness reference is made not only to the thermodynamic flux of matter and energy as in classical definitions. Reference is made to the processing of information and to the mutual modelling adopted by interacting agents. Behaviorism, as introduced by Skinner, is a good example of theory using thermodynamic rather than logical openness: stimuli and reactions are carried across borders by matter-energy, but they are not processed by cognitive models. ”Logical closure” means, in this case, a lack of cognitive processing of information, the interactions being reduced to stimuli. With reference to an observer, by avoiding objectivistic assumptions, it is possible to consider, for instance, different degrees of logical openness. 7. Modelling emergence The problem of modelling emergence is a crucial one in modern science. The issue relates to the modelling process and observer, theoretically and integral part of the process itself, assuming and S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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iteratively redefining such models. Modelling emergence is still an open issue. To cope with this problem we need more than dynamic modelling: dynamics is required not at the same level of description (dynamics of data), but between different levels of description (dynamics of models). The subject relates to modelling as in logical openness [Minati et al., 1998] mentioned above. The subject may be considered, in some ways, as being related to user modelling when observer and observed process both interactively change. 8. Systemic meaning of theoretical approaches such as those of Quantum Field Theories (QFT). The systemic meaning of theoretical approaches such as those of Quantum Field Theory (QFT) in physics with related applications (e.g., biology, brain, consciousness, dealing with long-range correlations), making reference, for instance, to the concept of quantum, quantic vacuum, simultaneity of effects, and long range correlations [Pessa, 1998]. These concepts are already applied not only in the discipline of physics, but in the study of the brain and in theories about consciousness [Vitiello, 2001]. The urgency to adapt and improve the current reductionist systemic approach comes from the need to deal with problems in various disciplines, such as those listed above, and with results reached in specific disciplinary research (such as in physics) having such a level of architectural abstraction that they require re-formulation within a systemic view, suitable for trans-disciplinary usage more than to be just popularised or only metaphorically generalised. This is also a challenge for systems thinking. Conclusion The mission of the systems community is to continue the approaches introduced by L. von Bertalanffy not only by applying and popularising, but also by innovating them within the context of new disciplinary results. We think that the systems community has the mission not just to diffuse methodologies (often based on reductionist concepts of system), but to care about procedures of scientific and artistic production and application of knowledge dealing with technological, scientific, ethical, and humanistic aspects within the framework of emergence. Transdisciplinarity is the core value and to honour it we should continuously S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

deal with disciplinary and interdisciplinary results obtained thanks to systemic approaches applied in various disciplines within the general framework of emergence. If the process of establishing General System Theory as Theory of Emergence does not occur explicitly, supported by the systems movement, then it will be established anyway, emerging from research in the various disciplines, but without the extended generalisation that the systems movement can bestow upon it.


References: see Bibliography.


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Appendix B

Evolution of the ”good continuation” principle1 Shelia Guberman2 ”Wherever the understanding of humanity will take a step forward, there people will honour the name of Max Wertheimer and turn back to his thought with a sense of gratitude and affection” (Solomon Asch, 1946)3

B.1

Introduction

For five decades computer scientists have tried to implement models of human intelligence based on psychological knowledge using computers. In particular, many were pattern recognition and image understanding problems. Naturally, this adopts the use of the basic principles of Gestalt psychology. It is always a challenge to represent psychological theories to a computer: the computer demands an absolutely clear description of terms, notions and procedures, while psychology suffers from fuzziness of many definitions. Therefore, an implementation of any psychological model on a computer takes a lot of work in clarifying psychological terms and notions. Only then could a step toward creating an intelligent computer be made. From such attempts not only 1 This Appendix is based on a paper published in the Proceedings of the 6th Systems Science European Congress, E.N.S.A.M., Paris, France, Sept. 9-22, 2005. 2 Author’s address: Digital Oil Technologies, Cupertino, California, USA 3 Asch, Solomon E., 1946, ”Max Wertheimer’s Contributions to Modern Psychology,” Social Research, 13(1) 81-102

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computer science, but, hopefully, psychology itself will benefit. The imprecise nature or ”softness” of psychological knowledge provides no advantage to the more ”exact” computer science, and does not leave computer science in a superior position. Psychology is still the only basis and source of ideas for Artificial Intelligence - the main road of computer development. In his book ”Productive Thinking” [Wertheimer, 1943] M. Wertheimer in 1943 (before the computer was invented!) forecast many of the problems that computer science would meet over the following 50 years [Guberman and Izvekova, 1972]. He warned about potential mistakes in its development, and proposed a number of solutions. Unfortunately, the computer community did not heed that warning, until now. At the same time, however, there are several examples of successful applications of real psychological knowledge, and particularly of Gestalt Psychology. That paper represents an analysis of one of the basic principles in Gestalt Psychology - the ” good continuation” principle - from the computer (read ”mechanical”, or ”physical”) point of view with all its limitations. By the way, Wertheimer did not counterpose the physics approach to the Gestalt approach. On the contrary, he thought that wenn wir Wissenschaft treiben wollen, wird oft hinzugef¨ ugt, dann m¨ ussen wir ja doch analysieren, auf die Elemente gehen; wer wollte denn wissenschaftlich versuchen, ein solches Fließendes, Str¨ omendes irgend zu fassen? Und dabei tut solches die Physik dauernd! Und dabei ist es bloß ein altes erkenntnistheoretisches Vorurteil, daß die Physik rein mit St¨ ucken arbeite, sondern gerade dies: das Fließende, das Str¨ omende, von Ganzgesetzlichkeiten Beherrschte, ist Arbeitsgebiet der Physik seit mehreren Jahrzehnten [Wertheimer, 1925].

B.2

Good continuation - what does it mean?

All basic Gestalt principles (similarity, proximity, good continuation and so on) help to recognize the organization of an image, i.e., divide the image into appropriate parts and find the relations between them. In the case of the simple drawing in Figure B.1, the image can be described as two intersecting lines ”ab” and ”cd”, or two touching angles ”ac” and ”bd”, or four lines ”aO”, ”bO”, ”cO”, ”dO”. The ”good continuation” principle helps describe the image (i.e., to represent our perception) as containing two parts - two intersecting lines ”ab” and ”cd”. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Why is this choice of representing (describing) the image preferable? What is the meaning of ”good continuation”? As a matter of fact, ”continuation” means a process, which develops over time. But the image is final (it does not change over time), so how can we apply a time-dependent process to that unchanging image? In most cases ”good continuation” is applied to a line so that it is a ”good continuation of the continuation of the line”. The direct interpretation of the term ”continuation” is prolongation of the line, say ”a-b”, beyond the point ”b”. This makes no sense because the drawing is already complete, and there is no intention of changing the drawing by elongating this line. The only reasonable interpretation is if ”continuation” is applied not to the given image itself, but to the imagined process of creating the line. If the process of drawing a given line is done smoothly, i.e., the direc-

Figure B.1: Example of ”good continuation” tion and/or curvature of the pen’s movement do not change much, or do not change at all (straight line), then the continuation of the drawing is easy, and this line could be called a line of ”good continuation” at any point along it (lines ”ab” and ”cd” in Fig. B.1). Thus, the ”good continuation” principle - one of the basic principles of Gestalt psychology - assumes that the perception of a drawing includes the imagined process of recreating (or imitating) the drawing. From all possible partitions of the whole, the set of parts which has the simplest description is preferred. The simplicity of the description reflects: 1) the number of parts (the smaller the number the simpler the description); 2) the relationships between the parts (touching, intersecting, above, to the right); 3) the simplicity of the description of each part. Therefore, the hypothesis of creating the image in Fig. B.1 by drawing the lines point-by-point and in random order has to be rejected as being extremely complicated and practically impossible. The number of parts in the cases of two intersecting lines and two touching S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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corners is the same - two, but to create the whole from the chosen parts is much more difficult in the case of the corners. It is simple to draw the first corner, but drawing the second one requires concentration. First, the vertex of the second corner has to coincide with the vertex of the first one. Second, the direction of the first leg has to be precisely the same as the direction of the appropriate leg of the first corner. That will ensure the smooth continuation through the point of intersection. The same conditions have to be met for the second leg. Overall, it is an arduous problem. This means that the relationships between the parts are very complicated. In the case of intersecting lines the relationships are described by only one condition: intersection. The simplest way to create Fig. B.1 is to draw two intersecting lines. The good continuation through the point of intersection of both lines is ensured by the nature of the pen’s movement - the inertia of the hand together with the pen mass. There are good reasons why imitating the way the drawing was created is a correct approach when looking for a short and sensible description. Before somebody begins to draw one creates a plan. The plan gives instructions about what has to be done and in which sequence. Usually, the plan is created and kept in memory, so the plan can not be too complex. It means that the number of parts in the plan has to be limited, and therefore the whole has to be divided into a reasonable number of parts. Each part has to be as meaningful as possible. This means that in our perception we try to reconstruct the plan, which was in the mind of the person that created the drawing. This also means that the organization we found in the stimuli is really the organization in the drawer’s mind - the organization of the plan. This is true not only when we are dealing with objects created by other human beings but also when we try to understand how any object in nature was created or how it could be created. This is why the first story in the Bible is the ”Creation”. As a matter of fact the main notions of our approach were understood by Wertheimer as early as 1923 in one of his most influential Gestalt papers [Wertheimer, 1923] in which he states: 1. ”On the whole the reader should find no difficulty in seeing what is meant here” clearly indicating that the issue being discussed is perception (”seeing”).” 2. ”In designing a pattern, for example, one has a feeling how successive parts should follow one another; one knows what a ”good” S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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continuation is, how ”inner coherence” is to be achieved, etc.” Here an imaginary action - ”designing a pattern” (which is the plan!) - is used for explaining the perception, and the process of redrawing the image is specified: creating genuine parts and drawing them in the right sequence. 3. Max Wertheimer’s point of view, expressed in his 1923 paper, was represented 60 years later by Michael Wertheimer et al. [Brett et al., 1994]: ”Assemblages of lines and dots are not perceived as unrelated, piecemeal units or as a chaotic mass, but are instead grouped into meaningful configurations based on their similarity, proximity, closure, continuity, and the like, and governed by dynamic processes such as Pragnanz, a tendency toward simple Gestalten”. This is the last part of our interpretation of the ”good continuation” principle - the description has to be as simple as possible. In this way, the interpretation proposed above of ”good continuation” is really a detailed development of Wertheimer’s point of view.

B.3

Wertheimer

Let us now apply this interpretation of the ”good continuation” principle - we will call it the ”imitation principle” - to more complicated drawings used by Wertheimer in 1923. In Fig. B.2 we see, as Wertheimer wrote, an ”arc and a tangent line”. How can such a description be explained by the ”imitation prin-

Figure B.2: Arc with tangent ciple” based on imitating the process of creating the drawing? Both versions (ab/c and ac/b) consist of two parts, and in each version the conditions of ”good continuation” are satisfied. But to draw the version ab/c is easy: one draws the arc and then the tangent line. To draw a tangent line is easy - it is enough to draw a line, which touches the arc; that line will necessarily be a tangent. It is not so easy to draw S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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the version ac/b - first the part ac, and then an arc, which is tangent to the given line at a given point. So, the simplest representation will be ”an arc and a tangent line”. As a matter of fact, in the process of perception we understand not only the right partition of the object but also how successive parts should follow one another: in drawing ”arc + tangent” it is much easier to draw an arc first and then the tangent than vice versa. Wertheimer also introduced other figures to which he ap-

Figure B.3: Wertheimer’s figures: good continuation and closure plied new principles, e.g., closure. From an inspection of Figs. B.3a and B.3b we are led to the discovery of yet another principle: The Factor of Closure. In some cases this factor, together with ”good continuation”, create a contradiction (Fig. B.3c): according to ”good continuation” the figure should be divided into a ”rectangular chain” and a ”smooth line”; according to the ”closure” principle it should be divided into three rectangles. Wertheimer remarks: ”In Fig. B.3c, for example, it is not the three self-enclosed areas but rather The Factor of the ”Good Curve” which predominates”. To clarify the problem let us analyze Fig. B.3d. In this case both factors are also applicable, but now The Factor of Closure will predominate in our perception: we perceive three self-enclosed units. Let us try to eliminate the contradiction by applying the ”imitation principle”. The simplest description for the partition of the second figure is ”three rectangles” and the relations of the parts are simple (they touch each other only at their corners). If we try to represent Fig. B.3c as consisting of three parts the description of each part will be complicated, and the conditions of the connections between the parts will be complicated. It is almost impossible to redraw the first figure by drawing sequentially the first quadrilateral, then the second one followed by the third one. Fig. B.3c creates a Gestalt that is common for a set of figures shown in Fig. B.4, but Fig. B.3d creates a Gestalt, which covers a quite different set of figures (Fig. B.5). As time passed a new definition of ”closure” emerged: the principle of closure applies when we tend to see complete figures even when part of the information is S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Figure B.4: Gestalt for a common set of figures

Figure B.5: Three rectangles: Closure predominates

missing (see appropriate examples in Fig. B.6a). How does the ”imitation principle” manage this situation? The instruction for reproducing Fig. B.6a would be as follows: ”start drawing a circle, continue, and stop before closing the curve”. The description of the closed circle (Fig. B.6b) would be ”start to draw a circle, continue, and stop on closing the curve”. Omitting small details both figures create the same description, the same pattern, the same Gestalt - a circle. The same could be said about Fig. B.6c which happens when a circle is drawn by hand. From a

Figure B.6: Closure of a circle even with missing information mathematical point of view the circle with a gap is not a circle (because a circle consists of all points at a given distance from the centre. It differs from an ideal circle in a number of ways: one has a closed curve, and the other does not; one has derivatives at each point of the curve, and the other does not at two points (the ends of the curve). In our perception we represent the figures not as geometrical abstracts but as tracks of movements in the real physical world, which are never precise and are exposed to perturbations. In this representation, contrary to the mathematical one, all the figures are the same: ”circles”. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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B.4

Kohler


Six years later, in 1929 W. Kohler published the book Gestalt psychology [Kohler, 1929] in which he expressed two important ideas. The first is that ”particular visual shape goes with the existence of a corresponding visual unit which, when segregated, has the shape” (p.108). It means that we perceive not the abstract shapes, but real objects which have that particular shape. The second idea is that ”the things around us are for the most part very stable entities” (p.110). Both ideas establish connections between our perception and the real world. In his book Kohler discussed similar problems using more complicated figures (see, for example, Fig. B.7a). Kohler posed a reasonable question: why don’t we see in Fig. B.7a shapes shown in Fig.s B.7b and B.7c? His answer is: ”because we perceive the image as ”a Maltese cross in a quadrangle”, we can’t see at the time other shapes”. This answer is not sufficient because it only leads to the next question: ”why do we perceive the cross without perceiving either shape B.7b or B.7c?” Kohler did not answer the latter question. What could be an answer

Figure B.7: Kohler’s shapes to that question according to the approach described above? ”Maltese cross in a quadrangle” is the simplest description of Fig. B.7a and that fact determines our perception. A description, which includes Fig. B.7b as a part of the whole would be extremely complicated: it is not easy to describe the shape of Fig. B.7b alone, it is not easy to describe the rest of the whole, and it is not easy to describe the structure of the whole, the relations between its parts. That is why unconsciously we perceive ”Maltese cross in a quadrangle”. We can perceive Fig. B.7c as part of the whole only consciously, only logically by isolating imaginarily this part from the rest, suppressing, in this manner, the rules of Gestalt perception. Other figures analyzed by Kohler are shown in Fig. B.8. He tries to explain why, in Fig. B.8a, nobody sees the ”4” and why in S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Figure B.8: Figures analyzed by Kohler

Fig. B.8b the ”4” is seen at once. His first remark is ”it is by no means the unusual character of the environment, which prevents one seeing the ”4” in Fig. B.8a ”. But ”unusual” is not an explanation, it is an emotional response. His second remark is: ”In Fig. B.8a conditions of organization are such as to favor the formation of other objects. In Fig. B.8b an equally strange environment contains no such conditions, and therefore the number remains a segregated visual thing”(p.115). Because the meaning of ”favorable conditions of organization” was not defined, there is no explanation of the phenomena. Kohler’s third remark is: ”In Fig. B.8b the added lines do not tend to fuse with the various parts of the number 4” (p.114). This also is not an explanation, because ”fuse” is not defined. Yes, one can see that ”4” does not ”fuse” with surrounding lines, but why does it not? It can be shown that the problem is not in the strange or complicated environment. In Fig. B.8c the environment for ”4” is minimal (one additional short line) but the result is amazing - one does not see the ”4” but the trident. All these cases are explainable using the ”imitation principle”. Fig. B.8a has to be described as ”two unknown objects through which a horizontal line is drawn”(p.108). Any other description would be extremely complicated. So ”4” is not a part of that description of the whole and therefore can not be seen. Fig. B.8b can be described as ”4” + 6 straight lines + two waves + two circles, and can be reproduced that way. Thus ”4” is a generic part of the whole and can be seen. Fig. B.8c can be described as a 2-dimensional open box + central handle and is drawn that way. Therefore ”4” does not appear. As a matter of fact Kohler was close to the solution: he describes Fig. B.8b as ”4 and added lines” (see above the quote from page 114). This describes precisely the simplest way of creating Fig. B.8b, which is the essence of our approach. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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There is one strange thing in his book: discussing these problems Kohler did not mention the ”good continuation” principle (which leads our perception to seeing the horizontal line as part of the whole in Fig. B.8a) and the ”closure” principle (which determines our perception of two separate objects in Fig. B.8a).

B.5

Arnheim

In the 1950s R. Arnheim discussed the same problems, referring to them in his book ”Art and visual perception” [Arnheim, 1997]. As an example he used Wertheimer’s figure (see Fig. B.9). He understood the local nature of ”good continuation”: ”The local situation suggests one conception, the total context prescribes another. In restricted local terms the horizontal base slides as an undivided whole into the right wing of the curve, although the total structure breaks the same line into two sections, belonging to different subwholes” (p.77).

Arnheim’s conclusion is correct - as ”good continuation” is a local rule it is sometimes overruled by the context, by the whole, despite the description of the situation not being precise. In Fig. B.9 there are two lines with ”good continuation” - one mentioned by Arnheim, and the other the curved line. So, one can not say that ”good continuation” suggests the wrong partition, but one can say that ”good continuation” suggests two possible partitions and the final choice is made by considering the whole. Arnheim also challenged the ”holy banner” of

Figure B.9: Good continuation and total context holism - the whole is more than the sum of its parts: ”The statement is, however, misleading because it suggests that in a particular context the parts remain what they are, but are joined by a mysterious additional quality, which makes the difference. Instead, the appearance of any part depends on the structure of the whole, and the whole, in turn, is influenced by the nature of its parts” (p.78). S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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The statement ”the appearance of any part depends on the structure of the whole” is very similar to another banner of holism - the part depends on the whole, but contains a very important nuance: it talks not about a part, but about the appearance of a part in our perception. This means that the context does not change the part (which is physically impossible), but changes the interpretation of the part in the mind. This small but crucial difference was the cause of major problems in General System Theory. A more detailed analysis of this issue can be found in Guberman [Guberman, 2004]. In a number of cases Arnheim promotes the idea that redrawing, or imitating, the figure is a good way to learn about perception. For example, he describes a series of experiments (p.65), in which the observer of a visual stimulus memorizes the stimulus and reproduces it by drawing. ”According to the basic law of visual perception, any stimulus pattern tends to be seen in such a way that the resulting structure is as simple as the given conditions permit” (p.63).

At a glance, this statement looks very similar to our definition of the imitation principle of perception (see above): from all potentially possible partitions of the whole the set of parts with the simplest description is preferred. The simplicity of the description is defined by 1) diversity of the parts, 2) complexity of the parts, and 3) complexity of the relationships between parts (i.e., the structure of the whole). But, at a second glance some ambiguities appear: 1. What is a ”stimulus pattern”? Within the context of this sentence it has to be something that one can see (a particular drawing, figure, picture or, in general, - a visual stimulus). It exists outside our mind and does not depend upon the observer. But ”pattern” is not an image, ”pattern” does not exist outside our mind; pattern is a product of our perception. 2. What is the ”resulting structure”? The word ”structure” was used a number of times in Arnheim’s book, but there is no definition of a ”structure”. There are ”structural features” that ”can be described by distance and shape”. There is a ”structural skeleton” which is ”created in perception by material shapes, but rarely coinciding with them” (p.93). Examples illustrating the use of ”structural skeleton” do not clarify the issue. In Fig. B.10, b is the structural skeleton of a. The notion of skeleton is well known in computer geometry. When any drawing is represented as an image on a computer screen, the strokes have some final thickness, S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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measured in pixels. In most cases the thickness is in the range of 5-15 pixels. The skeleton is an axial line of the strokes and it has a thickness of 1. Consequently, figure b is the skeleton of a. As a matter of fact, skeleton b is an instruction on how to redraw cross a: take a brush of an appropriate size and move it along the skeleton. The skeleton represents the general description of a cross, the idea of the cross, the pattern, the Gestalt. As Arnheim puts it: ”The pair of axes determines the character and identity of the shape” (ibid ). Using different brushes one obtains different crosses. In that case Arnheim found the right solution in complete accordance with the ”imitation principle”. But it is not clear why b is the structural skeleton, and what the two-way arrows mean. In Fig. B.11 five triangles are represented. In each triangle its

Figure B.10: Figure with its structural skeleton as a general description

Figure B.11: Wertheimer’s five triangles structural skeleton is shown. Arnheim wrote: ”The structural skeleton of each triangle derives from its contours through the law of simplicity: the resulting skeleton (sic! A new term - not a ”structural” skeleton, but a ”resulting” one) is the simplest structure obtained with the given shape” (p.94). Here is how Arnheim describes triangle a : ”Triangle a is characterized by a main vertical and a secondary horizontal axis, which S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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meet at right angles” (p.94). That short sentence poses many questions, without answers. In the previous example (the cross) the two strokes, which represent the skeleton, are really the axes, axes of symmetry, middle lines of the bars, but in this case why is the vertical line drawn outside the triangle its axis? What is the difference between these axes and adjoined legs? Why is the vertical axis the ”main” one: is it because it is ”vertical”? or because it is long? Either guess has a contradictory example (b and c). In b the main axis is the axis of symmetry. In general, structural skeletons considered separately or even collectively can not be rationally explained. The sequence of images in Fig. B.11 is one of Wertheimer’s examples. It was produced as follows: the right corner of the first triangle was continuously moved down transforming the triangle; some of the transformed triangles are shown. ”Wertheimer noted that as the moving point continuously slides downward, changes occur in the triangles that are not continuous. Rather, there is a series of transformations culminating in the five shapes shown” (ibid, p.94). For reasons discussed above, the explanations of this fact proposed by Arnheim (different structural skeletons) is not acceptable. Another explanation can be derived from the ”imitation principle”. All five triangles have a simple description, and all intermediate triangles have a complex description. The descriptions of the trangles shown are: a) right-angled triangle, b) isosceles triangle, c) equilateral triangle, d) isosceles triangle, e) rightangled triangle. Each of these descriptions represents a class of images, a pattern of particular types of triangles, a Gestalt. The intermediate triangles require a description of all three sides and can serve as a description only of one particular triangle. That is why these five, as Wertheimer noted, are culminating shapes in the discussed transformation. Wertheimer was brilliant as always.

B.6

The Imitation Principle and the Spirit of Gestalt psychology

Let us show that such an approach is in complete agreement with the spirit of Gestalt psychology. 1. Partition of the whole is the central theme in Gestalt psychology. Wertheimer emphasized the role of parts in representing the whole. He distinguishes the parts of the whole from pieces: ”. . . the S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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parts are not mere pieces in additional relation together, but parts of the whole” [Wertheimer, 1923]. It states that only the real parts (together with their relations) adequately represent the whole. K. Koffka wrote: ”To apply the Gestalt category means to find out which parts of nature belong as parts to functional wholes, to discover their position in these wholes” [Koffka, 1935]. This was echoed later by L. von Bertalanffy: ”If, however, we know the total of parts contained in a system and the relations between them, the behavior of the system may be derived from the behavior of the parts.” 2. The involvement of reality in perception is the way Wertheimer follows in his book ”Productive thinking”. For example, the ”Area of the parallelogram” problem was resolved by a purely mental process that includes imagined cutting with scissors and moving parts in 3D space. The concept of ”continuation” is based upon modeling the process of creating an image taking into consideration the features of the real physical world (time, velocity, mass, etc.) as well. It also uses the implicit and very reasonable assumption that parts are created in sequence, one after another. In Fig. B.1 this means that the hypothesis that the first couple of points of the line ”ab” were drawn, then some points of the line ”cd”, then back to the first line - is completely unacceptable. One more example of how our perception takes into consideration not only the perceived, but also the reality of the physical world, is represented in Fig. B.12. The simplest way of how the drawing can be created is as follows: 1) draw a set of parallel lines, 2) cut the drawing with scissors along the line ab, 3) shift the right part up. As a matter of fact, on geological cross-sections this pattern identifies a fault and a shift. Let us recall that Wertheimer’s very early experiments with shifted lines demonstrate the effect of movement. From our point of view the perception of the alternating lines has to be interpreted in terms of how this situation can be produced. The only way in the real world to generate this situation is to move the line from one position to another. 3. The perception of Fig. B.1 as ”two intersecting lines”, as a matter of fact, represents not only the given image, but also a set of images (as in Fig. B.13, first row) which our perception will refer to one class, which carry the same pattern, the same Gestalt. One of the important features of that pattern is stability: one S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Figure B.12: A fault with a shift along the faultline can change some parameters of an object (curvature of the lines, intersection point, or length of lines) but the resulting image will still carry the same Gestalt. On the contrary, if one chooses to describe Fig. B.1 as consisting of two angles some changes in the parameters will create a set of images (Fig. B.13, second row), which will not be accepted by our perception as belonging to the same class, to the same pattern, to the same Gestalt, as the initial image does. The characteristics of the Gestalt ”are applicable not only to the individual case in hand but to an infinite number of other cases as well” (ibid, p.133). This generalization function

Figure B.13: Description of figure B.1: First row - as two crossed lines; Second row - as a combination of two angles of Gestalt is remarkable. Over the past 50 years Artificial IntelS.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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ligence has developed a fruitful method for generalizing experimental data (particularly in geology and medicine) by teaching a computer using a set of examples: pattern recognition. But the Gestalt demonstrates the ability of our mind to generalize on the basis of a single example. 4. As a matter of fact, most drawings we see in books, posters, screens, etc. are created not by hand and pen, but by lithography (the complete drawing at once) or by rastering line-by-line. But as soon as the process is finished and we see the final image we perceive it as if it had really been drawn by hand and pen. This is the right thing to do, because the publisher intentionally creates an image which we will interpret as a drawing. These examples emphasize once more that the parts, the smooth movements, the right sequence of drawing parts are products of our perception and are not elements of reality. Also the observed movement of the bar in Wertheimer’s classic experiments does not correspond to any real movement - it is only our interpretation of the visual stimuli.

B.7

Art and technology

Let us take a look at how the principles of ”good continuation” and ”closure” work in applications. We examine two main areas - art and technology. In art it is difficult (and may be impossible) to decide what is right and what is wrong. In technology one can always test whether or not the technology works.

B.7.1

Handwriting

The idea that we perceive a drawing not merely as a static image, but as a dynamic pattern as well, has it roots in psychology. Alexandre Luria, the father of Neuropsychology, described a patient with alexia [Luria, 1970]. After brain damage, this patient lost the ability to read: he was unable either to recognize or to utter handwritten characters or words. During the rehabilitation process, it was discovered that he could read a given character if he traced this character with his finger. In a month, the patient could do it by tracing the character in the air, without touching the paper. In six months he did it while holding his hand in his pocket, but still moving the finger in the pocket. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Many facts support the idea that a character is not only an image pattern but also a movement pattern. One example is very simple but extremely impressive. Try to recognize a character that has been drawn on your back by somebody with his finger. You will generally succeed even without previous experience in doing this. You do not need to ”learn” these images nor do any intellectual work trying to reconstruct the appropriate picture in your mind logically. You only have to understand the movement. In any handwriting, you can reconstruct the path of the pen. You can recognize the starting point of each stroke, the direction of the pen’s movement, the pen’s path in the air, and the sequence of strokes. When we try to recognize an illegible writing sample, we consciously search for the path of writing. Our fingers move unconsciously along this path. Some people write characters in an unusual manner. For example, an ’O’ could be written in a clockwise direction – opposite to the regular (counterclockwise) one – but the resulting image appears the same and readers interpret it as being normal (written in a counterclockwise direction) recognizing the character correctly. For non-connected characters, the direction of writing strokes does not matter. The resulting image will not differ whether or not it is written in the standard direction. The situation changes dramatically when characters (or their parts) are connected. The links force you to follow the path by which the writing was actually done. If the writer uses a regular style of writing characters, we will not have difficulty in recognizing them. But if s/he writes some characters in the opposite direction, we can not interpret them correctly because the links require us to follow this opposite direction, and we fail to recognize this hitherto unknown movement. Try to recognize a character written on your back in a non-regular direction. As an illustration let us consider some examples. The first image in Fig. B.14a will undoubtedly be interpreted as an ’o’ and it does not matter which way it was written. The next one shows the character ’o’ in connection with ’t’. The shape of this ’o’ is the same as in the first image but now we are sure that the ’o’ has been written counterclockwise. The third image contains the same image of an ’o’, but in this case, we are sure that it was written clockwise and interpret it as ’s’. In Fig. B.14b the first character is ”t” and the usual way of writing it is by drawing a vertical bar (from top to bottom) and then crossing it with a horizontal bar (from left to right). Sometimes we encounter people who write the horizontal bar in ”t” from right to S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Figure B.14: Handwriting examples showing the importance of strokes over shapes left. This can not be discerned when the bars are written separately, but if the writer does not lift his pen while writing the ”t”, this could create problems in understanding the writing. The second character was written the regular way and there are no problems in recognizing it as a ”t”. The next character was produced by a writer drawing the horizontal bar from right to left without lifting the pen, and the result is difficult to recognize as a ”t”. In the next character the horizontal bar was drawn first (from left to right) and the vertical bar was drawn after without lifting the pen. The last case is the worst: one will positively recognize the character as a ”4”. The approach based on the ”imitation principle” (by reconstructing the trajectory of drawing) was a breakthrough in the thirty-year-long attempt to develop software for computer handwriting recognition [Guberman and Andreewsky, 1996]. The software developed on these principles was used by both leading software developers - Apple Computers and Microsoft.

B.7.2

Art

I. We have a unique opportunity to compare the analyses made by two different scholars on the same visual object (Michelangelo’s Creation of man) with the same purpose: to explain the perception of the painting from a Gestalt psychology point of view. The first analysis was made by Arnheim [Arnheim, 1997]. ”The structural skeleton (B.15) reveals the dynamic theme of the story”. When one looks at B.10b - the skeleton of the cross - one obtains the essence of the cross from that drawing. When one looks at B.15, which idea could be extracted? Which story does it represent? No idea and no story. But the trick is that Arnheim represents not the ”structural skeleton” of the painting - he represents the ”structural skeleton” on the painting B.16. Here everybody can recognize the sketches of two bodies. Two skeleton lines belong to the S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Figure B.15: Structural skeleton of Michelangelo’s Creation of Man

Figure B.16: Sketch of Michelangelo’s Creation of Man right figure (God). One represents the corpus + legs, another - the right arm, but why is the left arm missing? Three skeleton lines represent the left figure (Man): one line represents the left arm; a second, the left leg; a third, the body + right leg; but why is the right arm missing, and why is the corpus joined with the right leg? None of these questions have answers if we obtain the skeleton only from that sketch. There are more lines in the skeleton, which can not be explained from the sketch. To try to answer these questions let us refer to the original painting (Fig. B.17). Now one can see that the rest of the skeleton lines are parts

Figure B.17: Extract from Michelangelo’s Creation of Man of the borders of two local backgrounds. There is no explanation why borders are called ”skeletons”. Then it turns out that the painting alone is not enough to get the S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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right perception of the painting: ”The story of Michelangelo’s Creation of man is understood by every reader of the book of Genesis” (p.458). Now the viewer knows 1) from the caption: the two bodies are the Creator and the man created and the moment of creation is represented, 2) from the Bible: the magic transformation was made by breathing a living soul into the body of clay, but that is not what one can see: there is no contact between Creator’s mouth and the body of the man. But there is a touching contact with the tip of Creator’s finger. Then the idea comes to mind that according to the Bible there was another act of magic transformation - touching with the hand (or with a wand). So, the viewer has to make the sophisticated substitution in the attempt to understand the meaning of the painting. Only after all this intellectual activity can one write: ”The Creator reaches out toward the arm of Adam as though an animating spark, leaping from His fingertip, were transmitted from the maker to the creature. The bridge of the arm visually connects two separate worlds: the self-contained compactness of the mantle that encloses God and is given forward motion by the diagonal of his body; and the incomplete, flat slice of the earth, whose passivity is expressed in the backward slant of its contour. There is passivity also in the concave curve over which the body of Adam is molded. The desire to get up is indicated as a subordinate theme in the left leg.” (p.460). To create that essay one has to know the Bible, be a very articulate person, and live, at least, in the XVIII century (understanding the metaphor ”animating spark” demands some notion of electricity). This text defines the main objects of that scene (marked in the quote in italics): Creator’s arm, Adam’s arm, mantle, Creator’s body, contour of the earth, Adam’s body, left leg. Only after this can these bodies be chosen for representation with lines, which could be called ”skeletons”, and the sketch in Fig. B.16 be created. But there is no way to create such a set of ”skeletons” from the visual stimulus by applying rules of Gestalt psychology. II. The same painting was analyzed by R. Zakia fifty years later [Zakia]. The title of the paragraph with that analysis is ”Closure”: ”Nearly complete lines and shapes are more readily seen as complete (closed) than incomplete. In Michelangelo’s painting of ”The Creation of Man” the distance between the finger of God the Creator and the finger of man is critical. Each time we view the painting, we are invited to form closure S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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by completing the action” (p.119). The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

Starting with the ”complete shape”, which is a well-defined notion in Gestalt psychology, the author quickly substitutes this term with ”complete action”, which has no definition and does not belong to the basic rules of visual perception. The correct way to apply the Gestalt principle of closure is to fill the gap between fingers and to show that as a result we obtain a complete shape, which consists of the Creator and Adam. But there is no such shape - the two figures are definitely different objects. Now we can conclude that both attempts to apply Gestalt principles to analyzing the famous work of art failed. The reason for the failure is that it is wrong to try to create a complicated object from very primitive parts (for example, to try to build a car by assembling molecules). The Gestalt principles work by assembling the parts of the whole at the basic level. When we deal with relatively simple drawings (as most examples above) the partition created by Gestalt principles is final and solve the problem of understanding the stimuli. But in more complicated stimuli, in paintings, for example, the initial partitions created using Gestalt principles has to be processed at higher levels with the use of cultural, religious, and technical knowledge. III. But what can Gestalt principles really do in the case of Michelangelo’s painting? To be sure that we use only well defined notions and principles let us do it using a computer. Let us represent an image as a completely disorganized set of points (as it is, in fact, represented in the computer memory). Let us divide the image into background and foreground (which can be done by the computer). The results are shown in Fig. B.18: the foreground is black, the background is white. Now we can apply computer techniques which implement the ”closure” procedure. This procedure is described in detail by Guberman and Wojtkoski [Guberman and Wojtkowski, 2002] and is based on the ”proximity principle” of Gestalt psychology. It closes the gaps in a binary (black-and-white) image (i.e., transforms Fig. B.18a into Fig. B.18b). If the object has a ”leg” (offshoot) as in Fig. B.18c, then the background will have an indent (Fig. B.18e). The closure procedure applied to the background will fill the indent. After returning to the foreground (i.e., reversing the image) one returns to the initial object without the ”leg” (Fig. B.18f). The ”closure” procedure could be described as a way of obtaining a rough (or simplified) S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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Figure B.18: The Closure procedure based on the Proximity Principle approximation of the shape of a given object. In the case of a circle with a gap (or with an indent) the ideal circle is an approximation of the given object. Let us apply the ”closure” procedure to the ex-

Figure B.19: Closure applied to simplified representation of Michelangelo’s Creation of Man

Figure B.20: Closure applied to the background in Figure B.19 tremely simplified Michelangelo painting (Fig. B.19). Applied to the background (the white) in Fig. B.19 it erases the ”legs” in both black objects and represents roughly the main two bodies in the image (see Fig. B.20). Applied to the foreground (black) in Fig. B.19 it closes the gap between the two main objects by connecting the ”legs” (Fig. B.21). S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Thus, there are two main solid objects about the same size (conclusion from Fig. B.19). The ”legs” are directed face-to-face and about to create a bridge between the two main bodies as shown in Fig. B.21 where the gap is closed. There are two main solid objects about the same

Figure B.21: Closure applied to the foreground in Figure B.19 size. The ”legs” are directed face-to-face and about to create a bridge between the two main bodies. It is important to emphasize that the ”leg” has nothing to do with the human body part, but is a technical term, as ”bridge” is a technical term introduced by Guberman and Wojtkoski [Guberman and Wojtkowski, 2002] as a connection between two bodies, and is different from its use in the essay quoted above. This is what can be done by applying the basic Gestalt principles at low levels of image processing and is quite effective: a version of partition of the whole together with a rough description of the parts and their mutual relationships. Now, however, more general Gestalt principles have to be applied. To understand the whole it has to be represented by its genuine parts, so that each part is sensible and the whole, which consists of these parts, is sensible. First, we have to check whether the parts are sensible. As a matter of fact, nowadays this can also be done by the computer through the following steps. 1. The two human figures can be separated from their local backgrounds and recognized as figures. 2. The ”legs” can be identified as arms. 3. The contact points of the arms can be identified as tips of the fingers. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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So, the parts make sense. Now, to check whether the whole is sensible, we need a lot of high level knowledge of the Bible. Contemporary computer science is not yet ready for this and will not be until a computer can write an essay similar to that quoted above. IV. Zakia [Zakia, 2004] gave a good example of the ”good continuation” principle applied to art analysis. In E. Weston’s photograph ”Nude 1936” a woman sits, both arms embracing her legs (p.118). Her face is not visible, just the top of the tilted head, with the hairline where the hair is parted. The hairline coincides nicely with the continuation of the contour of the left arm. ”It turned out to be a beautiful composition, a perfect gestalt” (p.119). The example is good and the analysis is good, but the conclusion has to be the opposite one. The aim of all basic Gestalt principles allows our perception to create a correct partition of the whole. In that case the smooth line, which includes the hairline and the arm, was perceived as an indivisible line - a border of an indivisible part. But in reality there is no such body part. As a result our perception can not create a sensible whole - that strange part does not fit the shape of the human body. For the viewer, this creates psychological tension until the moment s/he resolves the puzzle, this being the cause of the artistic effect. As a matter of fact, a great number of work of modern art use the same idea - finding particular cases, in which a combination of lines, bodies, and colors initiate perceptions that conflict with common sense. So, in the photograph ”Nude 1936” the rules of Gestalt perception lead to the wrong partition and destroy the whole. This is why the concluding remark of the above analysis should be not ”perfect Gestalt”, but ”perfect anti-Gestalt”.

B.8

Bad continuation

In the 1920s and ’30s M. Wertheimer continued to develop the Gestalt theory. The culmination of his achievements was the book ”Productive thinking”, in which he shows how the way of perceiving the world, in accordance with Gestalt principles, crucially influences the way of thinking. His approach not only explains some of the mysteries of problem solving but also produced a guide for the forthcoming computer era, for future attempts to create Artificial Intelligence. A more detailed analysis of this book can be found in Guberman and Wojtkowski S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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[Guberman and Wojtkowski, 2001]. During the same period another line of development was explored transferring the main ideas and notions of Gestalt psychology, which explains the main rules of our perception, to the physical world, attempting to explain the organization of nature. Let us mention some milestones along that road, particularly regarding ”good continuation” and ”closure”. 1. Early attempts to expand Gestalt psychology beyond its boundaries were discussed by I. Verstegen [Wertheimer, 1925]: ”When Sedlmayr wrote the ”Einleitung” to the essays in 1928, he outlined the ways in which he felt that Gestalt psychology could explain Spengler’s impressionistic approach to historical cycles. When Wertheimer, or others, affirmed that visual forms possessed a real emergent form (”Gestalt”) and not so many blind, atomic components, they only had perceptible forms in mind. Sedlmayr, however, extended the analysis to history itself. He asks: ’Is there in historical events a unified direction?’ It is immediately clear that a directionality in history is completely different from a directionality in a seen figure” (p.140).

K. Koffka came forward with a more general statement, which linked the Gestalten to the whole of Nature [Brett et al., 1994]: ”To apply the Gestalt category means to find out which parts of nature belong as parts to functional wholes, to discover their position in these wholes, their degree of relative independence, and the articulation of larger wholes into sub-wholes.” Goldstein expanded Gestalt psychology as a study of perception to Gestalt psychology as a study of the whole person (based largely on Koffka’s work [Koffka, 1935]). His views appeared in ”The Organism” in 1939, and came to be known as ”organismic theory.” 2. An attempt to use the ”good continuation” and ”closure” principles in psychiatry was undertaken by E. Levy in 1935 [Guberman, 2004]. ”An ordinary question intends its answer. It calls for it, requires it. In itself it is incomplete and establishes a vector towards completion”. As the components of the ”vector” were not defined, it is only a metaphor. ”Once a proper answer is given, question and answer form a complete closed whole.” One can combine any objects in a unit and consider it as a ”whole” but the attributes ”complete” and ”closed ”, which characterize the whole, are not defined. It seems that ”closed” was used only to establish connections with the terminology of Gestalt psychology. In Gestalt psychology the basic principles (good continuS.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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ation, closure, proximity, etc.) serve human perception for discovering the organization of the whole and an adequate division of the whole into parts. The ”question - answer” as a whole does not have this problem. The parts are known - the ”question” and the ”answer”. Furthermore, the problem does not belong to the field of perception at all. As E. Levy himself admits, it is a semantic problem: ”the answer must deal with the question’s topic” (ibid ). ”The direction of the answer must be in good continuation with the question in order to achieve its closure.” It looks like just another attempt to establish connections with Gestalt psychology. But all the words - ”direction”, ”continuation”, and ”closure” - in that context failed to be filled with meaning. The only word that makes sense is ”good”, so the statement becomes: ”The answer must be ”good” but it has nothing to do with Gestalt Psychology.” 3. General System Theory was established by von Bertalanffy as a direct descendant of Gestalt psychology [Luria, 1970]. His explicit intention was to apply the notions and basic rules of perception (organization, whole, parts, structure) to the objects of perception itself. He decided to create a ”normal” science, where the participation of a human mind in a theory is not acceptable. So, he discards the child with the bath water, and neither he himself nor the army of his followers ever succeed. Despite the existence of dozens of journals, hundreds of conferences, and thousands upon thousands of articles, which use the words ”system theory”, the basic notions like ”system, part, emerging characteristics, etc.” have not been defined and therefore no theory could be developed. A more detailed discussion of this topic can be found in [Guberman and Wojtkowski, 2001]. Conclusion As mentioned by his son in 1994 [Brett et al., 1994], Wertheimer’s main obsession in his later years, as throughout much of his career, was centred upon the psychology of thinking. Moreover, Kohler believed that Wertheimer ”saw with disappointment that in this country his name was connected with details of perception while his main contribution to human thought was looked upon with distrust”. Now, 60 years later, we can see that his outstanding intuition leads him in exactly the right direction: the process of perception plays a crucial role in productive thinking. If we accept the extension of the ”good continuation” principle (corresponding to that described above S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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as the ”imitation principle” and agree that the essence of Gestalt is the simplest possible description of the perceived, we have to admit that the effectiveness of our perception depends upon the vocabulary we use for describing the parts, and the grammar we use for describing the relationships between the parts. The vocabulary and the grammar constitute the language of perception. Here we have to mention an important contribution of computer science to psychology and particularly to pattern recognition and decision making. A fundamentally important statement was made in 1970 by the outstanding Russian mathematician I. Gelfand: the language of description of a given situation or a given object is crucial for problem solving; it has to be described using an adequate language. Then M. Bongard proposed a method of creating an adequate language - the use of a language in which the creation of an object could be described [Bongard, 1970]. Over the following decade this approach helped to resolve a number of fundamental practical problems: 3D body shape recognition, oil exploration, earthquake prediction, handwriting recognition. To illustrate these ideas, let us briefly explain the computer handwriting recognition problem. From the very beginning the idea was to collect a number of examples for each character and compare every new sign with all stored examples when looking for the best match. Of course before the comparison, the input signs have to be ”normalized”, i.e., transformed to the size, slope and thickness of the example. It seemed natural, that these are the intelligent processes, which occur in our mind during character recognition. Hundreds of papers have been published and hundreds of millions of dollars spent developing that approach, without success. Success came only when the handwritten characters were represented using an adequate language - not as geometrical figures, but as a dynamic track of pen movement (see the ”handwriting recognition” section above). As a result, the pen’s trajectory does not depend upon the thickness of the pen stroke, and the elements of the trajectory are indifferent to the size and the slope. So, all intelligent operations, which provide the normalization, turn out to be unnecessary, and the decision rules became very simple. The only job our mind has to do is create an adequate language of perception. The same process occurred in other applications mentioned above (geological and medical): as soon as the traditional description was rejected and an adequate language was used, the effectiveness of the decision making improved dramatically, and at the same time it became S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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extremely simple if not primitive. Wertheimer demonstrated the power of changing the description of a situation in ”Productive thinking” in the chapter ”Two boys play badminton”. So, the problem of how our perception represents the real word, and in which language it is expressed, is a crucial problem of thinking. The fruitlessness of 40 long years of research in Artificial Intelligence (AI) was predetermined by the set of problems chosen. The vast majority of these problems were games, in which the environment, the rules and the acting objects were completely determined. So, no problems of describing the environment, of discovering the objects, of creating an adequate language appeared - all of them were solved before the computer started to perform the task. As a result the fundamental problems of intelligence, of productive thinking were not even touched. It is no wonder that some local achievements in AI (including the victory of the chess program) teaches us nothing about any principles of human brain function. Wertheimer was damn right to keep in mind the problem of thinking and working so much on perception, i.e., on understanding the way our mind describes the world. It could be that Kohler’s evidence that Wertheimer was disappointed with too much attention being paid by his fellow psychologists to his work on perception and their negligence of his results concerning thinking, should be interpreted in another way: Wertheimer was disappointed that the psychological community did not recognize that the perception problem is a crucial part of productive thinking.



Appendix C

Wholes and parts – analysis of concepts S.A. Guberman1 and W. Wojtkowski2 Introduction At the beginning of the 20th Century a new movement emerged claiming that the analytical approach for the investigation of natural phenomena did not always work. The cause of that failure was attributed to the fact that when studying an object (the whole), and when that whole is divided into parts, ’something’ is gone. The first solution to this enigma came from the psychological sciences with the emergence of Gestalt psychology. The predominance of the approaches used in the exact sciences (physics, mathematics) was so strong that even Gestalt psychologists resolved to construct physical models ad hoc as a basis of their important psychological discoveries (models based on the interaction between electrical and chemical fields in the brain). So it is understandable that scientists working within the basic sciences (physicists and mathematicians) endeavoured to invent a basic theory of the whole and parts excluding from their theories - of course - the human being. Nevertheless, it is noteworthy that a majority of systems theorists (including the founder of General System Theory, von Bertalanffy) are extremely sensitive towards a general discussion of the problem. Many emphasize the main issue - the connection between the whole and the part. Most employ only natural objects as examples of systems. But as soon as anyone starts to construct a physical or mathematical model of that object, the potential involvement of the human being - the observer - is completely excluded. 1 Author’s

2 Author’s

address: Digital Oil Technologies, Cupertino, California, USA address: BSU, Boise, Idaho, USA

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C.1

Wholeness


Wholeness is the main notion of the systems approach. We examine two statements describing wholeness. These are: 1. The part depends upon the whole; 2. The whole is more than the sum of its parts. Despite the fact that these statements have been repeated thousands of times their meanings are still unclear. Let us ask some ingenuous questions. 1. What is the whole? Anything which someone may choose to be a whole. The Universe could be considered as the whole. The Solar System could be considered as the whole. A man could be considered as the whole. A family could be considered as the whole. The whole can be created by definition: a) Anything that belongs to the Universe. b) The Sun and anything moving around it belong to the Solar System. In neither of these two cases do we know all the objects which belong to that whole. If one wants to investigate the behavior of that kind of whole, an approximation of the whole has to be chosen. For example, for Copernicus, Newton and Galileo, the Solar System consisted of 6 planets and the Sun. Later it turned out that in the Solar System there are more planets, a number of comets and a huge number of asteroids. The whole can be created by an explicit description: c) The alphabet. d) United Nations. The whole can be created by representing a finite number of examples: e) Mankind. No one has seen all the people in the world but everybody has seen a number of them, can generalize, and thus decide in each case whether a being in question belongs to mankind. This works well in the vast majority of cases. There is only one restriction on what can be called ”the whole” it has to contain parts. ”The definition cannot exist as a whole without the part” (Aristotle, Metaphysica, Book 5.10 ). ”We say that the vessel S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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holds the liquid and the city holds men and the ship sailors; and so too that the whole holds the parts. (Aristotle, Metaphysica, Book 5.23 ). The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

C.2

What are parts of the whole?

a) First, what parts are not. Each slice of bread is still bread, so, they are not parts of the whole (bread). To be a part it has to be of a different nature than the nature of the whole. A gallon of water is not a part of the water in the barrel. Aristotle, Metaphysica, Book 5.26 : ”those to which the position (of parts - S.G.) does not make a difference are called totals, and those to which it does, wholes. Water and all liquids are called totals”. b) The parts have to satisfy conditions similar to those when a mathematical set is divided into parts. If S is the set, and S1 , S2 , S3 . . . Sn are the parts, then S = S1 ∪S2 ∪S3 ∪. . .∪Sn and S1 ∧S2 ∧. . .∧Sn = 0. So, if the Solar System is the whole, it would be wrong to define the parts of that whole as: the Sun, the planets, and the African plate on the planet Earth. If a car represents the whole, it would be wrong to state that the constituent parts are the engine, the body, the electrical system, the brakes and so on plus three valves of the engine. c) Any part of a natural whole can be considered as a whole itself and consist of more elementary parts (down to the subnuclear level). The human body as a whole consists of a head, body, limbs, heart, lungs, liver, and so on. Each of these parts consists of tissues (muscle, bone, nerves, etc). Each of these tissues consist of a variety of cells, each cell consists of molecular conglomerates, and so on. Because the partition of each part has to satisfy condition (b) the second level parts all together will also have to satisfy condition (b) as well. This means that all second level parts taken together could be considered as parts of the whole. This creates a hierarchy of levels in the partition of the whole. d) The list of parts of the whole together with a list of their relationships and interactions constitute a description of the whole. Thus, the hierarchy of levels of partition defines the hierarchy of levels of description. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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e) The whole can be divided into parts in different ways. The human body can be described as consisting of organs (as described in (c) ), or of different kinds of tissues: bone tissue, muscle tissue, nerve tissue, dermis, epidermis and so on. The global economy can be represented by sectors (energy, transportation, information, commodity, and so on) or by countries, or by developed markets, emergent markets, undeveloped markets. Every subdivision of the whole creates pieces of the whole, but not always parts of the whole. Let us look at the the face drawn in Figure C.1a. It is trivial to name the parts of that drawing: the hair, the eyes, the eyebrows, the nose, the mouth, the wrinkles, the ears, the chin, the neck. The necessary conditions (b) are satisfied: all parts together completely cover the whole drawing, and no parts are overlapping. In Figure C.1b the same face is divided into pieces by a number of arbitrary lines. What is the difference between the parts and the pieces? Each of the parts has sense - it is a well known notion and it has a name. On the contrary, none of the pieces has sense - none of them corresponds to a known notion, or has a name, or could be described (one piece of the face is shown in Figure C.1c).

Figure C.1: Parts and Pieces of the Whole f) The main problem of systems analysis is the partitioning of the whole in an appropriate way. Based on the above considerations an appropriate partition is one which satisfies the three following conditions: 1) condition (b) described above, 2) each part is meaningful, and 3) the whole is meaningful. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Another example of finding the right partition is shown in Figure C.2a. The printed word is the whole. The word can be cut into arbitrary pieces (as in Figure C.2b). They satisfy the first condition (not overlapping) but do not satisfy the second one (being meaningful). So, they are not parts. If the word is sectioned vertically, all of the sections are meaningful - characters of the English

Figure C.2: Finding the correct partition alphabet. Because all together these characters constitute a word in a vocabulary (i.e., it is meaningful), all three conditions are satisfied and the characters are parts of the whole. In Figure C.2c the word is also sectioned vertically. All sections except one are meaningful (i.e., belong to the English alphabet) - ”o”, ”m”, ”e”, ”r” , but the first one - the ligature ”co” - isn’t. One can fix this by dividing the ligature into ”c” + ”o”. So, now all parts of the whole are meaningful (Figure C.2d), but the whole word is not - ”comer” is not an English word. The partition failed to satisfy the third necessary condition. On the next round of searching for appropriate partition one can try to divide the ”m” (which looked suspicious from the beginning) into ”r” + ”n” - two meaningful signs (Figure C.2e). After that it turns out that the whole word is meaningful as well - it is the word ”corner”. The partition problem is successfully resolved.

C.3

Do the parts depend upon the whole?

The above analysis opens the opportunity for interpretation of the statement ”parts depend upon the whole”. What does ”the part depends upon the whole” mean? Is it not the same as ”a slice of bread is bread”? As discussed above, in that case, according to Aristotle ”bread” is not a ”whole” but a ”total”. The existence of the part as a legitimate ”part of the whole” in itself depends upon the whole because the conditions of existence demand that ”the whole is meaningful” (the third condition). In the example in Figure C.2 the ”m” could not be accepted as a part of the word because the third condition was not satisfied (the S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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word ”comer” is meaningless). As shown, the correct partition contains the characters ”r” and ”n” instead of ”m”. As a matter of fact the visual stimuli of that part did not change at all. What really did change is our interpretation of that part of the visual stimuli. In Figure C.1 everybody recognizes a face and all its parts (nose, eyes, mouth, etc). At the same time all these parts of the face are identical visual stimuli - ellipses. But the interpretation of each of the ellipses is different. It depends on the whole. In paintings a red stroke of paint could be a King’s coat, or a rose-petal, or Marilyn Monroe’s lips. So, the real meaning of ”parts depend upon the whole” is ”the interpretation of parts depends upon the whole”. It is important to mention that Aristotle’s judgment that water is not a ”whole” is conditional. At his time water was basic simple matter and consisted of a number of volumes of water only. So, the parts and the whole were the same, accordingly the water could only be a ”total”. Nowadays water can be represented as consisting of H2 O molecules, so within that representation it is a whole. Explanation of the whole using lower level descriptions (the second level downwards) in most cases has no sense. It is fruitless to describe a car at the molecular level - it would be impossible to understand how the car works. This is what can be called reductionism. But it is wrong to proclaim - as many ”antireductionists” do - that the whole can not be explained on the basis of its parts and their interactions. The reason for multiple unsuccessful attempts to solve complicated problems (such as problems in economy, ecology, culture, life and many others) is not the ”reductionist approach”, i.e., description of the whole through its parts per se, but the inadequacy of that description. The description of the whole can be inadequate because a low level of description was chosen. For example, the attempts of electroneurophysiology to explain psychological phenomena at the neuron level were unsuccessful because the level is too low. To succeed it is necessary to find a higher level description adequate for the problem. Another kind of inadequate description originates when the basic top level description is wrong. And when the basic description is wrong any model of the whole becomes extremely complex but still unsatisfactory. It seems that this is the cause of failures in economy - the existing top level descriptions are wrong. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


C.4

181


Is the whole more than the sum of its parts?

There are hundreds of sites on the Internet quoting the statement ”the whole is more than the sum of its parts” and all of them refer it to Aristotle. There are two translations of his Metaphysics on the Internet and technically it is easy to find the quote. Surprisingly, a direct search of the translations for the full statement or for the main words in that statement was unsuccessful. Moreover, an examination of each appearance of the word ”whole” throughout the entire book failed to find a statement even close to the famous quotation. A control experiment was conducted: a search for another quote from within Aristotle’s Metaphysics was successful. In the vast majority of cases there is no precise reference to the quote, but in some cases there is one and it is always the same: Aristotle, Metaphysics, 10f-1045a. (1045a is the number of the paragraph in the overall numbering of paragraphs in the book). Here are the appropriate excerpts from two translations. The translation by Hugh Tredennick: ”what is the cause of the unification? In all things which have a plurality of parts, and which are not a total aggregate but a whole of some sort distinct from the parts, there is some cause”. Let us try to understand the meaning of this statement. Aristotle is talking about ”things” (”objects” in modern vocabulary), which are wholes in contrast to total aggregates. The notion of total aggregate is described in previous parts of the book using as examples ”water” and ”numbers”. Each part of water is water, so, the nature of all parts of the ”whole” is the same as the nature of the ”whole”. That kind of ”whole” are called by Aristotle not wholes but totals. So, the ”plurality of parts” in the quote means that the parts are different and that means that they are not parts of a ”total aggregate” but parts of a ”whole”. Further on in that sentence Aristotle repeats the basic features of the whole (which distinguish it from a ”total”) - the whole, which is distinct from the parts, i.e., whose nature is different from the nature of the parts. The quote thus repeats, in short, the basic feature that accordingly Aristotle characterizes the ”whole” and differentiates it from the ”total”: the nature of the whole is different from the nature of the parts. And when the whole and the parts are of a different nature, it is impossible to compare them - the whole and the parts (taken separately or in any combination), to judge which is bigger and S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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which is smaller. This means that if our interpretation of that piece of Aristotle’s text is correct, it contradicts the statement ”The whole is more than the sum of its parts” (whatever meaning may be given to the word ”sum”). Here is another translation of the same paragraph by W.D. Ross: ”what is the cause of their unity? In the case of all things which have several parts and in which the totality is not, as it were, a mere heap, but the whole is something beside the parts, there is a cause.” By comparing the translations one can see: 1. Unity vs. unification is acceptable; 2. Plurality of parts vs. several parts is not acceptable, because ”several” refers to the number of parts only (”more than one” - which is trivial) while plurality of parts means different kinds of parts, and that is exactly what Aristotle meant; 3. Total aggregate vs. a mere heap is adequate; 4. Distinct from the parts vs. something beside the parts is not equivalent. The first one requires that the whole and the parts have to be of a different nature (which is in agreement with the context of the book). The latter merely states that the whole is not the parts. It seems to be undisputed that this so-called ”Aristotle quotation” ”The whole is more than the sum of its parts” is not a verbal quote. Aristotle’s writings don’t contain a sentence like that. Perhaps somebody tried to sum up some ideas in Aristotle’s metaphysics in such a way. At least in German this seems to be the case3 . For the German ”Das Ganze ist mehr als die Summe seiner Teile” there is usually a specific source given in the metaphysics different from what you are citing: Metaphysik 1041 b 10 (VII. Buch (Z)). There are two translations of this, one with and one without the decisive formulation. The first by Adolf Lasson (Jena 1907, Diederichs) states: ”Das was aus Bestandteilen so zusammengesetzt ist, daß es ein einheitliches Ganzes bildet, nicht nach Art eines Haufens, sondern wie eine Silbe, das ist offenbar mehr als bloß die Summe seiner Bestandteile. Eine Silbe ist nicht die Summe ihrer Laute ...” 3 Gerhard

Stemberger, President of the Society for Gestalt Theory and its Applications (GTA), kindly supplied us with this information S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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The translation of Franz F. Schwarz (Stuttgart 1970, Reclam) however does not contain this formulation, it just says: The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

Das was in der Weise zusammengesetzt ist, da das Ganze Eines ist, ist nicht wie ein Haufen, sondern wie ein Silbe. Die Silbe aber ist nicht dasselbe wie ihre Buchstaben . . .

It seems that in the original this Aristotle sentence is incomplete, page somehow damaged - anyway: the words ”mehr als bloß die Summe seiner Bestandteile” in the first translation (by Lasson) were ADDED BY THE TRANSLATOR LASSON. At http://perseus.mpiwg-berlin.mpg.de/cgi-bin/ptext?lookup=Aristot.+Met.+7.1041b

the relevant passage reads: Now since that which is composed of something in such a way that the whole is a unity; not as an aggregate is a unity, but as a syllable is2 –the syllable is not the letters, nor is BA the same as B and A; . . .

footnote 2 states: This sentence is not finished; the parenthesis which follows lasts until the end of the chapter. The conclusion is obvious: the statement ”The whole is more than the sum of its parts” 1) was not written by Aristotle, and 2) it is a misinterpretation of Aristotle’s point of view. By the way, the founder of the General System Theory, von Bertalanffy himself refused to support the discussed principle (the whole is more than the sum of its parts). In his main book von Bertalanffy explained that when the partition is wrong, (i.e., when the ”whole” is divided into inappropriate pieces ) the ”whole” can not be understood and reconstructed from those pieces. If, however, ”we know the total of parts contained in a system and the relations between them, the behavior of the system may be derived from the behavior of the parts” [von Bertalanffy, 1968, p.55] I would like to conclude this section by quoting some comments by Gianfranco Minati during our discussion about this appendix. He said: ”Reading the two translations of Aristotle and your comments led me to the following considerations. Totals are established by parts in a passive way, that is by reproducing the same properties of its elements. Our use of the term ”total” explains that we do not consider just heaps without even the properties of parts, but combinations of parts having the same property of parts. This S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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relates to the modern interpretation based on using the term sum: by adding, replicating the same property we get the same property. We now may say that the term ”sum” relates to linear combinations of the same property. Any linear combination is intended not as a cause, but just as a linear extension of the original property. In this we may amplify the same property, but without having a new one. To consider ”several” parts is then suitable in this view. Wholes are generated by a plurality of different parts and have a cause. Parts are different and a linear combination of them may just produce a balance and not a whole having properties different from those of the parts. The cause is any reason why they are not simply the sum total of their individual behavior: for instance, non-linear relations, interaction and role of the observer. To consider ”plurality” of parts is then suitable from this point of view. Parts are to be intended as different not only when they are nonhomogeneous, but also when they have different behavior and different roles in such a way as to make insignificant their linear combination (e.g., collective behavior establishing laser light, ferromagnetism, swarming and flocking). 1. ’The whole is more than the sum of its parts’: I do not know the precise origin of this statement. I am inclined to retain this expression imprecise rather than wrong. 2. On the one hand it is possible to understand ’sum’ as any linear combination. On the other, I think we are in the typical situation where we face the truth, but not all the truth and only the truth. The point is that it is impossible to do science with only one of them, and this often occurred with Systemics. ”

C.5

Algorithmic approach to partition

From all the above it follows that the problem of partition (i.e., dividing the whole into parts) is the main constructive problem of Systems Theory. The principles of partition have to be formulated in general terms applicable to any phenomenon in any branch of science or technology. To create an adequate partition the three conditions mentioned above have to be satisfied. Two of them require rationality - the whole and each part have to be meaningful. Clearly, the judgement on ”being meaningful” can only be made by a human being - the observer. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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But can we analyze the meaning of ”meaningful”? Such analysis and modeling of partial aspects of ”rationality” could provide a deeper understanding of that notion and could lead to the creation of practical tools useful for system investigation. The three conditions are tests for a correct partitioning and have to be applied to any given partition. This leads to a crucial question: how to avoid the total search of all possible partitions, which is terribly time-consuming. In the Addendum, is a description of the ”DD algorithm”, which implements one of the fundamental features of wholeness (interpretation of the part depends upon the whole), introduces a formal analogy of the notion of ”being meaningful” (in a very restricted sense), and demonstrates an ability to avoid the full search. Let us formulate the basic ideas of the DD algorithm: 1. The division of the whole into parts and the interpretation of these parts should take place simultaneously. 2. A description of any part of the image must be done in terms applicable to all basic parts. 3. The subdivision should be performed not by means of searching through all elements, but by the ordered examination of a strongly limited class of subdivisions. 4. The aim of the subdivision is to identify a reasonably approximate description. 5. A reasonably approximate description presupposes the presence of all elements of a particular level of the description and the absence of all elements at lower levels. The DD algorithm realizes the following premises as described above: (1) the identification of an object and its interpretation take place simultaneously and for the entire image; (2) an object is that which can be reasonably interpreted, and such an interpretation is considered as reasonable, that is, in agreement with the interpretation of all other objects. These ideas are of paramount importance not only for solving problems identifying geological bodies. The DD algorithm has been successfully implemented in solving the very intricate problem of computeraided analysis of chest X-ray photos [Gel’fand et al., 1981], in analyzing the distribution of the density of galaxies in the Universe, in oil and S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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gas exploration, amongst others, but the importance of this algorithm goes far beyond its usage in solving problems of a practical nature. Over the past few decades, in various fields of knowledge, the problem of non-local data interpretation, the problem of wholeness, has become much more urgent.

C.6

Conclusions

1. The statement ”The whole is more than the sum of its parts” is not a quote from Aristotle’s ”Metaphysics”. We agree with von Bertalanffy’s opinion: ”if we know the total of parts contained in a system and the relations between them, the behavior of the system may be derived from the behavior of the parts” [von Bertalanffy, 1968, p.55] 2. It is more correct to state ”The interpretation of the parts depends upon the whole and upon the rest of the parts” than the popular statement ”The parts depend upon the whole”. 3. Our interpretation of the notions of whole and parts is in accordance with the spirit and letter of Aristotle’s book. 4. This discussion has opened a new vista on the interpretation of Aristotle’s text connected to the ”cause of wholeness”. Addendum ”Damn the details” (DD) algorithm Let us describe an algorithm which models the ability of our visual perception to interpret the parts of the whole while taking the whole into consideration. The practical task is how to describe an image in general, avoiding the details. Let us first see how this algorithm works in the case of a one-dimensional image. The curve y(x) (Figure C.3a) intersects the axis x at the points x0 , x1 , . . . xN *. These points [zero values of the function y(x)] would pre-assign an approximate description of the curve; this description retains information about points where the sign of the function y(x) changes, but it disregards the value of the divergence of the function from zero. This rough description of the function y(x) may be represented as the function Y0 (x) (Figure C.3b) that would change its sign at the points x0 , x1 , . . . xN (zero points) and assume constant values of + 1 or - 1 in between them. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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Figure C.3: Subdivision of the curve y(x)

The number of intervals between the zero points of the function y(x) is equal to N. Let us find the shortest of these intervals. Let this be the interval (xk , xk+1 ) of length l1 . Now let us perform the operation of eliminating the shortest interval. For this purpose we exclude the boundaries of this interval xk and xk+1 from the set of zero values. As a result, instead of three intervals (xk−1 , xk ), (xk , xk+1 ) and (xk+1 , xk+2 ), one interval (xk−1 , xk+2 ) with a constant sign is formed (Figure C.3c). We then repeat the operation of eliminating the shortest of the remaining intervals (of length l2 ≥ l1 ), and continue in the same way until all intervals between the zero points have been eliminated. Now let us construct the function n(l)/N where n(l) is the number of intervals remaining after the elimination of the intervals of length l. The function n(l)/N is equal to 1 at l = 0, it decreases jump-wise by 2/N at all values of l equal to the length of a minimum interval at any single stage of the process of eliminating intervals, and maintains a constant value between them. In other words, this is the stepwise steadily decreasing function. Two cases may be considered: (1) the function n(l) declines steadily, (2) the function n(l) declines jump-wise in large steps, and the short intervals of rapid decrease alternate with long intervals of S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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a constant value of n(l). The presence of a step in the function n(l)/N corresponds to the following properties of the initial function: (a) at the i-th stage in the process of eliminating intervals, several intervals of approximately the same length (l0 ) are formed; (b) after their elimination the remaining intervals have a length exceeding l0 by several times; (c) the length of the interval eliminated at the (i1)th stage is several times smaller than l0 . The function n(l)/N constructed for the curve y(x) is of the same step-wise nature (Figure C.4). The position of the step

Figure C.4: The graph n(l)/N determines the size which is characteristic of the details on the curve l0 , and the subdivision in which all details of a size less than l0 are absent identifies characteristic objects on the curve. On the curve Yi (x) three objects of length l0 (Figure C.3d) are identified, and they are also well defined visually on the initial curve y(x). The presence of a step on the curve n(l)/N is a formal criterion of the fact that the identification of objects on the curve would be worthwhile. The more distinctly the stepwise nature of the curve n(l)/N is expressed, the better organized is the initial curve (the degree of organization of the function is an ability to describe a function with the large number of variables by a smaller number of parameters). The algorithm for the identification of objects described here is non-local, since the question of whether a particular interval is a meaningful object or not is solved depending upon the size of all other objects being identified. One and the same segment of a curve may either be an object or not, depending upon the context, i.e., on the rest of the curve. It is important that the criterion for the existence of objects [the existence of a step in the function n(l)] is intrinsic rather than pre-assigned from the outside. In the two-dimensional case, the function of brightness is pre-assigned on a plane as the function of S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy


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two coordinates (half-tone image). In this case the lines of the zero level of the function of brightness Φ (x, y) (with respect to the mean value) are the analogs of the zero values of the one-dimensional function. The lines of the zero level demarcate relatively light and dark fields of the image. The operation of excluding details involves eliminating a light (or dark) field of the minimum area. In Figure C.5 the curve is a geo-

Figure C.5: Breakdown of a gamma-ray logging curve by means of the DD algorithm physical borehole profile: the relationship between the radioactivity of rocks and their depth of occurrence (with respect to the mean value.) On the curve the alternation of sandy and clayey rocks is reflected. Clayey rocks have high radioactivity levels, whereas sandy rocks have low ones. The largest formations in the profile are members consisting of beds. A sandy member contains mainly sandy rocks, but also contains clayey beds. In turn, the beds are complicated by interlayers of another composition. Such a three-level structure of the profile is reflected in the curve n(l) by the presence of three steps (Figure C.4). The different steps correspond to different levels of approximation in the description of the curve (and thus, also of the geological profile). In various problems, the description of the profile with various levels of approximation proves to be meaningful. In planning rates of drilling a very rough description of a borehole profile (breaking it down into sandy, clayey, and carbonaceous members) proves to be sufficient. The same rough description can be used in the calculation of undiscovered reserves of oil and gas on a basin-wide scale. The description of a borehole at the next level of detail (at the level of identifying beds) corresponds to the tasks of correlating borehole profiles and estimating mineral reserves within the limits of a field. The most detailed description of a borehole profile is needed, for example, in the task of working out conditions for field development. It should be stressed that not each curve has a high degree of organization (i.e., having the function n(l)/N of a clearly defined step-like nature). Correspondingly, for each curve, one can not indicate a stable subdivision, i.e., present a curve in a reasonably rough form. S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

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Of course, one can carry out a formal approximation for each curve, namely, excluding all intervals whose thickness is less than an arbitrary constant l0 from the description. However, such an approximation of the curve is impermissible (without special stipulations), for the following reason. When a geologist or a geophysicist receives an approximate description of a borehole profile, s/he believes that the approximation has been carried out in a reasonable manner and, consequently, the following condition would be fulfilled: if in a description of the borehole profile the minimum thickness of a bed is equal to l0 , then (1) with the approximation, only beds much smaller than l0 in thickness would have been excluded from the description; (2) there are no beds close to a thickness of l0 in the borehole profile; (3) beds of about l0 or more than l0 in thickness would not have been excluded from the description. Thus, a reasonably rough description would contain a degree of its level of roughness. In somewhat more general terms, this property of a reasonably rough description can be expressed in the following way: in a reasonably rough description either all objects belonging to the particular level of description, or none of them, should be represented.



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(B. A. Huberman, ed.), Elsevier North Holland, Amsterdam, pp. 77115. The electronic edition of this book is not sold and is made available in free access. Every contribution is published according to the terms of “Polimetrica License B”. “Polimetrica License B” gives anyone the possibility to distribute the contents of the work, provided that the authors of the work and the publisher are always recognised and mentioned. It does not allow use of the contents of the work for commercial purposes or for profit. Polimetrica Publisher has the exclusive right to publish and sell the contents of the work in paper and electronic format and by any other means of publication. Additional rights on the contents of the work are the author’s property.

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Index abduction, 25, 54, 63, 67, 68, 70

94, 99–107, 111–113, 117, 119, 132, 134–136, 138, 142, 162, 173, 183, 185 emergence, 1, 3, 5, 8, 10, 11, 13, 19, 31, 34–43, 68, 70, 72, 73, 82–85, 87, 100, 103, 104, 106, 107, 111, 114, 116, 121, 123, 124, 127, 128, 131–145, 175 existence, 17, 30, 34, 71, 77, 89, 92, 126, 154, 172, 179, 188

behavior, 2–7, 9, 11–13, 22, 23, 26, 28, 32, 33, 37–40, 48–52, 66, 69, 70, 72, 73, 77, 83– 86, 89, 91, 92, 100, 103, 106–108, 111, 113, 114, 116, 117, 124, 132, 134, 136– 138, 141, 160, 176, 183, 184, 186 Bertalanffy, 1, 3, 4, 7, 9–11, 30, 89– 92, 98, 99, 101, 126, 128, 131, 135, 136, 144, 160, generalization, 22, 23, 36, 43, 58, 172, 175, 183, 186 61, 94, 117, 128, 161 Bongard, 31, 59, 61, 65, 94, 173 Gestalt, 5, 27, 30, 58, 59, 61, 63, 65, 67–71, 90, 94, 98, 128, collective, 7, 11, 19, 21, 22, 28, 32– 147–150, 152–154, 158–162, 34, 37–41, 47, 66, 70, 72, 164, 166, 167, 169–173, 175, 73, 83, 84, 86, 106, 107, 182 110, 114, 116, 117, 124, good-continuation principle, 128 132, 133, 137, 139, 141, 142, 184 health, 111, 119, 120, 122, 123 consciousness, 39–41, 99, 101, 144 constructivism, 71, 128, 132, 133, image understanding, 147 139 imitation principles, 128 inter-disciplinarity, ix, 43, 117, 131, de-emergence, 34–36, 40–42 132, 139, 140 elements, 2–8, 10, 11, 13, 20, 22, interaction, ix, 2–6, 8, 9, 14, 16, 19, 24, 27, 28, 30–39, 41, 47, 26–28, 30, 32–34, 37, 39, 53, 55, 62, 64, 69, 72, 73, 41, 42, 47, 53, 55, 62, 64, 75–77, 79, 83, 89, 90, 92, 66, 67, 75, 77, 79, 84, 89, 199

200



91, 92, 94, 99–101, 103, reduction, 2, 3, 5, 8, 82, 102, 103, 104, 106–108, 110–113, 117, 105, 108, 111, 116, 121, 121, 123, 124, 127, 128, 139 134, 136–139, 175, 177, 180, structured sets, 113, 122 184 sub-symbolic, 19, 36, 37, 65–68, 70– 72, 80, 82–87, 127, 135, levels of description, 19, 25, 26, 32, 138 37, 38, 40, 54, 72, 73, 83, symbolic, 19, 39, 66–68, 70, 71, 80, 87, 100, 102, 103, 105, 107, 83, 85–87, 127, 128, 135, 109, 116, 117, 136, 138, 138 144, 177 linear, 16, 17, 53, 55, 60, 77, 107, systems, 1–3, 5–11, 14, 16, 21–26, 28–34, 36, 38–41, 47–49, 109–114, 116, 119–122, 184 53–56, 58–62, 64–68, 75– 82, 84, 86, 87, 89–94, 98, model, 1, 6, 10, 11, 13, 15–17, 19, 107, 109, 110, 112–114, 116, 21–24, 26, 28–31, 33, 34, 120, 122, 126–129, 131– 36, 37, 45–50, 52–54, 56, 142, 144, 145, 147, 175, 64–70, 72, 73, 75–79, 82– 176, 178, 184 86, 89, 92, 94, 106, 110, 114, 116, 117, 121, 123, 124, 127–129, 132, 133, 137– trans-disciplinarity, ix, 43, 63, 117, 131–133, 139–141, 144 144, 147, 175, 180, 186 variables, 6, 12, 13, 19, 20, 22, 50, observer, 1, 4–6, 8, 10, 12–14, 19– 51, 54, 62, 84, 86, 122, 21, 23–26, 28, 30, 33, 34, 123, 127, 188 37, 38, 40, 48, 53–57, 59, 61, 62, 66, 75–79, 81, 83, whole, 1, 2, 10, 16, 20–22, 30, 53, 84, 86, 87, 89–94, 99–108, 55, 62, 64, 66, 75–77, 89– 111, 112, 116, 117, 126– 92, 98–109, 111, 114, 128, 128, 132, 137, 138, 143, 141, 149, 150, 154–157, 159, 144, 157, 175, 184 160, 167, 169–172, 175– 186 partition of the whole, 20, 53, 55, 58–60, 63, 76, 77, 92–94, 159, 169, 170, 177 pattern recognition, 16, 17, 147, 162, 173 reality, 3, 8, 24–26, 29, 32, 46, 128, 133, 136, 160, 162, 170 S.A. Guberman, G. Minati Dialogue about Systems c 2007 Polimetrica International Scientific Publisher Monza/Italy

Gianfranco Minati (2004) Teoria Generale dei Sistemi, Sistemica, Emergenza: un'introduzione. Progettare e Processi Emergenti: Frattura o Connubio per l'Architettura? Polimetrica Publisher, Italy. ISBN 88-7699-003-8 Shelia Guberman, Gianfranco Minati (2007) Dialogue about Systems Polimetrica Publisher, Italy. ISBN 978-88-7699-061-5

related publication:

Valerio Di Battista, Giorgio Giallocosta, Gianfranco Minati, eds. (2006) Architettura e Approccio Sistemico. Polimetrica Publisher, Italy. ISBN 88-7699-020-8


Sistemica ed Emergenza series editor Gianfranco Minati


Dr. Shelia Guberman graduated in Electronics in Odessa and in Mathematics from Moscow State University. He worked as a geophysicist in the oil fields of Central Asia and the Urals. He obtained his PhD in Nuclear Physics and a PhD in Computer Science from the Russian Academy of Sciences. He was invited by the outstanding XXth-century mathematician, Prof. Israel Gelfand, to the Institute of Applied Mathematics (Russian Academy of Sciences). There, as a Chief Scientist, Dr. Shelia Guberman managed a number of projects in Applied Mathematics, Geology, Geophysics, Medicine, Psychology, and Computer Science. For the past 15 years he has lived in the USA. Author of core technologies for five US companies (handwriting recognition, X-ray image interpretation, image search and understanding, oil exploration). He is the author of the first application of Pattern Recognition as well as his work on the Theory of D-waves, the best approach to computer handwriting recognition (licensed by Microsoft and Apple computers) and revolutionary oil exploration technology. He has published 3 books and more than 170 scientific papers. Professor Gianfranco Minati graduated in Mathematics from the University of Milano (Italy). He was then involved in various professional activities including: software engineering, telecommunications and management (influenced by the The Age of Discontinuity by P. F. Druker). Since 1985, after reading the seminal Bertalanffy book General System Theory and working with Systems Institutions and scholars in the US and Europe, he has dedicated himself to research on Systems. He is founder and President of the Italian Systems Society (AIRS), doctoral lecturer on systems science at the Polytechnic University of Milan 'Building Environment Sciences and Technology' Department and invited lecturer at several Italian universities. He is the author of numerous academic publications (14 books, 42 papers) and has given a number of invited lectures in Italy and abroad. His current research interests are: Modeling Emergence; Multiple-systems; Collective Beings; Dynamic Usage of Models; Collective Behavior; Ethics; Systems and Architecture; Music and Systems; Consent Manipulation; Torah and Systems; Systemics for disability.


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