Design for a Brain

Ashby, W.R. . Design for a Brain – The origin of adaptive behaviour . John Wiley & Sons (second edition revisited) . 1960

Preface

This is a model for the adaptive behavior of the nervous system. The basis is the fact that the nervous system is adaptive and the hypothesis that it is mechanistic. It is attempted identify the properties the nervous system must have if it is both adaptive and mechanistic. To that end a logic of mechanism is required. Only what can be expressed in mathematical form is accepted so as to protect the rigor of expression. A coherent whole is developed from the concepts of organization, behavior, change of behavior, part, whole, dynamic system, co-ordination, &c.

Chapter 1, The Problem

1/1 The brain resembles a machine. The living organism behaves in a purposeful and adaptive way. The aim is to show that a system can be both mechanistic and adaptive. With the developed methosd it is possible to make a machine’s behavior adaptive.

Behaviour, Reflex and Learned

1 /2 Reflex behavior is genetically determined and not altered by individual experience. Learned behavior is not genetically determined and it is modified by an individual experience.

1/3 Reflex behavior is not in the scope of this research: each reflex is produced by some neural physico-chemical reflex to produce some behavior; this is complex but no difficulty of principle is involved.

1 /4 We are concerned with the second type, learned behavior; man produces many examples of this kind of behavior. The nervous system in people and animals is capable to develop behavior that is not genetically determined nor specified by a gene pattern in detail.

1/5 The principal concern here is with learning that changes behavior for the better; the exact meaning of ‘better’ will be discussed later on, but it relates to the bettering of the individual’s chances of survival. The problem in preliminary form: what are the cerebral changes occurring during the learning process? / Why does the behavior generally change for the better? / What type of mechanistic process can show the same advancement of behavior?

1/6 A perceived change can result in a response or change many times bigger through the spreading of the effect. The nerve cells can rouse mechanical power through their control of the muscles. The nerve cells have potentiality for action. The question how it changes for the better isn’t answered by the increase of activity; in real-life examples there is no relation between the change in energy prior to and after learning. The same counts for the level of activity: the correlation between more activity and an improvement of the situation can be negative.

The Relation of Part to Part

Normality at the level of components’ behavior bears no relation with normality at the level of the behavior of the organism, because the two forms of normality have no definite relationship.

1/8 Neural activities are composed of excitations, inhibitions and other physiological processes the correctness of which is not determined by the process itself but by its relations with other processes. ‘These considerations reveal the main peculiarity of the problem. When the nervous system learns, its behaviour changes for the better. When we consider its various parts, however, we find that the value of one part’s behaviour cannot be judged until the behaviour of the other parts is known; and the values of their behaviours cannot be known until the first part’s behaviour is known. All the valuations are thus conditional, each depending on the others. Thus there is no criterion for ‘better’ tha can be given absolutely, i.e. unconditionally. But a neuron must do something. How then do the activities of the neurons become co-ordinated so that the behaviour of the whole becomes better, even though no absolute criterion exists to guide the individual neuron?’ (p 7). NB: this is descriptive of the behavior of a wide variety of complex systems and how local and global behavior relate. Also it is descriptive of the control that the global behavior has as a context, an ambience, an environment over the local actors.

The genetic control of cerebral function

1/9 The development of adaptive behavior is genetic in the sense that the extent of the adaptive capabilities varies per species.

Restrictions on the concepts to be used

1/10 In this book the brain is treated as an organ that has been developed in evolution as a specialized means of survival.

1/11 Living matter is assumed similar to other matter. The only reason admitted for the behavior of some component is its own state and the condition of its immediate surroundings led by the usual laws of nature.

1/12 The ‘operational method’ will be followed and no concept will be used unless it can be shown to exist in objective form in non-living systems.

1/13 No teleological explanation for behavior will be used. The assumption is that a machine or an animal behaves in some way because its nature and its circumstances at some point allow it no other behavior.

1/14 Each component, of the observed system and the system’s environment alike, is assumed to function determinedly; this means it functions in one way, namely the way it is directed by its particular surrounding components. Strong proof exists that memory, as part of the nervous system, behaves determinately (ex. Skinner p 10). But this is part of the question and the statement that components are, will be tested.

1/15 The consequence of answering the research question is that, directly or by implication, will enable the specification of an artificial system to be made that will be able to develop adaptation in its behavior such as the living brain.​​​ Thus is the requirement to the quality of the answer to the research question: that a brain can be built based upon the specifications developed. NB: This is a very ambitious criteria: can’t this be a requirement for the development of a firm also?

1/16 The concept of consciousness is not included in the argumentation in this book, because it is not necessary to explain the subject of study of this book, learning. Example: to turn left with a bicycle one steers right first. Every bike rider has learned it and practices it, but not consciously so. This is not an argument against the existence of consciousness, but an argument against its use here: ‘This knowledge of personal awareness, therefore, is prior to all other forms of knowledge. If consciousness is the most fundamental fact of all, why is it not used int his book? The answer, in my opinion, is that Science deals, and can deal, only with what one man can demonstrate to another. .. And until such a method, or its equivalent, is found, the facts of consciousness cannot be used in scientific method’ (pp. 11-12).

1/17 State some well-known practical problem as a type-problem so that general problems may refer to it. NB: what could the equivalent of this question be concerning a firm? The summary of the research is: assumptions: the organism is mechanistic, the organism is composed of parts, the behavior of the whole is the outcome of the compounded actions of the parts, organisms change their behavior by learning and that they change it so that the latter behavior is better adapted to the environment than the earlier: ‘Our problem is, first, to identify the nature of the change which shows as learning, and, secondly, to find why such changes should tend to cause better adaptation for the whole organism’ (p 12).

Chapter 2. Dynamic Systems

2/1 It is important to define properties of dynamical systems because there is ample room for ambiguity and confusion. A first assumption is that with regards to the brain we are dealing with a dynamical system, something that changes with time; it will be referred to as the ‘machine’ and no restriction is applied to it.

2/2 The objective of this chapter is to construct a method for the study of this machine; the principal axioms as per 1/10 -15 are:

(1) it is precisely defines and in operational form (2) it must be applicable to all material machines, animate and inanimate (3) its procedure for obtaining information from the machinne must be objective (demonstrable to other observers) (4) it must obtain all information from the machine and no other source is permitted. ‘The method proposed here must have the peculiarity that it is applicable to all; it must, so to speak, specialise in generality’ (p 14). NB: some such condition s relevant to firm theory also, because there is no limitation to the number of staff, the turnover or the product range and it cannot be limited to some stage in the firm’s ontogeny; it must apply to every conceivable firm.

Variable and system

2/3 In this book we are concerned with the relations between parts and the focus will be on the behavior of the individual parts. To do that he focuses on any number of variables; a variable is defined as a measurable quantity which at every instant has a definite numerical value (if it can be represented by a pointer on a dial, even if the reading is 0 and the entity is absent): ‘Eddington’s statement on the subject is explicit: ‘The whole subject matter of exact science consists of pointer readings and similar indications. Whatever quantity we say we are ‘observing’, the actual procedure nearly always ends in reading the position of some kind of indicator on a graduated scale or its equivalent’’ (p 15).

2/4 Every real machine embodies an infinite number of variables, the lion’s share of which must be ignored; those considered by the observer are the system. If a new set of variables is drawn up, then a new system is considered.

2/5 As a consequence, first an observer must be given. The system is defined as the set of variables that the observer selects from the set available on the machine. The system therefore is different from the machine. On the list of variables, system is kept separated from time and time is not included in the variables of the system.

2/6 The state of a system at a given time is the set of numerical values of its variables at that instant. Two states are equal if and only if all of the pairs of numerical values of their variables are equal.

The operational method

2/7 In the book only the case is considered where the observer can control every variable and so that he has access to every state of the system. The postulate implies that any variable can be forced to follow some prescribed course. If a variable of the system cannot be set to the desired value, then the observer waits for it to occur (e.g. astronomical and meteorological systems). The observer also has control over the variables that are not a part of the system but that have an effect on it. This is assumed to arrive at a basis model; complications to not have full control over every variable can be added later.

2/8 The primary operation means that the observer enforces a particular state of the system by selecting the variables of the system; and he selects the variables of the environment, sets their values; and he allows a unit of time to elapse. He observes the state that the system goes to as it moves under the drive of its own dynamic nature; he observes a transition from a particular state under particular circumstances. The experimenter observes how one variable changes over time while another is kept constant or caused to change in some prescribed way.

2/9 This objective approach is required as the source of the knowledge must not be the previous experience of the observer, because it is not wholly reliable. The unexpected must be allowed to happen: ‘and the only way to be certain of the relation between parts in a new machine is to test the relation directly’ (p 19). The transition by this method is an objective and demonstrable fact.

2/10 The power of the method is that the experimenter can repeat it with variations and relate the ddifferent responses to the variations; after an operations te next may be varied a) include new or omit old variables, b) change of the initial state, and c) change of the surrounding states. These variations may be applied to yield second-order (and more) relations between responses and different levels. All our concepts will be expressed in terms of this method.

Phase-space and field

2/11 A line of behavior is specified by a succession of states and the time-intervals between them.

2/12 and 2/13 Representations of a system can be graphical, tabular (the most factual, suggesting nothing else), phase space (time is eliminated from the graph; a maximum representation of 3 variables is possible in a graph).

2/14 ‘A system’s field is the phase-space containing all the lines of behaviour found by releasing the system from all possible initial states in a particular set of surrounding conditions’ (P 23). The concept of a field defines all the characteristic behaviors of a system under constant conditions ‘frozen into one unchanging entity that can be thought of as a unit. Such entities can readily be compared and contrasted, and so we can readily compare behaviour with behaviour, on a basis that is as complete and rigorous as we care to make it’ (p 24). NB: what happens to a firm if some initial characteristic value of a variable is varied and it is ‘released’ into a static environment. The variable would have to pertain to the memeplex at the basis of the firm.

The Natural System

2/15 If a system is to be studied with profit its variables must have some naturalness of association: 1) if an active and relevant variable is left unobserved then the system becomes capricious; if the state is known and the external conditions then the transition is known; if the pairs C (external condition, input) and S (state, transition) invariably lead to the same transition given some C and / or some S then the system is a machine with input. A special case is a state-determined system where all the events in one field (all the system’s behaviors in some constant C) occur in one set of conditions, e.g. a pendulum: at no point of the field of a state-determined system do the lines of behavior cross.

2/16 What does a natural association of the variables mean? A definition must have these properties: 1) it must have the form of a test, separating all systems in two classes 2) its application must be objective 3) it must agree with common sense in typical and undisputed cases. Because of 3) no verbal definition is possible but a working hypothesis that must be used. A basis hypothesis in scientific research is that given a set of variables a larger set can be found that a) includes these variables and b) is state-determined. This is implicit in many scientific research and never mentioned explicitly. NB: ‘The assumption is known to be false at the atomic level. We, however, will seldom discuss events at this level; and as the assumption has proved substantially true over great ranges of macroscopic science, we shall use it extensively’ (p 28).

Strategy for the complex system

2/17 Theories are of various types: Newton is simple, precise and exactly true. ‘Darwin’s theory, on the other hand, is not so simple, is of quite low accuracy numerically, and is true only in a partial sense – that the simple arguments usually used to apply it in practice (..) are gross simplifications of the complex of events that will actually occur. The theory attempted in this book is of the latter type. The real facts of the brain are so complex and varied that no theory can hope to achieve the simplicity and precision of Newton’s; what then must it do? I suggest that it must try to be exact in certain selected cases, these cases being selected because there we can be exact… This scientific strategy is by no means as inferior as it may sound; in fact it is used widely in many scoences of good repute’ (p 29). NB: this is the level of the firm theory attempted also and so this can prove to be useful as a quote.

Chapter 3. The Organism as Machine.

3/1 In accordance with S. 1/11 it is assumed that living organism in its nature and processes is not different form other matter. The truth of this assumption will not be discussed. The chapter will deal with the technique of applying this assumptions to the complexities of biological systems.

The specification of behaviour

3/2 Is the behavior of a system capable of being specified by variables, given that their representation can be by dial readings (S. 2/3)? In principle the measurement of bodily functions can be represented by variables, though their measurement is with technical difficulty in practice.

3/3 But can not only ‘straightforward’ physico-chemical, but ALL biological events be represented by readings on dials? To that end it every associated variable is presumed present, but as long as it is unused to represent a system’ s behavior, its value remains 0. Now this method of description can be used in a wide range of phenomena. If there is no relation between the measurements then they can be cardinal instead of ordinal, provided that it is used systematically throughout the system and over time.

3 /4 The behavior of the organism must be measured and so subjective elements (what it thinks or feels) are ruled out and if the complexity increases then more than one variable can be applied to describe the system.

3/5 –

3/6 the nervous system in a physiological experiment can be assumed to be state-determined.

3/7 the animal in an experiment concerning conditioned reflexes can assumed to be state-determined.

3/8 ‘Given an organism, its environment is defined as those variables whose changes affect the organism, and those variables that are changed by the organisms behaviour. It is thus defined in a purely functional, not a material, sense’ (p 36) NB: the variables are internal to the system or internal to the environment. Their interface is the behavior of the organism and the environment respectively as isolated systems. The functionality implies that the boundary between environment and organism is functional also (and not material). The environment is a) representable by dials, b) objective, c) explorable by primary operations and d) state-determined.

Organism and environment

3/9 The free-living organism and its environment, taken together as one system can be represented with sufficient accuracy by a set of variables that forms a state-determined system. The organism and its environment can be treated by identical methods because the same assumptions are made about them.

3/10 ex.

3/11 The organism affects the environment and vice versa; the system has feed-back. Systems without feed-back are a special class of systems with feed-back.

3/12 If organism and environment are observed as one then the dividing line between them becomes conceptual if the view is not material but functional. If this flexibility of division is allowed then no bounds can be put to its application. In this sense, the cortex can have to deal with different environments within the body (eating without biting its tongue, playing without exhausting itself, talking without getting out of breath). The system now means not only the nervous system, but the organism-cum-its-environment; if the system has a property it belongs to the whole; detailed study is required to identify the contributions of the components. NB: this is relevant to identify the system that is a firm: following this description it is the components that identify a firm per se plus the environment (or environments) that it is associated with. It is relevant because it is assumed in my book that the firm is a resultant of the beliefs that are widely held in society and that for via patterns in the behavior of the people associated with the firm, a firm. ‘In some cases the dynamic nature of the interaction between organism and environment can be made intuitively more obvious by using the device, common in physics, of regarding the animal as the centre of reference. In locomotion the animal would then be thought of as pulling the world past itself’ (p 41). NB: this is an interesting way of experimenting wth the idea of how a firm would behave, ‘pulling the world past itself’.

Essential variables

3/14 The biologist must see the brain as a means of survival. As per 2/10 survival must be translated into the standard form here to say what it means in standard operations: the essential variables of a system are those that may change over the course of time and then show mere small deviations, other variables show large deviations initially that at some later stage become even larger until eventually the machine changes into something else. The first are the essential variables; they indicate whether an organism is or isn’t alive. NB: this relates to my question: ‘What is the invariant in the life time of the the firm?’ Translated to this theory: ‘What variables change with large variations and keeps changing at later stages of its life time?

3/15 The essential variables do not indicate lethality in the same way or with the same urgency. Survival can now be defined: ‘We can now define survival objectively and in terms of a field: it occurs when a line of behaviour takes no essential variable outside given limits’ (p 43). NB: How does this definition of survival relate to the viability condition as an extension of the autopoiesis theory?

Chapter 4. Stability.

4/1 Cube, sphere and cone resting on a horizontal surface are in stable, neutral and unstable equilibrium; stable equilibrium is used a lot here.

4/2 Stability is an aspect of a material body. We do not study physical bodies but entities abstracted from them; to that end we must define them as results of primary operations (S. 2/10):

4/3 The state of stability does not belong to a body but to a field.

4/4 Given a field then a state of equilibrium from which the representative point does not move. A transition from a stable point is to itself only. This is a point in phase-space and it does not mean that the object is not moving.

4/5 and 4/6 –

4/7 If a system is stable, then, after some displacement, it is possible to define a bound to the next movement of the representative point in phase-space. If it is unstable then this is not possible or it depends on something outside of the system.

4/8 ‘Given the field of a state-determined system and a region in the field, the region is stable if the lines of behaviour from all points in the region stay within the region. ’ (p 48) ‘A field will be said to be stable if the whole region it fills is stable; the system that provided the field can then be called stable’ (p 49).

4/9 –

4/10 If a line of behavior re-enters itself, the system undergoes a recurrent cycle. If the cycle is contained in a region and the lines lead into the cycle then the cycle is stable.

4/11 –

The diagram of immediate effects

4/12 and 4/13 the arrow between the representations of variables represents a relation between them (not a material connection between them). The chain of cause and effect is re-entrant. The diagram can be derived wholly from the results of primary operations. By reversing the arrows between the variables, the immediate effects between variables can be tested.

Feedback

4/14 The nature of the feedback usually have an effect of the stability of the system or its instability (runaway, vicious circle).

4/15 ‘But here it is sufficient to note two facts: a system which possesses feedback is usually actively stable or actively unstable; and whether it is stable or unstable depends on the quantitative details of he particular arrangement’( p 54). NB:

4/16 Stable systems have the property that if they are displaced from their equilibrium, then the subsequent response is such that the system is brought back to its equilibrium: ‘A variety of disturbances will therefore evoke a variety of matched reactions’ (p 54). This is specific for the behavior of a pendulum but not for the behavior of living organisms. This can be referred to as ‘goal seeking’. A stable system is not necessarily a rigid system and restricted only in the sense that it does not show the unrestricted divergences of instability. NB: this is relevant where it concerns the way in which a state in an evolutionary process restricts to possible configurations of the next state.

Stability and the whole

4/18 A system’s stability is a property of the entire system and can be contributed to no part of it. The stability belongs to the combination and it cannot be related to the parts considered separately. Examples are given of operations (combination with another system, separation from another system) on systems such as to render them stable or unstable.

4/19 ‘The fact that the stability of the system is a property of the system as a whole is related to the fact that the presence of stability always implies some co-ordination of the actions between the parts. .. as the number of variables increase so usually do the effects of variable on variable have to be co-ordinated with more and more care if stability is to be achieved’ (p 57).

Chapter 5. Adaptation as stability.

5/1 and 5/2 The definition must be precise and it must be given in terms that can be reduced to primary operations.

Homeostasis

5/3 ‘I propose the definition that a form of behaviour is adaptive if it maintains the essential variables (S. 3/14) within physiological limits’ (p 58). NB: to fully justify it involves an impossibly large task. It must however be sufficiently discussed to show how fundamental it is and how wide its applicability. First an outline of the concept of homeostasis as per Cannon: 1) each mechanism is ‘adapted’ to its end, 2) its end is the maintenance of the values of some essential variables within physiological limits and 3) almost all behavior of an animal’s vegetative system is due to such mechanisms. When an essential variable is driven outside its normal limits by an external disturbance then another process is started by the same external change activating a mechanism that opposes the disturbance. The essential variable is maintained in narrower limits than if the effects of the disturbance remained unopposed. ‘The narrowing is objective manifestation of the mechanism’s adaptation’ (p 61).

5/5 These mechanisms of 5/4 act mostly through the body but some of them act through the environment also. The extremes of homeostatic mechanisms are: those that work within the body alone and mechanisms that work largely through the environment.

Generalised homeostasis

5/6 The same criterion of homeostasis for adaptation can be used to judge the behavior of the free-living animal in its learned reactions. The cat regulates her distance to an open fire so as to optimize body heat while refraining from direct contact with the fire: ‘Such behavior is ‘adapted’: it preserves the life of the animal by keeping the essential variables within limits. The same thesis can be applied to a great deal, if not all, of the normal human adult’s behaviour. .. Many of the other conveniences of civilisation could, with little difficulty, be shown to be similarly variation-limiting. .. The thesis that ‘adaptation’ means the maintenance of essential variables within physiological limits is thus seen to hold not only over the simpler activities of primitive animals but over the more complex activities of the ‘higher’ organisms’ (pp. 62-3). NB: I find this remark about the limiting of variation very important because it seems to me to be very close to some generalized driving force of all organization to reduce the amount of variation (or rather uncertainty) that the organism has to deal with in its environment. Check the relation of this thesis with the thesis of Wagensberg concerning the reduction of uncertainties in the environment of an organism and also the thesis of Jagers te Opperhuis (?) about the utility of diversity with the consequence that to increase universal utility, order must increase or decrease. For order to increase or decrease, the level of organization must increase or decrease. If order increases for increased organization, order decreases also.

5/7 The first stage of the process of learning occurs when the animal ‘learns’ and it changes from an animal without to an animal with the mechanism, the second stage is when the developed mechanism changes from inactive to active.

5/8 ‘We can now recognize that ‘adaptive’ behaviour is equivalent to the behaviour of a stable system, the region of the stability being the region of the phase-space in which all the essential variables lie within their normal limits’ (p 64). Also quoted Starling, Cannon, Pavlov and McDougall.

Survival

5/9 and 5/10 The constancy of essential variables is crucial to adaptive behavior and the activity (change) of the other variables is important only to the extent that it contributes to this end.

Stability and co-ordination

5/11 Up to this point, the relation between stability and adaptation were discussed; now it is argued that co-ordination has an important connection with stability. Co-ordination means the combination of the behavior of several components such that the resulting movement of the whole is as appropriate.

5/12 Of stable systems we have so far only discussed the property of keeping variables in limits; other properties are: 1) the lines of behavior may not directly return to their stable state (but only after moving away from it first) and 2) an organism reacts to a variable with which it is not directly in contact; co-ordination will first occur between part and part and then between part and environment and reciprocally between environment and part and then between part and part: ‘Here we should notice that the co-ordination of the behaviour of one part with that of another part not in direct contact with it is simply an elementary property of the stable system’ (p 70). NB: this is the mechanism of coupled dancing landscapes: the transmission of information through components of the system to others and interactions with the environment.

5/14 The problem can be stated as: ‘A determinate machine changes from a form that produces chaotic, unadapted behaviour to a form in which the parts are so co-ordinated that the whole is stable, acting to maintain its essential variables within certain limits..’ (p 70).

Chapter 6. Parameters.

6/1 A system is formed by selecting some variables out of all variables; forming it, variables are divided into two classes: within the system and without. Their relation to the system is different.

6/2 Given a system, a parameter is a variable not included in it, a variable is within the system. The closeness of relation between a parameter and a system varies from no effect to a large effect.

Parameter and field

6/3 A change in the value of an effective parameter changes the field. A system can show as many fields as the total number of combinations of values of its parameters.

6/4 A change in a variable leads to a change of state; this is a change that IS behavior. A change in a parameter leads to a change of field; this is a change of behavior.

Stimuli

6/5 Many stimuli can be represented as a change of value of a parameter; the effect of a sharp parameter change is that the field briefly changes whereby the point is carried away from its initial position. When the parameter is returned to its original value, the original field is restored and the representative point is away from its initial position, on another line of behavior and as it returns to its initial position (or another equilibrium point if multiple exist), and it responds. This is called an impulsive.

Joining dynamic systems

6/6 Joining occurs whenever one system has an effect on another, such as communication, forcing, and signaling. To join systems A and B such that A affects B, some parameters of B must become a function of the variables of A. If a joining is made in two directions, then feedback is set up between the two systems.

Parameter and stability

6/7 ‘Because a change of parameter-value changes the field, and because a system’s stability depends on its field, a change of parameter-value will in general change a system’s stability in some way’ (p 77). A change in a parameter substitutes the field; this leads to any change in behavior: stable or unstable, cyclic, single or multiple states of equilibrium. ‘..in a state-determined system, a change of stability can only be due to change of value of a parameter, and a change of value of a parameter causes a change in stability’ (p 78).

Equilibria of part and whole

6/8 If system A with variables u and v is joined with system B with variables x, y and z and the joint of A and B (with variables u, v, x, y, z) is in equilibrium, then the transition is from that state to itself. Given the constancy of its parameters x, y and z, the values of the variables of A are unchanged and conversely, given the constancy of the parameters u and v of B, its variables x, y and z remain constant also. A and B are both in a state of equilibrium as is their whole: ‘So, the whole’s being at a state of equilibrium implies that each part must be at a state of equilibrium, in the conditions provided (at its parameters) by the other parts’ (p 79). Conversely, if, given the values of their reciprocal parameters (the conditions given them by the other parts), A is in equilibrium and B is in equilibrium, then their whole is in equilibrium also.

6/9 If a single part of a whole is not in equilibrium, then it will again change, changing the conditions (the parameters) of the other parts and in turn start them moving again. Any part of the system can prevent the whole to enter a state of equilibrium, it has the power of veto over the states of equilibrium of the whole.

6/10 ‘..each part acts selectively towards the set of possible equilibria of the whole’ (p 79). NB: A smallest common denominator of all variables of the whole (the variables of all parts) detemines whether there can be some specific state such as an equilibrium.

Chapter 7. The Ultrastable System.

7/1 How does the kitten change from not having a mechanism to show no adaptive behavior to having one that does show adaptive behavior?

The implications of adaptation

7/2 In accordance with S. 3/11 and S. 4/14 (if the organism and the environment mutually affect each other’s stability, the system has feedback) the kitten and environment are to be considered as interacting. System and environment interact (have feedback) if they influence each other’s stability. R is a system that belongs to the organism and that acts when the organism reacts to a signal; the arrows between R and the environment and between R and the organism represent the motor and sensory channels. A change of parameters (represented by S) affect the behavior of the kitten; the change in S do not (directly) affect the environment; the number of distinct values of parameters S must be at least as great as the number of distinct behaviors of the kitten.

7/3 If the environment and R or both affect the essential variables of the organism, then its survival is at risk; the more interesting case being the external threat.

7/4 ‘To be adapted, the organism, guided by information from the environment, must control its essential variables, forcing them to go within the proper limits, by so manipulating the environment (through its motor control of it) that the environment then acts on them appropriately’ (p 82). R in this sense can be thought of as an organism trying to control the output of the environment, a black box the contents of which is unknown to it. The procedure to know the contents of a black box is to feed it input and to register the output; to do things to it and act in accordance with the way they affected the environment; the kitten can know the situation by proceeding by trial and error. This test procedure is a necessity in the case of a black bow, because it is the only way can the reuired information be obtained. From the viewpoint of success trial and error is a second rate method, but from the viewpoint of gaining information it ranks higher.

7/5 The essential variables are to have an effect on which behavior the kitten must produce for them to remain inside their limits; a channel must exist from the essential variables to the parameters S. The organism now has a motor output to influence the environment and two feedback loops: sensory input and a carrier of information whether the values of the essential variables are within their limits and it acts on parameters S: the first feedback plays a part within each reaction, the second determines which reaction will occur.

7/6 1) with essential parameters within their limits the overt behavior of R is such as follows from a parameter set is S1 and 2) with the essential parameters outside of their limits, the overt behavior of R is such as follows from a parameter set S2. The overt behavior changed such that S2 is not equal to S1: the different values at the essential variables led to different values of S; a change of essential variables has led to a change of parameters.

7/7 If a trial is unsuccessful then change behavior. If and only if an outcome is successful then retain the way of behavior.

7/8 This is necessary: ‘That is to say, any system that has essential variables with given limits, and that adapts by the process of testing various behaviours by how each affects ultimately the essential variables, must have a second feedback formally identical (isomorphic) with that described here’ (p 85).

The implications of double feedback

7/9 In what material form will the above mechanism necessarily show adaptive behavior?

7/10 –

7/11 The whole consists of two parts coupled: 1) R plus the Environment, and 2) the essential variables and S. The whole can only be in equilibrium if the parts are. S is in equilibrium if the essential variables are. The whole can have such states of equilibrium as allow states of equilibrium in both S and in the essential variables; S is at equilibrium only if the essential variables are within the given limits; if the whole is at some state and it goes to an equilibrium along a corresponding line of behavior, then the equilibrium is always an adapted one. This is a sufficient condition and together with S. 7/8, the necessary condition it is the solution to the original question.

7/12 Assume for sake of clarity that the variables in the environment and in R vary continuously and those in S vary discreetly.

Step-functions

7/13 – 7/18

7/19 Systems tend to show changes of a step-function form if their variables are driven far from some usual value. The nervous system may not be different in that respect.

Systems containing step-mechanisms

7/20 Can a machine be determinate and capable of spontaneous change?

7/21 A system with continuous variables A and B and step variable S can be said to be state-determined in one field. But the system of main variables A and B can be said to have as many kinds of behavior as the step-variable(s), in this case S, has (combinations of) values: ‘And if the the step-mechanisms are not accessible to observation, the change of the main variables from one form of behaviour to another will seem to be spontaneous, for no change or state in the main variables can be assigned as its cause’ (p 95).

7/22 and 7/23 By changing the value of the step function, the system transitions into different fields; each new field can have a new state of stable equilibrium as well as critical states. Once the system has entered a region where it is attracted to such a stable state, it will remain there. If the organism is displaced moderately from this region it will return to it, demonstrating instances of adaptation.

7/24 This field will therefore persist indefinitely. The trial and error exercise has proven bloody and exasperating, but it was successful for finding a stable solution in phase-space. This trial and error is efficient if the result is also used many times to increase performance.

7/25 ‘It should be noticed that the second feedback makes, for its success, no demands either on the construction of he reacting part R or on the successive values that are taken by S. Another way of saying this is to say that the mechanism is in no way put out of order if R is initially constructed at random or if the successive values at S occur at random. (The meaning of constructed at random’ is given in S. 13/1)’(p 97)

The ultrastable system (definition)

7/26 ‘Two systems of continuous variables (that we called ‘environment’ and ‘reacting part’) interact, so that a primary feedback (through complex sensory and motor channels) exists between them. Another feedback, working intermittently and at a much slower order of speed, goes from the environment to certain continuous variables which in their turn affect some step-mechanisms, the effect being that the step-mechanisms change value when and only when these variables pass outside given limits. The step-mechanisms affect the reacting part; by acting as parameters to it they determine how it shall react to the environment’ (p 98)

7/27 –

Chapter 8. The Homeostat.

8/1 The homeostat is a physical instance of an ultrastable system.

8/2 and 8/3 –

8/4 and 8/5 Diagram of immediate effects a) 12, b) 1→2→3→1. NB: how can an interaction as per Knorr Cetina be represented in a diagram of immediate effects? ‘The nervous system provides many illustrations of such as series of events: first the established reaction, then an alteration made in the environment by the experimenter, and finally a reorganisation within the nervous system, compensating for the experimental alteration. The Homeostat can thus show, in elementary form, this power of self-reorganisation’ (p107).

8/6 and 8/7 If the configuration of the main variables of an ultrastable system is such that their field is unstable, then the system will change the field such that the system becomes stable.

Training

8/8 The process of training in relation to ultrastability. All training involves punishment and or reward. In the required form punishment means (S. 7/19 and 9/7) that a sensory organ was stimulated causing a step-change causing the system to enter a different field. The operations following a reward are assumed to be similar than following a punishment (but they are more complex). The trainer a) plans the experiment deciding on the rules that should be obeyed and b) the trainer plays a part in the experiment and obeys the established rules: this part of the ‘training’ situation implies that the ‘trainer’ or some similar device is an integral part of the trained system. Consider this system Trainer Animal to be ultrastable; the step-mechanisms are assumed to be confined to the animal.

8/9 To say that the trainer has punished the animal is equivalent to saying that the system has a set of parameter values that make it unstable. ‘In general, then, we may identify the behavior of the animal in ‘training’ with that of an ultrastable system adapting to another system of fixed characteristics’ (p 115).

8/10 If it has to adapt to two alternating environments an ultrastable system will be selective for fields that adapt to both environments (the field that is terminal for one environment will be lost at the next change).

8/11 What will happen if the ultrastable system is given an unusual environment, namely an environment where some of the parameter values are unusual. The ultrastable system will always produce a set of step-mechanism values, which will in conjunction with the parameter settings, produce stability. If the parameters have unusual values, then so will the step-mechanisms lead to compensating values that are unusual in the same vein.

Some apparent faults

8/12 this model cannot match the richness of adaptations of higher animals in reality.

8/13 if the critical surfaces are not disposed in proper relation to the limits of the essential variables then the system may seek an inappropriate goal or may fail to take action.

8/14 this model cannot deal with sudden discontinuity.

8/15 sufficient time must elapse between the trials so the system has enough time to get away from the region of the previous, critical state.

8/16 Systems may encounter easy environments with few independent variables; in difficult environments the encounter many interlinked variables.

Chapter 9. Ultrastability in the Organism.

9/1 Some further considerations concerning the relation between the organism and the theoretical construct more specifically as per Figure 7/5/1.

9/2 When one real machine is examined by the observer with a variety of technical methods, it can give rise to a variety of systems and of diagrams of immediate effects; sometimes two methods give rise to the same diagram (of IE): When this happens we are delighted, for we have found a simplicity; but we mustn’t expect this to happen always’ (p 122). Physical systems of which the design in some way resembles Figure 7/5/1 are not the only pattern; ‘for there are also systems whose parts or variables have no particular position in space relative to one another, but are related dynamically in some quite different way. Such occurs when a mixture of substrates, enzymes, and other substances occur in a flask, and in which the variables are concentrations. The the ‘system’ is a set of concentrations, and the diagram of immediate effects shows how the concentrations affect one another. Such as diagram, of course, shows nothing that can be seen in the distribution of matter in space; it is purely functional. Nothing that has been said so far excludes the possibility that the anatomical-looking Figure 7/5/1 may not be of the latter type. We must proceed warily’ (p 123). NB; this points at auto-catalytic systems: apparently they can be ultrastable systems; however Maturana and Varela rule them out as AP systems; this is a conseuence of their lack of topological structure. Auto-catalysis can be ultrastable but it can not be autopoietic; this means that auto-catalytic systems can be adaptive at some point for a finite period, but they cannot be adaptive for an infinite period.

9/3 –

Step-mechanisms in the organism

9/4 What to look for? For instance not: where to look, because that implies they are located somewhere – anatomically or in another way not applicable to the variable.

9/5 – 9/7 –

A molecular basis for memory?

9/8 – 9/9 –

Are step-mechanisms necessary?

9/10 Does evidence exist that the process of adaptation implies the existence of step-functions?

9/11 The way a system is observed, for instance the time lapse (micro-seconds, years) of the observation of a system is important for the categorization of the system as a step-function.

9/12 The behavior of a step-function is simple compared to the behavior of a full-function (continuous?); not every real object can be made to show such simple behavior; to say that something can show step-function-type behavior is unconditionally true; if a three dimensional system can be shown to show behavior in a field on two two-dimensional planes then this is special, because not all systems show this characteristic.

9/13 The nervous system often shows some persistence in its behavior: make a trial, persist for some time, make another trial, persist again &c. The shown behavior is less than fully complex by a full-function; every trial represents a field, each field persists for some time and so the behavior can be said to be discreet. Full functions could not represent this discrete character (from trial to trial) and so that they may be s represented is meaningful restriction on their nature. ‘If we now couple this deduction with what has been called Dancoff’s principle – that systems made efficient by natural selection will not use variety or channel capacity much in excess of the minimum – then we can deduce that when organisms regularly use the method of trials there is .. evidence that their trials will be controlled by material entities having (relative to the rest of the system) not much more than the minimum variety. There is therefore strong presumptive evidence that the significant variables in S (of Figure 7/5/1) are step-functions, and that the material entities embodying them are of such a nature as will easily show such functional forms’ (p 130). NB: can this be said of firms also? Is Dancoff’s principle also relevant for social systems, namely for all evolving systems with selection?

Levels of feedback

9/14 Are the two channels of feedback of Figure 7/5/1 relevant in reality? a) an impulsive disturbance to the main variables of the system (fire flares up) and the adaptive system reacts (kitten moves away a bit), and b) a parameter to the whole system changes (from a value it had during many impulsive perturbations). ‘The impulse made the system demonstrate its stability, the change at the parameter made the system demonstrate (if possible) its ultrastability. Whereas the system demonstrates, after the impulse, its power of returning to the state of equilibrium, it demonstrates, after the change of parameter-value, its power of returning the field (of its main variables) to a stable form’ (p 131). The latter are of a step-functional form. ‘When the disturbances that threaten the organisms have, over many generations, had the bi-modal form just described, we may expect to find that the organism will, under natural selection, have developed a form fairly close to the ultrastable, in that it will have developed two readily distinguishable feedbacks’ (p 131).

The control of aim

9/16 The systems discussed so far sought constant goals through the development of a variety of fields. If he critical states’ distribution in the main variables’ phase-space is altered then the ultrastable system will be altered in the goal it seeks; the ultrastable system will always develop a field of which the representative point is kept within the region of the critical states.

9/17 Starting at Figure 7/5/1: 1) the environment is given arbitrarily 2) the channel by which the environment affects the essential variables is given arbitrarily 3) the essential variables and their limits are determined genetically (species’ characteristics) 4) the reacting part R has three inputs: a) sensory input from the environment (quasi-continuous change) b) the values of its parameters in S (genetic, change between trial and trial) and c) parameters developed during embryonic development (changes once in a lifetime) and 5) the relation between the essential variables and the variables in S, namely that the essential variables force the variables in S to change if their values are threatened to go outside their limits; and not to change otherwise (changes ad-hoc and this can only be based on genetic sources).

9/18 ‘For ultrastability to have been developed by natural selection, it is necessary and sufficient that there should exist a sequence of forms, from he simplest to the most complex, such that each form has better survival-value than that before it’ (p 135). NB: this implies a ratchet.

9/20 ‘To some extent, the generality of the ultrastable system, the degree to which it does not specify details, is correct. Adaptation can be shown by systems far wider in extent than the mammalian ad the cerebral, .. . Thus the generality, or if you will, the vagueness, of the ultrastable system is, from that point of view, as it should be’ (p 137) NB: how wide, can it include the workings of social systems?

Chapter 10. The Recurrent Situation.

10/1 So far the basis; now complications can be added to better model living systems. It seems that living systems when adapting follow a path that is not so far from the path involving the least energy, time and risk.

10/2 Let’s return to first principles. Success or adaptation to an organism means that, in spite of the world showing its worst side, the organism lives to reproduce at least once. What the world did to the organism can be regarded as a Grand Disturbance and the response of the organism as the Grand Response to eventually lead to the Grand Outcome, success or failure to reproduce. The partial disturbances (the whole of which forms the GD) and the partial responses (the whole of which forms the GR) can be interrelated to any degree, zero to complete. In the latter case, the GO is a function of all the partial responses forming a very complex relation between GO and GR. This is rare in reality, because the GD of the real world contains a lot of constraint: ‘Thus the organism commonly faces a world that repeats itself, that is consistent to some degree in obeying laws, that is not wholly chaotic. The greater the degree of constraint, the more can the adapting organism specialise against the particular forms of environment that do occur. As it specialises so will its efficiency against the particular form of environment increase.’ (p 139). NB: this is reminiscent of Oudemans’ increasing restrictions or limitations on the following configurations, it reminds of Wolfram, namely with regards to the units of computation that will be equal as well as the powers of perception of people that are of the same order of complexity as the processes they are trying to perceive and analyze (and that themselves are produced by). A few lines previous: ‘Were it common, a brain would be useless (I. To C. 13/5). In fact, brains have been developed because the terrestrial environment usually confronts the organism with a GD that has a major degree of constraint within its component parts, of which the organism can take advantage’ (p 139). This attributes a natural role to the brain: to ferret out the regularities in the environment of the organism. How is the analogy brain : organization with firm : organization?

10/3 –

The recurrent situation

10/4 Consider the case in which disturbances are sometimes repetitive; in those cases if a response is adaptive on the disturbance’s first appearance, it is also repetitive on later appearances. This is not automatic, because in some cases a disturbance’s appearance depends on the number of times it has appeared before. In this chapter disturbances are studied that are independent of where it appears in the sequence of previous appearances; the only condition is that if a response is adaptive to the first appearance it also is on later occasions. The advantage is that exploratory trial and error is required only at the first appearance and not at the later appearances. If an organism can adapt to multiple (different kinds of) disturbances, then these can be considered multiple environments; an extension of the environments it can adapt to, means an increase of its chances of survival: this organism can accumulate adaptations.

10/5 The alternative is that the system does not jump to conclusions; in a pré-bait kind of situation it would perform better than the rat. But if the environment is constrained in its possible behaviors, then the system is at a disadvantage.

10/6 and 10/7 –

The accumulator of adaptations

10/8 Step mechanisms can be thought of as information about the way that the essential variables of an ultrastable system have behaved in the past. They must be split into classes and they cannot belong to the same set, because on the occurrence of some new event, the stored information will be overwritten; separate stores must exist for different kinds of occurrences.

10/9 et it be given that the organism adapts to P1 initially in a process of trial and error and if P1 occurs a second time it adapts at once. The same counts for P2; from this is follows that te step-mechanisms must be divided into non-overlapping sets, that the reactions to P1 and P2 are due to their particular set. The presentation of the problem value of P) must determine which set is brought to bear, while the remainder is left inactive.

10/10 The subsets of S need not be efficiently organized and can be random processes. A mechanism for a gating mechanism (the selection of appropriate subset for the problem at hand) is presented in 16/13. The basic requirements are easily met. Even thought eh arrangement may not be as tidy as the abstract design here.

10/11 In many cases a specific sequence exists between various situations. The design of Figure 10/9/1 caters for this naturally, as P1 is followed by P2 &c (first do not touch the teapot, then don’t wipe the jam, don tip over the milk jar, then reach for the cookie). Only certain fragmented situations allow this kind of environment; if it is then a mechanism such as presented above improves the organism’s adaptive capabilities. How the entire regulatory device of an organism develops depends on the situations of the environment presented to it.

10/13 The mechanisms of adaptation are not due to star dust or excellent cerebral design; adaptivity can be a ‘dumb’ process which can occur in a non- neurophysiological environment such asa a computer.

Chapter 11. The Fully Joined System.

11/1 A basis version of the ultrastable system can work; not consider some complications. the first of which is a large number of components.

Adaptation time

11/2 Suppose the Homeostat is made up with 1,000 units (instead of 4) and suppose that all but 100 are shorted out, the order of magnitude of essential variables in a living organism. Because they are essential, they must all remain in their limits; suppose that the step-mechanisms give a 50% chance to each variable to stay within limits and an independent 50% chance to move outside the limits. How many trials are necessary on the average before adaptation? At this rate the probability is (½)¹⁰⁰ ; at 1 pr second this implies that it will take approximately 1022 years to arrive at a situation where all are within limits; this in fact means very close to never; and yet the human brain can do this in a reasonable period of time, does it use the ultrastable mechanism? ‘It can hardly be that the brain does not use the basic process of ultrastability, for the arguments of S. 7/8 show that any system made of parts that obey the ordinary laws of cause and effect must use this method’ (p149).

11/3 and 11/4 similar outcomes as 11/2

11/5 The processes are so time consuming because partial successes go to waste with regards to the establishment of the Grand Success. Consider a case where it isn’t: N events, independent chance of success of p, A covering fraction p of the circumference of each wheel and B the remainder, 1 spin takes 1 second: case 1) all N wheels are spun and when all N are A it stops (this requires (1/p)N spins, (1/2)1000 if N=1,000, p=2), case 2) the first wheel is spun until it is A, then the second wheel is spun until it is A and so on until all are A (this requires N/p spins, 1,000/p if N is 1,000, p=2) and case 3) of all the wheels initially spun, the ones that are A remain, the remaining contingent is spun again and the ones that are B are spun again &c (this requires 1/p spins, if N=1,000, p=2). Case 1 requires 10293 year, case 2 requires 8 minutes and case 3 mere seconds.

11/6 Case 2 and case 3 can use partial successes to built the Grand Success where case 1 cannot. ‘The examples show us the great, the very great, reduction in time taken that occurs when the final Success can be reached by stages, in which partial successes can be conserved and accumulated’ (p 152).

11/7 If the cases are applied to the selecting of a number registration on cars ending 1, then 2 then 3 up to and including 9, then using the method of case 1 this requires 10 billion cars to pass by, using case 2, 50 suffice.

11/8 ‘A compound event that is impossible if the components have to occur simultaneously may be readily achievable if they can occur in sequence or independently’ (p 153).

11/9 The difference between the Homeostat and a living organism is exactly that the organism does not engage in trials until all comes right at once, but instead while making trials, achieves and retains (accumulates) successes as it goes, until the Grand Success is possible. A combination lock is an example where human organism and Homeostat fail alike.

Cumulative adaptation

11/10 The organism has many essential variables; the organism manages to reach adaptation fairly quickly; what can be deduced from this? ‘It has thus been shown that, for adaptations to accumulate, there must not be channels from some step-mechanisms (e.g. S3) to some variables (e.g. M12), nor from some variables (e.g. M3) to others (e.g. M12). Thus, for the accumulation of adaptations to be possible the system must not be fully joined. .. This is the point. If the method of ultrastability is to succeed within a reasonably short time, then the partial successes must be retained. For this to be possible it is necessary that certain parts should not communicate to, or have an effect on, certain other parts’ (p 155). NB: this is a very important argument for the way the system retains information in this case so as to get work done in a reasonable time-frame. But why should it be required that it does this in a reasonable time-frame? Brains have developed for there are regularities in the environment that it can anticipate; had there been no regularities ata ll then there would not have been a need for a brain. Now that there is a brain, all it needs to do is to anticipate the event before it occurs; if it does not do so then it is useless after all and the world would appear to be just as random as it does without any regularity. I reckon that this is what Wolfram refers to if he suggests that the processes that developed people’s brains are the same processes that occur in nature.

11/11 Because we worked with systems that were assumed to be richly connected there could not be a discussion about integration or mechanisms that work in separate parts: ‘The reacting parts and the environments that we have discussed have so far been integrated in the extreme’ (p 156). NB: this is where the channels M sit. This Statement seems to bear a relation with the (Wagensberg) interface that the system has with the environment.

11/12 The Homeostat is too well integrated, too much cross-joined, and as an ultrastable system takes too long to adapt: to what level should it be cross-joined? The separation into parts and the union into a whole are extremes on the scale of connectedness; in the above sense adaptation requires independence of unrelated activities as well as integration of related activities. NB: this refers to an example of a driver keeping a car on the road while clutching and changing gears.

11/13 ‘They do this by developing partial, fluctuating and temporal independencies within the whole, so that the whole becomes an assembly of subsystems within which communication is rich and between which it is more restricted’ (p 157).

Chapter 12. Temporary Independence.

12/1 Physical separation or connection is useless as a criterion of independence.

12/2 No relation necessarily exists between the direction of control and the direction of the flow of matter or energy if the situation is such that all the system’s parts are freely supplied with energy.

Independence

12/3 X and Y are variable sin a system. Set X and observe the value of Y. Reset X and reset Y. Set X to a value different from the first trial. Observe Y. If the value of Y is now the same as it was the first time then Y is independent of X. Dependent means ‘not independent’; the concept needs 2 transitions.

12/4 If Y is independent of X regardless every possible value of the other variables, then Y is unconditionally independent of X. Y is independent of X in every field of the system. However, this is possible without conditions only if the system is suitably simple, else additional information must be provided.

12/5 Because independence varies one system can give a wide variety of diagrams of immediate effects.

12/6 If X is independent of Y and Y is not independent of X then X dominates Y.

12/7 Of every variable of an entire system A is independent of every variable in system B then system A is independent of system B. A may in addition dominate B and a mutual dependence can exist.

12/9 The definition makes independence dependent on one time, step, click, or infinitesimal time if continuous. If Z depends on Y and Y depends on X, then if X changes then Y changes and, one step later Z changes. So Z depends on X delayed. The diagram of ultimate effects shows the dependencies if time is allowed for all the effects to work around the system.

The effects of constancy

12/10 If component C depends on component B and component B depends on component A and A, B and C all contain various variables, then to make A and B independent requires that the variables in B are null-functions, implying separation at B by a wall of constancies. This also implies that this is not necessarily the case at every field: A and C can be sometimes joined and sometimes independent.

12/11 –

12/12 The diagram of ultimate effect can take a different shape if one or more of the variables in the system are constant; this includes the reversal of dominancy between variables.

12/13 –

The effects of local stabilities

12/14 For a system to have temporary independencies it must have variables that are temporarily constant. Any subsystem that is constant is in a state of equilibrium. If its surrounding parameters are constant then the subsystem has a state of equilibrium in the corresponding field; if it stays constant if the parameters change, then that is an equilibrium state in all the fields occurring. Constancy in a subsystem implies it is in an equilibrium state; constancy in the presence of small disturbances implies stability. Constancy, equilibrium and stability are closely related.

12/15 These kind of systems are common, see S. 15/2; two types worth noting are: 1) with a probability p some randomly selected state of a system is equilibrial and 2) all states are stable if some parametric value is below a threshold and few or none are if it exceeds that value. The latter can easily generate varying connections between variables by readily giving constancy.

12/16 Consider ABC, then if B is equilibrial for all values from A and C, then A and C are independent. If however, B is equilibrial for some and not for other values from A and / or from C, then A and C will sometimes be and sometimes not be dependent: ‘Thus we have achieved the first aim of this chapter: to make rigorously clear, and demonstrable by primary operations, what is meant by ‘temporary functional connexions’, when the control comes from factors within the system, and not imposed arbitrarily from outside’ (p 169). NB: this statement is relevant with regards to autopoietic systems: the control lies within the system. The difference is that adaptive systems are adaptive to their environment at once and not necessarily in an evolutionary process a/p autopoiese.

12/17 ‘The same ideas can be extended to cover any system as large and richly connected as we please’ (p 169). Constancies, in other words, can cut a system to pieces.

12/18 –

Chapter 13. The System with Local Stabilities.

13/1 Rigor and precision are possible examining the kinds of systems that show the above behavior; it is required to define a set with certain properties and the statements must be precise and concern the properties of the set: we are now not talking about individual systems but about a set of systems. NB: how is this relevant to the definition of individual firms or of a set of firms with some specific properties? The discussed systems are random in the sense that they are generic with typical properties such as to arrive at a precise deduction about the defined set of systems.

13/2 A polystable system is any system whose parts have many equilibria and that has been formed by taking parts at random and joining them at random.

13/3 –

13/4 In a state-determined system, if a sub-system has been constant and it starts to show change, then it can be deduced that a change must have occurred in one or more of its parameters. If a sub-system that is a part of a state-determined system, it is stable, and its parameters (variables of other subsystems) are constant, then it is trapped in equilibrium; only an external source can allow it to change.

Progression to equilibrium

13/5 –

13/6 let i be the number of components in a system that is in equilibrium and let n be the number of components. If i=n then every component is in equilibrium and the whole is also. If i<n and n-i components are not in equilibrium and they will assume a new value at each step and a new state of the whole appears.

13/7 In a particular system its behavior is determinate if the system and its initial state is given. In a set of systems this is not the case, except at the two extremes, namely richly connected and hardly connected.

13/8 How will i behave if every component is connected to all others, meaning n(n-1) arrows in the diagram of immediate effects? If p is independent and unequal 1 and n is large then the probability that the whole is in equilibrium is small and i will be approximately np. The line of behavior starts a random walk and the systems meets and equilibrium in case i by chance becomes n. The time to get there is of geological (astronomical) timescales.

13/9 A special case is when i is close to n: at the next step, its value will average away from n and so the number of elements in equilibrium decreases. Such a system will fall back to an average state; it is typically unable to retain partial or local successes.

13/10 Consider a system will large n, independent p and the elements not much connected. This resembles the situation where p is very close to 1: many elements remain in equilibrium for long periods of time; they are constant and leave large areas in the system isolated, in effect this means they are not much connected. Consider a case where none of the n variables is connected with any of the others: this is a system only in the nominal sense; once in equilibrium an element stays in equilibrium because it cannot be disturbed. So all elements that contribute to i (set of elements in equilibrium) at an earlier state, must contribute to i at a later state; and as a consequence the value of i cannot fall with time (or clicks). This type of system goes to its final state of equilibrium progressively in the sense of Case 3 of S. 11/5 and the time the system takes is not excessively long.

13/11 The more interesting kind is the systems that near the limit of disconnection, where i has the tendency to move to n: ‘This is the sort of system that, after the experimenter has seen i repeatedly return to n after displacement, is apt to make him feel that i is ‘trying’ to get to n’ (p 177).

13/12 –

13/13 Connection is an important determinant for the way in which a system goes to equilibrium; when the connection is rich then the behavior tends to become complex, the time to reach n is long and if some high i is reached then it cannot retain the excess over the average. When the connection is poor (either by few joints or by many constancies), the line of behavior is short and the time lapse for the whole to arrive at equilibrium is short. When a state is met where a large number of variables are stable, the excess of the average is retained for a time; local equilibria are accumulated and equilibrium for the whole is progressed.

Dispersion

13/14 This is the phenomenon that, given arbitrary sections of the behavior of a system, the variables that are active in a previous section are different from the active variables in a later section; the sections can come from the same line or from different lines. The essential feature is that even if the sections differ in one or few variables, namely their dependency, the changes that result may distribute the activations to different sets of variables, namely to different places in the system: ‘Thus the important phenomenon of different patterns (or values) at one place leading to activations in different places in the system demands no special mechanism: any polystable system tends to show it’ (p 179).

13/15 If the two places are to have minimal overlap then the parts should have almost all their states equilibrial; then the number active will be few: if the fraction is r, then the fraction of the overlap is r². If the proportion of the equilibrial states is nearly 1, then r is correspondingly small. ‘Thus the polystable system may respond, to two different input states, with two responses on two sets of variables that may have only small overlap’ (p 179).

13/16 Dispersion is used widely in the sense organs and in the nervous system. NB: it is possible to translate this to the workings of organizations.

13/17 ‘The fact that neuronic processes frequently show threshold, and the fact that this property implies that the functioning elements will often be constant (S. 12/15) suggest that dispersion is bound to occur, by S. 12/16’ (p 180).

Localisation in the polystable system

13/18 How will the set of active variables be distributed over the whole set? The answer to whether activity is restricted to a certain variables only is ‘yes’; the answer to whether the variables occur in no simply describable way is ‘no’: the variables can be determined from local circumstances but the outcome on a global scale is random.

13/19 ‘The set of variables activated at one moment will usually differ from the set a later moment; and the activity will spread and wander with as little apparent orderliness as the drops of rain that run, joining and separating, down a window-pane. But though the wanderings seem disorderly, the whole is reproducible and state-determined; so that if the same reaction is started again later, the same initial stimuli will meet the same local details, will develop into the same patterns, which will interact with the later stimuli as they did before, and the behavior will consequently proceed as it did before’ (p 182). This describes the dichotomy between local behavior and global behavior and how a pattern must occur and how it can be repeated because of its deterministic character. It is stable in the face of the removal of material: ‘For in a large polystable system the whole reaction will be based on activations that are both numerous and widely scattered. And, whole any exact statement would have to be carefully qualified, we can see that, just as England’s paper industry is not to be stopped by the devastation of any single county, so a reaction based on numerous and widely scattered elements will tend to have more immunity to localised injury than one whose elements are few and compact’ (pp. 182-3).

13/20 –

Chapter 14. Repetitive Stimuli and Habituation.

14/1 Two reasons: 1) Exercise in discussing polystable systems in terms that are both general and precise and 2) the behavior of a system in equilibrium is often perceived as ‘boring’ in the sense of a run down clock. However, when a complex system nears an equilibrium this involves complex (and interesting) relations between the states of the various parts of the observed system. This chapter shows how a system running to equilibrium under a complex and repetitive input produces interesting behavior.

14/2 Definition: when there are many states of equilibrium in a field and every line of behavior terminates at some state of equilibrium, the lines of behavior collect into sets, such that the lines in each set terminate into one common point or cycle of termination; the field can be divided into regions such that one region contains one and only one state or cycle of equilibrium to which each line of behavior in the region eventually comes; this region is called a confluent (this is a basin of attraction DPB). Important properties of the confluent are: a) a line cannot leave it if arepresentative point is released within it, and b) it will go to the equilibrium or cycle, where it remains sso long as the parametric conditions remain unchanged: ‘The division of the whole field into confluents is not peculiar to machines of special type, but is common to all systems that are state-determined and that have more than one state of equilibrium or cycle’ (p 185).

Habituation

14/3 Impulsive parametric changes can bring the system into a new confluent, given sufficient delay between the applications for the line of behavior to find the equilibrium. There it can again be brought to another and another, or it can be trapped inside the confluent; some confluents can hold the line inside while others can’t: the process is selective.

14/4 –

14/5 The polystable system is selective, because at some point the line will be transported to a confluent where the stimulus cannot shift it from. ‘And, if there is a metric and continuity over the phase space, this distance that the stimulus S finally moves the point will be less than the average distance, for short arrows are favoured. Thus the amounts of change caused by the successive applications of S change from average to less than average. .. What we should notice is that the outcome of the process is not symmetric. When we think of a randomly assembled system of random parts we are apt to deduce that its response to repetitive stimulation will be equally likely to decrease or to increase. The argument shows that this is not so: there is a fundamental tendency for the response to get smaller. .. If the responses have any action back on their own causes, then large responses tend to cause a large change in what made them large; but the small only act to small degree on the factors that made them small. Thus factors making for smallness have a fundamentally better chance of surviving than those that make for largeness. Hence the tendency to smallness’ (p 187).

14/6 –

14/7 ‘The argument of this chapter suggests that it is to be expected to some degree in all polystable systems when they are subjected to a repetitive stimulus or disturbance’ (p 189).

Minor disturbances

14/8 If the arrow S does not represent a single response but a distribution of responses, inside and outside of the confluent. The answer is roughly the same. The confluent who’s arrows go far is left by the representative point and the ones who’s arrows remain in its own confluent act as a trap. Thus the polystable system selects the equilibria that are immune to the actions of small irregular disturbances (and will be destroyed by large field shifts).

14/9 –

14/10 Bizarre fields are selectively destroyed when the system is subjected to small, occasional, and random disturbances. ‘Since such disturbances are inseparable from practical existence, the process of ‘roughing it’ tends to cause their replacement by fields that look like C of Figure 14/9/1 and act simply to keep the representative point well away from the critical states’ (p 191). NB: this resembles Wolfram’s remark that selection smooths out the edges and polishes existing order to a workable and simpler design.

Chapter 15. Adaptation in Iterated and Serial Systems.

15/1 Let us resume the task of considering how a large and complex system can adapt to a large and complex environment without taking almost an infinite time to do it. The facts are as follows: 1) the ordinary terrestrial environment has a distribution of properties very different from what was assumed earlier (S. 11/2), 2) against the actual distribution of terrestrial environments, the process of ultrastability can give adaptation in a reasonably short time, 3) when environment gets more complex then the time of adaptation of an ultrastable system goes up, not only theoretically but in real living systems, and 4) when the environment is excessively complex and closely-knit, the theoretical ultrastable system and the living system fail alike.

15/2 An ordinary terrestrial environment has these features: 1) many of the variables are constant over considerable amounts of time such that they behave as part-functions, 2) most variables of the environment have an immediate effect on only a few of the totality of variables; this operates as a system of part-functions. ‘A total environment, or universe, that contains many part-functions, will show dispersion, in that the set of variables active at one moment will often be different from the set active at another. The pattern of activity within the environment will therefore tend, as in S. 13/18, to be fluctuating and conditional rather than invariant’ (p 195). NB: what are (examples of) these constants and temporary or quasi relations between variables and variables and variables and parameters? In my mind’s eye it is visualized as blocks of temporarily invariant situation where interaction between the e.g. an animal and the environment occurs. How does this view on interacting relate to the view of Knorr-Cetina, namely the establishment of a third body? As an interaction with an environment takes place, now this set is active, now that set. If some set is active for a long time and others sets are inactive and inconspicuous, then the observer may call the first part the environment. And if later the activity changes to another set, he may call that also a (second) environment.

15/3 Previews to cases: 1) a whole of which the connections between the parts is zero 2) subsystems are connected in a chain 3) subsystems are connected unrestrictedly in direction so that feedback can occur and 4) chapter 16: systems with non-rich connections in all directions; these kinds of systems can be thought of as constructed from sub-systems that are internally richly connected with feedback loops between them that are much poorer.

Adaptation in iterated systems

15/4 Consider from a field of interactions between elements one configuration where some feedback loops are closed; the entire system contains a number of subsystems; functionally this represents an organism dealing with its environment by several independent reactions. The whole is said to consist of iterated systems. If i is the number of subsystems in equilibrium then i will not fall but can only rise as a consequence of S. 13/10.

15/5 Whether the feedbacks are first-order or second-order is irrelevant; if the system has essential variables and step-mechanisms it will go to equilibrium and the system’s adaptation will develop cumulatively and progressively. The process of trial and error takes place in the different subsystems independently of the developments in the others.

15/6 The time it takes for the iterated set to become adapted is of the order T3; this means of the order of one of its subsystems.

15/7 If the components are not connected then each can adapt independently (parameters are constant) and the time of the whole to equilibrium is of the order T3. If two components are connected then one cannot reach equilibrium until the other has; the time to reach equilibrium is of the order 2 x T3 if the step-mechanisms of the component systems are connected and of the order T1 (almost indefinite) if the systems’ reaction parts are connected: a joining from the reacting part of A to that of B can have the effect of postponing the whole’s adaptation almost indefinitely.

Serial adaptation

15/8 As per S. 15/3 the second stage of connectedness occurs when parts of the environment are joined as a chain: ‘Thus we are considering the case of the organism that faces an environment whose parts are so related that the environment can be adapted to only by a process that respects its natural articulation’ (p 200).

15/9 As an illustration: the environment allows only that an organism learns to walk before learning how to run; additional examples: falcons, chimpanzees, children.

15/10 Part A, the avoiding system: objects are noticed by the organism via skin and eyes; objects are handled via muscles. Part B, the feeding system: the blood glucose level is communicated to the brain; the brain instructs the muscles to get food; the muscles get food. As a consequence of a process of dispersion A and B may share variables (brain, muscle). A and B interact. Assume that no step-changes in A occur while adaptation of B occurs; the adaptation is now in Part B alone, interacting with ‘an environment’ A. Whatever the particularities of the conditions of the domain of A, B will be forced to adapt within the scope defined by them. NB: this is relevant to the case of a firm: everything but the firm’s memeplex is external to it; the memeplex interacts with those things such as to adapt to them; these include elements traditionally considered internal to the firm such as employees. PS: if viewed anatomically, the (sets of) variables are grouped differently from a functional view: anatomically, two variables are external to the system, functionally, all of the variables are part of the whole system and organized into an adapting part (B) to which A is the environment. Now, given that adaptations in A only occur in between step-changes in B, collisions between A and B will not occur.

15/11 In a sequence of nested sub-systems, every sub-system will be affected (and will adapt to) every disturbance in every (sub-) system in the chain it is dominated by as well as every reaction to those disturbances. If the channel capacity of the connections is high then so much disturbance is transmitted to the sub-systems that their adaptation is postponed indefinitely. If the capacity is low then the adaptation is so rapid that C, though affected by B, may be unaffected by disturbances in A and so on. In this way, if the connections get weaker then the adaptation tends to be more sequential, first A thenn B and so on, and limiting to the iterated set. If sequential the behavior tends to Case 2 (turn each wheel until A, then turn the next wheel &c.) and the time will be of the order T2. ‘Thus adaptation, even with a large organism facing a large environment, may be achievable in a moderate time if the the environment consists of sub-systems in a chain, with only channels of small capacity between them’ (p 204).

Chapter 16. Adaptation in the Multistable System.

16/1 Consider sub-systems of the environment that are connected unrestrictedly in direction so that feedback occurs between them. The type may vary according to the amount of communication between sub-system and sub-system, of special interest are: 1) it is near maximum and 2) the amount is small.

The richly joined environment

16/2 In this case, the division into subsystems ceases to have a basis.

16/3 Examples of large richly connected systems are rare, as the terrestrial environment is highly subdivided: combination lock, mathematical examples where the behavior of every sub-system depends on the behavior of all others.

16/3 ‘Thus the first answer to the question: how does the ultrastable system, or the brain, adapt to a richly joined environment: is – it doesn’t’ (p 207).

The poorly joined environment

16/5 This was shown in S. 15/2 to be the case in most terrestrial environments: sub-systems affect each other only occasionally, weakly, or via other systems. If the degree of interaction varies, at the lower end is the iterative system of S. 15/4, at the upper end is the richly connected systems of S. 16/2.

16/6 What is now assumed: 1) the environment consists of large numbers of sub-systems that have large numbers of states of equilibrium as per S. 15/2, 2) whether because of few connections or because equilibria are common, the interactions are weak, 3) the organism coupled to this environment will adapt by the method of ultrastability and 4) the organism’s reacting part is itself divided into sub-systems between which there is no direct connection: each sub-system is supposed to have its own essential variables and second order feedback.

16/7 ‘In other words, within a multistable system, subsystem adapts to subsystem in exactly the same way as animal adapts to environment. Trial and error will appear to be used; and, when the process is completed, the activities of the two parts will show co-ordination to the common end of maintaining the essential variables of the double system within their proper limits. Exactly the same principle governs the interactions between three subsystems. If the three are in continuous interaction, they form a single ultrastable system which will have the usual properties’ (p 210). NB: this appears to explain how social behavior of people gets to be correlated.

16/8 –

16/9 What modifications are required to allow that in a multistable system the number and distribution of the sub-systems active changes at each moment? Adaptation of the whole will occur, whether dispersion occurs or not. Dispersion destroys the individuality of the sub-systems. If the adaptation of the multistable system is tested by displacing its representative point then the system’s sub-systems will be found to react in a way co-ordinated to some common end. ‘But though co-ordinated in this way, there will, in general, be no simple relation between the actions of subsystem on subsystem: knowing which subsystems were activated on one line of behaviour, and how they interacted, gives no certainty about which will be activated on some other line of behaviour, or how they will interact’ (p 213). In other words: what is sub-system A and what is B can change from moment to moment.

16/10 NB: the structure changes from moment to moment, the content and the process interchange. And in addition, no anatomical or histological existence may exist of these functionalities.

16/11 What is the time required of these kinds of multistable systems to adapt? This largely depends on the richness of connection of the systems.

Summary If the actual richness is not high then the time required to reach adaptation is reasonable in practical terms.

Retroactive inhibition

16/12 Figure 7/5/1 breaks up into a multistable systems like Figure 16/6/1. Questions: 1) can a multistable system take advantage of a recurring situation? As a reminder: polystable systems have dispersion; the number of active variables they have in common is limited; a different line of behavior results in changes in their respective sets, which may or may not overlap. In the case of a multistable system, the outcomes that would be the same given two different disturbances sufficiently separated, is P1 x P2. ‘Thus the multistable system, without further ad-hoc modification, will tend to take advantage of the recurrent situation’ (p 216).

16/13 If the disturbances vary widely then the multistable system tends to direct the activations to widely different sets of step-mechanisms providing a functional equivalent of the gating mechanism of S. 10/9.

16/14 If two disturbances are nearly equal, then the overlap of the activated sets is larger; chances increase that the effects of the last disturbance destroys the effects of the first one. New learning destroys old learning: retroactive inhibition. In a multistable system the more the newer stimuli resemble the old, the more will the new upset the old. This is matched by a similar tendency in the nervous system.

16/15 Adaptability or the power to accumulate adaptations means that later adaptations shall not be destructive to earlier ones; this is the opposite of retroactive inhibition meaning that later adaptations shall be destructive to earlier ones. A brain model should show both. The homeostat shows retroactive inhibition maximally, iterated systems with a gating-mechanism shows adaptive behavior maximally and the multistable system of some intermediate degree of connection can show both. The latter will resemble the living organism.

Chapter 17. Ancillary Regulations.

17/1 Some objections (other than processing time) to the thesis that the brain is to a large extent multistable are discussed.

Communication within the brain

17/2 Why are in the multistable system and its Figure no connections between the parts of the brain, namely in the lower part, the organism; why are the connections in the environment?

17/3 Dispose of the idea that the more communication within the brain, the better. Three ways in which a function can be successful only if certain pairs of variables are not allowed to communicate or only to a certain degree: (1) in S. 8/15 it was shown that the essential variables must change the step-mechanism such that there is sufficient time between (discrete) trials; in that way the essential variables change slower than the rate of the main variables; if the essential variables change too fast there is not enough time to communicate the appropriateness of the values around the system and the environment as they are implementing their trial; changing too fast means acting before communication has arrived: ‘And if it takes ten years to observe adequately the effect of a profound re-organisation of a Civil Service, then such re-organisations ought not to occur more frequently than at eleven-year intervals. The amount of communication from essential variables to step-functions can thus become harmful if excessive’ (p 219), (2) When presented with a recurrent situation A and then with Band again with A, a system can act on A appropriately. It was shown in S. 10/8 that while adapting to B the step-mechanisms concerned with the adaptation to A must not be affected with what happens at the essential variables; allowing such communication would be harmful, and (3) It was shown in S. 16/11 that a system’s adaptation depends on its approximation of the iterated form; every addition of channels of communication takes it further away from that state and increases the time to adaptation: ‘Thus in adaptive systems, there are occasions when an increase in thee amount of communication can be harmful’ (p 219).

17/4 Another objection to the lack of connection between part and part is that coordination between part and part is required; this communication is not necessary: First, if the parts in the environment are not connected then no coordination (no communication) between parts of the organism is necessary because the changes in essential variables come (and can be responded to) independently. Second, if the parts in the environment are connected then the actions between the parts of the organism must be coordinated, because the state of all the essential variables must be kept within limits, each in relation to the others’ actions. To achieve this coordination however, communication does not necessarily take place between the organism’s parts, but can take place via the environment.

17/5 Two reasons for communication to exist between part of the organism are: 1) disturbances can come from the environment as well as from other parts; if they come from other parts it is useful if the communication is direct such that it arrives early,

17/6 and 2) the fewer the joins, the smaller the range of behaviors available to the organism (and conversely the larger, the wider the repertoire). In summary: some connections between the parts of the organism are realistically there.

17/7 With increasing connections between the (reacting) parts of the organism, the time to adapt also increases. The richness of connection between the parts of the brain has advantages and disadvantages and so the brain has to develop to reach some kind of optimum; the optimum is not a goal in itself, but is a condition for proper functioning between given limits: ‘Thus, for the organism to adapt with some efficiency against the terrestrial environment, it is necessary that the degree of connexion between the reacting parts lie between certain limits’ (p 224).

Ancillary regulations

17/8 The phrase ‘between certain levels’ above is not a circular argument, because two types (levels, orders) of adaptation are involved; in S. 3/14 it was assumed that certain essential variables, say E, remain within limits. In Chapter 11 the time for achieving equilibrium, say F, was added as an essential variable; time is different from other kinds of essential variables, but it must keep within limits also. The effect of F exceeding its limits on the behavior of a very essential (but not so essential that the organism dies from it) variable EE is that the system must now start to look for other essential variables than EE to change such that the system survives; the difference with an additional change in EE beyond some F is that the step-changes of EE do not suffice and, follwing the method of ultrastability, the step-mechanism of another E (one that remained unchanged while EE changed) is required; an example: the cat has tried every possible combination of levers to get out of the box and must now revert to mewing. Changes in E bring answers, F ‘helps’ only in the sense of forcing a change of set of essential variables hence step-mechanism. As a consequence the conclusion that certain parameters will have to be brought within certain limits does not imply a circular reference.

17/9 real systems are much more complicated than this thesis poses. The reaction part R can contain a multistable system and moreover, it can contain sub-systems of the same form and with its own sub-essential variables and sub-adaptations.

17/10 A mechanism to represent the human brain must find one that adapts really efficient. In S. 17/7 it was argued that this implies adjustment of the degree of intra-cerebral connectivity in the brain to within certain limits. Other parammeters that must be kept within limits also are: (1) duration of trial: this was hinted at in S. 8/15 but not how it is automatic, (2) the essential variables should via the step-mechanisms ‘hunt at bad’ and ‘stick with good´, but it is unclear how this relation works, (3) in S. 10/8 a gating-mechanism was introduced but it is unclear how the organism should get it, and (4) in S. 13/11 the importance was shown of the parameter: richness of equilibria among the states of the parts, but it is unclear how this parameter can be adjusted within limits. Another is discussed in the next paragraph.

Distribution of feedback

17/11 If in Figure 16/6/1 a disturbance is delivered by the environment of some part, it will affect the essential variables, through the corresponding step-mechanism, on to the reacting part and affect THE SAME environment that caused the disturbance initially. This indeed favors efficiency but it need not be so designed: the second-order feedback loops can be connected to another part. The system could not retain adaptations from the past and achieve an equilibrium in any efficient way in practical terms.

17/12 Following the above at least five ancillary regulations must be in place to achieve addaptation with reasonable efficiency and speed: how are they to be achieved?

17/13 The law of requisite variety states that if a certain quantity of disturbance is prevented by a regulator, then the regulator must be capable of exerting at least that quantity of selection. ‘The provision of the ancillary regulations thus demands that a process of selection, of appropriate intensity, exists. The biologist, of course, can answer the question at once; for the work of the last century and especially of the last thirty years has demonstrated beyond dispute that natural, Darwinian, selection, is responsible for all the selections shown so abundantly in the biological world. Ultimately, therefore, these ancillary regulations are to be attributed to natural selection’ (p 229 – 30).

17/14 The purpose of the next section is to show: ‘.. how the ancillary regulations must be developed in brains other than the living’ (p 230). A second purpose is to show that adaptation is the inevitable outcome of the process of causal relations starting at a general point.

Chapter 18. Amplifying Adaptation.

Selection the state-determined system

18/1 Selection is performed by every isolated state-determined system (also I. to C., S. 13/19): ‘In such a system, as two lines of behaviour can become one, but one line cannot become two, so the number of states that it can be in can only decrease’ (p 231). NB: this must connect with utility of diversity (how?) and also with Wolfram’s hunch that selection smooths existing patterns. Selection means that the system tends to achieve some equilibrium; in simple systems this seems trivial, such as a clock running towards its run-down state. The more complex the system gets, the more interesting this property becomes, ‘.. to show: (1) a high intensity of selection by running to equilibrium and (2) that the selected set of states, though only a small fraction of the whole (set of states), is still large enough in itself to give room for a wide range of dynamic activities’ (p 231). ‘Thus, selection for complex equilibria, within which the observer can trace the phenomenon of adaptation, must not be regarded as an exceptional and remarkable event: it is the rule. The cchief reason why we have failed to see this fact in the past is that our terrestrial world is grossly bi-modal in its forms: either the forms in it are extremely simple, like the run-down clock, so that we dismiss them contemptuously, or they are extremely complex, so that we think of them as being quite different, and say that they have Life’ (p 231-2).

18/2 These above are extremes of the same scale. Survival of Odds over Evens (and 0 over all alike) example.

18/3 The common denominator is that whenever a single-valued operator (the ‘law’ of the system) is performed repeatedly on a set of states, then the system tends to the states that are not affected by the operation or to a lesser degree: ‘In other words, every single-valued operation tends to select forms that are peculiarly able to resist its change-inducing action. In simple systems this fact is almost truistic, in complex systems anything but.’ (p 233). Think of the states of preference as a consequence of evolution on the earth: ’The development of life on earth must thus not be seen as something remarkable. On the contrary, it was inevitable’ (p 233). Consider the enormous amount of selection performed by this process, which in fact is the same as the processes we see around us everyday; the greater space available allows more forms to test and the greater period of time allows a greater level of intricate co-ordination. Under evolutionary processes forms in conjunction with their environments have developed powers to resist to the change-inducing actions of the world around them: ‘They are resistant, .. , in the dynamic and much more interesting way of forming intricate dynamic systems around themselves (their so-called ‘bodies’, with extensions such as nests and tools) so that the whole is homeostatic and self-preserving by active defenses’ (p 233). NB: can firms be seen as part of the defenses of people?

18/4 If an organisms deals with disturbances that are not adaptable, because they change over the long run (too fast for its gene-pattern) but remain the same during the generation, then it is advantageous to have the outline of the adaptive mechanism controlled by the gene-pattern and the details by the details within that generation: ‘This is the learning mechanism. Its peculiarity is that the gene-pattern delegates parts of its control over the organism to the environment. Thus, it does not specify how a kitten shall catch a mouse, but provides a learning mechanism and a tendency to play, so that it is the mouse which teaches the kitten the finer points of how to catch mice’ (p 234). NB: the environment of people changes faster than their gene-pattern can accommodate. Genes allow the environment including the firm to take some control over people?

18/5 The law of requisite variety must be applied to ancillary regulations, how the relevant parameters are brought to their appropriate values as follows: 1) some are injected by the genes and the organism is born with the correct values or 2) other ancillary regulations can be adjusted by the gene-pattern at one remove: the gene-pattern establishes a mechanism, a regulator that would then proceed at its own initiative to bring parameters to their appropriate values. However systems can seldom be arranged into distinct levels.

Amplifying adaptation

18/6 How much regulation does the gene-pattern achieve, considering the law of requisite variety? Under direct regulation some mechanism ensures that an essential variable is maintained within limits; under indirect regulation, a regulating mechanism of a parameter affecting the essential variable ensures that the parameter stays within limits which keeps the essential variable within limits. There is no relation between the amount of regulation to keep the essential variable within limits and the amount of regulation to keep the parameter within limits; as a consequence the amount of regulation to keep the parameter within limits can be small but the amount to keep the essential variable within limits can be large. Under direct regulation the amount is limited by what can be supplied by the law of requisite variety, under indirect regulation more regulation may be shown by the essential variable than is supplied to the parameter. Indirect regulation can amplify the amount of regulation.

18/7 ‘Living organisms came across this possibility aeons ago, for the gene-pattern is a channel of communication from parent to offspring..’ (p 236). NB: the meme-pattern is also a channel of communication from ‘parent’ to ‘offspring’ in a cultural sense. The gene-pattern leads to the growing in organisms of a brain that is partly adapted by details in the gene-pattern as well as by details in the environment: ‘The environment acts as the dictionary’ (p 236-7). Thus the information that comes to an organism via its gene-pattern is supplemented by the information supplied by the environment: ‘.. so the total adaptation possible, after learning, can exceed the quantity transmitted directly through the gene-pattern’ (p 237).

Summary

All state-determined dynamic systems are selective; from whatever initial state they go towards states of equilibrium; considering the change-inducing laws of the system, these states are exceptionally resistant: ‘Specially resistant are those forms whose occurrence leads, by whatever method, to the occurrence of further replicates of the same form – the so-called ‘reproducing’ forms’ (p 238). Local equilibria take the shape of sub-systems that are exceptionally resistant to local disturbances; the parts of such a stable local equilibrium are co-ordinated in their defence against disturbances. If the class of disturbance changes from generation to generation then the organism can be more resistant if it is born with a mechanism that the environment will make it act in a regulatory way against the particular environment – the learning organisms.