The abstract characteristics of living systems

This paper [[by G. Sommerhoff](https://en.wikipedia.org/wiki/Gerd_Sommerhoff)] is published for the first time, in this volume. Snippets of text (from the beginning, maybe the middle, and the end) appear below, to give a sense of the content for the chapter. For more depth, the original source is cited, above. ---

## Preface > If the concept of organization is of such importance as it appears to be, it is something of a scandal that biologists have not yet begun to take it seriously but should have to confess that we have no adequate conception of it (J. H. Woodger).

The physico-chemical picture of the living organism is only half the truth. The missing half concerns the nature of the organizational relationships that make the behaviour of obviously living systems uniquely different from that of obviously non-living systems and give it a teleological quality not found elsewhere. In many ways this is the more important half. For here lie the differences between life and death, and between higher and lower forms of life as they affect us most. Here too lies the key to the true function of the living brain, for this function is nothing if not an organizing and teleological one. The distinctive organization of living systems shows itself in the goal-directedness and directiveness of their activities. Aristotle's 'absence of haphazard and conduciveness of everything to an end' are not two separate criteria of life. We infer the former from the latter. The lesson to be learnt from cybernetics is that we are dealing here with objective system properties which, in principle at least, are susceptible to mathematical analysis. [p. 147]

But they are very abstract properties, and to get a clear conception of the distinctive nature of vital organization in general and the distinctive functions of the brain in particular we must above all acquire the ability to think of living systems in sufficiently abstract terms. We also require the _purest form of behaviourism_. That is to say, we must start by thinking of the living organism as no more than a 'black box' which reacts to its environment in certain observable ways, and then analyse mathematically _what_ it does, without preconceived ideas of _how_ it does it. [pp. 147-148]

Biologists, psychologists and neurologists have been all too slow to realize the importance of abstract and accurate analysis along these lines. They are still content to leave it to the cyberneticists. But cybernetics has its origin in control engineering, and so it is not surprising that the biological sciences have to pay for their omissions by an undue servitude to engineering concepts. That is why the writer continues to press for independent pure research in this field - for what he has called _analytical biology_.

## 1\. Introduction 1\.1. Even if we knew down to the last molecular detail what goes on inside a living organism, we should still be up against the fact that a living system is an organized whole which by virtue of the distinctive nature of its organization shows unique forms of behaviour which must be studied and understood at their own level, for the significance of all living things depends on this. The most distinctive character of the behaviour of higher organisms is its goal-directedness, its apparent purposiveness. In fact, it is largely through this apparently teleogical nature of their activities that living organisms betray their exceptional organiza- tion. And their position on the 'scale of life' is largely determined by the degree to which they possess those characteristics. The task of analytical biology is to concern itself with the systematic study of these abstract characteristics of life, and with the precise analysis of the ordering relations in space and time on which they depend. To understand this particular aspect of life is important not only for the biologist: it profoundly concerns also the psychologist, philosopher, and automation engineer. [p. 148] [....]

1\.2. Many animal activities are patently goal-directed in a way which makes it clear that we are dealing here with an objective system-property - a property, moreover, which we can assume to be compatible with the basic laws of physics and chemistry. We can assume this because we know of servo-mechanisms and automata that are capable of essentially similar types of behaviour. [p. 149] [...]

1\.3. Frequently, indeed almost invariably, various different forms of goal-directedness or directiveness are all present and intimately inter-related in the same biological situation. This is a common source of confusion. [....] These are organizational relationships, and this type of coordination and integration is of the essence of vital organization. We are dealing here with a higher, teleological, type of order that is quite distinct, for instance, from the mere geometrical order that distinguishes the molecular structure of solids and forms the subject of classical entropy studies. The ordering relations here are in time as well as in space. [....] [p. 150] [....]

1\.4. It is only in recent years that these characteristic properties of living systems have come to be looked upon as objective system-properties that require an independent abstract analysis within the framework of a general and exact systems research. They are elusive properties which, partly because of the vague and ambiguous terms in which they were discussed, have been the subject of much inconclusive speculation in the history of biology. But the elusive must be grasped and bounds must be set to the vague. [....] [p. 152] [....]

1\.5. The working biologist may often refer explicitly to the goal-directedness or directiveness of biological activities. But many of his key concepts imply it; concepts like adaptation, coordination, control, regulation, learning, maturation, instinct, drive, etc. At present most of these concepts suffer from a degree of ambiguity and uncertain meanings which hamper the progress of theoretical biology. This is also true of psychology and ethology, as the history of behaviour theory well shows. [p. 152] [....]

1\.6. The psychologist is preoccupied with the mind rather than the brain. That means that he is interested in the subjective rather than the objective side of goal-directed behaviour. We know from introspection that in some cases goal-directed behaviour (in the objective sense) is achieved through the instrumentality of conscious thought processes - through the conscious striving after some future goal which is retained as some kind of idea or image. But since we also know that an action does not necessarily have to be consciously purposed in order to be goal-directed in the objective sense of the term, it is advisable to maintain a strict distinction between 'purposive' in the subjective sense and 'goal-directed' in the objective sense. The present paper deals only with the latter. This does not preclude the possibility of making a transition to the subjective aspects of behaviour at a later stage. But it could not be the other way round. [pp. 153-154] [....]

## 2\. Some Fundamental Physical Concepts 2\.1. Throughout our analysis, the organism and its environment will be treated as a dynamical physical system. In the context of the discussion this system is a macroscopic one and the analysis can therefore be based on the conceptual framework of classical physics. The following is a brief outline of some of the concepts that will be used later on. An isolated physical system in the classical sense is _state-determined_. This means, _inter alia_, that the state of the system at any instant can be represented as a single-valued function of the _initial state_ and the _time_ co-ordinate. For instance, the velocity and displacement of a simple pendulum at any instant can be expressed as a single-valued function of the velocity and displacement with which the pendulum was released and the time that has elapsed since. [....]

2\.2. The physicist deals with the complexity of concrete objects and events by inventing abstract models or representations in which certain factors are singled out and the others discarded as irrelevant. [...] In such theoretical representations the state of the system at any given instant is defined by specifying the values for that instant of a selected set of variables. These may be called the _state variables_. Their number depends, of course, on the degree of abstraction and simplification that are made in the model and on the _conditions_ that are assumed to be constant for the purpose of the investigation in hand. [....] [p. 155] [....]

2\.3. We shall assume throughout that the organism-plus-environment system is state-determined, so that the current state of the system can be expressed in terms of single-valued functions of the initial state and the time. [p. 156] [....]

2\.4. When the state of a physical system is described in terms of N epistemically independent state variables, it may be represented as a point in an iV-dimensional space. The N numbers defining the state of the system are then the N components of the position vector of the _representative point_. And the behaviour of the system in time is reflected in the movement of the representative point in the _phase space_. As it moves it traces out the _line of behaviour_ of the system. In a state-determined system every possible initial state determines a single line of behaviour only. And although different lines of behaviour may at one point or another fuse, they can never bifurcate. [pp. 157-158] [....]

## 3\. Preliminary Analysis of Goal-Directed Behaviour 3\.1. To discover what the exact relationships are that distinguish a system showing goal-directed behaviour from one that does not -- and so to give a precise meaning to this concept in the language of mathematics and physics -- is not a simple task of translating one language into another. For one thing, we are dealing here with a term which as yet has no uniform usage. The first step therefore must be to clarify further the sense in which the concept is to be understood here. [p. 159] [....]

3\.2. To follow this up, let us take a concrete example and examine what operational procedures we would adopt to verify the existence of goal-directed behaviour. As we want to concentrate on what the thing does without being distracted by how it comes to do it, we may borrow for this purpose the familiar engineering concept of a 'black box'. [....] [p. 160] [....]

3\.3. Provisionally we may sum up this point as follows: If in an environment E an action A is directed towards a goal G, this implies: i. That _there exists a set V of hypothetical variations of the environment such that each member of V requires a specific modification of the action A if the goal-event G is to result_, and ii. The organisms or machine at the time is so conditioned that _if any of these variants had in fact been the case, the action A would have shown the required modification._ [p. 162] [....]

## 4\. Final Analysis of Goal-Directed Behaviour 4.1. The analysis of the last section has brought out one essential ingredient of the concept of goal-directedness. [....] [p. 163] In all, the concept of goal-directedness implies that the relations between the action, the environment, and the goal-event satisfy all of three criteria. These will be discussed in turn below. [p. 163]

_Criterion I_ In goal-directed behaviour the action itself is not a sufficient condition for the occurrence of the goal-event. In all cases the occurrence of the goal-event is conditional on the action having a specific relation to the environment. More specifically, the situation is always one in which it is a necessary condition for the occurrence of the goal-event that one or more action variables stand in a particular relation to one or more environmental vari ables. [p. 164] [....]

_Criterion II_ Secondly, the concept of goal-directedness implies that the variables a and e in the function F, introduced above, are mutually orthogonal. [p. 165] [....]

_Criterion III_ Finally, the third implication of goal-directedness is the one that was discussed at length in section 3. The concept implies that the animal or machine produces the appropriate action (and satisfied F(ak, ek) = 0 not only under the actual environmental conditions, but also that it would have produced an appropriately modified action under a variety of alternative circumstances each requiring a specific modification of the action. [p. 165] [....]

## 4\. Final Analysis of Goal-Directed Behaviour 4.1. The analysis of the last section has brought out one essential ingredient of the concept of goal-directedness. [....] In all, the concept of goal-directedness implies that the relations between the action, the environment, and the goal-event satisfy all of _three criteria_. These will be discussed in turn below. [p. 163]

_Criterion II_ Secondly, the concept of goal-directedness implies that the vari- ables a and e in the function F, introduced above, are mutually orthogonal (p. 164). For the implication always is that F(ak, ek) = 0 is a condition that must be _brought about_ by the mechanism involved. It is not implied by the axioms of the system. Indeed, random combinations of a and e are conceivable initial states of the system. [p. 165] [....]

## Summary of analysis 4\.2. This completes the main analysis of the fundamental ingredients of the concept of goal-directed behaviour. They may be brought together in the following summary. _If an action is directed towards a goal G, then the following relations exist in respect of an arbitrarily chosen initial point of time t0, provided this precedes the action by a sufficient interval .... [p. 167] [....]

### Degrees of goal-directedness 4/.3. Can a precise meaning be given to the idea of different degrees of goal-directedness? The following illustrates one way in which this may be done .... [p. 168] [....]

### Probability and goal-directedness 4\.4. To indicate the theoretical relation between the degree of goal-directedness and the probability of G occurring, we may briefly say this. [p. 169] [...]

### Unsuccessful goal-directed behaviour 4\.5. In section 4.2 it was assumed that the actual value of u0 is a member of the set S0. The actual action therefore satisfies F(ak, ek) = 0, which we postulated to be a necessary condition for the success of the action. But this does not mean that the action must be successful. For a necessary condition is not the same as a sufficient condition. Other requirements may have to be fulfilled by the action. [pp. 169-170] [....]

### Response functions 4.6. Biologists tend to think about animal behaviour in terms of 'stimuli' and 'responses', whereas engineers compare the 'input' of a servo-mechanism with its 'output'. The notion of 'response' is not a simple one. We can equate the 'output' of a machine with the motor activities of a living organism, but not with its 'responses'. [p. 170] [....]

A _stimulus situation_ may then be defined as the aggregate of the values of the independent environmental variables that enter as arguments into a response function. And, in particular, a _stimulus_ may be defined as any binary variable that is defined on this aggregate. This would conform with the practice of regard- ing a stimulus as a factor that is either present or absent. [p. 171] [....]

### Appendix: a quantitative example 4.7. The purpose of the present investigations is purely analytic and descriptive. [p. 171] [....]

## 5. Directive Correlation and Examples ### Definition of directive correlation 5.1. [....] It is now expedient to comprise these characteristic system properties in the definition of a single specific concept, which we shall call _'directive correlation'._ [p. 174] [....]

### The black box and the football player 5\.2. [....] [p. 176]

### The concept of adaptation 5\.3. The concept of adaptation is one of the most general and important concepts that the biologist uses when dealing with the directive aspects of vital activities. [....] In all these three cases we are referring to a specific form of directive correlation and it is only in terms of the details of this correlation that the essential differences be- tween these three applications can be made clear. We shall find that the main difference lies in the length of the back-reference period (as defined in section 5.1); in other words, in the magnitude of _a variable that is never explicitly referred to in ordinary discourse and only emerges as the result of a precise analysis._ This shows the enormous importance of such a detailed analysis before any precise definition of a concept like adaptation is attempted. [p. 177] [....]

### Phylogenetic adaptation 5\.4. The directive correlations of the last examples had very short back-reference periods. Now let us take the opposite ex- treme - phylogenetic adaptation. As a simple example consider the adaptation of the colour of a population of caterpillars to that of its habitat, i.e. cryptic colouration. For simplicity let the (modal) colour of the caterpillars and that of their habitat be represented by two single variables, c and h, respectively. [p. 180] [....]

### Learning 5\.5. We are not here, of course, concerned with theories of learning, but merely with an accurate description of the directive element in the learning process. Speaking generally the directive element here consists of a directive correlation in which the appropriate back-reference period extends over the life span of the animal during which the learnt responses were acquired, e.g. the training period in a typical laboratory experiment. [....] [p. 181] [....]

### Learning to discriminate 5\.6. As another example of medium-term directive correlation we may take the case of a bird that has been taught to discriminate between iV different geometrical shapes painted on the lids of a number of N similar food bowls, only one containing the food. [....] [p. 181] [....]

### Self-regulation and feedback 5\.7. As an example of self-regulation, consider an imaginary black box with a radar scanner locking on a moving target and keeping the image of the target at the centre of a display screen. The case is analogous to visual fixation. [....] [p. 182] [....]

### Co-ordination 5\.8. When a number of activities are co-ordinated - and it does not matter whether they are the part-activities of a single organism or whether they are the activities of separate individuals (as in a football team) - we can say this .... [p. 184] [....]

### Instinctive behaviour 5\.9. [....] Instinctive behaviour shows a high degree of phylogenetic adaptation, but that is not the most remarkable thing about it. Other forms of behaviour show that too. The real hallmark of instinctive behaviour is the comparative absence of _medium-term directive correlations_. [p. 186] [....]

## 6\. Organic Integration ### The concept of integration 6\.1 . In section 5 we defined the mathematical concept of 'directive correlation' and illustrated how this concept enables us to express in precise terms the objective goal-directedness of organic activi- ties and processes. It also enabled us to show at once the formal similarity of different patterns of adaptive behaviour and yet reveal their essential differences. [....] [p. 187] [...] .... _The concept of an integrated sequence of activities, therefore, stands for a relation between these activities which enables us to attribute an individual goal to each, and at the same time an ultimate goal to the whole sequence._ Our next step must be to find the exact nature of this relation. [p. 188]

### The integration theorem 6\.2. To this end we shall prove an important theorem which follows from the definition of directive correlation .... [p. 188] [....]

### Social integration 6\.3. Complex patterns of directive correlations may exist not only between an organism and its environment, but also between members of an aggregate of individual organisms. And to the extent that these directive correlations form an integrated system of the kind outlined in the last section, they can impart a measure of organic integration and unity to such an aggregate. [....] [p. 190] [....]

### Potential directive correlations 6\.4. We have found that the goal-directedness of an action is an objective system property, and that to define it we must refer not only to what the system does under the given circumstances but also to what it would have done under certain alternative conditions. In this respect the property is not unique; many other physical properties can only be defined in the same general way. We can now take this a step further. Suppose that in a given situation an animal is inactive but is in a state of _alertness_. [....] [p. 191] [....]

### Learning by trial and error 6\.5. Learning has been defined as 'that process which manifests itself by adaptive changes in individual behaviour as result of individual experience' .... [....] [p. 194] [....]

## 7 Brain-Like Mechanisms Before saying a word about brain-like mechanisms, two different but widely held fallacies must be cleared up. * One is that the goal-seeking behaviour of organic systems and servo-mechanisms is not fundamentally different from the equilibrium-seeking behaviour of inorganic systems. * The other is the view that goal- seeking behaviour is co-extensive with error-controlled behaviour, i.e. with feedback control in the engineering sense. * The first deprives us of any clues about the structure of the brain altogether. * The second does have important structural implications but misleads us by presenting the brain as just a network of feed back loops. [p. 196, editoral paragraphing added]

### Goal-seeking is not the same as equilibrium-seeking 7\.1 Many biologists and cyberneticists tend to equate the characteristic directiveness of organic activities with the kind of directiveness that is shown by a physical system returning to a state of stable equilibrium. Although, of course, equilibrium-seeking processes of all kinds are essential ingredients of many organic activities, the characteristic goal-seeking quality of vital activities that has been our concern in this paper is of a different nature. [p. 196] [....]

### Directive correlation not co-extensive with feedback control 7\.2. Error-controlled devices, such as servo-mechanisms with feed back, can produce goal-directed behaviour in the full sense of our definition of directive correlation, provided they are seen in the broad context in which they are applied. [p. 198] [....]

### 'Brain-like' mechanisms 7\.3. Automata of all sorts are being designed today with the ex- press purpose of mimicking the behaviour of living systems, particularly that of the brain. But mimicry of this kind can be a very superficial thing, and its importance for the biological sciences is easily over-rated if we gloss over the question of how close an analogy to living systems they really achieve. [p. 199-200] [....]

## Summary and Conclusions 1\. The distinctive organization of living systems manifests itself in the goal-directedness of their activities (section 1). 2\. This goal-directedness is an objective system property which can be expressed in terms of mathematical relations between physical variables -- in fact a physical property (sections 3 and 4). 3\. The mathematical definition of 'directive correlation' (sec- tion 5.1) illustrates one way in which this system property may be given a precise definition. 4\. Goal-seeking is not the same as equilibrium-seeking (section 7.1) nor is it co-extensive with feedback control (section 7.2). [p. 201] 5\. A mathematical definition of directive correlation enables many biological key-concepts to be made precise. On this foundation a bridge may ultimately be built between the language of biology (and psychology) and that of the physical sciences (section 5). 6\. The main examples discussed were the concepts of adaptation, regulation, co-ordination, learning, instinct, and drive (sections 5 and 6). 7\. The fact that these definitions required an explicit reference to 'hidden' variables such as the 'coenetic variable' and the 'back-reference period' demonstrated that these concepts had inherent ambiguities which only a precise analysis can eliminate. 8\. The nature of the random element in trial-and-error learn- ing was discussed in section 6.5. 9\. Organic integration was explained in terms of hierarchies of directive correlations (section 6.1). 10\. The logical structure of these was established by the integration theorem stated in section 6.2. 11\. The objective substrate of social integration was outlined in sections 6.3 and 6.4. 12\. Among the wider concepts that appeared in a new light were those of life and death (section 6.1), consciousness (section 6.4), and freedom of the will (section 7.1). 13\. The significance for the neurologist of the various 'brain- like' mechanisms that are being developed in our time cannot be assessed until we have clearer formulations of the most generally distinctive functions of the brain. Here the concept of directive correlation, or the development of similar concepts, would seem to be an indispensable prerequisite (section 7.3). 14\. If agreement can be reached on this point, the mathematical definition of directive correlation will then yield equations which can serve as criteria for brain-like mechanisms, and as directions for their future development (section 7.3). [p. 202]