R E G U L A T I O N A N D C O N T R O L
The fourldation of all physiology must be the physiology of permanence.
(Darlington)
R E G U L A T I O N I N B I O L O G I C A L S Y S T E M S
Chapter 10
R E G U L A T I O N I N B I O L O G I C A L S Y S T E M S
10/1. The two previous Parts have treated of Mechanism (and the processes within the system) and Variety (and the processes of communication between system and system). These two subjects had to be studied first, as they are fundamental. Now we shall use them, and in Part III we shall study what is the central theme of cybernetics —regulation and control.
This first chapter reviews the place of regulation in biology, and shows briefly why it is of fundamental importance. It shows how regulation is essentially related to the flow of variety. The next chapter (11) studies this relation in more detail, and displays a quantitative law—that the quantity of regulation that can be achieved is bounded by the quantity of information that can be transmitted in a certain channel. The next chapter (12) takes up the question of how the abstract principles of chapter 11 are to be embodied—what sort of machinery can perform what is wanted.
This chapter introduces a new sort of machine, the Markovian, which extends the possibilities considered in Part I. The remain-ing chapters consider the achievement of regulation and control as the difficulties increase, particularly those that arise when the sys-tem becomes very large.
At first, in Part III, we will assume that the regulator is already provided, either by being inborn, by being specially made by a manufacturer, or by some other means. The question of what made the regulator, of how the regulator, which does such useful things, came itself to be made will be taken up at S.13/10.
10/2. The present chapter aims primarily at supplying motive to the reader, by showing that the subjects discussed in the later chapters (11 onwards) are of fundamental importance in biology.
The subject of regulation in biology is so vast that no single chap-ter can do it justice. Cannon’s Wisdom of the Body treated it ade-quately so far as internal, vegetative activities are concerned, but
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there has yet to be written the book, much larger in size, that shall show how all the organism’s exteriorly-directed activities—its
“higher” activities—are all similarly regulatory, i.e. homeostatic.
In this chapter I have had to leave much of this to the reader’s imagination, trusting that, as a biologist, he will probably already be sufficiently familiar with the thesis. The thesis in any case has been discussed to some extent in Design for a Brain.
The chief purpose of this chapter is to tie together the concepts of regulation, information, and survival, to show how intimately they are related, and to show how all three can be treated by a method that is entirely uniform with what has gone before in the book, and that can be made as rigorous, objective, and unambig-uous as one pleases.
10/3. The foundation. Let us start at the beginning. The most basic facts in biology are that this earth is now two thousand million years old, and that the biologist studies mostly that which exists today. From these two facts follow a well-known deduction, which I would like to restate in our terms.
We saw in S.4/23 that if a dynamic system is large and com-posed of parts with much repetition, and if it contains any prop-erty that is autocatalytic, i.e. whose occurrence at one point increases the probability that it will occur again at another point, then such a system is, so far as that property is concerned, essen-tially unstable in its absence. This earth contained carbon and other necessary elements, and it is a fact that many combinations of carbon, nitrogen, and a few others are self-reproducing. It fol-lows that though the state of “being lifeless” is almost a state of equilibrium, yet this equilibrium is unstable (S.5/6), a single devi-ation from it being sufficient to start a trajectory that deviates more and more from the “lifeless” state. What we see today in the biological world are these “autocatalytic” processes showing all the peculiarities that have been imposed on them by two thousand million years of elimination of those forms that cannot survive.
The organisms we see today are deeply marked by the selective action of two thousand million years’ attrition. Any form in any way defective in its power of survival has been eliminated; and today the features of almost every form bear the marks of being adapted to ensure survival rather than any other possible outcome.
Eyes, roots, cilia, shells and claws are so fashioned as to maximise the chance of survival. And when we study the brain we are again studying a means to survival.
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10/4. What has just been said is well enough known. It enables us, however, to join these facts on to the ideas developed in this book and to show the connexion exactly.
For consider what is meant, in general, by “survival”. Suppose a mouse is trying to escape from a cat, so that the survival of the mouse is in question. As a dynamic system, the mouse can be in a variety of states; thus it can be in various postures, its head can be turned this way or that, its temperature can have various val-ues, it may have two ears or one. These different states may occur during its attempt to escape and it may still be said to have sur-vived. On the other hand if the mouse changes to the state in which it is in four separated pieces, or has lost its head, or has become a solution of amino-acids circulating in the cat’s blood then we do not consider its arrival at one of these states as corre-sponding to “survival”.
The concept of “survival” can thus be translated into perfectly rigorous terms, similar to those used throughout the book. The various states (M for Mouse) that the mouse may be in initially and that it may pass into after the affair with the cat is a set M1, M2, …, Mk, …, Mn. We decide that, for various reasons of what is practical and convenient, we shall restrict the words “living mouse” to mean the mouse in one of the states in some subset of these possibilities, in M1 to Mk say. If now some operation C (for cat) acts on the mouse in state Mi, and C(Mi) gives, say, M2, then we may say that M has “survived” the operation of C, for M2 is in the set M1, … Mk.
If now a particular mouse is very skilled and always survives the operation C, then all the states C(M1), C(M2), …, C(Mk), are contained in the set M1, …, Mk. We now see that this representa-tion of survival is identical with that of the “stability” of a set (S.5/
5). Thus the concepts of “survival” and “stability” can be brought into an exact relationship; and facts and theorems about either can be used with the other, provided the exactness is sustained.
The states M are often defined in terms of variables. The states M1, …, Mk, that correspond to the living organism are then those states in which certain essential variables are kept within assigned (“physiological”) limits.
Ex. 1: If n is 10 and k is 5, what would the operation C(M7) = M9 correspond to?
Ex. 2: (Continued.) What would the operation C(M8) = M4 correspond to?
Ex. 3: What would be an appropriate definition of “lethal”, if C’s attack were invariably fatal to M?
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10/5. What is it survives, over the ages ? Not the individual organ-ism, but certain peculiarly well compounded gene-patterns, par-ticularly those that lead to the production of an individual that carries the gene-pattern well protected within itself, and that, within the span of one generation, can look after itself.
What this means is that those gene-patterns are specially likely to survive (and therefore to exist today) that cause to grow, between themselves and the dangerous world, some more or less elaborate mechanism for defence. So the genes in Testudo cause the growth of a shell; and the genes in Homo cause the growth of a brain. (The genes that did not cause such growths have long since been eliminated.)
Now regard the system as one of parts in communication. In the previous section the diagram of immediate effects (of cat and mouse) was (or could be regarded as)
We are now considering the case in which the diagram is
in which E is the set of essential variables, D is the source of dis-turbance and dangers (such as C) from the rest of the world, and F is the interpolated part (shell, brain, etc.) formed by the gene-pattern for the protection of E. (F may also include such parts of the environment as may similarly be used for E’s protection—
burrow for rabbit, shell for hermit-crab, pike for pike-man, and sword (as defence) for swordsman.)
For convenience in reference throughout Part III, let the states of the essential variables E be divided into a set η∇those that cor-respond to “organism living” or “good”—and not-η∇those that correspond to “organism not living” or “bad”. (Often the classifi-cation cannot be as simple as this, but no difficulty will occur in principle; nothing to be said excludes the possibility of a finer classification.)
To make the assumptions clear, here are some simple cases, as illustration. (Inanimate regulatory systems are given first for sim-plicity.)
(1) The thermostatically-controlled water-bath. E is its temper-ature, and what is desired (η) is the temperature range between, say 36° and 37°C. D is the set of all the disturbances that may drive the temperature outside that range—addition of cold water, cold draughts blowing, immersion of cold objects, etc. F is the
C→ M
D → F→ E
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whole regulatory machinery. F, by its action, tends to lessen the effect of D on E.
(2) The automatic pilot. E is a vector with three components—
yaw, pitch, and roll—and η is the set of positions in which these three are all within certain limits. D is the set of disturbances that may affect these variables, such as gusts of wind, movements of the passengers in the plane, and irregularities in the thrusts of the engines. F is the whole machinery—pilot, ailerons, rudder, etc.—
whose action determines how D shall affect E.
(3) The bicycle rider. E is chiefly his angle with the vertical. ,1 is the set of small permissible deviations. D is the set of those dis-turbances that threaten to make the deviation become large. F is the whole machinery—mechanical, anatomical, neuronic—that determines what the effect of D is on E.
Many other examples will occur later. Meanwhile we can sum-marise by saying that natural selection favours those gene-pat-terns that get, in whatever way, a regulator F between the disturbances D and the essential variables E. Other things being equal, the better F is as a regulator, the larger the organism’s chance of survival.
Ex.: What variables are kept within limits by the following regulatory mecha-nisms: (i) the air-conditioner; (ii) the climber’s oxygen supply; (iii) the wind-screen-wiper; (iv) the headlights of a car; (v) the kitchen refrigerator; (vi) the phototaxic plant; (vii) sun-glasses; (viii) the flexion reflex (a quick lifting of the foot evoked by treading on a sharp stone); (ix) blinking when an object approaches the eye quickly; (x) predictor for anti-aircraft gunfire.
10/6. Regulation blocks the flow of variety. On what scale can any particular mechanism F be measured for its value or success as a regulator ? The perfect thermostat would be one that, in spite of disturbance, kept the temperature constant at the desired level. In general, there are two characteristics required: the maintenance of the temperature within close limits, and the correspondence of this range with the desired one. What we must notice in particular is that the set of permissible values, η, has less variety than the set of all possible values in E; for η is some set selected from the states of E. If F is a regulator, the insertion of F between D and E lessens the variety that is transmitted from D to E. Thus an essen-tial function of F as a regulator is that it shall block the transmis-sion of variety from disturbance to essential variable.
Since this characteristic also implies that the regulator’s func-tion is to block the flow of informafunc-tion, let us look at the thesis more closely to see whether it is reasonable.
Suppose that two water-baths are offered me, and I want to
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decide which to buy. I test each for a day against similar distur-bances and then look at the records of the temperatures; they are as in Fig. 10/6/1:
There is no doubt that Model B is the better; and I decide this pre-cisely because its record gives me no information, as does A’s, about what disturbances, of heat or cold, came to it. The thermom-eter and water in bath B have been unable, as it were, to see any-thing of the disturbances D.
The same argument will apply, with obvious modifications, to the automatic pilot. If it is a good regulator the passengers will have a smooth flight whatever the gustiness outside. They will, in short, be prevented from knowing whether or not it is gusty out-side. Thus a good pilot acts as a barrier against the transmission of that information.
The same argument applies to an air-conditioner. If I live in an air-conditioned room, and can tell, by the hotness of the room, that it is getting hot outside, then that conditioner is failing as a regulator. If it is really good, and the blinds are drawn, I shall be unable to form any idea of what the outside weather is like. The good conditioner blocks the flow inwards of information about the weather.
The same thesis applies to the higher regulations achieved by such activities as hunting for food, and earning one’s daily bread.
Thus while the unskilled hunter or earner, in difficult times, will starve and will force his liver and tissues (the essential variables) to extreme and perhaps unphysiological states, the skilled hunter or earner will go through the same difficult times with his liver and tissues never taken to extremes. In other words, his skill as a regulator is shown by the fact, among others, that it prevents
Fig. 10/6/1
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information about the times reaching the essential variables. In the same way, the skilled provider for a family may go through difficult times without his family realising that anything unusual has happened. The family of an unskilled provider would have discovered it.
In general, then, an essential feature of the good regulator is that it blocks the flow of variety from disturbances to essential variables.
10/7. The blocking may take place in a variety of ways, which prove, however, on closer examination to be fundamentally the same. Two extreme forms will illustrate the range.
One way of blocking the flow (from the source of disturbance D to the essential variable E) is to interpose something that acts as a simple passive block to the disturbances. Such is the tortoise’s shell, which reduces a variety of impacts, blows, bites, etc. to a negligible disturbance of the sensitive tissues within. In the same class are the tree’s bark, the seal’s coat of blubber, and the human skull.
At the other extreme from this static defence is the defence by skilled counter-action—the defence that gets information about the disturbance to come, prepares for its arrival, and then meets the disturbance, which may be complex and mobile, with a defence that is equally complex and mobile. This is the defence of the fencer, in some deadly duel, who wears no armour and who trusts to his skill in parrying. This is the defence used mostly by the higher organisms, who have developed a nervous system pre-cisely for the carrying out of this method.
When considering this second form we should be careful to notice the part played by information and variety in the process.
The fencer must watch his opponent closely, and he must gain information in all ways possible if he is to survive. For this pur-pose he is born with eyes, and for this purpur-pose he learns how to use them. Nevertheless, the end result of this skill, if successful, is shown by his essential variables, such as his blood-volume, remaining within normal limits, much as if the duel had not occurred. Information flows freely to the non-essential variables, but the variety in the distinction “duel or no-duel” has been pre-vented from reaching the essential variables.
Through the remaining chapters we shall be considering this type of active defence, asking such questions as: what principles must govern it? What mechanisms can achieve it? And, what is to be done when the regulation is very difficult?
Chapter 11
R E Q U I S I T E V A R I E T Y
11/1. In the previous chapter we considered regulation from the biological point of view, taking it as something sufficiently well understood. In this chapter we shall examine the process of regu-lation itself, with the aim of finding out exactly what is involved and implied. In particular we shall develop ways of measuring the amount or degree of regulation achieved, and we shall show that this amount has an upper limit.
11/2. The subject of regulation is very wide in its applications, covering as it does most of the activities in physiology, sociology, ecology, economics, and much of the activities in almost every branch of science and life. Further, the types of regulator that exist are almost bewildering in their variety. One way of treating the subject would be to deal seriatim with the various types, and chap-ter 12 will, in fact, indicate them. In this chapchap-ter, however, we shall be attempting to get at the core of the subject—to find what is common to all.
What is common to all regulators, however, is not, at first sight much like any particular form. We will therefore start anew in the next section, making no explicit reference to what has gone before. Only after the new subject has been sufficiently developed will we beam to consider any relation it may have to regulation.
11/3. Play and outcome. Let us therefore forget all about regula-tion and simply suppose that we are watching two players, R and D, who are engaged in a game. We shall follow the fortunes of R, who is attempting to score an a. The rules are as follows. They have before them Table 11/3/1, which can be seen by both:
Table 11/3/l α β γR
D
1 b a c
2 a c b
3 c b a
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D must play first, by selecting a number, and thus a particular row.
R, knowing this number, then selects a Greek letter, and thus a particular column. The italic letter specified by the intersection of the row and column is the outcome. If it is an a, R wins; if not, R loses.
Examination of the table soon shows that with this particular table R can win always. Whatever value D selects first, R can always select a Greek letter that will give the desired outcome.
Thus if D selects 1, R selects β; if D selects 2, R selects α; and so on. In fact, if R acts according to the transformation
then he can always force the outcome to be a.
then he can always force the outcome to be a.