This dot stands for a unique state of the whole, which is to say that everything characterizing the system has been specified. A different state would be specified by a different dot. Thus we may imagine a system with a phase-space comprising millions of dots, i.e. any state possible in the system has a dot which represents it. Suppose now that a change is effected within the system. Then the systemic state will be indicated by a new dot which (we may imagine) lights up, whereas the dot previously lit up goes out. Then the apparent movement of light from dot 1 to dot 2 will be the *Trajectory* of the state-variable of the system.
Every Event changes the systemic state, therefore there is a continuous trajectory. But we may distinguish between states which support Homeostasis within this one system, and those which do not. Then let us collect the dots representing the stable state into a group and enclose them in a Circle. Now the trajectory of the state variable ought to describe a Movement within this circle. If the trajectory moves outside, then the system is out of homeostatic control.
When two such systems are coupled together, the concept of their joint homeostasis (which is the equilibrial condition of the metasystem comprising the two systems) may be invoked — and a meta-control operation may be envisaged. It works as a self-vetoing system, and is depicted in Figure 26.
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Each dot represents a total configuration of the system; dots contained in circles represent satisfactory states. The two systems are in equilibrium, because the trajectories of each (thick lines) remain within the circles
Figure 26. Ashby-type self-vetoing homeostasis operating between any two areas of Figure 25.
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We suppose firstly that each of the original systems is operating under local homeostasis, so that the trajectory of each state-variable is within its own circle. Then the messages travelling down lines A and B do not attempt to define the state of each system from moment to moment (the channels could not have requisite variety); they simply say ‘homeostasis’. This means that wherever one system impinges on the other, it recognizes a match which is normal to their coexistence. In the diagram, a few of these matched states are indicated by thin lines.
Well, this allows the two systems to communicate with each other about apparently elaborate states of affairs without disobeying the law of requisite variety, and without offending against the theorems of information theory where channel capacities are concerned. What the mathematical model really proposed was that each system could learn about the other, not in terms of understanding all about it, but in terms of recognizing it as being in normal operation. Then what is to happen when one of the systems is not normally operating, when its own trajectory leaves a homeostatic state, and when — consequently — a mismatch occurs between aspects of the two systems which impinge? The answer is that each system acts (having of course requisite variety) as controller of the other.
This act of meta-control is supposed to work like this. Instead of the A message declaring ‘homeostasis’, the A message reads ‘non-homeostasis’ as soon as the trajectory in A leaves its circle. This message causes the second system to change its own state, in a way indicated to A by changes in the relationships of events common to both systems. The effect of this change on A (the two systems being coupled) is to cause its state to change again, and therefore to alter the trajectory in A. This process is iterated round the meta-control loop for as long as it takes to get A’s state-variable back to ‘homeostasis’ and all is still again.
The first thing to note is that the restabilization of A under B’s meta-control may take a very long time. Indeed, if A goes a little wild as an internal system, it may be losing control of its own homeostatic equilibrium at a rate faster than this apparently random technique of trial-and-error government can operate to restore equilibrium. The analogous situation in the firm, and particularly in national control systems, should be thought about. The second difficulty is that in changing its own state, as a means of supplying A with control variety, B might inadvertently knock its own state-variable out of its circle — thereby losing control of its own internal equilibrium, and originating a ‘non-homeostasis’ B message. Then both systems are out of control — a classic *hunting* situation.
Ashby’s original theory of the homeostat appeared vulnerable to these two possibilities. I personally spent many years experimenting with the problem in three sorts of system. Firstly, there was the mathematical model (the sort of thing called a ‘paper machine’). Next there were actual machines devised for the purpose (a bit like the wood-and-brass machine of Part I). Thirdly, there were social systems within the firm. **In all three manifestations, the problems seemed to revolve around learning.** There is never requisite variety, never adequate channel capacity, and never enough time, to reach homeostasis at this meta-control level simply by inducing variations, although *formally* the process ought to work in the end. I learned how to modify all three experimental approaches from the study of Waddington’s work in genetics — for evolution has exactly the same problems in the rate at which adaptation can possibly occur. Random mutation, as first proposed by Darwin, ought to work; but again my calculations (see *Decision and Control*) showed that such an evolutionary mechanism was short of variety, of channel capacity, and, above all, of time. Despite the aeons of evolutionary time available, there does not seem to have been enough to evolve the well-adapted creatures alive today by a simple mutate-and-see-if-you-survive evolutionary kit. There has then, to be a further mechanism to do with the facilitation of survival-favourable trends and the extinction of time-wasting, if not actually damaging, development circuits.
Where Waddington spoke of an ‘epigenetic landscape’ in his evolutionary theory to deal with the problem, I inserted the algedonode into the theory of the anastomotic reticulum. In both cases the idea is that the movement of a trajectory (as here defined) changes the conditional probabilities along its path that this path will be used again. The criterion is of course the speed of success in adaptation — what engineers might call minimizing the relaxation time of the system. If the trajectory can find a natural return route to its circle, then this pathway will in future be facilitated. If it moves into an area of its phase-space from which return proves to be dangerously difficult and lengthy, then the probabilities change so that it is less and less likely to enter that area again. This means that the apparently unstructured phase-space of the system, to which we have so far admitted only one organized component — the original circle — will gradually grow in organizational structure, for other sets of dots than those indicating homeostasis will be grouped together in a self-organizing way and will be marked — designated — by their routes ‘home’, and the difficulties to be expected in realizing them.
These notions were incorporated in the 1960 mathematical model, and various experiments with machines and in firms were conducted too. The idea is to use the biggest switch to run this system across all six couplings of the four main groups of top-level control activity (remember Figure 25). Thus each group is held in control by the other three, and there is a matching process across the six couplings tantamount to a learning process which happens in synchrony. More follows on this topic in Part III. Meanwhile, there is one thing more to add.
In so far as the algedonodes really work, in so far then as the individual systems rapidly converge on both internal stability and corporate ultrastability, in so far as recognition and matching occur, so that organization extends across the intervening anastomotic reticulum, the whole switch is in danger of losing its flexibility and selectivity. It will become set in its ways. We see this happening in every kind of social situation: it leads to stereotyped behaviour, to taboos, to a lack of adaptivity as an outcome of too facile an adaptation. We know about it within evolution, too, in the over-specialization of species which leads to their becoming extinct. We see it in the firm which ‘really knows its business’ to the extent that it can no longer recognize either the new technological challenge or that the business is changing.
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(Brain of the Firm, 144–147) – This dot stands for a unique state of the whole, […]
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