That B must be in equilibrium, by the principle of the previous sec-
Tion. But B has been made so that this occurs only when the relay
Is non-energised. And B has been coupled to A so that the relay is
Non-energised only when A’s needles are at or near the centres.
Thus the attachment if B vetoes all of A’s equilibria except such
As have the needles at he centre.
It will now be seen that every graph shown in Design . . . could
Have been summed up by one description: “trajectory of a system
Tinning to a state of equilibrium”. The homeostat, in a sense, does
Nothing more than run to a state of equilibrium. What Design . . .
Showed was that this simple phrase may cover many intricate and
Interesting ways of behaving, many of them of high interest in
Physiology and psychology.
The subject of “stability” recurs frequently, especially in S.9/
That of the homeostat is taken up again in S.12/15.)
84
The complex of ideas involved in “stability” can now be
Summarised.
First there is the state of equilibrium— the state that is
Unchanged by the transformation. Then the state may become
Multiple, and we get the stable set of states, of which the cycle and
Basin are examples.
Given such a state or set of states and some particular distur-
Bance we can ask whether, after a disturbance, the system will
Return to its initial region. And if the system is continuous, we can
Ask whether it is stable against all disturbances within a certain
Range of values.
Clearly, the concept of stability is essentially a compound one.
Only when every aspect of it has been specified can it be applied
Unambiguously to a particular case. Then if its use calls for so
Much care, why should it be used at all ? Its advantage is that, in
The suitable case, it can sum up various more or less intricate pos-
Sibilities briefly. As shorthand, when the phenomena are suitably
Simple, words such as equilibrium and stability are of great value
And convenience. Nevertheless, it should be always borne in mind
That they are mere shorthand, and that the phenomena will not
Always have the simplicity that these words presuppose. At all
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Times the user should be prepared to delete them and to substitute
The actual facts, in terms of states and transformations and trajec-
Tories, to which they refer.
It is of interest to notice, to anticipate S.6/19, that the attempt to
Say what is significant about a system by a reference to its stability
Is an example of the “topological” method for describing a large
System. The question “what will this system do?”, applied to, say,
An economic system, may require a full description of every detail
Of its future behaviour, but it may be adequately answered by the
Much simpler statement “It will return to its usual state” (or per-
Haps “it will show ever increasing divergence”). Thus our treat-
Ment in this chapter has been of the type required when dealing
With the very large system.
85
TH E BL AC K B O X
Chapter
6
TH E BL A C K B O X
The methods developed in the previous chapters now enable
Us to undertake a study of the Problem of the Black Box; and the
Study will provide an excellent example of the use of the methods.
The Problem of the Black Box arose in electrical engineering.
The engineer is given a sealed box that has terminals for input, to
Which he may bring any voltages, shocks, or other disturbances he
Pleases, and terminals for output, from which he may observe
What he can. He is to deduce what he can of its contents.
Sometimes the problem arose literally, when a secret and sealed
Bomb-sight became defective and a decision had to be made,
Without opening the box, whether it was worth returning for repair
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