By showing that the feedback is positive, may not be reliable. (It
Shows also that feedback can be positive and yet leave the system
Stable; yet another example of how unsuitable is the concept of
Feedback outside its particular range of applicability.)
Undesirable stability. Stability is commonly thought of as
Desirable, for its presence enables the system to combine of flex-
Ibility and activity in performance with something of permanence.
Behaviour that is goal-seeking is an example of behaviour that is
Stable around a state of equilibrium. Nevertheless, stability is not
Always good, for a system may persist in returning to some state
That, for other reasons, is considered undesirable. Once petrol is lit
It stays in the lit state, returning to it after disturbance has changed
It to “half-lit”— a highly undesirable stability to a fireman.
Another example is given by the suggestion that as the more
Intelligent members of the community are not reproducing their
81
Ex. 1: Identify a, D and Tin Ex. 3/6/17. Is this system stable to this displacement?
Ex. 2: (Continued.) Contrast Ex. 3/6/19.
Ex. 3: Identify a and Tin Ex. 2/14/11. Is it stable if D is any displacement from
A?
Ex. 4 Take a child’s train (one that runs on the floor, not on rails) and put the line
Of carriages slightly out of straight. Let M be the set of states in whichthe
deviations from straightness nowhere exceed 5 °. Let T be the operation of
Drawing it along by the locomotive. Is M stable under T?
Ex. 5: (Continued.) Let U be the operation of pushing it backwards by the loco-
Motive. Is M stable under U?
Ex. 6: Why do trains have their locomotives in front?
80
A N I N T R O D UC T I O N T O C Y B E R NE T I C S
STA BI LIT Y
Kind as freely as are the less intelligent, the Intelligence Quotient
Of the community will fall. Clearly it cannot fall very low, because
The feebleminded can reproduce better than the idiot. So if these
Were the only factors in the situation, the I.Q. would be stable at
About 90. Stability at this figure would be regarded by most peo-
Ple as undesirable.
An interesting example of stability occurs in the condition
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Known as “causalgia”, in which severe pain, without visible
Cause, occurs in a nerve which has previously been partly divided.
Granit has shown that it is almost certainly due to conduction, at
The site of injury, of impulses from the motor (outgoing) to the
Sensory (incoming) nerves, allowing the formation of a regenera-
Tive circuit via the reflex centres in the spinal cord. Such a circuit
Has two states of equilibrium, each stable: conducting few
Impulses or conducting the maximal number. It is like a top-heavy
See-saw, that will rest in either of two extreme conditions but will
Not rest in between. The patient is well aware that “stability” can
Be either good or bad, for of the two stable states one is comfort-
Able and the other extremely painful.
E Q UI LI BRI U M I N PA RT A ND WH OL E
We can now notice a relation between coupling and equilib-
Rium that will be wanted later (S.12/14 and 13/19), for it has
Important applications.
Suppose some whole system is composed of two parts A and B,
Which have been coupled together:
A ← B →
And suppose the whole is at a state of equilibrium.
This means that the whole’s state is unchanging in time. But the
Whole’s state is a vector with two components: that of A’s state
And that of B’s. It follows that A, regarded as a sub-system, is also
Unchanging; and so is B.
Not only is A’s state unchanging but so is the value of A’s
Input; for this value is determined by B’s state (S.4/7), which is
Unchanging. Thus A is at a state of equilibrium in the conditions
Provided by B. (Cf. Ex. 5/3/11.) The similar property holds for B.
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