Zero is in fact forcing x to vary, copying y. Similarly, “making x
do the opposite to y” corresponds to “keeping x + y at some con-
Stant value”. And “make the variable w change so that it is always
Just twice as large as v’s (fluctuating) rate of change” corresponds
To “keep the quantity w – 2dv/dt constant”.
It is a great convenience in exposition and in the processes of
General theory to be able to treat all “targets” as if they were of the
Form “keep the outcome constant at a”. The reader must, however,
Not be misled into thinking that the theory beat’ only of immobil-
Ity; he must accustom himself to interchanging the corresponding
Concepts freely.
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214
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
REQ U ISI TE V A RI ETY
S O M E V AR I A TI ONS
In S.11/4 the essential facts implied by regulation were
Shown as a simple rectangular table, as if it were a game between
Two players D and R. The reader may feel that this formulation is
Much too simple and that there are well known regulations that it
Is insufficient to represent. The formulation, however, is really
Much more general than it seems, and in the remaining sections of
This chapter we shall examine various complications that prove,
On closer examination, to be really included in the basic formula-
Tion of S.11/4.
Compound disturbance. The basic formulation of S.11/4
Included only one source of disturbance D, and thus seems, at first
Sight, not to include all those cases, innumerable in the biological
World, in which the regulation has to be conducted against several
Disturbances coming simultaneously by several channels. Thus, a
Cyclist often has to deal both with obstructions due to traffic and
With disequilibrations due to gusts.
In fact, however, this case is included; for nothing in this chap-
Ter excludes the possibility that D may be a vector, with any
Number of components. A vectorial D is thus able to represent all
Such compound disturbances within the basic formulation.
Noise. A related case occurs when T is “noisy”— when T
Has an extra input that is affected by some disturbance that inter-
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Feres with it. This might be the case if T were an electrical
Machine, somewhat disturbed by variations in the mains’ voltage.
At first sight this case seems to be not represented in the basic for-
Mulation.
It must be appreciated that D, T, E, etc. were defined in S.11/3
In purely functional form. Thus “D” is “that which disturbs”.
Given any real system some care may b necessary in deciding
What corresponds to D, what to T, and so on. Further, a boundary
Drawn provisionally between D and T (and the other boundaries)
May, on second thoughts, require moving. Thus one set of bound-
Aries on the real system may give a system that purports to be of
D, T, etc. yet does not agree with the basic formulation of S.11/4.
Then it may be found that a shifting of the boundaries, to give a
New D. T, etc., gives a set that does agree with the formulation.
If a preliminary placing of the boundaries shows that this (pro-
Visional) T is noisy, then the boundaries should be re-drawn so as
To get T’s input of noise (S.9/19) included as a component in D. D
216
Is now “that which disturbs”, and T has no third input, so the for-
Mulation agrees with that of S.11/4.
There is, of course, no suggestion here that the noise, as a dis-
Turbance, can be allowed for magically by merely thinking differ-
Ently about it. The suggestion is that if we start again from the
Beginning and re-define D and T then some new transformation of
D may be able to restore regulation. The new transformation will,
Of course, have to be more complex than the old, for D will have
More components.
Initial states. A related case occurs when T is some machine
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