An exactly similar modification may be made to the theorem in
Terms of entropies, by supposing, not as in S.11/8 that
HR (E) > HR (D), but that
HR (E) > HR (D) – K.
H(E)’s minimum then becomes
H(D) – K – H(R),
With a similar interpretation.
The law states that certain events are impossible. It is
Important that we should be clear as to the origin of the impossi-
Bility. Thus, what has the statement to fear from experiment?
It has nothing to do with the properties of matter. So if the law
is stated in the form “No machine can …”, it is not to be over-
208
Thrown by the invention of some new device or some new elec-
Tronic circuit, or the discovery of some new element. It does not
Even have anything to do with the properties of the machine in the
General sense of Chapter 4; for it comes from the Table, such as
That of S.11/4; this Table says simply that certain D-R combina-
Tions lead to certain outcomes, but is quite independent of what-
Ever it is that determines the outcome. Experiments can only
Provide such tables.
The theorem is primarily a statement about possible arrange-
Ments in a rectangular table. It says that certain types of arrange-
Ment cannot be made. It is thus no more dependent on special
Properties of machines than is, say, the “theorem” that four
Objects can be arranged to form a square while three can not. The
Law therefore owes nothing to experiment.
Regulation again. We can now take up again the subject of
Regulation, ignored since the beginning of this chapter, for the law
Of Requisite Variety enables us to apply a measure to regulation.
I et us go back and reconsider what is meant, essentially, by “reg-
Ulation”.
There is first a set of disturbances D, that start in the world out-
Side the organism, often far from it, and that threaten, if the regu-
Lator R does nothing, to drive the essential variables E outside
Their proper range of values. The values of E correspond to the
“outcomes” of the previous sections. Of all these E-values only a
few ( η) are compatible with the organism’s life, or are unobjec-
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Tionable, so that the regulator R, to be successful, must take its
Value in a way so related to that of D that the outcome is, if possi-
Ble, always within the acceptable set 17, i.e. within physiological
Limits. Regulation is thus related fundamentally to the game of
S.11/4. Let us trace the relation in more detail.
The Table T is first assumed to be given. It is the hard external
World, or those internal matters that the would-be regulator has to
Take for granted. Now starts a process. D takes an arbitrary value,
R takes some value determined by D’s value, the Table deter-
mines an outcome, and this either is or is not in η. Usually the
Process is repeated, as when a water-bath deals, during the day,
With various disturbances. Then another value is taken by D,
Another by R, another outcome occurs, and this also may be either
in η or not. And so on. If R is a well-made regulator— one that
Works successfully— then R is such a transformation of D that all
the outcomes fall within η. In this case R and T together are act-
Ing as the barrier F (S.10/5.)
209
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
We can now show these relations by the diagram of immediate
Effects:
T
D
R
The arrows represent actual channels of communication. For the
Variety in D determines the variety in R, and that in T is deter-
Mined by that in both D and R. If R and T are in fact actual
Machines, then R has an input from D, and T has two inputs.
When R and T are embodied in actual machines, care must be
Taken that we are clear about what we are referring to. If some
Machine is providing the basis for T, it will have (by S.4/1) a set
Of states that occur step by step. These states, and these steps, are
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