Saves the animal’s life, though it may not have saved the animal
From discomfort.
Thus the presence of continuity makes possible a regulation
That, though not perfect, is of the greatest practical importance.
Small errors are allowed to occur; then, by giving their informa-
Tion to R, they make possible a regulation against great errors.
This is the basic theory, in terms of communication, of the simple
Feedback regulator.
The reader may feel that excessive attention has just been
Given to the error-controlled regulator, in that we have stated with
Care what is already well known. The accuracy of statement is,
However, probably advisable, as we are going now to extend the
Subject of the error- controlled regulator over a range much wider
Than usual.
This type of regulator is already well known when embodied in
A determinate machine. Then it gives the servo-mechanism, the
Thermostat, the homeostatic mechanism in physiology, and so on.
It can, however, be embodied in a non-determinate machine, and
It then gives rise to a class of phenomena not yet commonly occur-
224
Ring in industrial machinery but of the commonest occurrence and
Highest importance in biological systems. The subject is returned
To in S.12/11. Meanwhile we must turn aside to see what is
Involved in this idea of a “non-determinate” machine.
T HE M AR KOVI AN M ACHI NE
We are now going to consider a class of machine more general
Than that considered in Parts I and II. (Logically, the subject should
Have been considered earlier, but so much of those Parts was con-
Cerned with the determinate machine (i.e. one whose transforma-
Tions are single- valued) that an account of a more general type
Might have been confusing.)
A “machine” is essentially a system whose behaviour is suffi-
Ciently law-abiding or repetitive for us to be able to make some
Prediction about what it will do (S.7/19). If a prediction can be
Made, the prediction may be in one of a variety of forms. Of one
Machine we may be able to predict its next state— we then say it
Is “determinate” and is one of the machines treated in Part I. Of
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Another machine we may be unable to predict its next state, but we
May be able to predict that, if the conditions are repeated many
Times, the frequencies of the various states will be found to have
Certain values. This possible constancy in the frequencies has
Already been noticed in S.9/2. It is the characteristic of the Markov
Chain.
We can therefore consider a new class of absolute system: it is
One whose states change with time not by a single-valued trans-
Formation but by a matrix of transition probabilities. For it to
Remain the same absolute system the values of the probabilities
Must be unchanging.
In S.2/10 it was shown that a single-valued transformation
Could be specified by a matrix of transitions, with 0’s or 1’s in the
cells (there given for simplicity as 0’s or +’s). In S.9/4 a Markov
Chain was specified by a similar matrix containing fractions. Thus
A determinate absolute system is a special case of a Markovian
Machine; it is the extreme form of a Markovian machine in which
All the probabilities have become either O or 1. (Compare S.9/3.)
A “machine with input” was a set of absolute systems, distin-
Guished by a parameter. A Markovian machine with input must
Similarly be a set of Markovian machines, specified by a set of
Matrices, with a parameter and its values to indicate which matrix
Is to be used at any particular step.
The idea of a Markovian machine is a natural extension of the
225
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
TH E ERR O R- CO N TR O LLED REG U LA TO R
Idea of the ordinary, determinate machine— the type considered
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