If One and Two are quarrelsome, they can now fall into a dis-
Pute. One can maintain that the system shows no “memory”, i.e.
Its behaviour requires no reference to the past, because the appear-
Ance of behaviour B can be fully accounted for by the system’s
Present state (at I, A and Z). Two can deny this, and can point out
That the system of I and A can be shown as determinate only when
Past values of I are taken into account, i.e. when some form of
“memory” is appealed to.
Clearly, we need not take sides. One and Two are talking of dif-
ferent systems (of I + A + Z or of I + A), so it is not surprising that
They can make differing statements. What we must notice here is
That Two is using the appeal to “memory” as a substitute for his
Inability to observe Z.
Thus we obtain the general rule: If a determinate system is only
Partly observable, and thereby becomes ( for that observer) not
Predictable, the observer may be able to restore predictability by
Taking the system’s past history into account, i.e. by assuming the
Existence within it of some form of “memory”.
The argument is clearly general, and can be applied equally
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Suppose the important question is whether the part A does or does
Not show some characteristic behaviour B (i.e. follow trajectory
B). Suppose this is shown (followed) only on the simultaneous
Occurrence of
(1) I at state α
And (2) Z at state y.
Suppose that Z is at state y only after I has had the special value µ.
We (author and reader) are omniscient, for we know everything
About the system. Let us, using full knowledge, see how two
Observers (One and Two) could come to different opinions if they
Had different powers of observation.
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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 BL AC K B O X
well if the special, earlier, event ( µ) occurred not one step earlier,
But many. Thus in general, if earlier events E1, E2, . . ., Ek leave
Traces T1, T2, . . ., Tk respectively, which persist; and if later the
Remainder of the system produces behaviours B1, B2, . . ., Bk cor-
Responding to the value of T, then the various behaviours may be
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Related to, or explained by, either
The present value of T, in which case there is no need for the
Invocation of any “memory”, or
The past value of E, in which case the observer is compelled
To postulate some form of “memory” in the system.
Thus the possession of “memory” is not a wholly objective prop-
Erty of a system— it is a relation between a system and an observer;
And the property will alter with variations in the channel of com-
Munication between them.
Thus to invoke “memory” in a system as an explanation of its
Behaviour is equivalent to declaring that one cannot observe the
System completely. The properties of “memory” are not those of
The simple “thing” but the more subtle “coding”.
*Ex. 1: Prove the statement (Design. . S.19/22) that in an absolute system we can
Avoid direct reference to some of the variables provided we use derivatives
Of the remaining variables to replace them.
*Ex. 2: Prove the same statement about equations in finite differences.
*Ex. 3: Show that if the system has n degrees of freedom we must, in general,
Always have at least n observations, each of the type “at time t1 variable xi
Had value Xi” if the subsequent behaviour is to be predictable.
A clear example showing how the presence of “memory” is
Related to the observability of a part is given by the digital calcu-
Lator with a magnetic tape. Suppose, for simplicity, that at a cer-
Tain moment the calculator will produce a 1 or a 2 according to
whether the tape, at a certain point, is magnetised + or— , respec-
Tively; the act of magnetisation occurred, say, ten minutes ago,
and whether it was magnetised + or— depended on whether the
Operator did or did not, respectively, close a switch. There is thus
The correspondence:
switch closed ↔ + ↔ 1
switch open ↔ – ↔ 2
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An observer who can see the magnetic tape now can argue that
Any reference to the past is unnecessary, for he can account for the
Machine’s behaviour (i.e. whether it will produce a 1 or a 2) by its
State now, by examining what the tape carries now. Thus to know
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that it carries a + now is sufficient to allow prediction that the
Machine’s next state will be a 1.
On the other hand, an observer who cannot observe the tape can
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