Available, and the outcomes (E). Inspection of the table, as in Ex.
Would then enable him to decide whether, in all cases, he
Would get what he wanted.
There are, therefore, cases in which the regulation has to be
Exerted against a non-repetitive disturbance, but they are uncommon.
From here on we shall consider the case in which the distur-
Bance, and the regulatory response, occur more than once; for
Such cases show constraint, of which advantage can be taken.
The constraint occurs in the following way.
The basic formulation of the regulatory process referred to a set
Of disturbances but assumed only that the separate elements in the
Set were distinct, nothing more. Like any other quantity, a distur-
Bance may be simple or a vector. In the latter case, at least two
Main types are distinguishable.
The first type was discussed in S.11/17: the several components
Of the disturbance act simultaneously; as an air-conditioner might,
At each moment, regulate both temperature and humidity.
The second type is well shown by the thermostatically-control-
Led water bath, it can be regarded as a regulator, over either short
Or long intervals of time. Over the short interval, “the distur-
Bance” means such an event as “the immersion of this flask”, and
“its response” means “what happens over the next minute”. Its
Behaviour can be judged good or bad according to what happened
248
In that minute. There is also the long interval. After it has worked
For a year someone may ask me whether it has proved a good reg-
Ulator over the year. While deciding the reply, I think of the whole
Year’s disturbance as a sort of Grand Disturbance (made up of
Many individual disturbances, with a small d), to which it has pro-
Duced a Grand Response (made up of many individual responses,
With a small r). According to some standard of what a bath should
Do over a year (e.g. never fail badly once, or have an average devi-
ation of less than 1/2 °, etc.) I form an opinion about the Grand
Outcome— whether it was Good or Bad— and answer the ques-
Tion accordingly.
It should be noticed that what is “Good” in the Grand Outcome
does not follow necessarily from what is “good” ( η ) in the indi-
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Vidual outcomes; it must be defined anew. Thus, if I go in for a
Lottery and have three tickets, a win on one (and consequent loss
On the other two) naturally counts as “Good” in the Grand Out-
come; so here I good + 2 bad = Good. On the other hand, if I am
Tried three times for murder and am found not guilty for one, the
individual results are still I good + 2 bad, but in this case the
Grand Outcome must naturally count as Bad. In the case when the
Individual disturbances each threaten the organism with death,
Good in the Grand Outcome must naturally correspond to “good
In every one of the individual outcomes”.
These Grand Disturbances are vectors whose components are
The individual disturbances that came hour by hour. These vectors
Show a form of constraint. Thus, go back to the very first example
Of a vector (S.3/5). It was A; contrast it with B:
A
Age of car: ............
Horse power: ............
Colour:............
B
Age of Jack’s car: ............
,, ,, Jill’s,, ............
,, ,, Tom’s ,, ............
Obviously B is restricted in a way that A is not. For the variety in
The left-hand words in A’s three rows is three; in B’s three rows it
Is one.
Vectors like B are common in the theory of probability, where
They occur under the heading “sampling with replacement”. Thus,
The spin of a coin can give only two results, H or T. A coin spun
Six times in succession, however, can give results such as (H, H,
T, H, T, H), or (T, T, H, H, T, H), and so on for 64 possibilities.
(Compare S.9/9.)
What is important here is that, in such a set of vectors (in those
Whose components all come from the same basic class, as in B),
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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
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