Ride ions. So we get references to the petrol engine, the growing
Child the chronic drunkard, and to other objects in the singular,
When the reference is in fact to the set of all such objects.
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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
Q UA N TI TY O F V AR IE TY
Sometimes it happens that a statement is equally true of the
Individual and the set: “the elephant eats with its trunk”, for
Instance. But the commonness of such a double application
Should not make us overlook the fact that some types of statement
Are applicable only to the set (or only to the individual) and
Become misleading and a source of confusion if applied to the
Other. Thus a gramme of hot hydrogen iodide gas, at some partic-
Ular moment, may well be 37 per cent ionised; yet this statement
Must not be applied to the individual molecules, which are all
Either wholly ionised or not at all; what is true of the set is false of
The individuals. Again, the Conservative M.P.s have, at the
Moment, a majority in Parliament; the statement is meaningless if
Applied to an individual member. Again, a tyre on a motor-car
May well be travelling due west at 50 m.p.h. when considered as
A whole; yet the portion in contact with the road is motionless, that
At the top is travelling due west at 100 m.p.h., and in fact not a sin-
Gle particle in the tyre is behaving as the whole is behaving.
Again, twenty million women may well have thirty million
Children, but only by a dangerous distortion of language can we
Say that Mrs. Everyman has one and a half children. The statement
Can sometimes be made without confusion only because those
Who have to take action, those who have to provide schools for the
Children, for instance, know that the half-child is not a freak but a
Set of ten million children.
Let us then accept it as basic that a statement about a set may be
Either true or false (or perhaps meaningless) if applied to the ele-
Ments in the set.
Ex.: The following statements apply to “The Cat”, either to the species Felis
Domestica or to the cat next door. Consider the applicability of each state-
Ment to (i) the species, (ii) the individual:
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It is a million years old,
It is male,
Today it is in every continent,
It fights its brothers,
About a half of it is female,
It is closely related to the Ursidae.
The set, but has little meaning for any individual, each of whom
Either is or is not married. Examine each man as closely as you
Please, you will find nothing of “0.82” about him; and if he moves
To another village this figure may change to another without his
Having changed at all. Evidently, the “0.82” is a property of the
Village, not of the individual.
Nevertheless, it is sometimes found convenient to pretend that
The fraction has a meaning for the individual, and it may be said
That any one person has a “probability” 0.82 of being married.
This form of words is harmless provided it is borne in mind that
The statement, in spite of its apparent reference to the individual,
Is really a statement about the village. Let this be forgotten and a
Host of “paradoxes” arise, as meaningless and silly as that of
Attempting to teach the “half”-child. Later (in Chapter 9) we shall
Have to use the concept of probability in conjunction with that of
Machine; the origin and real nature of the concept should be borne
In mind perpetually.
Communication. Another subject in which the concept of a
Set plays an essential part is that of “communication”, especially
In the theory developed by Shannon and Wiener. At first, when
One thinks of, say, a telegram arriving, one notices only the sin-
Gleness of one telegram. Nevertheless, the act of “communica-
Tion” necessarily implies the existence of a set of possibilities, i.e.
More than one, as the following example will show.
A prisoner is to be visited by his wife, who is not to be allowed
To send him any message however simple. It is understood that
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They may have agreed, before his capture, on some simple code.
At her visit, she asks to be allowed to send him a cup of coffee;
Assuming the beverage is not forbidden, how is the warder to
Ensure that no coded message is transmitted by it? He knows that
She is anxious to let her husband know whether or not a confeder-
Ate has yet been caught.
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