The warder will cogitate with reasonings that will go somewhat
As follows: “She might have arranged to let him know by whether
The coffee goes in sweetened or not— I can stop that simply by
Adding lots of sugar and then telling him I have done so. She might
Have arranged to let him know by whether or not she sends a
Spoon— I can stop that by taking away any spoon and then telling
Him that Regulations forbid a spoon anyway. She might do it by
Sending tea rather than coffee— no, that’s stopped because, as
They know, the canteen will only supply coffee at this time of
Day.” So his cogitations go on; what is noteworthy is that at each
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Probability. The exercise just given illustrates the confusion
And nonsense that can occur when a concept that belongs properly
To the set (or individual) is improperly applied to the other. An
Outstanding example of this occurs when, of the whole set, some
Fraction of the set has a particular property. Thus, of 100 men in a
Village 82 may be married. The fraction 0.82 is clearly relevant to
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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
Possibility he intuitively attempts to stop the communication by
Enforcing a reduction of the possibilities to one— always sweet-
Ened, never a spoon, coffee only, and so on. As soon as the possi-
Bilities shrink to one, so soon is communication blocked, and the
Beverage robbed of its power of transmitting information. The
Transmission (and storage) of information is thus essentially
Related to the existence of a set of possibilities. The example may
Make this statement plausible; in fact it is also supported by all the
Work in the modern theory of communication, which has shown
Abundantly how essential, and how fruitful, is the concept of the
Set of possibilities.
Communication thus necessarily demands a set of messages.
Not only is this so, but the information carried by a particular mes-
Sage depends on the set it comes from. The information conveyed
Is not an intrinsic property of the individual message. That this is
So can be seen by considering the following example. Two sol-
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Diers are taken prisoner by two enemy countries A and B, one by
Each; and their two wives later each receive the brief message “I
Am well”. It is known, however, that country A allows the pris-
Oner a choice from
I am well,
I am slightly ill,
I am seriously ill,
While country B allows only the message
I am well
Meaning “I am alive”. (Also in the set is the possibility of “no
Message”.) The two wives will certainly be aware that though
Each has received the same phrase, the informations that they have
Received are by no means identical.
From these considerations it follows that, in this book, we must
Give up thinking, as we do as individuals, about “this message”.
We must become scientists, detach ourselves, and think about
“people receiving messages”. And this means that we must turn
Our attention from any individual message to the set of all the pos-
Sibilities.
V A RIE TY
Throughout this Part we shall be much concerned with the
Question, given a set, of how many distinguishable elements it
Contains. Thus, if the order of occurrence is ignored, the set
C, b, c, a, c, c, a, b, c, b, b, a
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Which contains twelve elements, contains only three distinct ele-
Ments — a, b and c. Such a set will be said to have a variety of
Three elements. (A qualification is added in the next section.)
Though this counting may seem simple, care is needed. Thus
The two-armed semaphore can place each arm, independently of
The other, in any of eight positions; so the two arms provide 64
Combinations. At a distance, however, the arms have no individu-
Ality—“ arm A up and arm B down” cannot be distinguished from
“arm A down and arm B up”— so to the distant observer only 36
Positions can be distinguished, and the variety is 36, not 64. It will
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Be noticed that a set’s variety is not an intrinsic property of the set:
The observer and his powers of discrimination may have to be
Specified if the variety is to be well defined.
Ex. 1: With 26 letters to choose from, how many 3-letter combinations are avail-
Able for motor registration numbers ?
Ex. 2: If a farmer can distinguish 8 breeds of chicks, but cannot sex them, while
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