QUANTITY OF VARIETY 7/5 



clearly relevant to 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 attempt- 

 ing 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. 



7/5. 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 singleness 

 of one telegram. Nevertheless, the act of "communication" 

 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 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 confederate has yet been 

 caught. 



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 possibihty 



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