QUANTITY OF VARIETY 7/9 



£".v. 8: (Continued.) If the closed transformation had n states what variety 



is there? 

 Ex. 9: If the Enghsh vocabulary has variety of 10 bits per word, what is the 



storage capacity of 10 minutes' speech on a gramophone record, assuming 



the speech is at 120 words per minute? 



Ex. 10: (Continued.) How does this compare with the capacity of a printed 

 page of newspaper (approximately) ? 



Ex. 11: (Continued.) If a pamphlet takes 10 minutes to be read aloud, how 



does its variety compare with that of the gramophone record ? 

 Ex. 12: What set is the previous Ex. referring to? 



Ex. 13: Can a merely negative event — a light not being lit, a neuron not being 

 excited, a telegram not arriving — be used as a contribution to variety ? 



CONSTRAINT 



7/8. A most important concept, with which we shall be much 

 concerned later, is that of constraint. It is a relation between two 

 sets, and occurs when the variety that exists under one condition 

 is less than the variety that exists under another. Thus, the variety 

 in the human sexes is 1 bit ; if a certain school takes only boys, the 

 variety in the sexes within the school is zero; so as is less than 1, 

 constraint exists. 



Another well-known example is given by the British traffic hghts, 

 which have three lamps and which go through the sequence (where 

 "+" means lit and "0" unlit): 



(1) (2) (3) (4) (1) ... 



Red: + + + 



Yellow: + + 



Green : + 



Four combinations are thus used. It will be noticed that Red is, 

 at various times, both ht and unht; so is Yellow; and so is Green. 

 So if the three lights could vary independently, eight combinations 

 could appear. In fact, only four are used; so as four is less than 

 eight, constraint is present. 



7/9. A constraint may be slight or severe. Suppose, for instance, 

 that a squad of soldiers is to be drawn up in a single rank, and that 

 "independence" means that they may stand in any order they please. 

 Various constraints might be placed on the order of standing, and 

 these constraints may differ in their degree of restriction. Thus, if 

 the order were given that no man may stand next a man whose 

 birthday falls on the same day, the constraint would be slight, for 

 of all the possible arrangements few would be excluded. If, 



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