QUANTITY OF VARIETY 7/25 



particular message, then as time goes on the amount of information 

 it stores can only diminish. Thus one of three messages might be 

 carried to a prisoner by a cup of coffee, the message depending on 

 whether it was hot, tepid, or cold. This method would work 

 satisfactorily if the time between despatch and receipt was short, 

 but not if it were long; for whichever of the three states were selected 

 originally, the states after a short time would be either "tepid" or 

 "cold", and after a long time, "cold" only. Thus the longer the 

 time between despatch and receipt, the less is the system's capacity 

 for carrying information, so far as this depends on its being at a 

 particular state. 



Ex. 1 : If a ball will rest in any one of three differently coloured basins, how much 

 variety can be stored ? 



Ex. 2 : (Continued.) If in addition another ball of another colour can be placed, 

 by how much is the variety increased? 



Ex. 3: That a one-one transformation causes no loss of variety is sometimes 

 used as a parlour trick. A member of the audience is asked to think of two 

 digits. He is then asked to multiply one of them by 5, add 7, double the 

 the result, and add the other number. The result is told to the conjurer 

 who then names the original digits. Show that this transformation retains 

 the original amount of variety. (Hint: Subtract 14 from the final quantity.) 



Ex. 4: (Continued.) What is the set for the first measure of variety? 



Ex. 5: (Another trick.) A member of the audience writes down a two-digit 

 number, whose digits differ by at least 2. He finds the difference between 

 this number and the number formed by the same digits in reverse order. 

 To the difference he adds the number formed by reversing the digits of the 

 difference. How much variety survives this transformation? 



Ex. 6: If a circuit of neurons can carry memory by either reverberating or not, 

 how much variety can the circuit carry? What is the set having the variety? 



£'.v. 7: Ten machines, identical in structure,, have run past their transients and 

 now have variety constant at zero. Are they necessarily at a state of 

 equilibrium? 



7/25. Law of Experience. The previous section showed that the 

 variety in a machine (a set being given and understood) can never 

 increase and usually decreases. It was assumed there that the 

 machine was isolated, so that the changes in state were due only 

 to the inner activities of the machine; we will now consider what 

 happens to the variety when the system is a machine with input. 



Consider first the simplest case, that of a machine with one para- 

 meter P that changes only at long intervals. Suppose, for clarity, 

 that the machine has many replicates, identical in their transforma- 

 tions but differing in which state each is at; and that we are observing 

 the set of states provided at each moment by the set of machines. 

 Let P be kept at the same value for all and held at that value while 



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