REGULATING THE VERY LARGE SYSTEM 



13/17 



13/16. Exactly the same measure may be applied to the design of a 

 Markovian machine. Thus the variety between the two Markovian 

 machines 



Y 



i. 

 4 

 1 

 2 

 J, 

 4 



and 



is just 1 bit, for we are choosing between two objects, whose inner 

 contents — the various fractions — ^are here irrelevant. (This quantity 

 of 1 bit is, of course, different from the 1-58 bits that would be 

 associated with the right-hand matrix regarded as an information 

 source that produces 1 -58 bits on the average, at each step (S.9/12).) 



13/17. Selection in stages. The process of selection may be either 

 more or less spread out in time. In particular, it may take place 

 in discrete stages. 



The driver about to choose a new car often proceeds in this way. 

 He first says, perhaps, 'Tt must cost less than £1000". This criterion 

 effects some reduction in the number of possibilities. Then perhaps 

 he adds that it must also be able to take five people. So he goes on. 

 Each new criterion makes the surviving possibilities fewer. If he 

 can buy only one car then the criteria must eventually reduce the 

 possibilities to one. Somehow this reduction must be made, even 

 if the spin of a coin has to be used as final selector. 



The abstract selection (or design) of a machine can similarly take 

 place in stages. Thus suppose the machine has the four states 

 a, b, c, d. The transformation T 



T:\ 



a 



— in which the asterisks are not yet decided on — leaves all possibilities 

 open. The change to transformation U 



U: j 



abed 



represents a partial selection. U also represents a set of trans- 

 formations, though a smaller set. So does V: 



17 



