SECT. 1.3.] Randomness and its scientific treatment. Ill 



purpose, as in drawing a card or tossing a die: it may be 

 the outcome of an extremely complicated interaction of many 

 natural causes, as in the arrangement of the flowers scattered 

 over a lawn or meadow : it may be of a kind of which we 

 know literally nothing whatever, as in the case of the actual 

 arrangement of the stars relatively to each other. 



This was the state of things had in view when it was 

 said a few pages back that randomness and design would 

 result in something of a cross-division. Plenty of arrange 

 ments in which design had a hand, a stage or two back, can 

 be mentioned, which would be quite indistinguishable in 

 their results from those in which no design whatever could 

 be traced. Perhaps the most striking case in point here is 

 to be found in the arrangement of the digits in one of the 

 natural arithmetical constants, such as TT or e, or in a table 

 of logarithms. If we look to the process of production of 

 these digits, no extremer instance can be found of what we 

 mean by the antithesis of randomness : every figure has its 

 necessarily pre-ordained position, and a moment s flagging of 

 intention would defeat the whole purpose of the calculator. 

 And yet, if we look to results only, no better instance can 

 be found than one of these rows of digits if it were intended 

 to illustrate what we practically understand by a chance 

 arrangement of a number of objects. Each digit occurs 

 approximately equally often, and this tendency developes as 

 we advance further; the mutual juxtaposition of the digits 

 also shows the same tendency, that is, any digit (say 5) is 

 just as often followed by 6 or 7 as by any of the others. In 

 fact, if we were to take the whole row of hitherto calculated 

 figures, cut off the first five as familiar to us all, and con 

 template the rest, no one would have the slightest reason 

 to suppose that these had not come out as the results of a 

 die with ten equal faces. 



