102 Randomness and its scientific treatment. [CHAP, v, 



individual occurrence. We might, in our statement of a 

 problem, as easily postulated number thought o/at random 

 as a shot fired at random , but no one would risk his chances 

 of gain and loss on the supposition that this would be done 

 with continued fairness. Accordingly, we construct a die 

 whose sides are accurately alike, and it is found that we may 

 do almost what we like with this, at any previous stage to 

 that of its issue from the dice box on to the table, without 

 interfering with the random nature of the result. 



6. II. Another characteristic in which the scientific 

 conception seems to me to depart from the popular or original 

 signification is the following. The area of distribution which 

 we take into account must be a finite or limited one. The 

 necessity for this restriction may not be obvious at first sight, 

 but the consideration of one or two examples will serve to 

 indicate the point at which it makes itself felt. Suppose 

 that one were asked to choose a number at random, not 

 from a finite range, but from the inexhaustible possibilities 

 of enumeration. In the popular sense of the term, i.e. of 

 uttering a number without pausing to choose, there is no 

 difficulty. But a moment s consideration will show that no 

 arrangement even tending towards ultimately uniform dis 

 tribution can be secured in this way. No average could be 

 struck with ever increasing steadiness. So with spatial 

 infinity. We can rationally speak of choosing a point at 

 random in a given straight line, area, or volume. But if we 

 suppose the line to have no end, or the selection to be made 

 in infinite space, the basis of ultimate tendency towards 

 what may be called the equally thick deposit of our random 

 points fails us utterly. 



Similarly in any other example in which one of the 

 magnitudes is unlimited. Suppose I fling a stick at random 

 in a horizontal plane against a row of iron railings and 



