SECT. 8.] Randomness and its scientific treatment. 105 



solution : &quot; Of the four lines, two must and two must not pass 

 within the triangle formed by the remaining three. Since 

 all are drawn at random, the chance that the last drawn 

 should pass through the triangle formed by the other three 

 is consequently J.&quot; 



I quote this solution because it seems to me to illustrate 

 the difficulty to which I want to call attention. As the 

 problem is worded, a triangle is supposed to be assigned by 

 three straight lines. However large it may be, its size bears 

 no finite ratio whatever to the indefinitely larger area out 

 side it ; and, so far as I can put any intelligible construction 

 on the supposition, the chance of drawing a fourth random 

 line which should happen to intersect this finite area must 

 .be reckoned as zero. The problem Mr Wilson has solved 

 .seems to me to be a quite different one, viz. &quot; Given four 

 intersecting straight lines, find the chance that we should, 

 at random, select one that passes through the triangle formed 

 by the other three.&quot; 



The same difficulty seems to me to turn up in most other 

 attempts to apply this conception of randomness to real 

 infinity. The following seems an exact analogue of the 

 above problem : A number is selected at random, find the 

 chance that another number selected at random shall be 

 greater than the former ; the answer surely must be that 

 .the chance is unity, viz. certainty, because the range above 

 any assigned number is infinitely greater than that below it. 

 Or, expressed in the only language in which I can under 

 stand the term infinity , what I mean is this. If the first 

 number be m and I am restricted to selecting up to n 

 (n &amp;gt; m) then the chance of exceeding m is n m:n; if I 

 am restricted to 2n then it is 2n m : 2n and so on. That 

 is, however large n and m may be the expression is always 

 intelligible ; but, m being chosen first, n may be made as 





