112 Randomness and its scientific treatment [CHAP. v. 



14. If it be asked why this is so, a rather puzzling 

 question is raised. Wherever physical causation is involved 

 we are generally understood to have satisfied the demand 

 implied in this question if we assign antecedents which will 

 be followed regularly by the event before us; but in geometry 

 and arithmetic there is no opening for antecedents. What 

 we then commonly look for is a demonstration, i.e. the re 

 solution of the observed fact into axioms if possible, or at 

 any rate into admitted truths of wider generality. I do not 

 know that a demonstration can be given as to the existence 

 of this characteristic of statistical randomness in such suc 

 cessions of digits as those under consideration. But the 

 following remarks may serve to shift the onus of unlikeli 

 hood by suggesting that the preponderance of analogy is 

 rather in favour of the existence. 



Take the well-known constant TT for consideration. This 

 stands for a quantity which presents itself in a vast number 

 of arithmetical and geometrical relations ; let us take for 

 examination the best known of these, by regarding it as 

 standing for the ratio of the circumference to the diameter 

 of a circle. So regarded, it is nothing more than a simple 

 case of the measurement of a magnitude by an arbitrarily 

 selected unit. Conceive then that we had before us a rod 

 or line and that we wished to measure it with absolute 

 accuracy. We must suppose if we are to have a suitable 

 analogue to the determination of TT to several hundred 

 figures, that by the application of continued higher magni 

 fying power we can detect ever finer subdivisions in the 

 graduation. We lay our rod against the scale and find it, 

 say, fall between 31 and 32 inches ; we then look at the 

 next division of the scale, viz. that into tenths of an inch. 

 Can we see the slightest reason why the number of these 

 tenths should be other than independent of the number of 



