252 Chance, Causation, and Design. [CHAP. X. 



the value of TT was accurately (the degree of accuracy is not, 

 I think, assigned) indicated by the ratio of the sides to the 

 height. The contention was that this result could not be 

 accidental but must have been designed. 



As regards the estimation of the value of the chance 

 hypothesis the calculation is not quite so clear as in the 

 case of dice or cards. We cannot indeed suppose that, 

 for a given length of base, any height can be equally possible. 

 We must limit ourselves to a certain range here ; for if too 

 high the building would be insecure, and if too low it would 

 be ridiculous. Again, we must decide to how close an 

 approximation the measurements are made. If they are 

 guaranteed to the hundredth of an inch the coincidence 

 would be of a quite different order from one where the 

 guarantee extended only to an inch. Suppose that this 

 has been decided, and that we have ascertained that out 

 of 10,000 possible heights for a pyramid of given base just 

 that one has been selected which would most nearly yield 

 the ratio of the radius to the circumference of a circle. 



The remaining consideration would be the relative fre 

 quency of the design alternative, what is called its a 

 priori probability, that is, the relative frequency with 

 which such builders can be supposed to have aimed at that 

 ratio ; with the obvious implied assumption that if they did 

 aim at it they would certainly secure it. Considering our 

 extreme ignorance of the attainments of the builders it is 

 obvious that no attempt at numerical appreciation is here 

 possible. If indeed the design was interpreted to mean 

 conscious resolve to produce that ratio, instead of mere re 

 solve to employ some method which happened to produce 

 it, few persons would feel much hesitation. Not only do 

 we feel tolerably certain that the builders did not know the 

 value of TT, except in the rude way in which all artificers 



