254 Chance, Causation, and Design. [CHAP. x. 



16. There still remains a serious, and highly interesting 

 speculative consideration. In the above argument we took 

 it for granted, in calculating the chance alternative, that 

 only one of the 10,000 possible values was favourable ; that 

 is, we took it for granted that the ratio 77- was the only one 

 whose claims, so to say, were before the court. But it is 

 clear that if we had obtained just double this ratio the result 

 would have been of similar significance, for it would have 

 been simply the ratio of the circumference to the diameter. 

 In fact, Mr Smyth s selected ratio, the height to twice the 

 breadth of the base as compared with the diameter to the 

 circumference, is obviously only one of a plurality of ratios. 

 Again ; if the measured results had shown that the ratio of 

 the height to one side of the base was 1 : A/2 (i.e. that of a 

 side to a diagonal of a square) or 1 : A/3 (i.e. that of a side 

 to a diagonal of a cube) would not such results equally show 

 evidence of design ? Proceeding in this way, we might 

 suggest one known mathematical ratio after another until 

 most of the 10,000 supposed possible values had been taken 

 into account. We might then argue thus : since almost 

 every possible height of the pyramid would correspond to 

 some mathematical ratio, a builder, ignorant of them all 

 alike, would be not at all unlikely to stumble upon one or 

 other of them : why then attribute design to him in one case 

 rather than another ? 



17. The answer to this objection has been already 

 hinted at. Everything turns upon the conventional estimate 

 of one result as compared with another. Revert, for sim 

 plicity, to the coins. Ten heads is just as likely as alternate 

 heads and tails, or five heads followed by five tails ; or, in 

 fact, as any one of the remaining 1023 possible cases. But 

 universal convention has picked out a run of ten as being 

 remarkable. Here, of course, the convention seems a very 



