between Stars forming Binary or Multiple Groups, 419 



33. Assuming that this conclusion will not be contested, — 

 that geometrical symmetry will never be accepted by a rea- 

 sonable man as a proof that hazard has prevailed instead of 

 design, "accident" against "cause," — we are necessarily led to 

 infer that the vague premiss of " scattering by mere chance as 

 it may happen," includes, as an essential conception, a sphere 

 of possibilities wider than that of throwing dice in the manner 

 supposed; and though we may be at first sight reluctant to 

 admit this, I conceive that the reductio ad absurdum proves 

 the necessity of it, and I shall endeavour to explain the kind 

 of enlargement of the notion of chance or random which I 

 conceive will meet the case. 



34. It is plain from Art. 32, that there does exist an actual 

 probability of symmetry when the chance of a given fall of 

 dice is. considered against the chances of any other given fall. 

 But there is something assumed as previously known or tried. 

 That something is the perfect indifference of the dice. This 

 may be either assumed as a fact — suppose upon the informa- 

 tion of the maker — or it may be ascertained by experiment. 

 In the latter case it can only be known by the long run of a 

 vast number of trials, proving that all faces turn up indiffer- 

 ently in the long run. But in the case of the stars we have 

 witnessed no such series of experiments. The actual proba- 

 bility of the number of the stars being as the area considered, 

 is here equivalent to the equality of balance of the dice in the 

 last problem. Neither dare be assumed where the premisses 

 are utterly vague. The result of many trials in the one case 

 would be the tendency of all the numbers on the dice to turn 

 up equally ; in the other, the equality of interspacing of stars ; 

 each a most unlikely event, considered as a solitary result, yet 



my mathematical friend was undoubtedly quite right. But if it mean the 

 probability of the given symmetrical result, compared to the probability of 

 some other given result not symmetrical, I hope to have shown that he is as 

 certainly in the wrong. Now it is with a case in esse, an event which has 

 occurred, not with a case in posse, an event which may or may not occur, 

 with the previous probability for which we are here concerned. To take 

 a very simple illustration. The chance of throwing heads and tails being 

 reckoned to be precisely equal, it is yet absolutely very unlikely as a predi- 

 cate result that on 1000 throws there should be exactly 500 heads and 

 500 tails. We know in fact that there are almost forty chances to one, that 

 some one of the other possible events shall happen instead of the required 

 one (Galloway on Probability, p. 134) ; but if we had seen the experiment 

 tried, and had seen 499 heads and 501 tails as the result, the individual re- 

 sult of absolute equality is more probable (upon obvious grounds) than 

 the individual result that there should be any given discordance; for the 

 fact that such a preponderance of probability for heads or for tails existed, 

 would be tantamount to an assertion that the chance was not indifferent, 

 but that the coin had really a bias, which is contrary to the hypothesis. 



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