10 Ellery W. Davis 



different sorts of sets of 1024 throws, of sets of these sets, of 

 sets of sets of sets .... ad infinitum. 



But what has it all to do with defining chance? 



Just this: 



A chance distribution of coin tossings is one in accordance 

 with the above indicated calculations. 



A chance distribution of events is one in which alike the 

 separate events, and all the possible combinations, and com- 

 binations of combinations, nay (combinations of ) ^ of the 

 events happen in accordauca with their numerical possibilities-. 



How such a distribution is brought about, we do not, we 

 cannot say. For that matter, we cannot even say that it is 

 brought about. Neither time nor space nor mind permits the 

 calculation of the.distribution in sets of sets of sets .... of an 

 infinite number of throws. xA.s far as we can see there may be 

 but chance, and so a modest agnosticism forbids us to postu- 

 late a law. The realm of chance is the realm of the unknown, 

 an infinite realm an eternal realm, but liable at any moment 

 to be invaded by the army of seekers after truth. 



Notice the perfection of agnosticism in this doctrine of 

 probabilities. Ignorance of any law as to coin tossings bids 

 us say "about half heads, half tails"; ignorance as to the 

 deviation from this law of igaorance bids us set up a scheme 

 of deviations occurring in a set of ten, all possible deviations 

 being treated with an impartiality possible only to a carefully 

 maintained ignorance; and so we go on, forever and forever 

 escaping from the assertion of any fixed law, always saying 

 "about," "about." 



But suppose there is a departure from this ideally agnostic 

 distribution. Let the ratio of heads to tails be markedly dif- 

 ferent from unity. We suspect a law; we ask why. Yet the 

 discrepancy may, after all, be a mere happen so. A hundred 

 heads in succession is to be expected once in enough millions 

 of millions of throws, and is as likely to come at the start as 



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