ON COMMON NOTIONS OP PROBABILITY. 127 



running ; one who handles 'them frequently knows that 

 such is sometimes the fact. Every very practised user 

 of those implements has seen still rarer sequences. Now 

 suppose that a society of persons had thrown the dice so 

 often as to secure a run of six aces observed and recorded, 

 the preceding argument would still he used against 

 twelve. And if another society had practised long 

 enough to see twelve aces following each other, they 

 might still employ the same method of doubting as to 

 a run of twenty-four, and so on, ad infinitum. The 

 power of imagining cases which contain long combin- 

 ations so much exceeds that of exhibiting and arranging 

 them, that it is easy to assign a telegraph which should 

 make a separate signal for every grain of sand in a globe 

 as large as the visible universe, upon the hypothesis of 

 the most space-penetrating astronomer. The fallacy of 

 the preceding objection lies in supposing events in 

 number beyond our experience, composed entirely of 

 sequences such as fall within our experience. It makes 

 the past necessarily contain the whole, as to the quality 

 of its components ; and judges by samples. Now the 

 least cautious buyer of grain requires to examine a 

 handful before he judges of a bushel, and a bushel be- 

 fore he judges of a load. But relatively to such enor- 

 mous numbers of combinations as are frequently pro- 

 posed, our experience does not deserve the title of a 

 handful as compared with a bushel, or even of a single 

 grain. 



Further to illustrate this point, let us turn back to 

 page 64, where we see that when an event has happened 

 m times running, it is m -f 1 to n that it shall happen 

 n times more. This proceeds upon the supposition that 

 the chances of the event were entirely unknown before 

 its happening, and the presumptions drawn are therefore 

 entirely derived from experience. When an event has 

 happened 1000 times one way, it is 1001 to 1 that it 

 happens in the same way next time. But it is only 

 1001 to 1000 that it happens 1000 times more the 

 same way, and only 1001 to 1,000,000 that it happens 



