610 THE POPULAR SCIENCE MONTHLY. 



he bets $4; if he loses that he bets $8; if be then gains he has lost 

 I + 2 + 4 = 7, and he has gained $1 more ; and no matter how many 

 bets he loses, the first one he gains will make him $1 richer than he 

 was in the beginning. In that way, he will probably gain at first ; 

 but, at last, the time will come when the run of luck is so against him 

 that he will not have money enough to double, and must therefore let 

 his bet go. This will probably happen before he has won as much as 

 he had in the first place, so that this run against him will leave him 

 poorer than lie began ; some time or other it will be sure to happen. 

 It is true that there is always a possibility of hjs winning any sum 

 the bank can pay, and we thus come upon a celebrated paradox that, 

 though he is certain to be ruined, the value of his expectation calcu- 

 lated according to the usual rules (which omit this consideration) is 

 large. But, whether a gambler plays in this way or any other, the 

 same thing is true, namely, that if plays long enough he will be sure 

 some time to have such a run against him as to exhaust his entire for- 

 tune. The same thing is true of an insurance company. Let the di- 

 rectors take the utmost pains to be independent of great conflagra- 

 tions and pestilences, their actuaries can tell them that, according to 

 the doctrine of chances, the time must come, at last, when their losses 

 will bring them to a stop. They may tide over such a crisis by ex- 

 traordinary means, but then they will start again in a weakened 

 state, and the same thing will happen again all the sooner. An act- 

 uary might be inclined to deny this, because he knows that the ex- 

 pectation of his company is large, or perhaps (neglecting the interest 

 upon money) is infinite. But calculations of expectations leave out 

 of account the circumstance now under consideration, which reverses 

 the whole thing. However, I must not be understood as saying 

 that insurance is on this account unsound, more than other kinds of 

 business. All human affairs rest upon probabilities, and the same 

 tiling is true everywhere. If man were immortal he could be per- 

 fectly sure of seeing the day when everything in which he had trusted 

 should betray his trust, and, in short, of coming eventually to hope- 

 less misery. He would break down, at last, as every great fortune, 

 as every dynasty, as every civilization does. In place of this we 



have death. 



But what, without death, would happen to every man, with death 

 must happen to some man. At the same time, death makes the num- 

 ber of our risks, of our inferences, finite, and so makes their mean 

 result uncertain. The very idea of probability and of reasoning rests 

 on the assumption that this number is indefinitely great. We are 

 thus landed in the same difficulty as before, and I can see but one 

 solution of it. It seems to me that we are driven to this, that logi- 

 cality inexorably requires that our interests shall not be limited. 

 They must not stop at our own fate, but must embrace the whole 

 community. This community, again, must not be limited, but must 



