MEMORIAL TO CLASSICAL STATISTICS 109 



For an answer to this question and others of the kind, S.M. offers the 

 following statement : 



Basic Theorem of Statistical Mechanics 



A system is more likely to be found in a slate of greater probability than 

 in a state of lesser probability 



It may be that no reader of these lines has ever seen the basic theorem of 

 S.M. set forth with such merciless candor, though in many a sober treatise 

 there is an elaborate statement which when analyzed turns out to be just 

 this and nothing more. Of course it is a tautological statement, and has no 

 value except insofar as it may help to drive some contradictory notion out 

 of the student's mind or to prepare that mind for some meaning or other 

 which is not yet in the statement but may be added to it later. Actually it 

 can serve both these offices. 



To be expelled from the mind of the student is first of all the idea that 

 S.M. is going to give him a description of the way in which the gas proceeds 

 from the surging state to the uniform. From an astronomer he may 

 learn the orbit of the moon from apogee to perigee. From an authority 

 on ballistics he may find the trajectory of the bullet from the muzzle of the 

 gun to the bull's eye on the target. From a railroad ofhce he may get a 

 timetable showing the passage of the train from mile to mile over the rails 

 from Boston to Chicago. All this sort of thing is out of the range of 

 statistical mechanics! If a railroad acted like a surging gas and its time- 

 table were devised in the spirit of S.M., one would go to the office and. be 

 told that the trains were enormously more likely to be in Boston than in 

 Chicago or anywhere in between. From this one would be expected to infer 

 that at any moment chosen at random the chance of finding a train anywhere 

 along the line except in Boston would be practically nil — unless indeed one 

 got a train and put it on the rails at Springfield, and even this would be of 

 little use for getting to Chicago, since at every subsequent instant the 

 train would almost certainly be in Boston. Not a very useful timetable, 

 and not a ver}^ useful railroad! 



S.M. thus starts off with a renunciation. It renounces the prospect of 

 telling just how the gas proceeds from the surging state to the uniform state. 

 To that smooth unbroken sequence of times and places whereby the moon 

 finds its way through the heavens and the bullet through the air and the 

 train along the rails, there is no counterpart presented. 



This of course is a serious matter, for the smooth unbroken sequence is 

 inseparably linked — or almost inseparably linked — with the notion of cause- 

 and-effect, the notion of natural law, the notion of man as a being who can 

 foretell the future. Mechanics harmonizes with these notions; for mech- 



