PROBABILITY AND ENTROPY 



151 



apparatus so that the balls are mixed, the first 

 distribution or two may show evidence of the 

 original sorting, but after one or two good mix- 

 insrs the balls enter the tubes in random ar- 

 rangements which follow 

 the simple laws of chance. 

 As the mixing continues 

 we do not get nearer and 

 nearer to the even distri- 

 bution of five blacks and 

 five whites in each tube ; on 

 the contrary, the arrange- 

 ment of six and four oc- 

 curs more frequently than 

 that of five and five, and 

 occasionally greater fluc- 

 tuations from the mean 

 occur. Indeed, if we have 

 patience to mix them two 

 or three hundred thousand 

 times, we shall probably 



come to the original well-sorted arrangement. 

 If we stop there and plot our records from the 

 original complete sorting to the final complete 

 sorting we shall obtain a zigzag curve which 

 shows no dissymmetry on the average with re- 

 spect to the beginning and the end. If instead 



Figure 24 



