PROBABILITY AND ENTROPY 137 



is completed that he then proceeds by purely 

 mathematical methods to ascertain the most 

 probable value of the density of mercury and 

 the limits of its probable error. 



The theory of probability deals with data 

 which it does not itself provide, but which are 

 taken from without. As the science of geometry 

 tells nothing about the dimensions of this room, 

 but calculates diagonal distance after the length 

 and breadth are given; so, if in tossing a coin 

 the chance of a head is one in two, the chance of 

 getting all heads in three independent throws is 

 calculated to be one in eight. But the theory of 

 probability does not attempt to prove that the 

 chance of throwing a head is exactly equal to 

 the chance of throwing a tail; and obviously it 

 is not, for even if we leave aside the mechanism 

 of tossing, the two faces of the coin are not me- 

 chanically identical. Nor can dice be made so 

 perfect that each one is not "loaded" in some 

 slight measure. 



While we never can draw a perfectly straight 

 line, the idea of a straight line is essential to 

 geometry. So we never actually meet an entirely 

 level chance. Having imagined an ideal coin 

 with two sides which are quite alike mechani- 

 cally, we must also invent an ideal tossing 



