NATURE OF EXACT SCIENCE 253 



observation of any kind of coincidence — or, as it is 

 usually expressed in the language of the general rela- 

 tivity theory, an intersection of world-lines. The 

 essential point is that, although we seem to have very 

 definite conceptions of objects in the external world, 

 those conceptions do not enter into exact science and 

 are not in any way confirmed by it. Before exact science 

 can begin to handle the problem they must be replaced 

 by quantities representing the results of physical meas- 

 urement. 



Perhaps you will object that although only the pointer 

 readings enter into the actual calculation it would make 

 nonsense of the problem to leave out all reference to 

 anything else. The problem necessarily involves some 

 kind of connecting background. It was not the pointer 

 reading of the weighing-machine that slid down the 

 hill! And yet from the point of view of exact science the 

 thing that really did descend the hill can only be de- 

 scribed as a bundle of pointer readings. (It should be 

 remembered that the hill also has been replaced by 

 pointer readings, and the sliding down is no longer an 

 active adventure but a functional relation of space and 

 time measures.) The word elephant calls up a certain 

 association of mental impressions, but it is clear that 

 mental impressions as such cannot be the subject 

 handled in the physical problem. We have, for example, 

 an impression of bulkiness. To this there is presumably 

 some direct counterpart in the external world, but that 

 counterpart must be of a nature beyond our appre- 

 hension, and science can make nothing of it. Bulkiness 

 enters into exact science by yet another substitution; 

 we replace it by a series of readings of a pair of cali- 

 pers. Similarly the greyish black appearance in our 

 mental impression is replaced in exact science by the read- 



