210 THE NEW QUANTUM THEORY 



freely his own bias for symbols with an arithmetical 

 interpretation. If we are to discern controlling laws of 

 Nature not dictated by the mind it would seem neces- 

 sary to escape as far as possible from the cut-and-dried 

 framework into which the mind is so ready to force 

 everything that it experiences. 



I think that in principle Dirac's method asserts this 

 kind of emancipation. He starts with basal entities 

 inexpressible by numbers or number-systems and his 

 basal laws are symbolic expressions unconnected with 

 arithmetical operations. The fascinating point is that 

 as the development proceeds actual numbers are exuded 

 from the symbols. Thus although p and q individually 

 have no arithmetical interpretation, the combination 

 qp — pq has the arithmetical interpretation expressed by 

 the formula above quoted. By furnishing numbers, 

 though itself non-numerical, such a theory can well be 

 the basis for the measure-numbers studied in exact 

 science. The measure-numbers, which are all that we 

 glean from a physical survey of the world, cannot be 

 the whole world; they may not even be so much of it 

 as to constitute a self-governing unit. This seems the 

 natural interpretation of Dirac's procedure in seeking 

 the governing laws of exact science in a non-arithmetical 

 calculus. 



I am afraid it is a long shot to predict anything like 

 this emerging from Dirac's beginning; and for the 

 moment Schrodinger has rent much of the mystery from 

 the />'s and qs by showing that a less transcendental 

 interpretation is adequate for present applications. But 

 I like to think that we may have not yet heard the last 

 of the idea. 



Schrodinger's theory is now enjoying the full tide 

 of popularity, partly because of intrinsic merit, but also, 



