Nowadays we do not encourage the engineer to build the world for us out of his material, but we turn to the mathematician to build it out of his material. Doubtless the mathematician is a loftier being than the engineer, but perhaps even he ought not to be entrusted with the Creation unreservedly. We are dealing in physics with a symbolic world, and we can scarcely avoid employing the mathematician who is the professional wielder of symbols; but he must rise to the full opportunities of the responsible task entrusted to him and not indulge too freely his own bias for symbols with an arithmetical [Pg 210] interpretation. If we are to discern controlling laws of Nature not dictated by the mind it would seem necessary 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 and individually have no arithmetical interpretation, the combination 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 Schrödinger has rent much of the mystery from the ’s and ’s 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.