On the right-hand side, besides (the atom of action) and the merely numerical factor , there appears (the square root of -1) which may seem rather mystical. But this is only a well-known subterfuge; and far back in the last century physicists and engineers were well aware that in their formulae was a kind of signal to look out for waves or oscillations. The right-hand side contains nothing unusual, but the left-hand side baffles imagination. We call and co-ordinates and momenta, borrowing our vocabulary from the world of space and time and other coarse-grained experience; but that gives no real light on their nature, nor does it explain why is so ill-behaved as to be unequal to . It is here that the three theories differ most essentially. Obviously and cannot represent simple numerical measures, for then would be zero. For Schrödinger is an operator. His “momentum” is not a quantity but a signal to us to perform a certain mathematical operation on any quantities which may follow. For Born and Jordan is a matrix—not one quantity, nor several quantities, but an infinite number of quantities arranged in systematic array. For Dirac is a symbol without any kind of numerical interpretation; he calls it a -number, which is a way of saying that it is not a number at all. I venture to think that there is an idea implied in Dirac’s treatment [Pg 209] which may have great philosophical significance, independently of any question of success in this particular application. The idea is that in digging deeper and deeper into that which lies at the base of physical phenomena we must be prepared to come to entities which, like many things in our conscious experience, are not measurable by numbers in any way; and further it suggests how exact science, that is to say the science of phenomena correlated to measure-numbers, can be founded on such a basis. One of the greatest changes in physics between the nineteenth century and the present day has been the change in our ideal of scientific explanation. It was the boast of the Victorian physicist that he would not claim to understand a thing until he could make a model of it; and by a model he meant something constructed of levers, geared wheels, squirts, or other appliances familiar to an engineer. Nature in building the universe was supposed to be dependent on just the same kind of resources as any human mechanic; and when the physicist sought an explanation of phenomena his ear was straining to catch the hum of machinery. The man who could make gravitation out of cog-wheels would have been a hero in the Victorian age.