Turning to the sphere of scientific research, we find electricity playing a role in the development of modern thinking remarkably similar to its part as a labour-force in everyday life. We find it associated with phenomena which, in Professor Heisenberg’s words, expose their mutual connexions to exact mathematical thinking more readily than do any other facts of nature; and yet the way in which these phenomena have become known has played fast and loose with mathematical thinking to an unparalleled degree. To recognize that in this sphere modern science owes its triumphs to a strange and often paradoxical mixture of outer accident and error in human thought, we need only review the history of the subject without prejudice.