The power of understanding symbols, i.e. of regarding everything about a sense-datum as irrelevant except a certain form that it embodies, is the most characteristic mental trait of mankind. It issues in an unconscious, spontaneous process of abstraction, which goes on all the time in the human mind: a process of recognizing the concept in any configuration given to experience, and forming a conception accordingly. That is the real sense of Aristotle's definition of Man as "the rational animal".
The world of physics is essentially the real world construed by mathematical abstractions, and the world of sense is the real world construed by the abstractions which the sense-organs immediately furnish. To suppose that the "material mode" is a primitive and groping attempt at physical conception is a fatal error in epistemology.
The faith of scientists in the power and truth of mathematics is so implicit that their work has gradually become less and less observation, and more and more calculation.... But the facts which are accepted by virtue of these tests are not actually observed at all.