We have a physically objective world, and then after a while we learn to measure in this world, and we gain experience with this world, through our senses. That is the objective world, and then we pass in to the mathematical world. In the mathematical world there are mathematical entities – “x”, “y”, numbers, and things of that kind. And we bring this mathematical world into isomorphism, or equality in structure with the objective world, so we can manipulate the mathematics and tell what the objective world is going to do; or, as Dirac – a great theoretical physicist – said, to calculate numbers which can be compared with experience, and such is the meaning of all mathematics.
The theoretical physicist, or the mathematical physicist, or the physicist, in the more elementary sense, is merely an artist and he’s attempting to depict the external world in terms of these formulations of which I speak, and the question is, if the theory is real. Take Newton, Newton did this; he was a great painter and he painted the field of mechanics for us in certain equational form. Now, the interesting thing is, and the powerful thing is that if you manipulate these equations, they behave in an analogy with the physical world so that by examining these equations, you can tell what the physical world is doing or should do.
Now, suppose it doesn’t do it? Why then you have a case where the theory in question has broken down. And when I spoke of Einstein, I was speaking of certain slight deficiencies in Newton’s world. Newton did it first, then along came Einstein and Einstein noticed certain discrepancies in the world described by Newton, so he tried a new formulation, generated a new formulation for the theory of relativity, and his theory also is subject to criticism as time goes on.
Point Source = John Vincent Atanasoff