The Law of Vector Fields

When I was 13, the intellectual world began opening up to me. I remember discussing with my friends the list of Sciences which we were soon to be offered. There was Chemistry, Biology, Geology, Astronomy, and Physics. We knew what Chemistry was. It was the study of Chemicals. Biology was the study of life, Geology studied rocks and Astronomy the stars and planets. But what was Physics ? Now, many years later, I can answer the question. Physics is that branch of Science which is described by Mathematics. Too naive ? Well any one line description of a subject must be naive, unless the subject is a one line subject. But this one liner has a great deal of truth to it and is in fact a point of view which provokes a lot of thought. For example, we can use it as a tool to examine two famous statements about Science and Mathematics. The first one says that the other Sciences should eventually “mature” and become as mathematical as Physics. Whether one can eventually describe life mathematically or not is the key to whether biology will “mature” or not. I would guess that biology will never mature, but if it did then it would be Physics according to my definition. So the maturing process is replaced by a devouring process in which the “maturing” Science is in fact being eaten up. That seems to be the case for parts of Chemistry. The second statement is really only a phrase. “The unreasonable effectiveness of Mathematics in Physics.” Our one line point of view that Mathematics is the tool of Physics suggests that it is not unreasonable that Mathematics is effective in Physics. The success of Physics goes hand in hand with the effectiveness of Mathematics in Physics. And yet there is something unusual about the way Mathematics describes Physics. Something fantastically beautiful. This something is the existence of a few general laws or principles which imply mathematically most of the known facts of Physics. By that I mean the following. If we regard the objects of physical studies as real things, they have the dual attribute of not being welldefined in the mathematical sense. But since they are real we can try to measure them or measure their interactions. Then measurements give rise to numbers, and then to equations and then mathematical statements. These statements combine logically and produce derived statements which must agree with experiment. That is new experiments verify the mathematical relationships derived by logic. What is remarkable is the fact that there are a few general laws which imply most of these mathematical statements.