The Apes—Points To Ponder

The Hypnotic Power of Mathematics

Mathematics is not a science per se. It is a very useful related discipline that provides scientists and engineers with extremely useful tools—statistics being just one of them. Nevertheless, the point needs to be understood at the outset that mathematics does not and cannot prove anything in relation to reality.

Albert Einstein said, famously;

“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”

He got it exactly right. There is only one area where mathematics aligns almost completely with reality. That is in the act of counting. You might argue philosophically that, say, “three apples” in the real world only embody the concept of “threeness,” but it is splitting hairs to distinguish that from their embodying the concept of “appleness.” When there are three apples, there are three apples. The counting numbers—the natural numbers, as mathematicians call them, can reasonably be taken to denote a reality of the real world.
Beyond that, when we talk in terms of negative numbers, real numbers, irrational numbers, or complex numbers, we are manipulating abstract concepts that cannot be demonstrated to exist in reality. They are inventions of the mind of man that can, nevertheless, be put to good use to model reality. And that’s just for starters. We can introduce algebra, geometry, calculus and all the various fields of mathematics, most of which can also be put to excellent use in modeling reality.

Contemporary science and engineering employ mathematics to model reality and, time and again, the models turn out to be so close to reality that it predicts the real world accurately. In some instances the very laws that science proposes can be expressed mathematically—as for example with Newton’s Laws of Motion.

Indeed, Newton serves as an excellent example of the productive use of mathematics, since his gravitational theory and its associated equations are pretty much all you need to spray space shots around our solar system. He formulated it more than 200 years before the first space shot.

And none of that proves Newton’s gravitational theory correct. In fact nowadays his gravitational theory is regarded as incorrect and has been superseded by Einsteinian gravitation. The mathematics did not and never could prove the theory correct, but it created a very close-to-accurate model of reality.