Simulating Reality

I came across an interesting article, which was written way back in 1960 by Eugene Wigner, titled The Unreasonable Effectiveness of Mathematics in the Natural Sciences. I wouldn’t normally reply to the deceased, but a few people have mentioned the article and support the viewpoint that it is a remarkable coincidence that we have laws of physics which can be expressed nicely by mathematics. I have had other discussions in which it was argued that the existence of laws of physics points to a higher intelligence of some sort (usually referred to as god).

The article excellently sums itself up in it’s conclusion,

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.

and I couldn’t disagree more (alright, maybe I could if he were a creationist or similar). To begin with, in much the same way that the universe is not fine tuned for life, mathematics as a whole is not particularly suited for describing reality. There have been many more mathematical theorems in history which are not used to describe any aspect of reality than those that have.

Mathematics is, at it’s most basic, an extension and continuation of formal logic. Because of this, some branch of mathematics can be used to describe any logically consistent system. Given that mathematics is just the study of logical conclusions, anything that obeys logic can be described by math. The fact that any particular bit of math applies to a particular situation in reality is mere coincidence. The only “remarkable” condition for the effectiveness of mathematics is that the universe be consistent. And, as we know from mathematics, if the universe had one inconsistency, then it would have to have every conceivable inconsistency (and probably some you can’t conceive of as well). Given that we have never observed even a single inconsistency, we can reasonably assume (though never completely prove, thanks Gödel!) that we live in a consistent universe. As such, it is perfectly reasonable (in fact, inevitable) that mathematics be so effective in the natural sciences.