The Unreasonable Effectiveness of Mathematics

July 2014

This post is a draft. Content may be incomplete or missing.

Brain Dump

Why does math appear so often when we talk about natural phenomenon?

What is math? We have a set of fundamental laws / axioms which we hold to be true. We build proofs out of those fundamental axioms to get higher-level axioms we also hold true. Does this sound like subroutines? Maybe it should.

Buy what about those fundamental axioms? Aren’t they just observations about our universe? What makes them correct? Also, how can this be the case of math is considered pure?

The answer is that we’re thinking backwards. Math isn’t an observation of natural phenomena; rather, certain natural phenomena can be mapped to mathematics.

When we see a system (or, to be precise, a model thereof) conforms to the fundamental axioms, then we cam go into the realm of math to draw.conclusions about that system.

So what makes math so unreasonably effective?

  • The axioms are few, making it easy to conform systems to those xioms
  • There is a huge library of mathematical.knowledge we.have ready built up over the centuries

And as a result, we find it’s easy to map math to things and draw useful conclusions about things.

Math isn’t really about numbers. As you get more and more advance, this becomes more and more apparent. It’s really about drawing conclusions from fundamental.premeses – its logic. It’s basically the standard library for logic, with extended support for numeric logic. But if you can get your job done with numbers, math can be an unreasonably effective tool.