Evolution of Math

I have largely solved a problem to my satisfaction that has been bothering me since I was about 20 years old: How did humans evolve to be able to do math and physics in a world with no obvious need for such mental capacities?

The key insight, I think, is that the language of logic is useful to describe many of the patterns that we humans have evolved to discover and recognize. Whereas mathematicians deal in inviolate rules, and indeed this seems to be at the heart of useful math, the language of logic deals efficiently in rules of thumb which are very often wrong. I speculate here on how biological information systems, ultimately the brain and nervous system, evolved. Humans are social and information held by one person is profitably conveyed to another thru language. If there was a reason to believe some proposition then there was very often a reason for another person to believe the same proposition without going thru the cost of acquiring it as the first person did. Such a transfer is indeed often mutually advantageous. “There are lions at the water hole in the evening” is a useful proposition to convey.

It is sometimes beneficial to X for X to cause someone else Y to believe something that is not true. The brain sorts information and builds larger models and requires that these models be consistent. This is a source of resistance to new information. Merely hearing a proposition became an untenable reason for belief. Sometime in the last few hundred thousand years we evolved language to describe why we believed things and the concept of proof arose. At the time this was to help fit the new information into older models, and perhaps to displace some parts of the old models. This new language was the logic.

The notion of propositions that were inviolate was the origin of mathematics. The noun phrases in such propositions were imperfect abstractions of things in the world. The real world had no inviolate propositions, but with these new ‘things’ (called “ideals” by Plato) we could deal with inviolate rules. This must have seemed mere sophistry to the practical people of the day but it led to the math and physics that underpins today’s technology.

The world then was complex as it is today. Dealing with the physical world was perhaps complex enough to develop our ability to think about complex situations, even with imperfect propositions. Dealing with other people (think politics) was even more challenging. That such a mental capacity can transfer to mathematical maturity is a bit of a stretch.

To count, Are big numbers real?, x,