[toddwprice]

I love articles like this. Thanks for sharing. Ultimately math is just a language invented to describe the world. Which is what any language does. And it's a really useful language for sharing certain kinds of intelligence. I got into a discussion with my son last night about sine waves. Which don't really exist, per se, but they are a useful language construct for thinking about waves (especially sound waves as we were discussing). Shared intelligence like this is, as some have maintained, a major differentiator between humans and pre-humans. So the very fact we can argue about what is a number is part of what it is to be human.

[kevin_thibedeau]

Sine waves do exist. They are the 2D projection of a circular spiral, which is fundamental to the properties of the physical world. This is rarely explained fully when these concepts are introduced in trigonometry (which should more properly be called "circleometry") because of the higher level maths required before introducing imaginary exponentials.

The computer your are using would not work without sine waves. The nanometer scale chips couldn't be manufactured without them. The high speed signals transmitted over its wiring would not reach their destination without knowing how to manipulate them.

A deeper question is what to make of "uncountable" transcendental numbers.

[tim333]

It may be more than a language to describe the world. Take Euler's identity, e^(i*pi)=-1. One of the most striking equations in maths and it doesn't really describe anything physical in particular and true regardless of the nature of the world.

[mzs]

I can visualize it as triangles.

https://www.math.toronto.edu/mathnet/questionCorner/epii.htm...