Mathematics is like a ruler using which you make straight walls.
This describes the relationship between axoims and reality. Also a good metaphor regarding it precision. Also about engineering-iness and tool-ness (external-ness) of it.
It is precise in itself, but we need to use it with imperfect objects.
It is for extending the mind. Thinking outside the brain.
It is nit intuitive: in extends and enhances your mind, it is beyond your natural senses, perception, counting, etc. It is about what the brain cannot do very well, it extends what brain can do imperfectly.
It is about doing, changing. It is for adapting the world and reality to it, rather than the other way.
I can count, but Maths is not intuitive for me? Mathematics is extending where the brain stops.
Historically mathematics was created by Babylonians to help them in their engineering. (Obviously it is a simplification).
It can be used to predict and theorize and simulate too. But that’s secondary to engineering.
This hasty note is just a hardening and congealing what I said vocally.
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