Steven Strogatz on chaos theory, game theory, and why math isn’t boring

In fact, natural numbers are the basis for almost all of mathematics. And natural numbers are a manifestation of counting. Information theoretically, to count, one needs two dimensions (or degrees of freedom.) Space for storage of the number. And time to increment the storage medium, again and again, at different points. You could use two dimensions of space instead, and you'd just draw two orthogonal lines..and say the area inside the rectangle is the product.

So if counting is fundamentally related to the relationship between two dimensions, then so is addition since addition is repeated/recursive counting. And multiplication is repeated/recursive addition.

Once you realize this, physics seems less fundamental than mathematics, when it comes to understanding the universe.

Multiplication and addition are related in the way that f(x) and repeat(f(x), y) are related. They distribute over eachother and have certain properties.

See: https://en.wikipedia.org/wiki/Ring_(mathematics)

So..the primes, the chaotic relationship between the modularity of addition over multiplication and the modularity of multiplication over addition, is due to the relationship between our universe's dimensions.

Want to study the universe at the most raw level? Mathematics. Want to study it a little higher? Physics. Want to study it at a higher level..maybe closer to the phaneron? Biology/neurochemistry.

https://en.wikipedia.org/wiki/Phaneron

Want to study it at the thinking level? Zen buddhism.

Choose your pick. The causal chain of human to universe doesn't discriminate. The whole chain could be the "real" reality. Pick your choice. It's all beautiful. It's all mystifying and enigmatic. Just do it.

But I don't know that my younger self had the maturity to see the deeper beauty. It was only starting college that I had the necessary complexity of thought (combined with wonderful professors).

It takes a while to develop a taste refined enough to perceive these things. In the meantime, rote memorizing your multiplication tables and polynomial expansions might be a necessary evil to have foundations strong enough to later support that kind of more abstract, artistic reasoning.

This goes for other fields too. You have to practice your chords to play Bach, and learn your conjugations to write a novel.

But it's nonsense that the natural numbers require two dimensions. Time appears nowhere in the Zermelo–Fraenkel axioms: https://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory

But space and time are natural, ie. you mention a physical interpretation. And a paradox one at that, because you are explaining counting (numbers) by counting (dimensions).

> Want to study the universe at the most raw level?

I'd rather offer that mathematics is about formalization of what you know, while physics is about exploration of what you don't know. Maths is intrinsic, abstract and relies on intuition. Physics is extrinsic, concrete and relies on experimentation. These separations are arbitrary and not useful, if they don't serve a purpose. Why divide like that at all? If you talk hierarchy, I'd say logic is higher up there.

To wrap it up, what's that got to do with bad teaching? I'd suppose that deductive reasoning cannot be taught, because it is learned before language is acquired, then used to acquire language. Maybe, memory can be trained, and curiosity can be stimulated, but school is hardly the right setting to inspire creativity, when most of the time there talking is forbidden.

> Zen buddhism

Sure, nihilism, or religion overall, is like an escape when you abandon all hope and try to recollect new hope. It is admitting you don't know anymore and going back to square one.