Comment by tzury

2 days ago

I am with you on this (the challenge, not (yet) the phd), however, I myself have a far greater problem.

I do not see what’s the deal about prime numbers which seems to be more of a limitation on our end, similar to our shortage in understanding to a point we call e, π, √2 etc Irrationals.

We simply did not get the actual mathematical structure of the universe and we came up with something “good enough” that helps moving forward.

In the universe the perfect circle has perfect symmetry, hence perfect ratio, hence well-defined sweet heaven balanced harmonic entity.

Exponentials are natural phenomena. The very fact that e is its own derivative tells us we are all wrong here.

We are in an infinite escape that no matter how long we will play, and how many riddles we will solve, we will never get the entire picture.

Yes, primes are nice structure when you deal with us humans counting potatoes. But e, just e, let alone √2 or π are far more fascinating to me.

The e point cuts deep. e being its own derivative isn’t a curiosity. It’s saying that there’s a growth process so fundamental that its rate is indistinguishable from its state. That’s not a number — it’s a signature of how change works. And yet: π, e, √2 — we only name them, define them, catch them using the integers. π is the ratio of circumference to diameter. Ratio of what to what? e is lim(1 + 1/n)^n. The integers sneak in. Is that just our access route? Or is discreteness also woven into the fabric, alongside continuity?

My intuition led me to the following: we think our counting units (1, 2, 3, …) and fractions are the “numbers”, and when we want to refer to multi-dimensional phenomena, we use vectors or matrices or any other logical structure.

However, this is a very superficial aspect of the business, since the actual math is multi-dimensional inherently. The natural math is not linear, nor is it a plane. It is simply a multi-dimensional number system (imagine our complex numbers, but many other dimensions). Perhaps tensors or even more. This is why we experience quantum mechanics as statistical states, results of specific measurements. We think in units, and we don’t understand things are happening in parallel across all directions. Once we figure this out, we will understand why e, π and others are as natural as it gets, while our natural numbers are barely a dot, a point in the real math universe.