Comment by Razengan | Hacker News Reader

Comment by Razengan | Hacker News Reader

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I'm a layman in this space but I've been thinking about the idea of numbers a lot, mainly for fictional world-building, how aliens may use them, and wondering if they really are universal..

One of the things that strikes me, is how we just started with integers and then tried to fit everything into them. I mean they're fine for counting, but kind of a hackjob for measuring. Like sure, integers may exist in reality insofar as there may be one tree, two trees... but what about weight, speed, gravitational acceleration?

An alien species may use entirely different systems for Counting vs. Measuring.

We even found out that numbers may be "complex", have multiple dimensions. Beings exitsting in 4+ spatial dimensions may "write" in 3D; using Platonic solids to represent integers and fractions, and spheres for measurements?

And just as how humans took a while to come up with the concept of zero, could such a hypothetical 4D being have a hard time thinking about the idea of 1?

Riemannian geometry is a geometry on differentiable structures (manifolds) equipped with a "metric tensor" that generalizes the idea of a length to curved shapes.

Symplectic geometry is, similarly, a geometry on differentiable manifolds equipped with a "symplectic form" that generalizes the oriented area spanned by two vectors known in flat structures as the determinant.

Now here's the fun part: Riemannian geometry may exist in 1, 2, 3... dimensions; but symplectic geometry exists in even dimensions only. For example: if you tried to think of a 3D sphere of radius 1, you couldn't pass a 4D sphere through its largest section (a bit like if you couldn't pass a 3D sphere through a circle-shaped hole of same radius.

I forget what was my point initially.

> a bit like if you couldn't pass a 3D sphere through a circle-shaped hole of same radius.

So a funny thing happened. When my eyes first skimmed over that part, I spotted the word "donut". When I read it a second later, it wasn't there.

Something in my brain literally substituted "donut" for "circle-shaped hole" to the extent that it appeared in my vision, for a single processing cycle.

What value is there in counting "one tree, two trees" given you have small trees, large trees, new trees, dead trees, and trees of different species? You can't substitute any given "two trees" with any other "two trees", much less practically substitute any individual person with another. I can easily imagine an alien culture that highly internalizes individuality and thus finds no need to apply an arbitrary value (count) to any group.

That's very interesting; imagining beings that effortlessly "name" or label everything individually..if that's what you're saying.

The idea still needs a bit of fleshing out to count for cases when you're working with hundreds of practically identical things, e.g. cells and atoms.

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