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Overcoming Bias Commenter's avatar

One relatively simple but interesting implication of living in 1KD is that protecting your faces is cheap but encasing them in a rigid structure is crazy expensive. What do I mean by this? Think of a single atom that you are trying to "shield" from possible collisions with other atoms. One idea is to put that atom inside a 1K-dimensional hypercube. But if you do that, you will need 3^1000 atoms since you will need to put the lone protected atom at the core of a 3X3X3X...X3X3X3 hypecube.

But if instead you are satisfied with just blocking possible collisions by adding an atom on each "face" of this hypercube, you could do so with as little as 2X1000 atoms, which might be manageable.

In the case of a 3D space, this corresponds to putting your atom between 6 atoms, two per dimension, making it the center of the "sandwich" along each dimension. If you wanted to complete the cube, you'd need to also add the atoms at the edges and corners of the cube, which amount to 26 in this case. Manageable in 3D, but not in 1KD.

So I'd conclude that protecting the "faces" of your body is cheap, but encasing them inside a rigid boundary is crazy expensive. So while you will likely find evolved systems with protection shields, this protection will never include filling up all the "corners", or you'll run out of atoms really fast.

Same would likely apply to the protection of wire/cables.

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CF's avatar

Maybe one way to get an intuition about what a high-dimensional universe might be like is to consider that our own universe is, in a certain sense, much more than 1000 dimensional. They're not spatial dimensions, but bear with me...

The quantum wave function is at least 3N-dimensional where N is the number of particles in the universe, since it assigns a complex number to every possible arrangement of every particle. (Actually there are more dimensions for spin and so on.) And what do we observe?

Well, the quantum wave function often "branches", never to reunite, due to high degrees of freedom. (Copenhagen folks call this "collapsing", since they imagine that the other branches disappear.) Also, it is very difficult to determine the dimension (i.e. number of particles). Different places (arrangements of all particles) quickly become inaccessible to each other. Most space (i.e. possible arrangements of particles) is empty (i.e. gets low weight under Born's rule). Agents work in much lower dimensions, due to locality (we call irrelevant degrees of freedom "distant objects"), and modding over symmetries (e.g. "the ball fell down" means "all the particles in the ball moved down", vastly simplifying the cognitive burden).

This maybe tells us something about what universes with many spatial dimensions may be like. (After all, what *exactly* qualifies a degree of freedom as "spatial"?) But it doesn't tell us much about the specific high-dimensional universes Robin is interested in, the ones that have something like molecules and so on, assuming such universes are even logically possible.

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