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Comment by chias | Hacker News Reader

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> n runners on a track of unit length, with constant speeds all distinct from one another, will each be lonely at some time—at least 1/n units away from all others.

Interesting conjecture! And okay, a lot of interesting problems end up being distilled into tangible if eccentrically named things. Like the "dining philosophers" in computer science to describe deadlock. I'm curious how this relates to a tangible problem.

> Implications

Nice, here we go!

> Suppose C is a n-hypercube of side length s in n-dimensional space.

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A hypercube is just the higher-dimensional analog of a cube. A 2-hypercube is a square, a 3-hypercube is a cube, and so on.

Edit: I know complaining about downvotes is against the rules, and I’m not complaining, because I really don’t care about my karma on this site — but I am really confused and curious how people could possibly be opposed to me explaining a mathematical concept to someone who expressed frustration at not knowing it.

chias knows what a hypercube is. Their complaint is it isn't the tangible/practical implication they were hoping for.

I didn't know what a hypercube was, I found the explanation helpful.

Mathematicians are generally interested in the implications to other bits of math.

Exactly why I had to leave the field.

It's like that in most fields though. A builder is interesting in applications to buildings. An economist is interested in applications to the economy. Few people see things all the way through, whatever that even means.

n-hypercubes are very relevant and tangible. they model the state of your computer, for one.

Please explain? Or link?

A vertex in the N-dimensional hypercube represents an N-bit number.

An edge in the hypercube is equivalent to a single bit flip.

image: https://en.wikipedia.org/wiki/Snake-in-the-box#/media/File:S...

The deterministic state of a computation block (aka, a computer) is 2^N where N is the total number of state-retaining elements plus inputs. Large portions of this space are inaccessible due to mutex conditions (e.g., two or more conditions that cannot be true at the same time).

How does an open curve on the edge of an N-dimensional hypercube (snake in the box, as you provided) describe the state of my computer? Your link said nothing about that.

Apologies, the link was intended to go to the image of the hypercube + binary representation (which is much more intuitive than the images Wikipedia displays on the hypercube page), but it failed on mobile: https://upload.wikimedia.org/wikipedia/commons/2/2c/Snake_in...

The Gray Code image is a lot more 'practical' from an engineering perspective, but I don't feel it's of the same quality: https://upload.wikimedia.org/wikipedia/commons/c/c2/Gray_cod...

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