3 ms·
Reading: > 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 fr
by chias 4y ago
Reading:
> 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.
:|
- ouid 4y agon-hypercubes are very relevant and tangible. they model the state of your computer, for one.
- sbf501 4y agoPlease explain? Or link?
- david_allison 4y agoA 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:Snake_in_the_box.svg https://en.wikipedia.org/wiki/Snake-in-the-box#/media/File:S...
- sbf501 4y agoThe 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.
- david_allison 4y agoApologies, 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_box.svg 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_code_tesseract.svg https://upload.wikimedia.org/wikipedia/commons/c/c2/Gray_cod...
- edflsafoiewq 4y agoMathematicians are generally interested in the implications to other bits of math.
- thefaux 4y agoExactly why I had to leave the field.
- thomasahle 4y agoIt'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.
- School-Cotton 4y agoA 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.
- IAmLiterallyAB 4y agochias knows what a hypercube is. Their complaint is it isn't the tangible/practical implication they were hoping for.
- diffrabox 4y agoI didn't know what a hypercube was, I found the explanation helpful.
- deleted 4y ago[deleted]