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If you lived in a 1000 dimensional space, would you actually be able to figure out the number of dimensions? You could try counting how many sticks you could p
by OscarCunningham 3y ago
If you lived in a 1000 dimensional space, would you actually be able to figure out the number of dimensions?
You could try counting how many sticks you could place at right angles to each other, but the problem is that you can arrange 1001 vectors so that they're all very nearly at right angles.
- msla 3y agoI don't know, us poor three-dimensional beings figured out that the continuous functions from R to itself form an infinite-dimensional vector space. https://math.stackexchange.com/questions/466707/what-are-some-examples-of-infinite-dimensional-vector-spaces https://math.stackexchange.com/questions/466707/what-are-som...
- Bootvis 3y agoThese beings can do experiments that get better and better to finally find that the number of dimensions can’t be more than 1000 but also not less.
- deleted 3y ago[deleted]
- rocqua 3y agoDon't pick sticks. Pick sides. Sides of a box. Every time you pick a direction with a stick, also set up two hyperplanes spaced appart. Effectively trying to build a hypercube. Once you have 1000 directions chosen (i.e. 2000 sides) you will have fully enclosed a volume. You probably won't have a perfect cube, but this trick works as long as the set of vectors you picked 'are in general position' which has probability 1.