4 ms·
> and this has opened my eyes to a lot of elegant, useful sources of intuition (and not just about geometry). Would you care to compile and share them?
by aesh2Xa1 6y ago
> and this has opened my eyes to a lot of elegant, useful sources of intuition (and not just about geometry).
Would you care to compile and share them?
- wizzwizz4 6y agoIt's hard to compile intuition; seeing that one diagram unlocked an entire category of possibilities that I hadn't spotted before, and I can feel that they're now accessible (and always were, but I hadn't looked). It's hard to enumerate them. Basically, a lot of things can be thought of as something vaguely geometric, and then enumerated discretely using some method of enumeration (e.g. a grid) to form an approximation to the value, which is a known bound. It feels like the general idea can be used for things other than approximating real values (something to do with property membership and graphs?) but I can't give any concrete examples of that. One of the ideas I got from this, which I think was what spurred me to write that comment, was doing it in reverse. You can think of certain discrete systems as being, in some nebulous way stronger than a bound, inextricably linked to a continuous function. Kind of like Pisot–Vijayaraghavan numbers,[0] but more so. There was something about the resource requirements of an algorithm and applying this technique to compiler optimisation, but that's an incomplete thought. Lots of things. [0]: https://en.wikipedia.org/wiki/Pisot%E2%80%93Vijayaraghavan_number https://en.wikipedia.org/wiki/Pisot%E2%80%93Vijayaraghavan_n...