3 ms·

(Yes. Low-discrepancy sequences are the WP link for "a special random number generator" in /unsort, and I considered that link to also cover quasi-Monte Carlo e

by gwern 2y ago

(Yes. Low-discrepancy sequences are the WP link for "a special random number generator" in /unsort, and I considered that link to also cover quasi-Monte Carlo etc. I'm not immediately sure what you mean by "φ in a circular space" though.)

082349872349872 2y ago
My bad, I'd just ^F'd with a purely syntactic search on a few terms. If you can arrange your space from 0,..1 and identify 1 with 0 to make it circular, obviously (consider 1/3, 2/3, etc.) advancing by any amount in ℚ will fail to explore a lot of the space. The flip side of this is that φ, or 1/φ, are the least-ℚ-like regular things in ℝ: if we consider good approximations to be places in the continued fraction where there's a large entry, that never occurs. (their continued fraction representation is repeated 1's) This comes up with "how do sunflowers know about φ?", the answer to which seems to be: they don't, they're just creating new seeds in the least-correlated place to all the existing seeds, and because of the property above, that tends to result in apparently-spiraling placements which can be fitted with fibonaccis or φs. Does that make sense?
- gwern 2y ago
  That makes sense. Sounds interesting - do you have a favored reference? Quickly looking, I did find https://gwern.net/doc/math/1974-mathai.pdf https://gwern.net/doc/math/1974-mathai.pdf
  - gradschoolfail 2y ago
    Top of my deadtree stack is Chazelle, The Discrepancy Method (1998) (Father of the regrettably more famous Chazelle, if you’re okay californicating rabbit holes)
    - gsf_emergency 2y ago
      Update: Now that I've pushed BC back to the stack, here's a ref that might be worthier of the (nonnewtonian) process heap https://archive.fo/4mlUU https://archive.fo/4mlUU (Pls use the usual Chinese bulk carrier resilient doi tricks as might be required) Lagniappe: https://hn.algolia.com/?dateRange=all&page=0&prefix=true&query=Chazelle&sort=byDate&type=comment https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...
      - 082349872349872 2y ago
        That sounds like the perfect swith* for me as well — I'd already been meaning to hide some imperative O(n)s behind functional-seeming O(n log n)s, but if soft heaps have no huge constant involved, maybe no rabbits have to be hidden in hats? * http://bitsnbobstones.watershipdown.org/lapine/unit12.html#:~:text=swith http://bitsnbobstones.watershipdown.org/lapine/unit12.html#:...
      - 082349872349872 2y ago
        Heh, not that any of us would be willing to tolerate getting stuff back in corrupted order ;) If the constant factors aren't intolerable, it seems like one really ought to be able to do something with the fact that corruption (galois connection connexion?) only happens in one direction (corruption monad as closure)... Lagniappe: https://www.youtube.com/watch?v=_yExwkQYcp0 https://www.youtube.com/watch?v=_yExwkQYcp0
        gsf_emergency 2y ago
        I would, ipso facto(rio), in the hope that some of these corruptions, like Shakespeare's monkeys, would rephrase the muddled messages I get from the aether in something worth remembering for all time..
        082349872349872 2y ago
        Maybe you could get a professor from the Academy of Projectors in Lagado to agree to advise, whereby you could get allocated some time on https://en.wikipedia.org/wiki/The_Engine https://en.wikipedia.org/wiki/The_Engine for your own research? (thanks for reminding me of "Have not I the most reason to complain, when I see these very Yahoos carried by Houyhnhnms in a vehicle, as if they were brutes, and those the rational creatures?"!)
  - 082349872349872 2y ago
    No favoured reference on my part, but Kragen's played around with this before, so he might have some ideas...

by gwern 2y ago

082349872349872 2y ago

My bad, I'd just ^F'd with a purely syntactic search on a few terms. If you can arrange your space from 0,..1 and identify 1 with 0 to make it circular, obviously (consider 1/3, 2/3, etc.) advancing by any amount in ℚ will fail to explore a lot of the space. The flip side of this is that φ, or 1/φ, are the least-ℚ-like regular things in ℝ: if we consider good approximations to be places in the continued fraction where there's a large entry, that never occurs. (their continued fraction representation is repeated 1's) This comes up with "how do sunflowers know about φ?", the answer to which seems to be: they don't, they're just creating new seeds in the least-correlated place to all the existing seeds, and because of the property above, that tends to result in apparently-spiraling placements which can be fitted with fibonaccis or φs. Does that make sense?

gwern 2y ago
That makes sense. Sounds interesting - do you have a favored reference? Quickly looking, I did find https://gwern.net/doc/math/1974-mathai.pdf https://gwern.net/doc/math/1974-mathai.pdf
- gradschoolfail 2y ago
  Top of my deadtree stack is Chazelle, The Discrepancy Method (1998) (Father of the regrettably more famous Chazelle, if you’re okay californicating rabbit holes)
  - gsf_emergency 2y ago
    Update: Now that I've pushed BC back to the stack, here's a ref that might be worthier of the (nonnewtonian) process heap https://archive.fo/4mlUU https://archive.fo/4mlUU (Pls use the usual Chinese bulk carrier resilient doi tricks as might be required) Lagniappe: https://hn.algolia.com/?dateRange=all&page=0&prefix=true&query=Chazelle&sort=byDate&type=comment https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...
    - 082349872349872 2y ago
      That sounds like the perfect swith* for me as well — I'd already been meaning to hide some imperative O(n)s behind functional-seeming O(n log n)s, but if soft heaps have no huge constant involved, maybe no rabbits have to be hidden in hats? * http://bitsnbobstones.watershipdown.org/lapine/unit12.html#:~:text=swith http://bitsnbobstones.watershipdown.org/lapine/unit12.html#:...
    - 082349872349872 2y ago
      Heh, not that any of us would be willing to tolerate getting stuff back in corrupted order ;) If the constant factors aren't intolerable, it seems like one really ought to be able to do something with the fact that corruption (galois connection connexion?) only happens in one direction (corruption monad as closure)... Lagniappe: https://www.youtube.com/watch?v=_yExwkQYcp0 https://www.youtube.com/watch?v=_yExwkQYcp0
      - gsf_emergency 2y ago
        I would, ipso facto(rio), in the hope that some of these corruptions, like Shakespeare's monkeys, would rephrase the muddled messages I get from the aether in something worth remembering for all time..
        082349872349872 2y ago
        Maybe you could get a professor from the Academy of Projectors in Lagado to agree to advise, whereby you could get allocated some time on https://en.wikipedia.org/wiki/The_Engine https://en.wikipedia.org/wiki/The_Engine for your own research? (thanks for reminding me of "Have not I the most reason to complain, when I see these very Yahoos carried by Houyhnhnms in a vehicle, as if they were brutes, and those the rational creatures?"!)
- 082349872349872 2y ago
  No favoured reference on my part, but Kragen's played around with this before, so he might have some ideas...