[gwern]

(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]

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]

That makes sense. Sounds interesting - do you have a favored reference? Quickly looking, I did find https://gwern.net/doc/math/1974-mathai.pdf

[gradschoolfail]

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]

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

(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&que...

[082349872349872]

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#:...

[082349872349872]

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

[gsf_emergency]

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]

No favoured reference on my part, but Kragen's played around with this before, so he might have some ideas...