Ben Weinstein-Raun @benwr@schelling.pt
I like understanding stuff; I like making things; I like it when people get what they want; I like it when the world doesn't end.
Joined Dec 2022
I've been enjoying Mastodon lately, but it occurs to me that this might be due to the fediverse's userbase being pretty similar to “the internet in 2002” instead of “facebook in 2023", and as soon as Threads gets hooked up there will be an eternal septummer of the mil-post-sends
Ben Weinstein-Raun
boosted
Now, suppose you want to impose a stronger condition: not only does your set need to contain a unit line segment in every possible orientation, you need to be able to take any one of these line segments and continuously rotate it through a 360° turn (possibly translating it as well), without it ever leaving the set, eventually bringing it back to its original position and orientation.
A set that meets that stronger condition is known as a Kakeya needle set, since the problem of finding such sets was posed by the Japanese mathematician Sōichi Kakeya in 1917.
To turn our Besicovitch sets into Kakeya needle sets, you need to add new pieces to the set to provide a route for the “needle” as it moves between the now-separated edges. If you rotate the needle around its midpoint by a small angle, it will sweep out two narrow segments of a disk centred on that midpoint. You can then translate it along its new orientation adding essentially no area (because the needle has infinitesimal thickness), until its midpoint lies on the edge you want to reach (or on a line that continues that edge beyond its endpoints). You can then rotate it back into its original orientation, again sweeping out a couple of narrow disk segments, and translate it into the desired position on the destination edge.
It's possible to construct a Kakeya needle set whose area is as small as you like!
New concept just dropped: "concept creep"
Note to self: The following generates a pretty good list of 2^10 common english words, in which I haven't found any offensive ones:
```
cat words_by_freq.txt | egrep -e '^\w{5,9}$' | head -n 1024
```
Add one more bit, though, and you get "fucking" and a couple others.
Note: It's okay to be angry! It's even okay to be guided by righteous anger! But don't mistake the feeling of righteous anger for actually being right!
People are stupid when they're angry. If someone wants you angry, there's a decent chance that it's because they want you stupid.
Awesome fact: It takes light 0.1337 seconds to travel around the earth. I will never again be a factor of 2 off on my earth-size-related fermi estimates.
I found an actual useful-to-me way to use a current-gen LLM
PSA: It has recently come to my attention that you can buy crackers that are actually made almost entirely from seeds (not just as a marketing gimmick like Mary's Gone Crackers, which are mostly rice and quinoa). They're excellent! Genuinely as-good-as-or-better-than their grain-based counterparts. I've tried two brands-Brad's Veggie Keto Crisps, and Ella's Flats-and have really enjoyed them both (I think Brad's Crisps are slightly better, though less purely seed-based since they include carrot)
Civil asset forfeiture is actually an amazing tool for people who want to commit large-scale bribery
I like understanding stuff; I like making things; I like it when people get what they want; I like it when the world doesn't end.
Joined Dec 2022
