Pinned toot

Anyone hear of this before, or can find something about it? It seemed kinda cool at the time, and I like this axiomatization.

Pinned toot

Background: A finite projective plane has point-line duality, and affine planes lack it. You can get a projective plane by adding a "line at infinity," and this is reversible.

Years ago I stumbled across this in constructing a counterexample to a graph conjecture, and I never found out if it was something people had realized or used before:
We can also recover point-line duality from an affine plane by just deleting one of the parallel classes of lines. <cont...>

Pinned toot
Pinned toot

that if a finite poset has a unique maximal $$x$$, then $$x$$ is maximum.

If not, there is a $$y_1||x$$. $$y_1$$ is not maximal, so there is $$y_2>y_1$$; we cannot have $$y_2<x$$, else transitivity would give $$y_1<x$$, and we cannot have $$y_2>x$$ because $$x$$ is maximal, so $$y_2||x$$. Continuing, we build a chain $$y_1<y_2<\dotsb$$ (with $$y_i||x$$ for all $$i$$), contradicting finiteness.

(This proof also suggests a construction of an infinite poset without the property.)

You MUST play AI Dungeon 2, a text adventure game run by a neural net.

@nickwalton00 built it using @OpenAI's huge GPT-2-1.5B model, and it will respond reasonably to just about anything you try. Such as eating the moon.

aiweirdness.com/post/189511103

"Can you throw the bones for me?" the young woman asked.
"What is your concern?" said the witch.
"I don't fit."
A common concern among the young, but... The witch threw the bones and read them. "You must change, to stay who you are."
"Who I... " The young man blinked. "Oh!"
#MicroFiction #TootFic #SmallStories

non mathematicians: i hate math because i hate numbers

me, a mathematician: what the frick is a number

Anyone else on mathstodon doing ? If there's enough of us, would it be worth setting up a private leaderboard?

I've been playing "binary sudoku". You have a 2nx2n grid, with some 0s and 1s and you have to fill it in according to some rules:
* each row and column has equal number of 0s and 1s
* no row or column has a run of three 0s or 1s
* no pair of rows is the same
* no pair of columns is the same

conjecture: there must be a pair of rows (or columns) that are "inverse" i.e. a pair of strings s t where s[i]=/=t[i] for all i.

I can see a boring case analysis proof but is there an "at a glance" proof?

Bechdelgrams illustrate of whether a movie passes the Bechdel test: boingboing.net/2019/11/24/bech

A nice use of color to highlight the information you're looking for in a social network: Here, the network consists of interactions between characters in a film, and the women and conversations not about men are given distinctive colors to show the test criteria: does the film have at least two named female characters, who speak to each other, about something other than men?

Great insight, does your website fit on a floppy disk? 💾
fitonafloppy.website
Mine doesn't (yet), not sure how to cut back on size on @GoHugoIO@twitter.com w/ academic theme What is a p value? And what's wrong with them? @david_colquhoun explained all in issue 02! chalkdustmagazine.com/features

Probing some mathematical minds here: how novel is this way of solving a general quadratic equation $$x^2 + Bx + C = 0$$? Kinda looks like a corollary of "completing the square", or am I mistaken?

3blue1brown on numberphile, with a dart game that connects to (spoiler, but it's in the title too) higher dimensions:

Sunday Blitz Riddle Part 1:
For each real number $$a$$, is there $$b \neq 0$$, such that $$\sin(ab) = \sin(a) \sin(b)$$ ?

Somebody at day-job dressed as Ruth Vader Ginsburg.

Lorenzo found his friend crying.
The mathematician sniffled. "I made this sequence of numbers but I worry they aren't useful."
Lorenzo patted his shoulder. "Don't cry. I'm sure they're more than the sum of their parts."
Fibonacci wailed.

Costume victory: One daughter is the Lunar Lander, one an astronaut. This makes me giddy. I hope their candy sample return containers overflow.

imgur.com/gallery/ojqvVeY#K7IE

I'm sure many of you have seen this, it's a couple of years old - there's a sort of lattice of quadrilaterals (a square is a rectangle is a parallelogram etc) but it's a bit ugly if you stick to standard named ones. Here a "kitoid" is introduced to make a really beautiful diagram

hambrecht.ch/blog/2017/7/26/th

But it got me thinking, is there any well defined sense in which these categories are exhaustive (for convex quads)? And if so how many are there for n-gons

In his latest alphabet entry "Platonic" (nebusresearch.wordpress.com/20) @nebusj writes that "it was obvious" that eight equal charged particles free to move on a sphere would space themselves out into the vertices of a cube. But sadly, in this case, the obvious is false. According to en.wikipedia.org/wiki/Thomson_ they form a square antiprism instead. A Mastodon instance for maths people. The kind of people who make $$\pi z^2 \times a$$ jokes. Use $$ and $$ for inline LaTeX, and $ and $ for display mode.