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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...>

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@jordyd

"...now lastly, set \(x=10\), ..."

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#proofinatoot 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.

https://aiweirdness.com/post/189511103367/play-ai-dungeon-2-become-a-dragon-eat-the-moon

"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

Figures show 11,000 have left UK universities in three years since referendum

Lib Dems warn of Brexit brain drain as EU academics quit

#Universities #Brexit #LiberalDemocrats #Academics #EuropeanUnion #Education #Highereducation #Politics #UKnews #Worldnews

Lib Dems warn of Brexit brain drain as EU academics quit

#Universities #Brexit #LiberalDemocrats #Academics #EuropeanUnion #Education #Highereducation #Politics #UKnews #Worldnews

Anyone else on mathstodon doing #AdventOfCode? 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: https://boingboing.net/2019/11/24/bechdelgrams-are-beautiful.html

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?

New blog post: Reconfiguring 3-colorings, https://11011110.github.io/blog/2019/11/25/reconfiguring-3-colorings.html

Great insight, does your website fit on a floppy disk? 💾

https://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! http://chalkdustmagazine.com/features/the-perils-of-p-values/

Ohhhh, Minesweeper has been fixed: https://pwmarcz.pl/kaboom/

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?

https://www.youtube.com/watch?v=6_yU9eJ0NxA

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

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

https://www.hambrecht.ch/blog/2017/7/26/the-quest-for-the-lost-quadrilateral

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" (https://nebusresearch.wordpress.com/2019/10/24/my-2019-mathematics-a-to-z-platonic/) @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 https://en.wikipedia.org/wiki/Thomson_problem they form a square antiprism instead.

Combinatorist (esp. graph theorist) turned Data Scientist

Joined Jun 2017