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I'm an analysis person which means that I believe inequalities > equalities (up to a constant factor that's independent of the particular inequality concerned)

(the problem I ran into is that noteheads constantly stray outside the staves by varying amounts, so if I wanted to avoid lopping off too many notes I'd have to crop by hand, and in any case the cropped rectangles wouldn't all have the same height)

an idea I had for a project that never panned out: start with some (digital) sheet music; crop out the individual staves and concatenate them end-to-end in order, giving a long continuous strip of music; then apply a conformal equivalence that maps the *infinite* horizontal strip {0 < Im z < 1} to the unit disc. You'd get a circular image (less a bit, corresponding to the fact that the starting strip wasn't infinite) with, say, the entire violin I part for Mahler 6 compressed into it

imo the notation around set differences should be X ∖ Y for Y ⊂ X and X - x for x ∈ X, because X ∖ {x} and X - {x} are terrible

oh, this is neat. Radon's theorem: a set of d + 2 points in ℝᵈ can be partitioned into two disjoint subsets whose convex hulls intersect. used to prove a couple other intriguing results about convexity in Euclidean spaces

hexbienium boosted
hexbienium boosted

using weighted markov chains to generate nonsensical alignment charts with corpora project data

this... was not what I was supposed to be working on today.

shout-out to Élie Cartan for the whole differential forms thing

I wonder whether any performances of Beethoven 9 since the mid-20th century have updated the text to "seid umschlungen, Billionen"

how I "read" German poetry: eyes tennis-balling back and forth between the original and an English translation; constantly surprised by what's elided (verbs, cases); "this word sounds exactly like 1000 other German words"; mostly just appreciating the meter and rhyme tbh

one of these days my mathematical knowledge will catch up with the state of the art at the beginning of the 20th century...

smooth jazz, piecewise-linear jazz, topological jazz

smooth collie, piecewise-linear collie, topological collie

on this day in 1665: Samuel Pepys's work habits are criticized by a guy named Mr. Hater

Poll: Majority of Americans Disapprove of Path-Connectedness

(a2ps on an empty file followed by ps2pdf worked)

spent 15 minutes earlier today trying to create a blank PDF file, folks

woah: "In the p-adic integers, congruences are approximations: for a and b in Zₚ, a ≡ b mod pⁿ is the same as |a−b|ₚ ≤ 1/pⁿ. Turning information modulo one power of p
into similar information modulo a higher power of p can be interpreted as improving an approximation."

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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.