Craig S. Kaplan

Mathematics, Computer Science, Art, Design, Music, Soup, Pedantry. he/him/anything

Last Notes

2026-03-23 01:25:57 UTC

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@nprofile…yxlh The video won’t play for me, but that looks like Arthur Ganson’s “Machine with 27 scraps of paper”, which has long been a favourite of mine.

2026-03-03 02:07:05 UTC

In my online undergraduate P5.js course, students are about to begin the module on motion and physics, including a bit of physics simulation using Matter.js. It suddenly occurred to me that I had never seen anybody put together this particular demo before, and I realized it had to be done. Messy source code at https://editor.p5js.org/isohedral/full/vJa5RiZWs.
https://media.mathstodon.xyz/media_attachments/files/116/162/786/689/835/359/original/62d579f72469c1d2.mp4

2026-01-29 18:08:12 UTC

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@nprofile…yxlh Yes, the notation is hard to beat! The trouble tends to come in the implementation, where a naive representation of geometric objects tends to require an exponential number of coefficients. I assume there's some nice research to be done in compilation methods for GA that perform static type inference on the objects being processed (which are usually quite tame) and emit efficient code. I haven't looked too hard to see what's already been done in this context.

2026-01-22 16:35:48 UTC

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@nprofile…jydu Brian Wyvill wrote a fun paper about drawing pictures based on the Gosper curve: https://webhome.cs.uvic.ca/~blob/publications/flowpaint.pdf.

2026-01-22 01:52:17 UTC

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@nprofile…zl3j That's just about perfect, thanks.

2025-12-21 16:32:54 UTC

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@nprofile…l4xy Well, I mean, I'm the site owner, and I can tell you that I didn't configure this message and have never seen it before. Presumably it's baked into our provider's web server. I suppose I could... just follow their instructions, and send them the request ID...

2025-12-21 02:40:18 UTC

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@nprofile…l4xy Weird. it's working for me, and I've never seen that error before. Are you using anything unusual in terms of browser / OS / extensions?

2025-11-11 13:44:12 UTC

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@nprofile…u6hy I talk about a few variations of Kepler’s tiling in an old Bridges paper. https://archive.bridgesmathart.org/2006/bridges2006-465.pdf

2025-10-12 20:38:56 UTC

The delusion that we can advance AI to the point where it rescues us from the mess we’ve created for ourselves is pure millenarianism. The CEOs of the big AI companies are a cult who believe that if they pray hard enough, AI Jesus will come down and grant us infinite abundance and prosperity.

2025-08-24 02:30:40 UTC

Over the summer I thought a bit about a few 2D geometric problems that I hadn't seen before. Here's the first one.
Let 𝑃 and 𝑄 be 2D points and let 𝑛 be an integer ≥ 3.
Let 𝑆 be a shape (say, a topological disk) with 𝑛-fold rotational symmetry, and place two non-overlapping copies of 𝑆 in the plane, one centred on 𝑃 and the other centred on 𝑄. The copies may be rotated and/or reflected differently from each other.
What shape 𝑆 should I choose, and how should I orient the two copies, so as to maximize the area of 𝑆?
I'm assuming the answer is two congruent regular 𝑛-gons, each with an edge on the perpendicular bisector of 𝑃𝑄. But I'm not sure I have a convincing proof of that fact.

2025-08-13 15:04:09 UTC

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@nprofile…yu7x @nprofile…svv0 I just read it yesterday. The ideas are lovely, though unfortunately I still struggle mightily with the discrete exterior calculus and discrete differential geometry that powers this work (and so much other beautiful contemporary research in computer graphics).

2025-07-28 14:11:04 UTC

My son informed me of a phenomenon that's well known among D&D players: a D12 (dodecahedron) rolls much farther than a D20 (icosahedron). Is there an obvious reason why this should be? I can imagine a couple of possibilities, but I wouldn't know how to verify them.
(I suppose I should tag @nprofile…dcr8, given his recent work on the physics of rolling dice.)

2025-07-26 14:43:16 UTC

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@nprofile…yu7x Dave Swart wrote a nice survey of symmetries of soccer balls: https://archive.bridgesmathart.org/2015/bridges2015-151.pdf. Mind you, a lot of the designs in that paper acquire their exotic symmetries through graphics printed on a standard 32-panel ball.
If you want balls on the far more experimental side, check out the beautiful work of Jon-Paul Wheatley, e.g., https://12p.com/pages/lab, https://www.instagram.com/jonpaulsballs. Of course, there's one design of his that I'm particularly attached to: https://12p.com/pages/the-hat-trick.

2025-07-20 16:31:56 UTC

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@nprofile…fa4k OK, sure, not actually a glitch, but from a typical zoom level it looks like there are some weird black pixels in the middle of nowhere. I had to zoom in to see what was clearly going to be a place with an interesting history.
https://media.mathstodon.xyz/media_attachments/files/114/886/510/137/788/705/original/3779bcb68743b74d.png

2025-07-20 07:44:56 UTC

In planning my travels around The Netherlands, I noticed a funny glitch on Google Maps near the souther border. It turns out that the town of Baarle-Nassau has 22 "holes" in it, self-contained enclaves belonging to Belgium (in which the town is called Baarle-Hertog). And more deliciously, a couple of them contain "counter-enclaves" that are Dutch again! I'm sure many people have seen this before, but it was new to me. https://en.wikipedia.org/wiki/Baarle-Nassau

2025-06-18 21:54:40 UTC

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@nprofile…saev Years ago I saw a similar error in an exhibit at the British Museum. I contacted them to point out the problem. They weren’t particularly concerned.

2025-02-28 13:10:04 UTC

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@nprofile…fa4k This reminds me of a rather nice piece of installation art from 2013, in which (from a mathematical viewpoint) a film sequence is projected onto the subspace spanned by a set of frames from another film. It’s titled “Theorem 8”, presumably based on whatever textbook the artist used as a reference. http://theorem8.concept-script.com/