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Scoopert!
(31 Aug at 22:34) |
OK! I am better now. Let's strive to keep it that way.
I spent my free time this month continuing work on the proof described in the previous post, basically a big custom numerical search which was a neat blend of geometry (a little bit outside my comfort zone but I can wrap my head around it) and high-performance systems stuff (rational interval arithmetic) which is up my alley. It was actually going quite well (and maybe we will try to finish it, or an improvement upon it) but a couple days ago we found out that somebody beat us to it! A convex polyhedron without Rupert's property just went up on arxiv.org last week, and it demonstrates a synthetic convex polyhedron that is not Rupert (cannot fit through a proper hole in itself). Ah! I proved plenty of things for my Ph.D., but nothing that anybody but me cared about, so I was getting fond of the idea that we might crack an open problem. But at the same time I am happy for the authors (they emailed me about my paper in April; I probably should have written back! Do you know how bad I am at e-mail? If you have ever e-mailed me then you probably do know!) and happy that we have a resolution to this problem.
The other thing I'm happy about is that I finally know how the video ends (😵💫 but 😂) and I feel motivated to finish it forthwith. It's up to 45 minutes now, but the end is in sight! I'm in the phase now where even my procrastination is high-productivity (e.g. I have been repointing and repainting my house) instead of something like anxiously reformatting source code, so that is a good sign.
While I was sick I started DOOM: The Dark Ages, which is pretty fun. They did a good job with the combat, which is good because that's all there is, and it is quite hard (mostly fair). It's incredible how incoherent the "plot" is, though, almost like it's satire. I also played through Shantae and the Seven Sirens. It is very silly, as expected, but has great music and the writing was pretty funny. I've liked all the Shantae games that I've played, but this one was not my favorite; I think just too much of it took place inside underwater tunnels for my tastes. |  |
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| It was a smart move to construct a provably non-Rupert polyhedron, but I still wonder whether the rhombicosidodecahedron is a Nopert. Either way, I'm dying to watch the video. And oh boy, 45 minutes! That's longer than ARST ARSW. Thank you Tom! |
Silksong tomorrow!
Hyped for the view video also hehe |
I'm glad the idea of a long video appeals to some, since I'm up to an hour now!
Getting very close. I'm not allowed to play Silksong until it's done, but my workaround has been to play Spelunky 2. :) |
Your blog homepage appears to be broken. It spends a suspiciously long time loading, and then the following error message appears underneath the navbar:
[an error occurred while processing this directive] |
| Oh hey, I got an error when I tried to post that comment. Now half a day later, reloading this browser tab posted the comment. The website is working just fine with no issues now, so false alarm I guess. |
Tom7 released a new video "https://www.youtube.com/watch?v=QH4MviUE0_s" . This is connected to the research described in the SIGBOVIK 2025 article about Rupert property of polyhedrons, but talks about some progress after the publication of the video.
You refer to the unit ball and unit cube. As a historical note, the definitions of these were standardized by the ICFP contest 2000 task specification "https://www.cs.cornell.edu/icfp/task.htm#sec:prim-objects" . POV-Ray does not consider the unit ball or unit cube particularly important. The POV-Ray function to create a sphere "https://www.povray.org/documentation/3.7.0/r3_4.html#r3_4_5_1_12" is parametrized by the center and radius of the ball, and the function to create a cube "https://www.povray.org/documentation/3.7.0/r3_4.html#r3_4_5_1_2" actually makes a cuboid with edges aligned with the coordinate system but is parametrized by two opposite corners of the cuboid.
I don't like the animation near "https://youtu.be/QH4MviUE0_s?t=2846". The order that you uncover the text seems unnatural.
For the hard polyhedrons, you split the parameter space according to which vertexes of the inner and outer polyhedron are on the convex hull of the projection. I wonder why you don't also assume that two vertexes of the hull of the projected inner polyhedron are on two different sides of the perimiter of the projected outer polyhedron. If there's a solution then there's always a solution of that form. Split the parameter space according to which two vertexes of the inner polyhedron touch the perimeter, and probably also according to which two edges of the outer polyhedron they touch. This would let you eliminate two of the seven real degrees of freedom, because the translation of the two polygons would be uniquely determined. This should work for any convex polyhedron, not
I have received an email reply from Tom, so I can testify that he is not completely bad at email.
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Hi Tom, this is a mostly unrelated question and you might have covered this before but I really want to ask -
How do you do the animated MSPaint(ish) drawings that appear in your videos? I've been trying to work it out.
On the one hand it doesn't seem like it could be an actual recording of the drawing process because they are drawn in a very unnatural way - blocking in colours before linework, random splodges of colour appearing that later turn out to be a small part of a face, etc.
On the other hand it also seems to have some artefacts in the animation that seem like they couldn't have been generated from a static final images - areas that get overdrawn or redrawn. |
| Thanks Tom this was a very dramatic video, respect |
Eli: I noticed this too, while deep in the guts of my video editing, which is the worst time to have a computer emergency. In case anyone is interested, it was a true "straw that broke the camel's back" scenario where a 20 year-old bug finally caused my server to regularly run out of memory and OOM-loop. I had been looking for obscure memory or resource leaks for years, but the bug turned out to be trivial: I didn't know this but shell scripts do not forward SIGTERM to their child processes! So when apache2 would helpfully recycle my processes to prevent memory leaks etc., it was actually just making them into zombies and filling up my poor server's meager RAM. The fix was just to "exec" the binary from the shell script. OMG.
Jonas: I wonder if I subconsciously remember that from the ICFP 2000 task! I fondly remember participating in that one as an undergrad.
> I don't like the animation near
Yeah. I recorded myself hand-lettering that section and gave myself hand cramps, but when I looked at the video I was capturing the wrong window the whole time. So I had to fake it with the auto-animate program. I am aware it looks silly but I thought maybe it would at least be amusingly silly.
Snapping vertices to edges: We did contemplate this kind of thing. It makes sense, although it also adds a significant proof obligation (and we're already pushing it) to show that this search strategy would be complete. The main thing is that this kind of geometric reasoning is hard to do when the hulls are not concrete (because the endpoints are intervals). Or rather: You can do it but without additional care to avoid the dependency problem, it often ends up being counterproductive.
Anonymous: Some of the drawings are screen captured from Photoshop, but I think you're asking about the automatic ones. This is software I wrote (technically part of BoVeX) to create a video from a final image. Mainly I don't want people to have to stare at a static image when the voiceover is more than a few seconds. You have a keen eye: It does draw over areas. This is because it first heuristically creates layers from the final image as part of its plan. It then simplifies them to create color blobs from disconnected pieces, or keeps the pen down when it's moving—as long as it knows that it will be inked over later. I agree that it often still looks unnatural... every time I use it I add some more tweaks!
Thanks Nels! |
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