Keenan Crane / is on Nostr

Digital Geometer, Assoc. Professor of Computer Science and Robotics at Carnegie Mellon. http://keenan.is/here

Last Notes

2025-05-29 04:07:37

Anyone interested in 3D printing some funky dice—like a "fair dragon" which can land in three different ways, or a single die equivalent to to 2D6?
We've now put printable STL files online: https://www.cs.cmu.edu/~kmcrane/Projects/RestingBodies/supplemental/dice_stl/
More info here: https://hbaktash.github.io/
https://media.mathstodon.xyz/media_attachments/files/114/589/147/448/040/306/original/a68de483631858e8.png

2025-05-22 11:19:08

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@nprofile…hr6z Embarrassingly, I didn't know about it! We are learning a lot through social media that even the reviewers didn't catch.
As noted in the paper, our model assumes zero momentum, and is really just about equilibrium under gravity. Under this assumption, the question of friction becomes secondary. Though we still empirically get good predictions, both in simulation and physically.
On the whole, my belief is that the behavior of the human roller dominates bias from any physical effect. Even for "fair" coin tosses, one finds empirically that statistics are not 50/50: https://www.scientificamerican.com/article/scientists-destroy-illusion-that-coin-toss-flips-are-50-50/#:~:text=%E2%80%9CWe%20can%20be%20quite%20sure,side%20bias%20of%2051%20percent.

2025-05-21 16:27:04

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In a nutshell, we show that the resting poses & statistics of a rigid body are easily computed from its geometry, without any dynamical simulation.
This simple geometric model enables us differentiate through dice designs, & optimize their shapes to match target statistics. 3/n
https://media.mathstodon.xyz/media_attachments/files/114/546/758/287/957/565/original/308e8dba09a1d6f7.jpg

2025-05-21 16:25:02

Fun new paper at #SIGGRAPH2025:
What if instead of two 6-sided dice, you could roll a single "funky-shaped" die that gives the same statistics (e.g, 7 is twice as likely as 4 or 10).
Or make fair dice in any shape—e.g., dragons rather than cubes?
That's exactly what we do!
https://media.mathstodon.xyz/media_attachments/files/114/546/747/517/310/915/original/ec4324b7af0a7089.jpg

2025-05-21 16:25:02

2025-03-27 11:19:03

OpenAI's new 4o image generation is pretty amazing.
It also fails on some utterly basic tasks.
Maybe a good metaphor for how easily we can be misled by algorithms based largely on fitting empirical data (i.e., machine learning) rather than deductive reasoning.
http://penrose.cs.cmu.edu
https://media.mathstodon.xyz/media_attachments/files/114/234/119/437/887/981/original/c4902de06fe04713.png

2024-11-12 11:55:33

Even though Newton's laws are deterministic, the behavior of many interacting bodies is so chaotic that it looks essentially "random."
Statistical mechanics effectively says: why bother with all those complex trajectories? Just go ahead and replace them with truly random motion.
https://media.mathstodon.xyz/media_attachments/files/113/469/849/520/077/911/original/5d04e366b2a0296b.mp4