31–40 of 125 posts
Doesn’t this sound like a sneaky way for a mathematician to work on time travel?
Baby steps, first is the roulette table.
I've been trying to understand as much of "maths" as I can (now enough to write that in quotes, as there isn't a "single" maths) and still a layman, I love reading about discoveries like these, and the fact that you still can have discoveries in things thought to be so fundamental..
Neat factoid: there is something special about rotations in 3D. They are not "simply-connected", which means that there are 2 distinct classes of rotations. And this property is deeply important in quantum physics.
Positive potential:
Simplified “undo” mechanism: this result suggests that a given traversal (sequence of rotations) might be “reset” (i.e., returned to origin) using a simpler method than computing a full inverse sequence. That could simplify any functionality in libraries, like SpinStep[0], that deal with “returning to base orientation” or “undoing steps.”
The libraries could include a method: given a sequence of quaternion steps that moved from orientation A to orientation B, compute a scale factor λ and then apply that scaled sequence twice to go from B back to A (or A to A). This offers a deterministic “reset” style operation which may be efficient.
Orientation‐graph algorithms: in libraries used in robotics/spatial AI, the ability to reliably reset orientation (even after complex sequences) might enhance reliability of traversal or recovery in systems that might drift or go off‐course.
Earlier quoted context omitted.
Neat factoid: there is something special about rotations in 3D. They are not "simply-connected", which means that there are 2 distinct classes of rotations. And this property is deeply important in quantum physics.
It's a bit more complicated than "2 classes of rotations", though there is magic indeed. I've tried to explain it in this post https://dandanua.github.io/2021/08/23/the-spin-of-a-human-bo...
Unfortunately this subject is above my pay grade, so I gave up :)
I was immediately reminded of the anti-twist mechanism, perhaps unrelated but "reset rotation, twice/half" comes up there as well. https://en.wikipedia.org/wiki/Anti-twister_mechanism
For those who struggle with the pay wall: check your local library's (online) membership, it might come with the worldwide library card, which might include the New Scientist magazine. Mine does, and therefore I can "borrow" (read for free) articles that make it to the mag.
I was immediately reminded of the anti-twist mechanism, perhaps unrelated but "reset rotation, twice/half" comes up there as well. https://en.wikipedia.org/wiki/Anti-twister_mechanism
What?! Thank you! I'm working on a robot with a very expensive slip ring, and need to send high fidelity data through it with shielding. I had no idea this was possible this will make things so much easier! I found a related video you might find interesting. https://www.youtube.com/watch?v=gZvimEf6DFw I'm currently studying group theory and SO3 rotations (quaternions & matrix groups) and I'm also curious about the co…
I was immediately reminded of the anti-twist mechanism, perhaps unrelated but "reset rotation, twice/half" comes up there as well. https://en.wikipedia.org/wiki/Anti-twister_mechanism
What?! Thank you! I'm working on a robot with a very expensive slip ring, and need to send high fidelity data through it with shielding. I had no idea this was possible this will make things so much easier! I found a related video you might find interesting. https://www.youtube.com/watch?v=gZvimEf6DFw I'm currently studying group theory and SO3 rotations (quaternions & matrix groups) and I'm also curious about the co…
For those who struggle with the pay wall: check your local library's (online) membership, it might come with the worldwide library card, which might include the New Scientist magazine. Mine does, and therefore I can "borrow" (read for free) articles that make it to the mag.