How does this help solve a rubix cube?
Mathematicians have found a hidden 'reset button' for undoing rotation
111–120 of 125 posts
Re: Mathematicians have found a hidden 'reset button' for undoing rotation
#112Earlier quoted context omitted.
Not talking about thermodynamics here. The discovery referenced in this article also does not solve for thermodynamics or entropy. And yes, you're right, the article does mention this later. I'm still bothered by the sensationalized introduction and title.
> Not talking about thermodynamics here. My mistake, you said "Classical Mechanics", so I took it as such. But thermodynamics is not required either. Chaos theory would be of important note here. Take the double pendulum for example. It is a chaotic function because unless you have the initial state you cannot make accurate predictions as to its forward time evolution. This is a deterministic system because there is…
Sorry, with all due respect, I'm not "throwing out" thermodynamics. It's just not relevant to the discovery referenced in the article, which is only concerned with classical mechanics. Thermodynamics is not part of the theory of classical mechanics. I think perhaps you are confusing classical mechanics with classical physics.
Re: Mathematicians have found a hidden 'reset button' for undoing rotation
#113Earlier quoted context omitted.
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...
Thanks for sharing. I'm very familiar with the basic mechanics of quaternion rotation, and I've been interested in a deeper understanding of this double-cover concept, but I just don't get it. I've seen the belt trick and it feels more like an illusion than an illustration of some deep truth. I like how you've connected it to spin, but I still don't understand how that is a real physical property rather than a mathem…
That look is not that different. I bring attention to the fact that a product of quaternions all close to 1 can be close to -1, which correspond to a 2pi rotation too. This fact is a bit simpler to grasp than a topological explanation, where you consider a topology on the space of all rotations and show that some paths that correspond to 2pi rotation are different than the others. There are multiple youtube videos explaining the topological argument, see, e.g., this one https://www.youtube.com/watch?v=ACZC_XEyg9U.
The topological argument gives a larger picture and probably better understanding, but it is definitely harder.
Re: Mathematicians have found a hidden 'reset button' for undoing rotation
#114This article leads to a paywall where I am, making it of no use. Perhaps someone else has done a better job of summarizing the paper elsewhere, and that should be posted instead?
Re: Mathematicians have found a hidden 'reset button' for undoing rotation
#115For 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've been doing this for New Scientist and a few other magazines and there's always a few articles that I have found interesting that don't make it to hacker news (the whole magazine with ads comes digitally), though many of the pieces are very short half page articles that mention something new that one has to follow up on one's own for detailed information and there's regular columns like book reviews. This magazin…
I got an iPad many years ago from my employer. I literally only use it for libby :-)
Re: Mathematicians have found a hidden 'reset button' for undoing rotation
#116Earlier quoted context omitted.
> Not talking about thermodynamics here. My mistake, you said "Classical Mechanics", so I took it as such. But thermodynamics is not required either. Chaos theory would be of important note here. Take the double pendulum for example. It is a chaotic function because unless you have the initial state you cannot make accurate predictions as to its forward time evolution. This is a deterministic system because there is…
Sorry, with all due respect, I'm not "throwing out" thermodynamics. It's just not relevant to the discovery referenced in the article, which is only concerned with classical mechanics. Thermodynamics is not part of the theory of classical mechanics. I think perhaps you are confusing classical mechanics with classical physics.
https://en.wikipedia.org/wiki/Classical_mechanics
See the beginning and the Limits of Validity section. It's "classical mechanics", "quantum", and "relativity".
Thermaldynamics can overlap with quantum but there is a classical regime. Which, let's be clear
Re: Mathematicians have found a hidden 'reset button' for undoing rotation
#117Earlier quoted context omitted.
As meindnoch points out, the connection needs to loop over the rotating object. That is no problem if the only affect of the rotation that interests you is the centrifugal force. When you give plasma (not whole blood) the nurses use a centrifuge machine that seems impossible: one tube goes from you to it (carrying whole blood), another tube goes from it back to you (carrying plasma depleted blood). The mechanism of D…
What a fascinating project. It looks a real labor of love, and I wish I understood it more deeply. I've been making my own visualization sandboxes like this to explore configuration spaces and groups - but for much simpler, more intuitive physical systems. I went down a few rabbit holes on the site - is this program also written in Basic?
Yes, specifically the PowerBasic console compiler version 4 (later versions don’t do animation nearly as well). The PowerBasic compilers are no longer being sold and the company appears to be defunct. Anyway, you can do a lot with a good BASIC compiler.
Re: Mathematicians have found a hidden 'reset button' for undoing rotation
#118Quaternion libraries have work to do now. 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 cou…
Please don't use ChatGPT to advertise your GitHub repositories. As other commenters have noted, this comment doesn't really make sense: it's not a good contribution to the discussion, and it's spam.
Re: Mathematicians have found a hidden 'reset button' for undoing rotation
#119Earlier quoted context omitted.
1 - A copy of me is not me. 2 - There might be a form of hubris in thinking that replicating a conscious person by copying all their neurotransmitters is enough to have a continuity between the original and the copy. It can be easily evidenced if you consider that the people who tend to believe this, will have a level of granularity in their beliefs that depend on their era and their own knowledge, so maybe a century…
> enough to have a continuity Who said continuity mattered? How would a copy or original know which they were? Does it even matter? How would you even know you were in a simulation? We seemingly don't have the tools to know. Whatever the case, if you're the copy in the hell simulator getting thrown into the meat grinder, I don't really think the distinction of "original vs copy" is the most pressing issue. > while ma…
> Who said continuity mattered? How would a copy or original know which they were? Does it even matter?
Continuity matters because I do not care if this imaginary (digital or physically reconstructed) artifact you came up with sometime in the future lives in a simulation of (your understanding of) my real life or in Sim city.
This thing is not "me", and I was replying to your assertion that
> Maybe it'll be eternal heaven - just gifted to us without reason or cause
This is not "us". This hypothetical is just a bunch of Sims characters running around in some virtual universe.
Re: Mathematicians have found a hidden 'reset button' for undoing rotation
#120Earlier quoted context omitted.
Thanks for sharing. I'm very familiar with the basic mechanics of quaternion rotation, and I've been interested in a deeper understanding of this double-cover concept, but I just don't get it. I've seen the belt trick and it feels more like an illusion than an illustration of some deep truth. I like how you've connected it to spin, but I still don't understand how that is a real physical property rather than a mathem…
That look is not that different. I bring attention to the fact that a product of quaternions all close to 1 can be close to -1, which correspond to a 2pi rotation too. This fact is a bit simpler to grasp than a topological explanation, where you consider a topology on the space of all rotations and show that some paths that correspond to 2pi rotation are different than the others. There are multiple youtube videos ex…
I see, thanks. Sounds like I was overthinking it.