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Mathematicians have found a hidden 'reset button' for undoing rotation

newscientist.com

41–50 of 125 posts

Re: Mathematicians have found a hidden 'reset button' for undoing rotation

#41

Doesn’t this sound like a sneaky way for a mathematician to work on time travel?

In Ernst Mach's Opera Omnia, his Principia had a `gedenken experiment' visiting a related question about angular inertia, as an affection of all the matter in the universe and its simultaneity with local causation. He inferred by simile of unwinding the trajectory of a toy spinning top on the possibility of reversing the arrow of time.

Re: Mathematicians have found a hidden 'reset button' for undoing rotation

#42
post #19

Earlier quoted context omitted.

Baby steps, first is the roulette table.

Kardashev Type III civilization: Reverse the light cone, resimulate all moments of the past down to the neurotransmitter level. The thoughts, feelings, and memories locked inside your head. From Neanderthal to Shakespeare to you, we could bring back everyone who has ever lived and put them in a theme park without any of them ever even knowing. Some simulation instances might be completely accurate. For historians or…

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 ago you'd think copying the nerve/neuron arrangement would be enough, and a few decades later someone would've said that you need the exact arrangement of molecules or atoms, while maybe in 2025 we'd be thinking in terms of electron clouds or quarks.

But to think that today we have finally arrived at a complete and final understanding of the basic blocks and surely, there is no possible finer understanding that would make our current view quaint in the eyes of a person from 2085 is the hubris I'm talking about.

Re: Mathematicians have found a hidden 'reset button' for undoing rotation

#43
post #7

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…

There's a bit of a caveat with the anti-twister mechanism, namely, that the wiring must be loose enough to pass around the supplied rotating part.

Re: Mathematicians have found a hidden 'reset button' for undoing rotation

#44
post #21

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.

If you use an ad blocker, just disable inline scripts

Or, you know, you could use a mechanism that actually guarantees them some revenue and doesn't just burn the publication to the ground because you feel entitled to free access.

Re: Mathematicians have found a hidden 'reset button' for undoing rotation

#45
post #19

Earlier quoted context omitted.

Kardashev Type III civilization: Reverse the light cone, resimulate all moments of the past down to the neurotransmitter level. The thoughts, feelings, and memories locked inside your head. From Neanderthal to Shakespeare to you, we could bring back everyone who has ever lived and put them in a theme park without any of them ever even knowing. Some simulation instances might be completely accurate. For historians or…

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 maybe in 2025 we'd be thinking in terms of electron clouds or quarks.

We can't fathom what level of control over the physical world an advanced intelligence might have. Maybe they can create entire universes. Maybe there are structures and dimensions beyond our understanding. I don't know and can't reason about them, but I'm willing to prescribe them god powers on account of the fact I have no idea.

Maybe our logic and intuition, tools like Occam's Razor, are fixed to an artificial distribution of event occurrences that is entirely constructed. Perhaps not unlike the fundamental constants of the universe. We wouldn't know any differently.

None of this is not measurable. Indistinguishable from fantasy.

Re: Mathematicians have found a hidden 'reset button' for undoing rotation

#47
This article is written in a very annoying and misleading way. The discovery is not that rotation can be "reset". That is obvious and not surprising at all. Physical systems governed by classical mechanics are reversible just by perfectly inverting all forces, velocities, and rotations. The actual discovery is the shortcut to the original position without the need to perfectly inverse the full sequence of rotations.

Re: Mathematicians have found a hidden 'reset button' for undoing rotation

#48

Quaternion 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…

I must be missing something major here, but given a sequence of rotations combined into a quaternion orientation, can’t you just get the inverse rotation back to the original orientation by inverting the quaternion?

Re: Mathematicians have found a hidden 'reset button' for undoing rotation

#49

Quaternion 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…

>using a simpler method than computing a full inverse sequence

What are you even talking about? Rotations form a group. Any orientation "A" can be reached from any other orientation "B" with a single rotation. It's an O(1) operation. Always has been. What you wrote makes no sense whatsoever.

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