51–60 of 125 posts
This made me wonder if there are knots you can't untangle.
Yup, the trefoil knot is one
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.
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…
https://en.wikipedia.org/wiki/Surface_Detail
>Each chapter of the book covers one or more of the six main protagonists—Lededje Y'breq, a chattel slave; Joiler Veppers, an industrialist and playboy; Gyorni Vatueil, a soldier; Prin and Chay, Pavulean academics; and Yime Nsokyi, a Quietus agent. Some of the plot occurs in simulated environments. As the book begins, a war game—the "War in Heaven"—has been running for several decades. The outcome of the simulated war will determine whether societies are allowed to run artificial Hells, virtual afterlives in which the mind-states of the dead are tortured. The Culture, fiercely anti-Hell, has opted to stay out of the war while accepting the outcome as binding.
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..
Does it imply that some for some functions F(x) = y, you can compute x given the value of y without computing the inverse of F ?
If so, what constraints does F need to meet for this ?
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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.
You could, in principle, have a totally internal system, but with arms that grab and release the cable at intervals so that the looped portion can pass by them. You could arrange the timing so that electrical contact is never lost. But you are still making/breaking contact and it starts to lose some apparent advantages compared to a slip ring.
That's not to say it isn't still useful for some purposes, like maybe a radio antenna that isn't too impacted by a cable moving in front on occasion. But it doesn't eliminate all uses for a slip ring.
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.
#2: His point is that this could be applied compute that single rotation.
Any implications for MRI/ NMR here? The basis of arguably most pulse sequences is undoing rotation in some way, it’s not immediately obvious if this finding could provide any new refocusing sequences.
Can anyone comment on the difficulty of solving trigonometric Diophantine equations? Most of the resources I am familiar with only deal with linear or exponential versions.
Earlier quoted context omitted.
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.
Earlier quoted context omitted.
>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.
#1: BM. #2: His point is that this could be applied compute that single rotation.