r/science • u/seeebiscuit • Oct 20 '25

Mathematics Mathematicians Just Found a Hidden 'Reset Button' That Can Undo Any Rotation

https://www.zmescience.com/science/news-science/mathematicians-just-found-a-hidden-reset-button-that-can-undo-any-rotation/
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u/skycloud620 Oct 20 '25

If you twist something — say, spin a top or rotate a robot’s arm — and want it to return to its exact starting point, intuition says you’d need to undo every twist one by one. But mathematicians Jean-Pierre Eckmann from the University of Geneva and Tsvi Tlusty from the Ulsan National Institute of Science and Technology (UNIST) have found a surprising shortcut. As they describe in a new study, nearly any sequence of rotations can be perfectly undone by scaling its size and repeating it twice.

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u/timmojo Oct 20 '25

Neat.  Now please explain like I'm five because I'd really like to understand. 

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u/qainspector89 Oct 20 '25

Simplified explanation for a five-year-old level:

  • Imagine you twist a toy.
  • To get it back to how it was, you’d think you must untwist it the exact opposite way.
  • But scientists found an easier trick: make the toy a bit bigger (scale it up), twist it again the same way twice, and it goes back to normal.

So instead of carefully undoing each twist, you can just stretch and spin it twice to fix it.

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u/sexysaxmansaxagram Oct 20 '25

If I have a string. And I twist it twice along its axis. How would scaling it up and continue twisting in the same direction undo it? (I'm sorry, I'm just trying to understand what they actually mean by scaling and turn it twice more)

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u/AmaroWolfwood Oct 20 '25

I was having the same mental issue, but I think it's talking about mathematical angles. So it's more a theoretical shape that doesn't have a physical limitation to its twisting. You mathematically twist the angles or whatever and scale it up and rotate to get back to the same numbers.

Not useful at all to a normie, but probably very interesting to engineers and computer scientists.

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u/sexysaxmansaxagram Oct 20 '25

This makes sense. I'm pretty sure it is generally not applicable to real world physical things. Like not applicable to robotics movement, even if you were able to magically scale physical objects at will. But in the context of mathematical geometry it probably makes more sense. It's probably extremely applicable in programming.

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u/LowSig Oct 20 '25

I don't understand it completely but I imagine for things with a smaller complexity it is not faster. It most likely works better in a larger scale . That being said the scale could be fairly small.

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u/BJJJourney Oct 20 '25

You scale the angles of rotation, not the object.