4 ms·

Here's a short article that gave me some insight into the matter: https://nautil.us/blog/the-strange-numbers-that-birthed-modern-algebra https://nautil.us/blog

Here's a short article that gave me some insight into the matter: https://nautil.us/blog/the-strange-numbers-that-birthed-modern-algebra https://nautil.us/blog/the-strange-numbers-that-birthed-mode... "Place your phone face-up on a flat surface, for example. Spin it 90 degrees to the left, and then flip it away from you. Note which way the camera points. Returning to the original position, flip it away from you first and then turn it to the left second. See how the camera points to the right instead? This initially alarming property, known as non-commutativity, turns out to be a feature the quaternions share with reality "

dhosek 5y ago
It's worth noting that one of the early finite groups that is taught in abstract algebra are the dihedral groups which model exactly this sort of behavior (For your phone example this would be D₄. Knowing that mattress flipping is modeled with D₂ makes it trivial to prove that that there is no combination of flip and rotate that will allow you to always do the same move to your mattress to get it into the four possible positions for optimal wear.
- galaxyLogic 5y ago
  Interesting Applied Mathematics