Timeline for The advantage of asymmetric objects
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Jul 1, 2022 at 21:06 | review | Close votes | |||
| Jul 3, 2022 at 5:52 | |||||
| Jul 1, 2022 at 18:47 | answer | added | Vladimir Dotsenko | timeline score: 3 | |
| Jul 1, 2022 at 17:43 | comment | added | Maxime Ramzi | When an object has no automorphism, it is typically quite simple to prove that some other object is isomorphic to it (if it is, of course): there is only one possible choice of isomorphism, so you can't go wrong ! In another direction, bundles of objects with no automorphisms are trivial - for instance any manifold is $\mathbb Z/2$-orientable | |
| Jul 1, 2022 at 16:15 | history | edited | Glorfindel | CC BY-SA 4.0 |
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| Jul 1, 2022 at 4:21 | comment | added | Michael Engelhardt | @LSpice - At its core, I think all that was meant was that the symmetrized object does not reveal what the symmetry does, being invariant under the symmetry. You have to pick a representative to see it. Simple as that is, it can take interesting guises. E.g., the most direct understanding of the rotating rigid body is in the body-fixed frame; viscerally, you have to get on the merry-go-round to fully experience it. In a gauge theory, physical degrees of freedom only become evident upon fixing a gauge (e.g., the Coulomb gauge in classical electrodynamics, which renders the waves transverse). | |
| Jul 1, 2022 at 1:48 | comment | added | LSpice | @MichaelEngelhardt, do you have any interesting examples of putting that aphorism into practice? (I suspect my thoughts on it are shallower than those of someone who thinks about it professionally, so I'd like to hear yours!) | |
| Jul 1, 2022 at 1:13 | comment | added | Michael Engelhardt | One of the aphorisms I remember from one of my mentors is, "Everything we've ever learned about symmetries we learned by breaking them. Think about it." | |
| Jul 1, 2022 at 0:42 | history | became hot network question | |||
| Jul 1, 2022 at 0:40 | history | edited | Veronica Phan | CC BY-SA 4.0 |
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| Jul 1, 2022 at 0:17 | comment | added | LSpice | Asymmetric objects in your sense are often called rigid. One nice (almost-)example is algebraic tori, which have no connected algebraic group of automorphisms. | |
| Jun 30, 2022 at 23:33 | answer | added | Timothy Chow | timeline score: 12 | |
| Jun 30, 2022 at 17:23 | answer | added | Peter LeFanu Lumsdaine | timeline score: 22 | |
| Jun 30, 2022 at 16:42 | history | asked | Veronica Phan | CC BY-SA 4.0 |