Timeline for Does Conway's game of life admit a notion of energy?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Jul 19, 2022 at 4:54 | comment | added | Ville Salo | My reading is that they are not really making a mathematical statement about GoL, but more stating that there are no "a priori"/obvious local conservation laws. Also it seems they have only performed some simulations, so if they are making a statement, I am suspicious of it. | |
| Jul 18, 2022 at 18:55 | comment | added | I. J. Kennedy | @VilleSalo sci-hub.se/10.1038/342780a0 | |
| Jul 18, 2022 at 14:21 | comment | added | Ville Salo | I did not find it on scihub, have to retry | |
| Jul 18, 2022 at 13:16 | comment | added | Mormegil | @VilleSalo: FWIW, the Nature letter is on Sci-Hub, but I have no idea where/if the study itself was published. | |
| Jul 17, 2022 at 19:41 | comment | added | Hollis Williams | @The_Sympathizer Are you asking why Noether's theorem only applies to continuous and not discrete symmetries? | |
| Jul 17, 2022 at 11:11 | comment | added | Ville Salo | I just would've thought that's much beyond what we currently know, so I was surprised. Doesn't this rule out things like immortal creatures that survive in every context? | |
| Jul 17, 2022 at 10:25 | comment | added | Carlo Beenakker | @VilleSalo a "locally conserved functional" relates changes in that functional on some compact region to a current through the boundaries; a formal definition is in Additive conserved quantities in discrete-time lattice dynamical systems --- I do not know of a proof that the Game of Life lacks such a functional, the paper I cite in the post states this without proof. | |
| Jul 17, 2022 at 7:53 | comment | added | Carlo Beenakker | @The_Sympathizer --- indeed, the discretization is not the main obstacle to an application of Noether's theorem to the Game of LIfe, it's the absence of a Lagrangian. | |
| Jul 17, 2022 at 7:52 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
added 108 characters in body
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| Jul 17, 2022 at 7:26 | comment | added | Ville Salo | Mainly, I was wondering what "it is not possible to define a locally conserved energy functional" means exactly. | |
| Jul 17, 2022 at 7:21 | comment | added | Ville Salo | I cannot access this paper, does it contain mathematical theorems, and could you quote some relevant ones? | |
| Jul 17, 2022 at 7:15 | comment | added | The_Sympathizer | That's interesting. But the discrete-time analogue of differentiation is the finite difference. What causes a finite-difference analogue of the theorem to fail to "go through", i.e. where does an attempt to prove it in analogous fashion to the continuous case, break? | |
| Jul 17, 2022 at 7:10 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |