Timeline for Moshe Rosenfeld's Salmon Problem
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 30, 2010 at 0:54 | vote | accept | Cap Khoury | ||
| Jan 21, 2010 at 2:48 | comment | added | Cap Khoury | I agree. I'm pretty sure the "center of gravity" argument can be made rigorous, but the following argument is easier (for me) to be convinced by. If on some time interval $[t_0,\infty)$ there are no deaths, then the configuration is necessarily periodic on that time interval. Since each salmon's eventual range of motion is a closed interval (not the whole circle), each individual salmon spends as much time going one way as the other. So the total amount of time spent going clockwise in one period, summed over all salmon, equals the corresponding thing for counterclockwise. | |
| Jan 20, 2010 at 22:00 | comment | added | Douglas Zare | Yes, I came up with the same basic argument. If a salmon lives forever, it has 0 average speed, but if an odd number of salmon live forever then the sum of the speeds is a nonzero constant. | |
| Jan 20, 2010 at 21:56 | comment | added | domotorp | I checked the paper and there he asks another problem. Is it possible for an odd number of salmons to survive forever? I think that this is clearly not possible as if there are an odd number of salmons then the ``center of gravity'' of the salmons must be moving clockwise or counterclockwise. But this implies that sooner or later one of the salmons must make a complete cycle and thus die. What do you think? | |
| Jan 20, 2010 at 21:14 | history | answered | Cap Khoury | CC BY-SA 2.5 |