Timeline for An asymptotic expression for the solution to the squares problem suggested by statistical mechanics
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 11, 2010 at 17:27 | comment | added | fedja | At Michael: If you change it to "diatribe about Why Physicists Are So Poorly Trained In Mathematics", I'll agree. "Bad" is a meaningless word in such contexts. | |
| Sep 11, 2010 at 17:23 | comment | added | fedja | I'm not sure what you mean by "supported by experiments". Usually it means that the formulae and the models are tailored to what is observed so that the discrepancy is no longer obvious. Anyway, I do not mind back of envelope approximations: I do them all my life myself. What I mind is pretending they work in the ranges of parameters beyond where they can be proved. Yes, the surface area is a reasonable approximation in general, but the declared range is exactly where it fails miserably. | |
| Sep 11, 2010 at 17:09 | comment | added | Michael Lugo | Downvoted, because this really feels like a diatribe about Why Physicists Are Bad. | |
| Sep 11, 2010 at 13:55 | comment | added | QHLIU | fedja: I admit that physical way of reasoning usually loses the mathematical rigor, but it is supported by the experiments. Besides, physical reasoning enriches the mathematical studies, such as the Fourier series, distribution theory, etc. All primitive physical results are then mathematically proved correct; no exception is so far identified. Why isn’t it wrong? The approximate solution to the squares problem is easily attainable by treating the lattice (hyper-)spherical surface as a smooth one, and the number of the solutions is then nothing but the area of the surface area. | |
| Sep 11, 2010 at 13:07 | history | answered | fedja | CC BY-SA 2.5 |