Timeline for Why is differentiating mechanics and integration art?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jun 9, 2011 at 6:46 | comment | added | vonjd | @Deane: I would very much appreciate that - thank you! | |
| May 31, 2011 at 18:30 | comment | added | Deane Yang | vonjd, any local operation can be made global (by just doing it everywhere). I'll add a few more vague comments to my answer when I get some time. | |
| May 31, 2011 at 17:01 | comment | added | vonjd | @Deane: Now I am totally confused - on the one hand Tao says that differentiation is inherently local - and therefore easier. On the other hand I thought (and said it above) that differentiation is also global (in a way) because you are trying to find a function which satisfies the whole domain (and not only one point). Now Gowers seems to support this point. Isn't this a contradiction? The whole matter gets more and more mysterious (at least to me)... | |
| May 31, 2011 at 16:13 | comment | added | Deane Yang | I have only circular arguments on why linearization is simpler than the reverse, namely what I say in the penultimate paragraph. Somehow linearization is formally (algebraically) a nice operator, whereas reconstructing a nonlinear function from its linearization is not. But otherwise I can understand your skepticism. | |
| May 31, 2011 at 15:59 | comment | added | gowers | I'm not sure I buy your argument that the linearization "is somehow a simplification". True, linear functions are simple, but the linearization we perform when differentiating varies from point to point in a nonlinear way, and it's the entire derivative we're interested in here rather than just the derivative at a point. (This is particularly clear if we look at functions of more than one variable, when the derivative is a decidedly more complicated object than the original function.) | |
| May 30, 2011 at 23:30 | history | answered | Deane Yang | CC BY-SA 3.0 |