Timeline for Most harmful heuristic?
Current License: CC BY-SA 2.5
4 events
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| Mar 1, 2010 at 12:39 | comment | added | jvkersch | Somewhat related is the assertion that "differentiation is more fundamental", since it is "easier" and usually taught first. Not only is this misguided for the reasons you and Scott cite, but following Roger Penrose we can also turn the argument upside down in the complex plane by using Cauchy's theorem to define the derivative of a function by means of a contour integral. I've always hoped there was some alien civilization in another spacetime where derivatives were actually introduced this way. | |
| Oct 24, 2009 at 22:38 | comment | added | S. Carnahan♦ | I think your argument is more effective against a slogan like, "all interesting functions are differentiable". In my (limited) experience, differentiation tends to be algorithmic in practice, although it can be unstable in numerical applications. This is in contrast to integrals, which exist much more often and tolerate numerical error well, but are generally very difficult to compute. | |
| Oct 24, 2009 at 22:18 | history | edited | Qiaochu Yuan | CC BY-SA 2.5 |
Clarified a point.
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| Oct 24, 2009 at 21:58 | history | answered | Qiaochu Yuan | CC BY-SA 2.5 |