On Tue, Feb 12, 2008 at 03:04:13AM -0800, Andrew Lentvorski wrote: > >Ever heard of the chain rule? df/dx = (df/du) * (du/dx) . > > > >Technically this is not correct because f is either is function of x > >or u but not *both*. > > It is quite technically correct. If you write out the whole partial > derivative mess and then collapse the terms that go away because u is a > function solely of x, your formula is quite fine (in fact, all of the > calc books *I* have do indeed give a pointer to the fact that the chain > rule is a simplified partial derivative even if it is in a footnote).
*We* both understand what the chain rule really means. Notice it took you a whole paragraph to decode your understanding. You mentioned simplifications, footnotes and other gymnastics. Why make the poor student go on a scavenger hunt for all that implicit knowledge? Sussman is just suggesting that you can focus all that gymnastics into a laser sharp computer program. That's all we're saying. Nothing more. > We model at varying levels of abstraction and call them correct. This > is quite acceptable, TYVM. And, in this instance, the result is > actually correct. Be careful calling things "wrong" when they are not. Yes but you need *precise* way to communicate even just within your chosen layer. I'm not saying abstractions and layers are a bad idea. We're just suggesting the software is superb method of precise *communication*. > The ability to abstract at different levels of correctness and > completeness is a hallmark of modern science and engineering. The > inability to accept different levels of abstraction and correctness is a > hallmark of mathematics. Both have their place--see: Dirac delta function. Straw man. See my comments above. I'm not arguing against abstraction. > And what have *you* been smoking. Students learn what gets them through > their immediate problem. I'm not much different. Yes and a software algorithm would be the most efficient means to get through immediate problems. > I'm not going to learn all of formal lambda calculus to understand > lisp/scheme. I'm not going to learn deep pure math to balance my > checkbook. etc. Another straw man. See above again. > Sorry, normal programming languages are *lousy* constructs to match to > mathematics and physics. Maybe, maybe not. But informal English verbage is even more lousy. > Why do you think Mathematica and Matlab are so amazingly popular? These would be fine too. Chris -- [email protected] http://www.kernel-panic.org/cgi-bin/mailman/listinfo/kplug-lpsg
