[EMAIL PROTECTED] wrote:
*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?
You've switched arguments.
Sussman is talking pedagogy (when you teach what) as opposed to full
understanding (which you will get in multivariable calculus or advanced
analysis).
Imagine being bashed with multithreading in CS101 while trying to just
learn how programs work for a similar argument.
And, the people who *do* need this level of abstraction already have a
very fine, very precise language for expression. It's called mathematics.
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*.
I don't agree.
Mathematics is precise. Programming is not. It took some very smart
people to place computation (a restricted form of general programming)
on a decent precise mathematical foundation. And, even so, it is *very*
hard to formally prove all but the simplest things about computer
programs because of "assignment" (read "side effects").
And, if you don't have assignment, well, you have math. And we have a
very nice, very formal, very stable language for that.
Sorry, normal programming languages are *lousy* constructs to match to
mathematics and physics.
Maybe, maybe not. But informal English verbage is even more lousy.
That's why we use mathematics. What took me a paragraph to say is
probably about 20 mathematical glyphs.
-a
--
[email protected]
http://www.kernel-panic.org/cgi-bin/mailman/listinfo/kplug-lpsg
