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Re: More /.{I->-1} craziness

• To: mathgroup at smc.vnet.net
• Subject: [mg106713] Re: More /.{I->-1} craziness
• From: AES <siegman at stanford.edu>
• Date: Thu, 21 Jan 2010 04:57:09 -0500 (EST)
• Organization: Stanford University
• References: <200912300915.EAA17299@smc.vnet.net> <hhhmn8$o9t$1@smc.vnet.net> <hhpl28$9lf$1@smc.vnet.net> <hip8gf$t4d$1@smc.vnet.net> <8304354.1263643340634.JavaMail.root@n11> <hiuur1$919$1@smc.vnet.net> <hj130e$bcn$1@smc.vnet.net> <hj40q4$sgk$1@smc.vnet.net>

In article <hj40q4$sgk$1 at smc.vnet.net>,
 Richard Fateman <fateman at cs.berkeley.edu> wrote:

> But can you show they learn more 
> calculus if they have Mathematica at hand?

Speaking only for myself (and noting that my calculus-learning days are 
far in the past, and that I'm not at all sure what the operational 
meaning of "learn more calculus" might be), I can only say that having 
Mathematica at hand whenever I'm doing any kind of "maths" ­­ whether 
it's learning more about some familiar or new mathematical topic, or 
trying to solve some real problem using math ­­ certainly enables me to 
gain immensely more insight and/or intuition into what the symbols on 
the paper mean, or how the mathematically described system of interest 
will actually behave.  Mathematica can really be "insanely great" at 
helping do that, and I'm grateful for it.

But it's Mathematica that's the "tool" for producing results here, and 
the conventional mathematical symbols as conventionally written on paper 
and the real physical systems that are the important realities ­­ the 
things that most of us want to concentrate on ­­ not the arcane and 
sometimes inconsistent or even bizarre innards of Mathematica.

Which is why it's so egregious and some of us so unsympathetic when 
attempts to apply Mathematica to some conventional mathematical input in 
what would seem a sensible and consistent fashion instead trigger some 
arcane Mathematica "gotcha"; and Mathematica acolytes then try to 
convince us that, hey, that's the way Mathematica works, and we must 
therefore accept it as near divinely inspired, and focus unlimited 
energies on learning the arcane (and often very ill-documented) details 
of what Mathematica does, not the tasks we want to accomplish with it.

Mathematica is a _commercial tool_, not a divinely endowed 
accomplishment of human creativity before which we must all bow down 
(and that remains true not withstanding the large amount of great human 
creativity that has obviously gone into developing it).