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Re: Mathematica and Lisp
*To*: mathgroup at smc.vnet.net
*Subject*: [mg129737] Re: Mathematica and Lisp
*From*: Richard Fateman <fateman at cs.berkeley.edu>
*Date*: Sat, 9 Feb 2013 00:45:11 -0500 (EST)
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On 2/8/2013 2:10 AM, John Doty wrote:
<big snip, most of which suggest we agree on some things>
>
> But the rule-based paradigm is fundamental here.
>Formal proof in mathematics is rule-based.
Not necessarily. There's a substantial literature that
shows how to prove theorems by algebraic construction.
For example, geometry theorems are often convertible to
algebraic system solution.
I think the reality of rules is that too many of them are
confusing as a programming paradigm. Few people have the
knowledge and discipline to write rule sets which are
defined without overlaps, in a more-or-less unstructured
problem domain, where the solution is, as you say, "emergent".
> Mathematica implements a formalist vision of mathematics filtered
> through a physicist's pragmatism. That's why it's so good at mathematics
>, especially the applied mathematics of science and engineering.
That's partly why it fails so spectacularly on the mathematics examples
which I've pointed out again and again.
In
>Mathematica, programming is secondary: partly emergent and partly added on.
> If programming is your primary focus, Mathematica should probably not be your language of choice.
And so we agree, that if programming a solution to a problem
is the key to reaching your goal, perhaps you should not be
using Mathematica.
RJF
>
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