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Re: Mathematica and Lisp


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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