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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <kcqkv4$lq5$1@smc.vnet.net> <kct7fj$sgo$1@smc.vnet.net> <kf2iv5$3o7$1@smc.vnet.net>

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 >