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Re: scope all wrong? in Mathematica 4.1
*To*: mathgroup at smc.vnet.net
*Subject*: [mg31860] Re: [mg31827] scope all wrong? in Mathematica 4.1
*From*: Andrzej Kozlowski <andrzej at tuins.ac.jp>
*Date*: Fri, 7 Dec 2001 05:56:58 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
On Friday, December 7, 2001, at 10:42 AM, Richard Fateman wrote:
>
> The whole situation
>> reminds me of the traditional division in mathematics between these
>> mathematicians who consider foundations of mathematics as an important
>> and central subject and those who think of it as something totally
>> unimportant. Suppose an unresolvable flaw was discovered in the
>> foundations of Mathematics, say a basic inconsistency in all known
>> axioms of set theory. What would be the reaction of people studying
>> partial differential equations? Most would just shrug their shoulders
>> and go on doing what they were doing, and in my opinion would be quite
>> right to do so. These subject do not rest on the "foundations", it's
>> only the people who who work on foundations who flatter themselves
>> that it is so. You talk of mathematics in terms of "axioms". Of course
>> there are many mathematicians who think in this way. But there are
>> many more, including myself (and I mean pure mathematicians dealing
>> with abstract objects like manifolds or complexes) who hardly ever
>> mention this word in their work.
>
>
> But you are using as a tool, a program in which transitivity of equality
> fails. That is, a==b and b==c does not imply a==c.
> This matters even in partial differential equations.
>
> You are using a tool in which the identity function Function[x,x] is
> not
> a function, but a kind of pattern in which the basic notions of free
> and bound variables -- essential for referential transparency -- the
> substitution of equals for equals -- fails.
>
> Now of course if all your programs are not really programs, but
> commands like
> if you see f(x,x) change it to g(x).
> or commands like "compute the totally understood result of
> the polynomial resultant of two polynomials with exact integer
> coefficients" then you are OK.
>
> If you try to build a robust system of substantial complexity,
> the tools must not have hidden flaws.
>
Well, to me at least, these remarks show that you are engaging in
rhetoric designed to discredit Mathemaitca or Wolfram rather than an
objective argument. You know perfectly well that non-transitive notions
of "equality" are quite common in mathematics dealing with approximate
and uncertain quantities, indeed there are a whole subjects (for example
something called "fuzzy geometry") based on such notions. In fact you
yourself have pointed out that comparisons of this kind between
approximate quantities ought to be avoided. In fact Mathematica has a
strict notion of equality (SameQ) and this worn argument is just a red
herring. As for the other point, well Mathematica is clearly a pattern
matching language with a functional syntax, which makes it easier to
use, but may be misleading to those who have not studied it carefully.
But one can no more blame it for not being like Lisp as for not being
like C or Java.
>
> I can do this in Lisp, since Macsyma has those pieces, though these
> parts of Mathematica are probably OK. Well actually, the evaluation
> of integrals has problems...
Presumably you would argue that the reason why Macsyma never really
managed to gain any popularity outside a few departments of mathematics
or computer science (it was there when I was beginning to teach in the
US, before Mathematica, yet today it seems to be even less well known
than in those days) is somehow the result of failure of people to
realize its superior excellence. But claims like this are common,
particularly by the authors of the less successful products.
>
>
> I actually disagree. Look at the disclaimer at the front of the book
> that says not to use Mathematica for computations involving life, or
> property.
>
> Regards
> RJF
>
>
Hm, are you saying that you would be willing to accept personal
liability for any damage to life or property that could result from a
bug in Macsyma? If so I find it very admirable since I am not aware of
any other software developer who has the courage to take this attitude.
Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/
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