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Re: Re: scope all wrong? in Mathematica 4.1

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  • Subject: [mg31899] Re: [mg31874] Re: [mg31827] scope all wrong? in Mathematica 4.1
  • From: David Withoff <withoff at>
  • Date: Mon, 10 Dec 2001 06:14:42 -0500 (EST)
  • Sender: owner-wri-mathgroup at

> > 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.
> I don't know about fuzzy geometry, and I certainly do not encourage
> people to compare for equality of floating point numbers except in
> a very limited sense.  (Typically a convergence criterion that says
> "did the last iteration change the result AT ALL" ... but even so
> this is generally not a good idea). But that the programming language
> itself would have a notion of equality that was not transitive... this
> is bizarre, and I think unique to Mathematica.

I don't understand this.  What does "the programming language itself"
having "a notion of equality" mean?  Mathematica supports several
functions that are typically used as measures of equality, and users
can of course program their own.  Some of those operations will be
transitive and some will not.  Would the language be better if all
built-in functions for non-transitive measures of equality were removed?
Conversely, what if such functions were added to standard C and Fortran
libraries.  Would doing so make those languages worse?

None of this has anything to do with the message "Subject" of course.
I am concerned that the subject may have transmogrified to include
so many things that it is not very meaningful any more.

Dave Withoff
Wolfram Research

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