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Re: Why?

• To: mathgroup at smc.vnet.net
• Subject: [mg110563] Re: Why?
• From: Noqsi <jpd at noqsi.com>
• Date: Sat, 26 Jun 2010 03:08:44 -0400 (EDT)
• References: <hto93n$kt8$1@smc.vnet.net> <hviapu$h6s$1@smc.vnet.net>

On Jun 21, 12:11 am, Richard Fateman <fate... at cs.berkeley.edu> wrote:
> Noqsi wrote:

> > Approximation is often puzzling. The ideological war you wage against
> > WRI is unhelpful here. The wise person understands that there are
> > multiple points of view.
>
> If it is required to be wise in the ways of WRI's (unusual) arithmetic
> to use WRI software, then that is more than a user interface problem.

You must be wise in the ways of the tool to use it. That's always
true. There's nothing wrong with being "unusual": Mathematica is
unusual in quite a few ways, and that's key to its ability to quickly
dispose of problems that are more difficult with other tools. When a
different tool is better, just use that and quit carping.

>
>   Your IEEE754-based ideology has its own
>
> > weaknesses: abuse of the concepts of "rational" and "finite", and weak
> > connection to the real number system. Matthew 7:3 applies.
>
> I'm not sure what you mean by IEEE754-based ideology.

The ideologue never understands his own ideology.

>  Probably the
> whole community of numerical error analysts agrees on a model that is
> different from WRI's.

In other words, your fellow ideologues agree with you. Unanimity in an
area as tricky as this is a sure symptom of groupthink: difficult
problems demand *multiple* points of view for truly effective
understanding. Even in physics, where we think we are all working with
a common reality, we have multiple ways of looking at it. Numerical
analysis lacks that common reality: it serves a diversity of
applications, with a diversity of requirements.

Where I fault Mathematica's design here is that "Real" wraps two
rather different kinds of objects: fixed-precision machine numbers,
and Mathematica's approximate reals. Both are useful, but
understanding and controlling which kind you're using is a bit subtle.
"Complex" is even more troublesome.