Date: Jun 2, 2013 12:23 AM
Author: Mark McClure
Subject: Re: Applying Mathematica to practical problems

On Sat, Jun 1, 2013 at 6:27 AM, Richard Fateman <> wrote:
> On 5/31/2013 12:16 AM, Andrzej Kozlowski wrote:

>> Naive users of Mathematica practically never use arbitrary
>> precision arithmetic.

> Practically never, but occasionally? Like slightly pregnant?

While I'd prefer to steer clear of the majority of this morass, I do
have one data point that might be useful. In fact, I wrote the
following on sci.math.symbolic back in 2008:
>>>> I've been teaching undergraduate students to solve numerical
>>>> problems in calculus, differential equations, linear algebra, and
>>>> more recently numerical analysis using Mathematica since version
>>>> 1.2 and I don't believe I've ever seen the types of problems you
>>>> describe arise in that setting.

Well, that was five years ago and, as I've continued to teach with
Mathematica and even developed a course *on* Mathematica, I can now
expand on that a bit. I have now seen a novice user develope some
serious confusion due to unexpected behavior surrounding significance
arithmetic - once.

Incidentally, the significance arithmetic was triggered, not by one of
RJF's standard tricks, but by a simple bug. In versions 6 and 7 of
Mathematica, entering AiryA[0.0] yielded a non-machine number with
Precision $MachinePrecision, rather than a machine number with
Precsion MachinePrecision. I was studying the structure of Julia sets
of Airy functions with an undergraduate research student and, as you
might imagine, it was, uhmm, inconvenient to iterate with
high-precision numbers. Danny can verify the bug at least, as he
fixed it.

Finally, the main reason I find this debate so uninteresting is that
it is just simple observation that loads of people are doing good
numerical work with Mathematica. We have better things to talk about.

Mark McClure