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Re: Numerical accuracy/precision - this is a bug or a feature?

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  • Subject: [mg120245] Re: Numerical accuracy/precision - this is a bug or a feature?
  • From: Noqsi <noqsiaerospace at>
  • Date: Thu, 14 Jul 2011 21:19:57 -0400 (EDT)
  • References: <ius5op$2g7$> <ius7b6$30t$>

On Jul 14, 2:23 am, Richard Fateman <fate... at> wrote:
> On 7/13/2011 12:11 AM, Noqsi wrote:
> ..
> >> see e.g.
> >> <>.
> ..
> Learning mathematics from a physicist is hazardous.

In some ways. But if you want to relate mathematics to reality, you
might do well to consider the viewpoints of physicists.

> Learning computer science from a physicist is hazardous too.

Learning computer science from computer scientists is in some ways
worse, unless your interest is pointless bit pushing. Matthew 23:24 is
very relevant (some things never change).

In extracting useful results from computers in the real world
ignorance of the application domain is more debilitating than
ignorance of computer science. One can muddle through the latter, but
not the former.

Consider the howler you yourself committed a little while ago,
discussing the role of computers in the Apollo moon landings:

> you've got to wonder how the Russians, probably WITHOUT much in the way
> of computers, put up an artificial satellite.

This illustrates a profound ignorance of the problem. If you don't
care what orbit you go into, the computations are readily performed by
slide rule ahead of time. But Apollo had to perform a series of
precise maneuvers using imprecise rockets, with repeated re-
computation of the trajectories. For the early missions, they didn't
even know the lunar gravity very well, so actual orbits diverged
rapidly from predictions even when the initial conditions were known.
Apollo's indirect "lunar orbital rendezvous" approach was thus a
triumph of computation. Even the Saturn V was not big enough to
support the less computationally intensive direct approach.

Perhaps the "programmer" I learned the most from in a long career was
a physicist whose code was littered with silly (from a CS point of
view) constructions like:

        IF(ABS(TA).GT.1.) TA=SIGN(.99999,TA)

What was so great about his code? It's that every program he wrote was
an illuminating exercise in extracting important knowledge from
measurable information. The sloppy technique didn't matter so much. He
put rigor into the place it really counted: serving the needs of his
research. There were several much better technical programmers in that
research group, but they were not as good at conceptualizing how to
actually *use* the computer, rather than simply programming it.

> Numbers in a computer are different from experimental measurements.

But the experimental measurements relate much better to reality.

> nevertheless, I like this article.  It says, among other things,
>         The technique of propagating the uncertainty from step to=
> throughout the calculation is a very bad technique. It might sometimes
> work for super-simple =93textbook=94 problems but it is unlikely to work =
> real-world problems.

Except that error propagation techniques are used successfully in many
fields. Your cell phone works because engineers found a good balance
of power consumption and radio sensitivity from error propagation
methods, rather than the impractical method of tracking each electron
through the circuits. Getting back to orbits, one extremely useful
application of error propagation is to use it "backwards" to determine
which observations would best improve knowledge of an orbit.

There is no universal method for tracking uncertainty that is accurate
and practical. Your own ideologically favored method, interval
arithmetic, yields unrealistically large estimates of error in many
cases, and that can be a very bad thing. Or it can be useful to have
an upper bound. What's good depends on what the *application* needs,
not some ivory tower ideology.

I am *really* tired of your smug, patronizing attitude. You're a blind
man attempting to explain a rainbow. Why not, instead of whining all
the time that Mathematica doesn't conform to your profoundly narrow
notions of what computation is, spend some time with it actually
computing something of relevance to the real world? If you were
actually interested in applications, you would *rejoice* in the fact
that there are a variety of approaches available. But instead, you
obviously see Mathematica as a threat to your narrow ideology.

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