Accuracy and error analysis (was Re: [Maxima] primes)

--- Albert Reiner  wrote:

> Oh no, please don't!  That is NOT what Heisenberg is about.

Heh - don't worry.  I'm having enough fun with normal unit work at this
point.  And if the unit package gets polished to perfection Feyncalc is
always there begging for a port.
 
> BTW, I have always found Mathematica's significance arithmetic
> annoying at best, certainly not useful.  It gives the inexperienced
> user an illusion of security that is really not there.  In my courses
> I always had fun ``proving'' by a convergent process that the square
> root of 4.0000000000000 was 0..  If you really want something like
> that, I think you should read about Mma's $MinPrecision etc. and ask
> yourself whether that is a price worth paying.

I think Robert is correct - the useful thing to do is impliment it in a
way that is useful for physical quantities, and warn when those
quantities get small enough that precision issues start getting to be
within a couple orders of magnitude of the quantities involved.  For
physical measurements the price of calculating error propagation MUST
be paid, at least at the macroscopic error level - it is integral to
getting a meaningful answer.  As long as numerically induced errors are
small relative to measurement error it's probably a moot point.  There
might even be some experimental way to evaluate the numerical error
associated with a particular calculation - I'll have to check into it -
but that's most likely the practical limit.  Anyway, it's quite a ways
down the line before such things become relevant - I've still got a
fair bit of work on the unit package itself to do.

CY

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