String to Float, without introducing errors

[Peter J. Holzer]

On 2022-12-19 09:25:17 +1100, Chris Angelico wrote:
> On Mon, 19 Dec 2022 at 07:57, Stefan Ram <ram at zedat.fu-berlin.de> wrote:
> > G = Decimal( 6.6743015E-11 )
> > r = Decimal( 6.371E6 )
> > M = Decimal( 5.9722E24 )
> 
> What's the point of using Decimal if you start with nothing more than
> float accuracy?

Right. He also interpreted the notation "6.67430(15)E-11" wrong. The
digits in parentheses represent the uncertainty in the same number of
last digits. So "6.67430(15)E-11" means "something between 6.67430E-11 -
0.00015E-11 and 6.67430E-11 + 0.00015E-11". The r value has only a
precision of 1 km and I'm not sure how accurate the mass is. Let's just
assume (for the sake of the argument) that these are actually accurate in
all given digits.

So G is between 6.67415E-11 and 6.67445E-11, r is between 6.3705E6 and
6.3715E6 and M is between 5.97215E24 and 5.97225E24. If we compute the
time for those deviations you will find that the differences are many
orders of magnitude greater than the effect you wanted to show. And that
still ignores the fact that a vacuum won't be perfect (and collisions
with a few stray atoms might have a similarly tiny effect), that gravity
isn't constant while the weight falls (it's getting closer to the center
of the earth and it's moving past other masses on its way) that Newton's
law is only an approximation, etc. So while the effect is (almost
certainly) real, the numbers are garbage.

I think there's a basic numeracy problem here. This is unfortunately all
too common, even among scientists. The OP apparently rounded their
numbers to 8 significant digits (thereby introducing an error of about
1E-8) and then insisted that the additional error of 1E-15 introduced by
the decimal to float conversion was unacceptable, showing IMHO a
fundamental misunderstanding of the numbers they are working with.

        hp

-- 
   _  | Peter J. Holzer    | Story must make more sense than reality.
|_|_) |                    |
| |   | hjp at hjp.at         |    -- Charles Stross, "Creative writing
__/   | http://www.hjp.at/ |       challenge!"
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