What exactly is "exact" (was Clean Singleton Docstrings)

[Rustom Mody]

On Tuesday, July 19, 2016 at 8:46:44 AM UTC+5:30, Steven D'Aprano wrote:
> On Tue, 19 Jul 2016 10:36 am, Rustom Mody wrote:
> 
> > I recollect — school physics textbook so sorry no link —
> > that in the Newton gravitation law
> > f = -GMm/r²
> > 
> > there was a discussion about the exponent of r ie  2
> > And that to some 6 decimal places it had been verified that it was
> > actually 2.000002
> 
> Because gravitational forces are so weak, it is very difficult to
> experimentally distinguish (say) an exponent of 1.999999 from 2.000002 from
> 2 exactly.
> 
> Most physicists would say that an experimental result of 2.000002 is pretty
> good confirmation that the theoretical power of 2 is correct. Only a very
> few would think that the experiment was evidence that both Newtonian and
> Einsteinian gravitational theory is incorrect.

Yes this was — if memory is right — the conclusion, viz.:
Experimentally it looks like 2.000002 (or whatever)
This is as good as we can measure
So concluding its 2 seems to be reasonable with that 0.000002 relegated to
experimental error

Nevertheless my main point was that such a math (aka analytic to a layman) 
looking entity like 2, may for a physicist be a quantity for synthetic verification

> 
> (Newton, for obvious reasons; but also general relativity, since Newton's
> law can be derived from the "low mass/large distance" case of general
> relativity.) 
> 
> But it's an interesting hypothetical: what if the power wasn't 2 exactly?

May be related to the margin of error for G being quite high