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

[Steven D'Aprano]

On Tue, 19 Jul 2016 01:25 am, Ian Kelly wrote:

> On Mon, Jul 18, 2016 at 3:29 AM, Steven D'Aprano
> <steve+comp.lang.python at pearwood.info> wrote:
>> On Monday 18 July 2016 14:16, Rustom Mody wrote:
>>> In short one could think of inexact and exact — in scheme's intended
>>> semantics — as better called scientific (or science-ic) and mathematic
>>> numbers.
>>
>> I don't think so. "Science" uses both experimentally-derived numbers
>> (e.g. G, c, the mass of the electron) and numbers known exactly (√2, e,
>> π).
> 
> Off-topic, c being a fundamental constant is actually in the latter
> category. Its *exact* value is 299792458 m/s.
> 
> The length of the meter, on the other hand, is defined as the distance
> traveled by light in a vacuum in 1/299792458 seconds and is subject to
> the precision of measurements.

You're right, of course, but that's a post-facto redefinition of both c and
the metre. Historically, the metre was defined first, then people spent a
lot of time measuring the speed of light (I believe it was Galileo who made
the first known attempt). Eventually, physicists decided that it was easier
to declare by fiat that c = 299792458 m/s EXACTLY, and use that definition
to imply a standard metre, rather than keep a standard metre and use that
to measure c.

That makes it a matter of convenience and practicality rather than purity.
It also reflects the current theoretical paradigm that sees c as a constant
and both distance and time subject to distortion. Had special and general
relativity been disproven, or never invented, it's unlikely that we would
have declared c to be more fundamental than distance.

(We haven't declared that G is exactly such-and-such a value, and used that
to define the kilogram.)



-- 
Steven
“Cheer up,” they said, “things could be worse.” So I cheered up, and sure
enough, things got worse.