Axioms [LWN.net]

Axioms

Posted Feb 23, 2021 13:10 UTC (Tue) by mathstuf (subscriber, #69389)
In reply to: Axioms by Wol
Parent article: An introduction to lockless algorithms

> Things like c, g, permittivity, that stuff, are all physical constants, which should be explainable in terms of maths.

But…why? What is this assumption based upon? Is it a bit of Platonic idealism?

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Axioms

Posted Feb 24, 2021 0:27 UTC (Wed) by Wol (subscriber, #4433) [Link] (6 responses)

I don't know why, I just remember coming across it somewhere that most of the physical constants could be defined in terms of other things, and the reason they had the values they did was because the maths didn't make sense otherwise.

Cheers,
Wol

Axioms

Posted Feb 24, 2021 21:58 UTC (Wed) by mathstuf (subscriber, #69389) [Link] (5 responses)

Sure, but (as stated elsewhere) your numerical values are limited to our arbitrarily defined units. A mole is a number of atoms of a substance in a number of grams equal to its molecular weight. A meter is basically an arbitrary nice length, Seconds are based on a breakdown of the rotational speed of Earth. Sure, we've rebased them onto more stable footing now, but the counts of those things into the units are "arbitrary" based on what we had before.

If we wanted, we could say that the speed of light is pi/e Wol_lengths/Wol_time intervals. Doesn't mean that those units are any more useful than our numerical value in m/s.

Axioms

Posted Feb 25, 2021 7:48 UTC (Thu) by jem (subscriber, #24231) [Link] (4 responses)

One fun fact about the base unit for mass, kg, is that it is derived (indirectly) from the size of the Earth. On a bigger Earth, we would have a different "kilogram", with a bigger mass. (And I'm not talking about the gravitational force, which would increase even more, because of the bigger mass of both a kilogram and the Earth.)

Axioms

Posted Mar 16, 2021 21:09 UTC (Tue) by nix (subscriber, #2304) [Link] (3 responses)

Not any more it isn't. In 2019 it was redefined in terms of the Planck constant -- though, of course, its *actual value* comes down to the original French Revolutionary definition: but even that was the mass of a cubic centimetre of water at the melting point of ice. This, of course, depends on atmospheric pressure (since they didn't use the triple point), and thus indirectly on the mass of the Earth and a bunch of other contingent values -- but the current definition depends on no such things.

Axioms

Posted Mar 17, 2021 10:37 UTC (Wed) by jem (subscriber, #24231) [Link]

>Not any more it isn't. In 2019 it was redefined in terms of the Planck constant

Well, I said derived, not defined.

Axioms

Posted Mar 18, 2021 10:14 UTC (Thu) by mgedmin (guest, #34497) [Link] (1 responses)

> mass of a cubic centimetre of water

a cubic *deci*meter (which is also one liter) of water.

Axioms

Posted Mar 20, 2021 1:24 UTC (Sat) by nix (subscriber, #2304) [Link]

I changed that repeatedly before posting... and picked the wrong one, despite the metric system being the only system I actually know. Sigh.

(And obviously you're right, unless water has suddenly become much, much denser than lead :) )