Re: From physical measurement to mathematics...

Christophe de Dinechin wrote:
Why can we add masses together and get a mass? This question may seem
stupid, but we can't do the same with time: we need to add a time and a
*duration* to get another time.

It seems to me like adding masses depends on various assumptions, like
"the mass of two identical cubes of metal is twice the mass of one
cube". But "identical" here includes the fact that they have the same
mass, which makes the definition recursive. How annoying. And then, it
does not work for, say, the outer surface: if I put two cubes together,
their volumes add up, but their outer surface does not. So why does it
work for mass?

Would you know of any research along the lines of "what are legitimate
operations on results of measurements"? I'm currently piecing together
thoughts on this topic (I regularly put the latest draft on
http://cc3d.free.fr/tim.pdf), and I would appreciate any reference on
the subject.

Quite often "adding" two masses gives a mass, but not the sum of the
two masses. The rest is taken up as binding energy.

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