[hugh4]

It should be noted that a "temperature scale" is a pretty non-obvious thing. The idea that the temperature we call "ten degrees" is as much colder than "twenty degrees" as that is colder than "thirty degrees" is something you'd never figure out without getting as far as the 18th century.

Even the concept of "temperature" is not obvious. Give someone a hot piece of bread and a hot piece of metal and the metal seems hotter even if they're at the same temperature.

[yomritoyj]

Statistical mechanics is a subject for which it is very hard to pin down the conceptual foundations. To read a thermometer I need to be sure it has reached "thermal equilibrium" with the object being measured. But how do you define thermal equilibrium in terms of underlying mechanical ideas? How do we identify the mechanical systems to which the concept of temperature and thermal equilibrium can be meaningfully applied? See http://philsci-archive.pitt.edu/2691/1/UffinkFinal.pdf We would be accusing statistical mechanics of 'mathiness' were it not the case that we know how to make it work for very many systems of practical interest. The main problem with economics is that it does not work as often.

[Mattasher]

Good points. I think the hidden terms here are "ratio variables" vs "interval variables". It's not obvious that 200 degrees (Kelvin) is twice as hot as 100 degrees. But almost everyone is going to agree that water at 300K feels hotter than water at 280K (though this may not work across materials, as you note).

What we can do with our temperature scale is build a model that says every time we convert n liters of oil into heat and direct it at x liters of water we get a change of temperature of y degrees. Reliably, and with small margin of error.

We can't do this with GPD, and if we declare that a 10% increase in education spending will lead to a 5% increase in GDP over 15 years, we don't have a testable scientific model, we have a guess based on our interpretation of extremely messy data.