[C]razy ideas are the sort of thing one needs when talking about the Big Bang. ...All the ideas I'm going to show you... are put forward by very... r… - Roger Penrose

[S]ome of these regions may be... indistinguishable, for example the air in the room. We might have molecules in some other places. You might like to say we don't care where the individual molecules are. We just care about overall parameters, and so we lump together the systems which look very much the same. ...[L]et's say with regard to macroscopic parameters we lump them together, and so we have these things called course graining cells in the phase space... [Y]ou then say, well let's measure the volume of these regions... <math>V</math>... and the logarithm of that volume is the entropy. This is a marvelous formula due to Boltzmann. This [<math>k</math>] is Boltzmann's constant, the only thing in the formula that wasn't due to Boltzmann... This was named afterwards. I don't think he was particularly interested in constants...

I have been arguing that such 'God-given' mathematical ideas should have some kind of timeless existence, independent of our earthly selves.

It seems to me that we must make a distinction between what is "objective" and what is "measurable" in discussing the question of physical reality, according to quantum mechanics. The state-vector of a system is, indeed, not measurable, in the sense that one cannot ascertain, by experiments performed on the system, precisely (up to proportionality) what the state is; but the state-vector does seem to be (again up to proportionality) a completely objective property of the system, being completely characterized by the results it must give to experiments that one might perform.