The first is what Garrett points out, that probabilities are map things, and it’s a bit… weird for our measure of a (presumably) territory thing to be dependent on them. It’s the same sort of trickiness that I don’t feel we’ve properly sorted out in thermodynamics—namely, that if we take the existence of macrostates to be reflections of our uncertainty (as Jaynes does), then it seems we are stuck saying something to the effect of “ice cubes melt because we become more uncertain of their state,” which seems… wrong.
For this part, my answer is Kolmogorov complexity. An ice cube has lower K-complexity than the same amount of liquid water, which is a fact about the territory and not our maps. (And if a state has lower K-complexity, it’s more knowable; you can observe fewer bits, and predict more of the state.)
One of my ongoing threads is trying to extend this to optimization. I think a system is being objectively optimized if the state’s K-complexity is being reduced. But I’m still working through the math.
For this part, my answer is Kolmogorov complexity. An ice cube has lower K-complexity than the same amount of liquid water, which is a fact about the territory and not our maps. (And if a state has lower K-complexity, it’s more knowable; you can observe fewer bits, and predict more of the state.)
One of my ongoing threads is trying to extend this to optimization. I think a system is being objectively optimized if the state’s K-complexity is being reduced. But I’m still working through the math.