Quoting from Eliezer's post on the second law of thermodynamics:

And don't tell me that knowledge is "subjective". Knowledge has to be represented in a brain, and that makes it as physical as anything else. For M to physically represent an accurate picture of the state of Y, M's physical state must correlate with the state of Y. You can take thermodynamic advantage of that - it's called a Szilard engine.

Or as E.T. Jaynes put it, "The old adage 'knowledge is power' is a very cogent truth, both in human relations and in thermodynamics."

And conversely, one subsystem cannot increase in mutual information with another subsystem, without (a) interacting with it and (b) doing thermodynamic work. Otherwise you could build a Maxwell's Demon and violate the Second Law of Thermodynamics - which in turn would violate Liouville's Theorem - which is prohibited in the standard model of physics.

Which is to say: To form accurate beliefs about something, you really do have to observe it. It's a very physical, very real process: any rational mind does "work" in the thermodynamic sense, not just the sense of mental effort.

(It is sometimes said that it is erasing bits in order to prepare for the next observation that takes the thermodynamic work - but that distinction is just a matter of words and perspective; the math is unambiguous.)

(Discovering logical "truths" is a complication which I will not, for now, consider - at least in part because I am still thinking through the exact formalism myself. In thermodynamics, knowledge of logical truths does not count as negentropy; as would be expected, since a reversible computer can compute logical truths at arbitrarily low cost. All this that I have said is true of the logically omniscient: any lesser mind will necessarily be less efficient.)

I think it is exactly this last "complication" with logical truths that I am asking about. Are there later LW posts with more formulated thoughts / comments about this?

Added: I found this post and I would be very eager to hear thoughts on how this connects to claims about mathematical truths. I think many arguments about ontology conflate mathematical entities with the ontologically basic mental things of this post. This quote seems to support what I am saying:

A "supernatural" explanation appeals to ontologically basic mental things, mental entities that cannot be reduced to nonmental entities.