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.
I am reading through the sequence on quantum physics and have had some questions which I am sure have been thought about by far more qualified people. If you have any useful comments or links about these ideas, please share.
Most of the strongest resistance to ideas about rationalism that I encounter comes not from people with religious beliefs per se, but usually from mathematicians or philosophers who want to assert arguments about the limits of knowledge, the fidelity of sensory perception as a means for gaining knowledge, and various (what I consider to be) pathological examples (such as the zombie example). Among other things, people tend to reduce the argument to the existence of proper names a la Wittgenstein and then go on to assert that the meaning of mathematics or mathematical proofs constitutes something which is fundamentally not part of the physical world.
As I am reading the quantum physics sequence (keep in mind that I am not a physicist; I am an applied mathematician and statistician and so the mathematical framework of Hilbert spaces and amplitude configurations makes vastly much more sense to me than billiard balls or waves, yet connecting it to reality is still very hard for me) I am struck by the thought that all thoughts are themselves fundamentally just amplitude configurations, and by extension, all claims about knowledge about things are also statements about amplitude configurations. For example, my view is that the color red does not exist in and of itself but rather that the experience of the color red is a statement about common configurations of particle amplitudes. When I say "that sign is red", one could unpack this into a detailed statement about statistical properties of configurations of particles in my brain.
The same reasoning seems to apply just as well to something like group theory. States of knowledge about the Sylow theorems, just as an example, would be properties of particle amplitude configurations in a brain. The Sylow theorems are not separately existing entities which are of themselves "true" in any sense.
Perhaps I am way off base in thinking this way. Can any philosophers of the mind point me in the right direction to read more about this?