Aaron6

Sensual experience too easily renders a task involving.

Say what?

I would love a sensory modality for code.

Constant: with dogs, you can point to examples and say "these animals, and animals closely related to these are dogs".

Eliezer: Have you read Scott Aaronson's work on the learnability of quantum states. There, the full space is doubly exponential in system size, but if we just want to predict the results of some set of possible questions (to some fixed accuracy), we don't need to train with nearly as many questions as one might think.

Hopefully Anonymous: the usual phrasing is not "time-reversible" for that, as that can be interpreted as "the laws of physics are the same under exchange of t with -t". One usual phrasing is "non-dissipative", though I hold out for "retrodictable". Even this isn't sufficient for entropy to be conserved -- what's necessary is conservation of phase space volume. I'm going to cheese out and say that as energy conservation is enough to do this, that my comment about "reasonable" physics covers this.

But statistical mechanics can still treat the case where it isn't. Yes, entropy can decrease. That violates the second law of thermodynamics. Note that it isn't a law of statistical mechanics, and that we do in fact observe entropy fluctuations that dip negative in real open systems, without making statistical mechanics inapplicable. Note also that at most one closed system exists -- the universe itself.

I'd recommend starting with one of his Ethshar series, actually. *With a Single Spell* is I think an excellent exemplar of the type of work you're admiring. The canonical starting point is *The Misenchanted Sword*, which has most of these elements, but is slightly weaker in my opinion.

Watt-Evans has used a version of the street-performer protocol to publish the latest two of the series online, essentially acting as the advance, before having them published on paper. The draft of one is still up at http://www.ethshar.com/thevondishambassador1.html but might not make as much sense without having read the previous books.

Doug S: Cite? I'd love to believe that. It would also explain how humans can subvert the matrix, if they are themselves running the simulation.

Eliezer: Any universe with a reasonable notion of energy and probability will have statistical mechanics. In a sense it is far deeper than most of the physics that gets studied. The fact that gas expands when you heat it is due to the form of the density of states. The fact that you can get heat engines, and that they have a maximum efficiency of T_2 - T_1 / T_2 is stronger than that.

The GHZ state might be a better illustration, since it doesn't have the inherent probabilistic elements of the EPR/Bell state.

Yes, exactly what Douglas Keith said. The kinetic portion of the Hamiltonian is "non-local" in the position basis in exactly the same way that the potential portion of the Hamiltonian is non-local in the momentum basis: it appears in (powers of) the derivative.

If you want to talk about locality in terms of minimizing interactions between different basis states, then the basis is in eigenstates of the Hamiltonian, which is going to be neither position nor momentum.

Please consider replacing "sentient" with "sapient" in each occurrence in this essay.