You make an interesting observation. I'm still trying to think it through, so I might not yet be making sense. But, right now, I have the following difficulty with accepting your argument.
Any simulation has "true" physical laws. These are just the rules that govern how in fact the simulation's algorithm unfolds, including all optimizations, etc.
However, we expect, a priori, the ultimate laws of reality to satisfy certain invariances. For example, perhaps we expect the ultimate laws to work identically at different points in real physical space. The true laws of the simulation might not satisfy such invariances with respect to the simulation. For example, the simulation's laws might not work identically at different points in the simulated physical space. [ETA: Optimization makes this likely. The simulation could evolve in a "chunkier" way far from us than it does close to us.]
So maybe this is how we can define what it means to hide the simulated nature of our universe from us: "Hiding the simulation" means "making our universe appear to us as though its laws satisfy all the expected invariances, even though they don't".
Here's the issue that I hope you address:
I'm convinced by your argument that "any time you destroy entropy by forcing some system, from your perspective, to be in fewer possible states, you also allow another system, from your perspective, to be in proportionally more possible states."
Say that, when I start out, system A could be in any one of the states in some state-set X. Then I learn about system B, and so, as you point out, system A could now be in any one of the states in some larger state-set Y, as far as I know.
But what if the larger state-set Y includes states that do not obey the expected invariances? And what if, as I learn more about the universe, the state-set that A's state must be in grows, all right, but eventually consists almost entirely of states that violate our expected invariances?
Wouldn't that amount to discovering the simulated nature of our universe? To avoid this discovery, wouldn't the simulators have to put more resources into making sure that A's set of possible states includes enough states that obey the expected invariances?
Good point -- I've struggled with the same problem, in different terms. Let me know if my statement of the problem matches the point you're making here:
"It's possible to discover, not just particulars about individual systems, but universal laws. These universal laws put a constraint on all future observations, thus reducing the subjective entropy of the universe, without (apparently) needing any corresponding gain of entropy."
It's something I was wondering about when going over the E. T. Jaynes papers and Yudkowsky's Engines of Cognition.
I hav...
Parapsychologists are constantly protesting that they are playing by all the standard scientific rules, and yet their results are being ignored - that they are unfairly being held to higher standards than everyone else. I'm willing to believe that. It just means that the standard statistical methods of science are so weak and flawed as to permit a field of study to sustain itself in the complete absence of any subject matter.
— Eliezer Yudkowsky, Frequentist Statistics are Frequently Subjective
Imagine if, way back at the start of the scientific enterprise, someone had said, "What we really need is a control group for science - people who will behave exactly like scientists, doing experiments, publishing journals, and so on, but whose field of study is completely empty: one in which the null hypothesis is always true.
"That way, we'll be able to gauge the effect of publication bias, experimental error, misuse of statistics, data fraud, and so on, which will help us understand how serious such problems are in the real scientific literature."
Isn't that a great idea?
By an accident of historical chance, we actually have exactly such a control group, namely parapsychologists: people who study extra-sensory perception, telepathy, precognition, and so on.
There's no particular reason to think parapsychologists are doing anything other than what scientists would do; their experiments are similar to those of scientists, they use statistics in similar ways, and there's no reason to think they falsify data any more than any other group. Yet despite the fact that their null hypotheses are always true, parapsychologists get positive results.
This is disturbing, and must lead us to wonder how many positive results in real science are actually wrong.
The point of all this is not to mock parapsychology for the sake of it, but rather to emphasise that parapsychology is useful as a control group for science. Scientists should aim to improve their procedures to the point where, if the control group used these same procedures, they would get an acceptably low level of positive results. That this is not yet the case indicates the need for more stringent scientific procedures.
Acknowledgements
The idea for this mini-essay and many of its actual points were suggested by (or stolen from) Eliezer Yudkowsky's Frequentist Statistics are Frequently Subjective, though the idea might have originated with Michael Vassar.
This was originally published at a different location on the web, but was moved here for bandwidth reasons at Eliezer's suggestion.
Comments / criticisms
A discussion on Hacker News contained one very astute criticism: that some things which may once have been considered part of parapsychology actually turned out to be real, though with perfectly sensible, physical causes. Still, I think this is unlikely for the more exotic subjects like telepathy, precognition, et cetera.