3 ms·

Let's say that for a given set of physical laws, you get some "computational power" P, which characterizes how hard it is do to computation using those laws. Yo

Let's say that for a given set of physical laws, you get some "computational power" P, which characterizes how hard it is do to computation using those laws. You could imagine a universe with lower P than ours, where light was much slower, or the only workable transistor had a switching time on the order of seconds. Given a universe with computational power P, you can simulate a "universe" of something like P * 10^-100. For example, a Minecraft world is a universe with different physical laws, in which you could perform even slower and worse simulations, and you can make "turtles all the way down" at lower and lower P. The claim that our universe is not simulated, then, is nearly equal to the claim that the physical laws we have is the absolute highest P that could ever exist. Since we know we can simulate universes of much lower P than ours, we ought to have very good reason to assert that there is no universe of much higher P than ours. Given a finite speed of light in our universe, yet nonlocal effects (Bell inequalities) which appear to take instantaneous effect, we could perhaps fathom a universe of higher P created by having a method of communication which occurred instantaneously. Add to this more dimensions in time and space, etc... literally nothing is off the table for a "smarter" universe to be conceived of, because the containing universe's physical laws need bear no resemblance to our own. Barring a literal divine intervention, though, it's all completely unfalsifiable, but I think it's more nuanced than "God did it".

teraflop 10y ago
I think the Minecraft analogy is illustrative. In Minecraft, you can use redstone circuits to construct logic gates, and use those gates to build computational devices that are Turing-complete, in theory. But it's not possible to scale such devices up arbitrarily; you can build a simple CPU, but nothing that even approaches being able to run a nested copy of Minecraft. There are hard upper bounds on the amount of data that the simulation can cope with at once. (You can imagine patching Minecraft to allow keeping more chunks loaded at once, but you can't scale it up by very many orders of magnitude before you end up with something that can't run efficiently on any hardware that physically exists.) Similarly, as Scott Aaronson describes in the article we're discussing, it's likely that there are finite bounds on how much computation can possibly be done before the heat death of our own universe. So it's fair to be skeptical that a tower of "turtles all the way down" could ever possibly exist, at least on a universal scale. If there's no tall hierarchy, then the anthropic argument (which says that we're unlikely to be at the top) breaks down. You can certainly hypothesize higher levels which have infinitely fast communication, or other kinds of special properties that make deep simulations more feasible. (Greg Egan proposed one such cosmology in his novel Permutation City.) But you don't get to assume that and still use simulations within our own universe as examples, because you're talking about something entirely different.
evanb 10y ago
Indeed, computational complexity depends on the physical laws of the universe. Suppose your universe admitted a computer where, with finite power, in the first second you could execute one instruction, and then you could run the next instruction in half a second, and the third in a quarter of a second... etc. What is "reasonable" to compute in a short amount of time in this universe has changed dramatically! For example, I want to prove the Goldbach conjecture. No problem! Just use this crazy computer to check every case, which is possible because this computer executes an infinite number of steps in two seconds. Unfortunately [word choice?], in our universe such a computer needs an infinite amount of energy and would collapse into a black hole long before you received your answer!

teraflop 10y ago

I think the Minecraft analogy is illustrative. In Minecraft, you can use redstone circuits to construct logic gates, and use those gates to build computational devices that are Turing-complete, in theory. But it's not possible to scale such devices up arbitrarily; you can build a simple CPU, but nothing that even approaches being able to run a nested copy of Minecraft. There are hard upper bounds on the amount of data that the simulation can cope with at once. (You can imagine patching Minecraft to allow keeping more chunks loaded at once, but you can't scale it up by very many orders of magnitude before you end up with something that can't run efficiently on any hardware that physically exists.) Similarly, as Scott Aaronson describes in the article we're discussing, it's likely that there are finite bounds on how much computation can possibly be done before the heat death of our own universe. So it's fair to be skeptical that a tower of "turtles all the way down" could ever possibly exist, at least on a universal scale. If there's no tall hierarchy, then the anthropic argument (which says that we're unlikely to be at the top) breaks down. You can certainly hypothesize higher levels which have infinitely fast communication, or other kinds of special properties that make deep simulations more feasible. (Greg Egan proposed one such cosmology in his novel Permutation City.) But you don't get to assume that and still use simulations within our own universe as examples, because you're talking about something entirely different.

evanb 10y ago

Indeed, computational complexity depends on the physical laws of the universe. Suppose your universe admitted a computer where, with finite power, in the first second you could execute one instruction, and then you could run the next instruction in half a second, and the third in a quarter of a second... etc. What is "reasonable" to compute in a short amount of time in this universe has changed dramatically! For example, I want to prove the Goldbach conjecture. No problem! Just use this crazy computer to check every case, which is possible because this computer executes an infinite number of steps in two seconds. Unfortunately [word choice?], in our universe such a computer needs an infinite amount of energy and would collapse into a black hole long before you received your answer!