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cousin_it comments on The mathematical universe: the map that is the territory - Less Wrong
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I disagree that you're responding to my argument. I'm not making an argument about whether the universe is simple or not: I'm making the argument that if the universe has an encoding, "cousin_it turns into a pheasant", it's not going to be an exception. If the universe has that encoding, we would find that cousin_it turns into a pheasant, and upon further study, would find this was predicted all along by the lower level rules. Simply because nothing exists beyond the lower level rules. We can't expect inconsistencies at higher levels because the higher levels are just derivative of the lower ones.
What do you mean? There's no law of nature saying laws of nature must be low-level in all possible worlds - that's just an observation about our world. I can write a simulator that runs the low-level rules as you'd expect, but also it's preprogrammed to search for cousin_it in the simulation at a certain moment, turn him into a pheasant, then resume business as usual. If all simulated worlds "exist", this one "exists" too.
On the one hand, it a matter of the definition of 'low-level': all laws of nature must be low-level or derived from a low-level law because if you had a law that wasn't derived from a lower-level law, that would make it low-level.
Yes, I agree and I'm generally interested in this case. But as I explained, this is only possible in a subset of a universe. The whole universe could not be such a simulation, because there would be nothing 'outside it' to swoop down and make the arbitrary change.
The hypothesis says that all universes that can be simulated by computer programs exist. It doesn't restrict those computer programs by saying they must use "only local laws", or "can't swoop down", or whatever. What does this even mean? Moving the universe one step forward in time according to the Schroedinger equation qualifies as "swooping down" just as much as turning me into a pheasant, they're both things that the program just does.
I assume you're thinking of some other hypothesis, like "all universes that exist must start from a simple core and proceed logically from there", but unfortunately no one has a "logicalness predicate" that would say whether a given program simulates a "logical" universe without "swooping down". In fact, looking at a program you may not even tell if it's "simulating" any universe at all, as opposed to moving some bytes around in weird patterns.
Perhaps it is a matter of relying on different analogies for our intuitions. I was thinking of each possible universe as being identified with a single self-consistent mathematical structure. In which case, I expect the universe to be organized and coherent because any set of mutually consistent initial facts would generate a universe with structure rather than one with haphazard and inexplicable events.
I hadn't thought of all possible computer programs each mapping to a universe ... what is the truth value of a random string of instructions? But since I don't know much about computer science, I don't expect that to work as an intuition pump for me.
Instead I was thinking along the lines of there being a universe -- say -- for each exotic algebra there might be and all the facts that are derived from it. An "algebra-generated-universe" wouldn't say something random or arbitrary; instead everything about the universe would be derivable from a few facts. (Note you couldn't have too many facts, or they'd self-contradict.)
I can remove contradictions by making up a new rule that specifies which rules take precedence over other ones.
Let's build a simpler intuition pump: instead of universes, we'll talk about infinite sequences of integers that can be specified by finite sets of rules. For example, (1, 1, 1, ...) is such a sequence. (1, 2, 3, 4, 5, ...) is another. Those look regular all right. But this sequence: (1, 2, 3, 4, ..., 999999, 1000000, 12345, 1000001, 1000002, ...) can also be specified by a finite and self-consistent set of rules, even though something seems to have "swooped down" and changed it in one place. There's no hard difference between "regular-looking" and "irregular-looking" sequences. All finite sets of rules have equal footing.
Does this make sense to you? Now imagine those integers encoding the time evolution of your toy universe...
It seems to me we're conflating 'possible as an output' and 'true' but since I don't really know what 'true' means in this context, let's conflate them.
The fact that you've written the sequence (1, 2, 3, 4, ..., 999999, 1000000, 12345, 1000001, 1000002, ...) is evidence that it's the possible output of an algorithm. (Indeed, it was the output of an algorithm you ran.) However, this means that the output was possible (and true) for a subset of the universe. How do you know this rule could be universally true?
I say that it could not be universally true, because it has this property of arbitrariness. I think to answer, 'what could possibly be universally true?', you would have to answer the question, 'what can be deduced as true from nothing?' or at best, 'what can be deduced as possibly true from nothing?' From nothing, the universe might deduce the natural numbers. By definition of what the natural numbers are they have an ordering 1, 2, 3, ..., n, n+1, ... This ordering really could not be different.
Suppose that the universe had a way of "knowing about" a single element '12345' that it places in a new position between 1000000 and 1000001. Simultaneously, it could have placed this element in any position, so universally, you would get a much, much larger structure in which (1, 2, 3, 4, ..., 999999, 1000000, 12345, 1000001, 1000002, ...) was only a tiny subset.
My point, whether I can figure out how to make it or not, is that the universe doesn't 'know about' 12345, it only knows about all the numbers and evolves this structure universally. You can look at particular components of the structure and observe that individual components seem arbitrary, but the entire structure cannot be.
Imagine a "universe" that consists of all streams of natural numbers that can be specified by algorithms. Is that fundamental and non-arbitrary enough for you? This universe contains many "sub-universes" that cannot communicate, so we can call them "universes" in their own right. One of them is my 12345 sequence, and many others have me spontaneously turn into a pheasant a week from now.
Exactly, yes.
How do you know they don't communicate? This would be a very non-trivial claim. I'm saying that the set of things that could be independently true (and thus universally true) might be extremely small, and certainly much smaller than the set of possibly-possible things you can think of. Most things we can think of as possible are going to be entangled in ways we aren't aware of with other truths.
Instead of being where you are thinking of things that could be ('I turn into a pheasant in 5 minutes'), you would need to turn it upside down and think if there was nothing, what would be true? Perhaps not so many things ... perhaps this experienced universe is the only one that was possible. How do we know without developing a theory about what truths self-generate from a void?
Same way I know natural numbers don't communicate. The output of one algorithm can't "communicate" with the output of another algorithm, whatever that means.
All that means is that 'cousin_it turns into a pheasant' has to be taken as an axiom for the algebra you're using...