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HalFinney comments on The Strong Occam's Razor - Less Wrong
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Years ago, before coming up with even crazier ideas, Wei Dai invented a concept that I named UDASSA. One way to think of the idea is that the universe actually consists of an infinite number of Universal Turing Machines running all possible programs. Some of these programs "simulate" or even "create" virtual universes with conscious entities in them. We are those entities.
Generally, different programs can produce the same output; and even programs that produce different output can have identical subsets of their output that may include conscious entities. So we live in more than one program's output. There is no meaning to the question of what program our observable universe is actually running. We are present in the outputs of all programs that can produce our experiences, including the Odin one.
Probability enters the picture if we consider that a UTM program of n bits is being run in 1/2^n of the UTMs (because 1/2^n of all infinite bit strings will start with that n bit string). That means that most of our instances are present in the outputs of relatively short programs. The Odin program is much longer (we will assume) than one without him, so the overwhelming majority of our copies are in universes without Odin. Probabilistically, we can bet that it's overwhelmingly likely that Odin does not exist.
This is a cool theory, but it is probably equivalent to another, less cool theory that yields identical predictions and does not reference infinite virtual universes. :)
Although it postulates the existence of infinitely many inaccessible universes, it may be simpler than equivalent theories which imply only a single universe.
I feel like this is an argument we've seen before, but with more hilarious self-referentiality.
If I am not mistaken, it is a bit more formalized version of Greg Egan's Dust Theory.
I was actually referring to the (slightly superficial) similarity to the MWI vs. collapse discussion that indirectly prompted this post.
Perhaps in The Finale of the Ultimate Meta Mega Crossover?
Should we stop on UDASSA? Can we consider universe that consists of continuum of UDASSAs each running some (infinite) subset of set of all possible programs.
If anyone is interested. This extension doesn't seem to lead to anything of interest.
If we map continuum of UDASSA multiverses into [0;1) then Lebesgue measure of set of multiverses which run particular program is 1/2.
Let binary number 0.b1 b2 ... bn ... be representation of multiverse M if for all n: (bn=1 iff M runs program number n, and bn=0 otherwise).
It is easy to see that map of set of multiverses which run program number n is a collection of intervals [i/2^n;2i/2^n) for i=1..2^(n-1). Thus its Lebesgue measure is 2^(n-1)/2^n=1/2.
Yep, I already arrived at that answer elsewhere in the thread. It's very nice and consistent and fits very well with UDT (Wei Dai's current "crazy" idea). There still remains the mystery of where our "subjective" probabilities come from, and the mystery why everything doesn't explode into chaos, but our current mystery becomes solved IMO. To give a recent quote from Wei, "There are copies of me all over math".