I’m confused by your intuition that team manipulation’s universe has similar complexity to ours.
My prior is that scaling the size of (accessible) things in a universe also requires scaling the complexity of the universe in a not-bounded way, probably even a super-linear way, such that fully specifying “infinite computing power” or more concretely “sufficient computing power to simulate universes of complexity <=X for time horizons <=Y” requires complexity f(x,y) which is unbounded in x,y, and therefore falls apart completely as a practical solution (since our universe is at age 10^62 planck intervals) unless f(x,y) is ~O(log(y)), whereas using a pure counting method (e.g. the description simply counts how many universe states can be simulated) gives O(exp(y)).
Since my intuition gives the complexity of Team Manipulation’s raw universe at >10^(10^62), I’m curious what your intuition is that makes it clearly less than that of Team Science. There are approximately 10^185 Planck volumes in our observable universe so it takes only a few hundred bits to specify a specific instance of something inside a universe, plus a hundred or so to specify the Planck timestamp. In particular, this suggests that the third branch of Team Science is pretty small relative to the 10^8 specification of an observer architecture, not overwhelmingly larger.
One antidote to feeling like simple Turing machines can’t contain complicated stuff is to consider Universal Search (I forget its real name if that’s not it) - this is a Turing machine that iterates over every Turing machine.
Turing machines can be put in an ordered list (given a choice of programming language), so Universal Search just runs them all. You can’t run them in order (because many never halt) and you can’t run the first step of each one before moving onto step two (because there’s an infinite number of Turing machines, you’d never get to step two). But you can do something in between, kinda like the classic picture of how to make a list of the rational numbers. You run the first Turing machine for a step, then you run the first and second Turing machines for a step, and you run the first, second, and third… at every step you’re only advancing the state of a finite number of Turing machines, but for any finite Turing machine, you’ll simulate it for an arbitrary number of steps eventually. And all of it fits inside Universal Search, which is quite a simple program.
As for finding us in our universe, your estimate makes sense in a classical universe (where you just have to specify where we are), but not in a quantum on (where you have to specify what branch of the universe’s wavefunction we’re on).
My issue isn’t with the complexity of a Turing machine, it’s with the term “accessible.” Universal search may execute every Turing machine, but it also takes adds more than exponential complexity time to do so.
In particular because if there are infinitely many schelling points in the manipulation universe to be manipulated and referenced, then this requires all of that computation to causally precede the simplest such schelling point for any answer that needs to be manipulated!
It’s not clear to me what it actually means for there to exist a schelling point in the manipulation universe that would be used by Solomonoff Induction to get an answer, but my confusion isn’t about (arbitrarily powerful computer) or (schelling point) on their own, it’s about how much computation you can do before each schelling point, while still maintaining the minimality criteria for induction to be manipulated.
I’m confused by your intuition that team manipulation’s universe has similar complexity to ours.
My prior is that scaling the size of (accessible) things in a universe also requires scaling the complexity of the universe in a not-bounded way, probably even a super-linear way, such that fully specifying “infinite computing power” or more concretely “sufficient computing power to simulate universes of complexity <=X for time horizons <=Y” requires complexity f(x,y) which is unbounded in x,y, and therefore falls apart completely as a practical solution (since our universe is at age 10^62 planck intervals) unless f(x,y) is ~O(log(y)), whereas using a pure counting method (e.g. the description simply counts how many universe states can be simulated) gives O(exp(y)).
Since my intuition gives the complexity of Team Manipulation’s raw universe at >10^(10^62), I’m curious what your intuition is that makes it clearly less than that of Team Science. There are approximately 10^185 Planck volumes in our observable universe so it takes only a few hundred bits to specify a specific instance of something inside a universe, plus a hundred or so to specify the Planck timestamp. In particular, this suggests that the third branch of Team Science is pretty small relative to the 10^8 specification of an observer architecture, not overwhelmingly larger.
One antidote to feeling like simple Turing machines can’t contain complicated stuff is to consider Universal Search (I forget its real name if that’s not it) - this is a Turing machine that iterates over every Turing machine.
Turing machines can be put in an ordered list (given a choice of programming language), so Universal Search just runs them all. You can’t run them in order (because many never halt) and you can’t run the first step of each one before moving onto step two (because there’s an infinite number of Turing machines, you’d never get to step two). But you can do something in between, kinda like the classic picture of how to make a list of the rational numbers. You run the first Turing machine for a step, then you run the first and second Turing machines for a step, and you run the first, second, and third… at every step you’re only advancing the state of a finite number of Turing machines, but for any finite Turing machine, you’ll simulate it for an arbitrary number of steps eventually. And all of it fits inside Universal Search, which is quite a simple program.
As for finding us in our universe, your estimate makes sense in a classical universe (where you just have to specify where we are), but not in a quantum on (where you have to specify what branch of the universe’s wavefunction we’re on).
I’m assuming that you’re using “Universal Search” to refer to Toby Ord’s Complete Turing Machine.
My issue isn’t with the complexity of a Turing machine, it’s with the term “accessible.” Universal search may execute every Turing machine, but it also takes adds more than exponential complexity time to do so.
In particular because if there are infinitely many schelling points in the manipulation universe to be manipulated and referenced, then this requires all of that computation to causally precede the simplest such schelling point for any answer that needs to be manipulated!
It’s not clear to me what it actually means for there to exist a schelling point in the manipulation universe that would be used by Solomonoff Induction to get an answer, but my confusion isn’t about (arbitrarily powerful computer) or (schelling point) on their own, it’s about how much computation you can do before each schelling point, while still maintaining the minimality criteria for induction to be manipulated.