We don’t think it has exactly the probability of 0, do we? Or that it’s totally impossible that the universe is infinite, or that it’s truly non discrete, and so on.
A lot of conceptually simple things have no exact representation on a Turing machine, and unduly complicated approximate representations.
edit: also it strikes me as dumb that the Turing machine has an infinite tape, yet it is not possible to make an infinite universe on it with finite amount of code.
Suppose there’s a special kind of stone you can poke with a stick, and it does something, and any time it does something, it’s defying the pattern, you have to add more code to your computable model for it.
Meanwhile there’s a simple model of those kind of stones as performing one or other kind of hypercomputation, and while it doesn’t let you use a computer to predict anything, it lets you use one such stone to predict the other, or lets you use a stone to run certain kinds of software much faster.
edit: to be more specific, let’s say, we got random oracle magic stones. That’s the weakest kind of magic stone, and it is already pretty cool. Suppose that any time you hit a magic stone, it’ll flash or not, randomly. And if you take a stone and break it in two, the binary flash sequences for both halves are always the same. Obvious practical applications (one-time pad). So, people say, ohh, those stones are random oracles, and paired stones do not violate locality. After some hypothesis testing, they’re reasonably skeptical that you can build an FTL communicator or an uberdense hard drive from those magic stones.
Except a particularly bone headed AI. Any time it taps a stone, it needs to add one bit to the stone’s description. The AI is not entirely stupid—it can use paired stones as an one time pad too. Except, according to the AI, the first stone to be tapped transmits bits to the second stone. The AI is ever hopeful that it’ll build an FTL communicator on those stones one day, testing more and more extravagant theories of how stones communicate. edit: or a has a likewise screwed up model with incredible data storage density in the stones.
We don’t think it has exactly the probability of 0, do we? Or that it’s totally impossible that the universe is infinite, or that it’s truly non discrete, and so on.
A lot of conceptually simple things have no exact representation on a Turing machine, and unduly complicated approximate representations.
edit: also it strikes me as dumb that the Turing machine has an infinite tape, yet it is not possible to make an infinite universe on it with finite amount of code.
It isn’t a testable hypothesis. Why would anyone attempt to assign probabilities to it?
Suppose there’s a special kind of stone you can poke with a stick, and it does something, and any time it does something, it’s defying the pattern, you have to add more code to your computable model for it.
Meanwhile there’s a simple model of those kind of stones as performing one or other kind of hypercomputation, and while it doesn’t let you use a computer to predict anything, it lets you use one such stone to predict the other, or lets you use a stone to run certain kinds of software much faster.
edit: to be more specific, let’s say, we got random oracle magic stones. That’s the weakest kind of magic stone, and it is already pretty cool. Suppose that any time you hit a magic stone, it’ll flash or not, randomly. And if you take a stone and break it in two, the binary flash sequences for both halves are always the same. Obvious practical applications (one-time pad). So, people say, ohh, those stones are random oracles, and paired stones do not violate locality. After some hypothesis testing, they’re reasonably skeptical that you can build an FTL communicator or an uberdense hard drive from those magic stones.
Except a particularly bone headed AI. Any time it taps a stone, it needs to add one bit to the stone’s description. The AI is not entirely stupid—it can use paired stones as an one time pad too. Except, according to the AI, the first stone to be tapped transmits bits to the second stone. The AI is ever hopeful that it’ll build an FTL communicator on those stones one day, testing more and more extravagant theories of how stones communicate. edit: or a has a likewise screwed up model with incredible data storage density in the stones.