On your argument, there is little need to flawlessly compute the universe. If a civilization sees that their laws are inconsistent with their observations, then they will change their laws to reflect their observations. Because there is no way to conclusively prove your laws are correct, it is impossible for a simulation to state that “Our laws are correct, therefore there is a flaw in the universe”. Furthermore, on the probability that our ancestors have obtained the computing power of running a simulation:
An estimate for the power of a (non-quantum) planet sized computer is 10^42 (R. J. Bradbury, “Matrioshka Brains.”) operation per second. Its hard to pin down how many atoms there are in the universe, but lets put it at around 10^80, and with 128 bits needed to hold each coordinate, to the degree of one pm, and another for its movement, that puts it at around 10^83 operations to run a simulation.
So at first it looks impractical to compute a universe, but this computer need to perform its operations in a seconds time. (Practical value of a computer that runs infinitely slowly), it can compute its values infinitely slowly. And so, no matter the size of the universe, a computer can simulate it. And because it can compute its values infinitely slowly, it can compute an infinite number of universes.
So in conclusion, there is a very low probability that a civilization evolves to the point where it can simulate a universe, and the motives are also dubious. But, because of that fact that if it does, there is no upper bound to the number of universes the civilization can simulate, and so we are almost certainly in a simulated universe, because the probability of us being in a simulated universe is determined by n/p, where p is the probability of a universe being simulated, and n is the number of universes being simulated, that ends up being a probability of infinity, and so we are most likely part of a simulated universe.
You seem to be assuming that we’d be simulated by a universe which is physically like our own.
Our simulations, at least, are of much simpler scenarios than what we’re living in.
I’m not sure what properties a universe would need to have to make simulating our universe relatively cheap and easy. I’m guessing at smaller and faster fundamental particles.
I’m not sure what properties a universe would need to have to make simulating our universe relatively cheap and easy. I’m guessing at smaller and faster fundamental particles.
Egan has some fun thoughts about this with his Autoverse in Permutation City. The inhabitants do eventually get stuck with some contradictions that arise from the initial conditions of their universe.
You’re right, that was one of the erroneous assumptions I made. The problem with that is that there are an infinite number of permutations of possible universes. Even if only a small fraction of them are habitable, and a small fraction of those are conducive to intelligent life, we still have the multiplying by infinity issue. I don’t know how valid using infinity in an equation is though, because when there are two infinities it breaks down. For example, if they’re are an infinite amount of dogs in New York, and 10% of dogs are terriers, technically the probability of the next dog you see being a terrier is equal to that of any other dog. That again simply doesn’t make sense to me
On your argument, there is little need to flawlessly compute the universe. If a civilization sees that their laws are inconsistent with their observations, then they will change their laws to reflect their observations. Because there is no way to conclusively prove your laws are correct, it is impossible for a simulation to state that “Our laws are correct, therefore there is a flaw in the universe”. Furthermore, on the probability that our ancestors have obtained the computing power of running a simulation:
An estimate for the power of a (non-quantum) planet sized computer is 10^42 (R. J. Bradbury, “Matrioshka Brains.”) operation per second. Its hard to pin down how many atoms there are in the universe, but lets put it at around 10^80, and with 128 bits needed to hold each coordinate, to the degree of one pm, and another for its movement, that puts it at around 10^83 operations to run a simulation.
So at first it looks impractical to compute a universe, but this computer need to perform its operations in a seconds time. (Practical value of a computer that runs infinitely slowly), it can compute its values infinitely slowly. And so, no matter the size of the universe, a computer can simulate it. And because it can compute its values infinitely slowly, it can compute an infinite number of universes.
So in conclusion, there is a very low probability that a civilization evolves to the point where it can simulate a universe, and the motives are also dubious. But, because of that fact that if it does, there is no upper bound to the number of universes the civilization can simulate, and so we are almost certainly in a simulated universe, because the probability of us being in a simulated universe is determined by n/p, where p is the probability of a universe being simulated, and n is the number of universes being simulated, that ends up being a probability of infinity, and so we are most likely part of a simulated universe.
You seem to be assuming that we’d be simulated by a universe which is physically like our own.
Our simulations, at least, are of much simpler scenarios than what we’re living in.
I’m not sure what properties a universe would need to have to make simulating our universe relatively cheap and easy. I’m guessing at smaller and faster fundamental particles.
Egan has some fun thoughts about this with his Autoverse in Permutation City. The inhabitants do eventually get stuck with some contradictions that arise from the initial conditions of their universe.
You’re right, that was one of the erroneous assumptions I made. The problem with that is that there are an infinite number of permutations of possible universes. Even if only a small fraction of them are habitable, and a small fraction of those are conducive to intelligent life, we still have the multiplying by infinity issue. I don’t know how valid using infinity in an equation is though, because when there are two infinities it breaks down. For example, if they’re are an infinite amount of dogs in New York, and 10% of dogs are terriers, technically the probability of the next dog you see being a terrier is equal to that of any other dog. That again simply doesn’t make sense to me