I’m concerned about how Solomonoff induction accounts for how many “steps into” a program the universe is. A program only encoding the laws of physics and the initial state of the universe would fail, because the universe has been running for a very long time. One could get around this by having the program simulate the entire beginning of the universe by looping through an execution of the laws of physics many many times before outputting anything, but this seems to have some unintuitive consequences. Since it would take bits to specify the length of the loop, shorter loops would result in shorter programs, and thus beliefs that the universe is younger would be considered more probable than beliefs that the universe is older. Additionally, though I’m not sure about this, perhaps the algorithm would believe the universe is more likely to be, say, 5 10^50 steps old that 4.49345820893410^50 steps old, simply because the latter can be written more compactly. That doesn’t seem quite right...
I’m concerned about how Solomonoff induction accounts for how many “steps into” a program the universe is. A program only encoding the laws of physics and the initial state of the universe would fail, because the universe has been running for a very long time. One could get around this by having the program simulate the entire beginning of the universe by looping through an execution of the laws of physics many many times before outputting anything, but this seems to have some unintuitive consequences. Since it would take bits to specify the length of the loop, shorter loops would result in shorter programs, and thus beliefs that the universe is younger would be considered more probable than beliefs that the universe is older. Additionally, though I’m not sure about this, perhaps the algorithm would believe the universe is more likely to be, say, 5 10^50 steps old that 4.49345820893410^50 steps old, simply because the latter can be written more compactly. That doesn’t seem quite right...