Assume for now that the universe is the expression of a computable function. Then there exists a universal turing machine with a binary alphabet that computes this function. By compressing its input we can get a single number identifying our universe. If we knew this number and hat enough computing power we could then compute the exact timepoint of the radioactive decay of any single atom. But the number in itself would be completely random, meaning it would not be itself determined by anything else. It’s just the universe that happened to have us as part of its execution. Would you count that as “truly random” or not?
You could of course argue that the universe might not in fact be a computable function. But that claim would go far beyond just random atomic decay since we could in principle encode the time points of all radioactive decays ever into the initial number from which to create our universal turing machine.
Assume for now that the universe is the expression of a computable function. Then there exists a universal turing machine with a binary alphabet that computes this function. By compressing its input we can get a single number identifying our universe. If we knew this number and hat enough computing power we could then compute the exact timepoint of the radioactive decay of any single atom. But the number in itself would be completely random, meaning it would not be itself determined by anything else. It’s just the universe that happened to have us as part of its execution. Would you count that as “truly random” or not?
You could of course argue that the universe might not in fact be a computable function. But that claim would go far beyond just random atomic decay since we could in principle encode the time points of all radioactive decays ever into the initial number from which to create our universal turing machine.