Can a hypercomputer solve random sequences? I would love to know the answer to this question. Lets have a hypercomputer which is capable of doing an uncountably many computational steps in finite time with infinite memory. Now could such a cumputer predict exactly all events that happened and will happen in our universe? That is model our universe with arbitrary precision? And if yes, would this machine need to know the initial state, or would it be able to also compute it? 
I thought a lot about this and came up with two different scenarios. First one is that if our universe (its laws of physics) are entirely deterministic, then the answer is surely yes, but the second scenario is the one which I would like to ask you about. That is lets say that the Copenhagen interpretation of quantum mechanics is correct and our universe behaves randomly. Would previously mentioned hypercomputer still be able to precisely model our universe? Or I could turn this question into maybe a more formal one, that is could such hypercomputer predict digits in a random sequence?
Thank you very much for your answer,
have a nice day.
 A: In a universe like ours where quantum randomness exists, the answer is clearly No. The randomness is built-in. Thus even a hypercomputer could not calculate when a particular unstable atom decays, only what its half-life is.
But even in an alternate universe where all laws of physics are known and all laws are  deterministic and somehow the initial state of the entire universe (which could be infinite) is known to infinite precision, the answer would still be No, unless perhaps if time and space was discrete. 
Calculating stuff to an arbitrary precision is not enough if the "stuff" can have any real number value. An arbitrary precision is not generally an infinite precision. And you need infinite precision if you want to claim being able to exactly predict every action from some starting point in time and on into infinity. 
If, however, the alternate universe had a smallest unit of time and space, it seems to me that a hypercomputer would be able to accurately predict any future event.
However, in such a universe, I'm not sure it would be possible to actually generate a truely random sequence. 
