The function exp(x—K) grows exponentially in x, but is nevertheless really, really small for any x << K. Unbounded resources for computing means that the analogue of K may be made as large as necessary to satisfy any fixed tolerance t.
Yes, for a fixed amount of time. I should have made that explicit in my definition of “describe”: for some tolerance t greater than zero, simulate results at time T with accuracy within t. Then for any t > 0 and any T there will always be a Turing machine that can do the job.
The function exp(x—K) grows exponentially in x, but is nevertheless really, really small for any x << K. Unbounded resources for computing means that the analogue of K may be made as large as necessary to satisfy any fixed tolerance t.
For a fixed amount of time. What if you wanted to simulate a universe that runs forever?
Yes, for a fixed amount of time. I should have made that explicit in my definition of “describe”: for some tolerance t greater than zero, simulate results at time T with accuracy within t. Then for any t > 0 and any T there will always be a Turing machine that can do the job.