[pino999]

It goes like this: We have two observers with a computer. A is outside a black hole. B goes over the event horizon. B is infinitely time dilated seen from A. It takes forever for B to reach the singularity from A standpoint. B reaches the middle in a finite time.

A starts computation. If it halts A sends a result, otherwise it won't.

B sees the result in a finite time. If it doesn't, the program didn't halt.

If time is discrete, it won't fly I think. This works because there is no smallest time unit in gr.

We are working with different types of infinities. A's computational steps take, the further B goes in, less time. Sort of Zeno's paradox. It is easy to map all natural numbers between 0 and 1 on the real line. Just not 1 to 1.

There are more problems.

How to get the information out and how to survive the divergent blue shift, it is somewhat unclear. B cannot talk back. But still a cool find.

[JadeNB]

> It is easy to map all natural numbers between 0 and 1 on the real line. Just not 1 to 1.

For the usual meaning of the term, you certainly can construct a 1-to-1 (that is, injective) map N \to [0, 1] (for example, n \mapsto 10^(-n)); the natural numbers just can't be mapped onto [0, 1] (that is, the map can't be surjective). That's the opposite of the problem we have: it's saying you can losslessly encode a countable amount of information in an uncountable amount of space; but I'm saying conversely that you can't perform an uncountable number of steps in a countably infinite amount of time.

[pino999]

But the computation steps are certainly countable, even if there are infinite. The amount of steps in time we can take is uncountable. We can always find a point between two other times.Time dilation does exactly this, making the time a computational step take smaller and smaller.