Under these circumstances, there is a "correct" use of the hypercomputer. While a civilization could use it to compute some strategy in a war, upload themselves into it for a form of immortality, or create a new world by instructing it to run some kind of Game of Life (https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life) program, a more practical use would be to compute the first few thousand digits of Chaitin's constant for a programming language. This is possible because we can finitely describe "attempt to run every possible source code and record if the result halts", we just need an infinite amount of time in order to finish the task. Importantly, although we can't know the exact value of \(\Omega\), the first few thousand digits are about just as good for mortal purposes.

I always imagined that, in the story, one civilization would be unsubtle and look down on the other, which would only want to use the hypercomputer for the "academic" purpose of knowing \(\Omega\) approximately, only to realize that this knowledge is possibly the most practical use of the machine.

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When I learned about this as an undergraduate I started telling people the following story: Suppose that, simultaneously, two space-faring civilizations discover a naturally-occurring closed timelike curve (https://en.wikipedia.org/wiki/Closed_timelike_curve) around a nearby black hole. Suppose further that these civilizations both know that this structure can be used to build a hypercomputer (https://en.wikipedia.org/wiki/Hypercomputation), a machine that can perform an infinite number of classical computational steps in a finite amount of time. In order to make our story more realistic, we add the following constraints:

(1) The hypercomputer can correctly perform an infinite calculation, but it must be described by a finite program.
(2) The hypercomputer can access an arbitrarily large amount of memory during calculation, but there is a fixed finite size for its output after the infinite calculation is over.
(3) A massive amount of resources are needed for each use of the hypercomputer. Perhaps it breaks after each use.

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