Let us stipulate the following.
- The universe is fundamentally discrete / deterministic. (Seems reasonably plausible.)
- There’s a way to perform hypercomputation, in the sense that one can build or leverage a Turing-complete mechanism which can perform infinitely many computations in seemingly finite time, and store an infinite amount of data in seemingly finite space. (Seems wildly implausible.)
Take your hypercomputer and write some trivial code that systematically executes every possible algorithm, in particular all of the non-computable functions that require an infinite amount of steps to run. Among just a few other things, this program will eventually stumble onto a perfect simulation of our own universe, and suppose you make sure that simulation has time to run until it catches up with the current moment, so your universe and the simulation are synced up temporally (from your reference frame, perhaps, if GR is an issue).
Then take a mallet and smash your hypercomputer.
By my reasoning, it seems like it should be turtles all the way down, with infinitely many copies of you and your universe simulation if you were to drill down and examine that stack. By assertion, these are perfect simulations of the universe, such that not only will you be unable to tell them apart, but to the point where they’re isomorphic and are arguably one and the same thing.
In the slightly ‘weaker’ version of this, there remains a ‘topmost reality’. Even though you seemed to begin there, subjectively it’s all the same, so you’re Almost Surely in one of the infinite simulations, meaning you and your universe will wink out of existence as soon as you destroy your copy of it. Of course, the only you that will actually care is the one that will continue to exist, as well as presumably conclude that the whole thing was very anticlimactic.
In the stronger version, the simulated universe and your universe truly are the same thing, so when you destroy it, you don’t leave behind even a single copy of yourself that can breathe a sigh of relief.
(Also posted at LessWrong.)