If hypercomputation anywhere, we are almost certainly in a simulation

The usual simulation argument relies crucially on counting - if the number of beings with experiences like ours that are in a simulation is greater than the number that are in "base realities", then by counting we are likely in a simulation. But if there were infinitely many simulations of "us", then we'd be living in a simulation with probability 1.

In this post I simply take "hypercomputation" to be a process which can take a finitely specified computer program, and run it for infinitely many steps in finite time. By "infinitely many steps" I mean steps which can be denoted by the natural numbers: 1, 2, 3, ...

Given a hypercomputation machine, it can - in one run - run every finitely specified algorithm (from a finite alphabet) infinitely many times. This follows from a completely analogous reasoning as in any proof that a countable union of countable sets is countable. (Easier way to "see" this, requiring no countable choice, is to notice that "set of all prime powers" is a union of countably infinite collection of disjoint countably infinite sets, each consisting of prime powers for just one prime, and it is a subset of ℕ.)

Hence, if our universe can be simulated at all, and if hypercomputation exists, our universe is easy to simulate infinitely many times. Given those assumptions finitude of our simulations requires that nobody runs the above, nor any similar program, ever. In particular, it also requires them not to simulate any hypercomputation-able universes which decide to simulate us!

One way that this argument could fail is that if there are infinitely many "real" copies of "us". That would make the ultimate nature of nature quite wasteful, but she's allowed be wasteful.

Anyway, I am not too swayed by this whole argument, but I wanted to record it nonetheless, in anticipation of one day learning exactly how I was wrong about our reality to have wanted to record it.