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. And if we have a hypercomputing process, there is quite a simple program which runs all the programs, infinitely many times, "in one run". Below's a quick sketch.
Denote the primes, with standard ordering, p1 = 2, p2 = 3, p3 = 5, ...
Our program doesn't do anything at steps 1-5, nor on the powers of 2, 3 and 5, nor on prime powers where the power is not a power of a prime.
Now let's take a program which traverses the tree of all computer programs; we run it on all numbers that are not primes nor prime powers. We run the kth step of the program found on the nth composite number, for the jth time, on the step pn+3pjk. (n+3 just because we skipped the first 3 primes, for simplicity)
Hence, the above program is run once, and we are simulated infinitely many times. So if hypercomputations exists, finitude of our simulations requires that nobody runs the above, nor any similar program, ever. (There's many other hidden assumptions here, but I'm trying not to overcomplicate things.)
One way that this argument could fail is that if there are infinitely many "real" copies of us. That makes the ultimate nature of nature quite wasteful, but she's allowed be wasteful.
If the above program is run, then there are also infinitely many simulations in which, today, the ordinary course of the simulation is broken up and an intergalactic tournament in ping-pong is played by the most capable species - so I guess the ordinariness of our reality is evidence in favor that simpler simulations somehow appear more often - but that metaprogram is (I think) more complicated than the above one, so—
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.