Their findings, published in the Journal of Holography Applications in Physics, go beyond simply suggesting that we’re not living in a simulated world like The Matrix. They prove something far more profound: the universe is built on a type of understanding that exists beyond the reach of any algorithm.
So first is to accept this is more philosophy/religious sort of discussion rather than science, because it’s not falsifiable.
One thing is that we don’t need to presume infinite recursion, just accept that there can be some recursion. Just like how a SNES game could run on a SNES emulator running inside qemu running on a computer of a different architecture. Each step limits the next and maybe you couldn’t have anything credible at the end of some chain, but the chain can nonetheless exist.
If U0 existed, U1 has no way of knowing the nature of U0. U1 has no way of knowing ‘absolute complexity’, knowing how long of a time is actually ‘long’, or how long time passes in U0 compared to U1. We see it already in our simulations, a hypothetical self-aware game engine would have some interesting concepts about reality, and hope they aren’t in a Bethesda game. Presuming they could have an accurate measurement of their world, they could conclude the observed triangles were the smallest particles. They would be unable to even know that everything they couldn’t perceive is not actually there, since when they go to observe it is made on demand. They’d have a set of physics based on the game engine, which superficially looks like ours, but we know they are simplifications with side effects. If you clip a chair just right in a corner of the room, it can jump out through the seemingly solid walls. For us that would be mostly ridiculous (quantum stuff gets weird…), but for them they’d just accept it as a weird quirk of physics (like we accept quantum stuff and time getting all weird based on relative velocity).
We don’t know that all this history took place, or even our own memories. Almost all games have participants act based on some history and claimed memories, even though you know the scenario has only been playing out in any modeled way for minutes. The environment and all participants had lore and memories pre-loaded.
Similarly, we don’t know all this fancy physics is substantial or merely superficial “special effects”. Some sci-fi game in-universe might marvel at the impossibly complicated physics of their interstellar travel but we would know it’s just hand waving around some pretty special effects.
This is why it’s kind of pointless to consider this concept as a ‘hard science’ and disproving it is just a pointless exercise since you can always undermine such an argument by saying the results were just as the simulation made them to be.