Oh man, Stephen Wolfram and Jürgen Schmidthuber are probably fuming at the fact that this is called a "new" mathematical framework. It's all very old, and quite conventional, even popular -- not exactly the road not taken.

What the author did was use the Physical Church-Turing thesis, and Kleene's second recursion theorem, to show that: (1) If a universe’s dynamics are computable (PCT), and (2) the universe can implement universal computation (RPCT), then (3) the universe can simulate itself, including the computer doing the simulating.

That's basically all. And thus "there would be two identical instances of us, both equally 'real'." (Two numerically distinct processes are empirically identical if they are indistinguishable. You might remember this sort of thing from late 20th c. philosophy coursework.)

He also uses Rice’s theorem (old) to show that there is no uniform measure over the set of "possible universes."

It's all very interesting, but it's more a review article than a "new mathematical framework." The notion of a mathematical/simulated universe is as old as Pythagoras (~550 BC), and Rice, Church-Turing, and Kleene are all approaching the 100-year mark.

Zero cost abstractions! I'd almost be interested in Bostrom's inevitable physics-based counter (if he wasn't such a racist bellend).

Like running Kubernetes in a Docker container.

The simulation hypothesis takes something reasonable, that reality is "virtual," and runs it into absurdity.

If the universe isn't "real" in the materialist sense, that does not imply that there's a "real" universe outside of the one we perceive, nor does it imply that we're being "simulated" by other intelligences.

The path of minimal assumptions from reality not being "real" is idealism. We're not simulated, we're manifesting.

Funny people still call that "simulation hypothesis". At some point they should try to do some Past lives regressions or Out of body experience (astral projection). Then they'll know for sure what this reality is about.

The author of the article on the site, is the author of the paper!

It's starting with the assumption that the simulation would reproduce the universe perfectly; this eliminates a lot of possibilities.

Many would expect that the parent universe would be more sophisticated, potentially with more dimensions, that we can only glimpse through artifacts of the simulation.

Hope folks involved in this type of exploration have it clear in mind that what they are reasoning about it’s strictly the model of the real world only. It’s far from obvious that nature follows anything remotely computational.

We can't even run docker inside docker without making things slower, the simulator hypotheses is frankly ridiculous

I always feel like these frameworks rely on a semantic sleight of hand that sounds plausible on the surface, but when you drill down a bit they render words like 'simulation' 'reality' or 'truth' as either unintelligible or trite, depending on how you define them.

Arxiv.org PDF:

https://arxiv.org/pdf/2404.16050

Here is one thing I don't understand about these kind of approaches. Doesn't a computational simulation imply that time is discrete? If so, doesn't this have consequences for our currently best physical theories? I understand that the discreteness of time would be far below what can be measured right now but AFAIK it would still makes a difference for physical theories whether time is discrete or not. Or am I mistaken about that? There are similar concerns about space.

By the way, on a related note, I once stumbled across a paper that argued that if real numbers where physically realizable in some finite space, then that would violate the laws of thermodynamics. It sounded convincing but I also lacked the physical knowledge to evaluate that thesis.

These models get things backwards. The universe is a wave function in logic space. It appears discrete and quantized because integers composed of primes are logically stable information entropy minimal nodes. In other words the universe is the way it is because it depends on math. Math does not depend on the universe. Logic is its own "simulation." Math does not illuminate physics, rather physics illuminates math. This can be shown by the construction of a filter that cleanly sorts prime numbers from composites without trial division but by analysis of the entropic harmonics of integers. In other words what we consider integers are not fundamental but rather emergent properties of the minimal subjunctive of superposition of zero (non existence) and infinity (anything that is possible). By ringing an integer like a bell according to the template provided by the zeta function we can find primes and factor from spectral analysis without division. Just as integers emerge from the wave as stable nodes so do quanta in the physical isomorphism. In other words both integers and quanta are emergent from the underlying wave that is information in tension between the polarity of nonexistence and existence. So what appears discrete or simulated is actually an emergent phenomenon of the subjunctive potential of information constrained by the two poles of possibility.

Related?

> Consequences of Undecidability in Physics on the Theory of Everything

https://news.ycombinator.com/item?id=45770754