New mathematical framework reshapes debate over simulation hypothesis
23 comments
·December 21, 2025A_D_E_P_T
HPsquared
I'm no mathematician, but doesn't this come up against Gödel's incompleteness theorem? My brain has that roughly as "If you have a system and a model of that system, but the model is also part of the same system, something something, impossible"
bananaflag
No, this sort of self-reflection is exactly what makes Gödel/Turing/etc impossibility results work ("strange loops" and all that).
keepamovin
Isn't GIT you can have a statement that is valid in a system, but can't be proven this way or that given the systems' axioms? And this is true for all such axiom systems? In other words the axioms are an incomplete description of the system.
Maybe the problem is axiomative deduction, we need a new inference-ology?
anthk
Any decent Lisp can reimplement eval, apply and the rest of functions/atom within itself.
ericpauley
It’s also a little silly for the same reasons discussions of theoretical compatibility often are: time and space requirements. In practice the Universe, even if computable, is so complex that simulating it would require far more compute than physical particles and far more time than remaining until heat death.
Borg3
Hehe yeah.. For me, its just inverted search for the God. There must be somethink behind it, if its not God, then it must be simulation! Kinda sad, I would expect more from scientist.
The big riddle of Universe is, how all that matter loves to organize itself, from basic particles to Atoms, basic molecues, structured molecues, things and finally live.. Probably unsolvable, but that doesnt mean we shouldnt research and ask questions...
FabHK
Yes, is that (obvious) point being addressed in the paper? At first skimming, it just says that a "sufficiently souped up laptop" could, in principle, compute the future of the universe (i.e. Laplace's daemon), but I haven't seen anything about the subsequent questions of time scales.
NoahZuniga
Thanks for this great comment!
> He also uses Rice’s theorem (old) to show that there is no uniform measure over the set of "possible universes."
I assume a finite uniform measure? Presumably |set| is a uniform measure over the set of "possible universes".
Anyway if I understood that correctly, than this is not that surprising? There isn't a finite uniform measure over the real line. If you only consider the possible universes of two particles at any distance from eachother, this models the real line and therefore has no finite uniform measure.
daoboy
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.
CuriouslyC
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.
EdgeCaseExist
Exactly, it's paradoxical; how would you define the universe as a simulation, without being on the same substrate! The title should have focused more on the computability of the universe, as we know it.
mgaunard
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.
te7447
I've always wondered how you'd be able to rigorously distinguish breaking out of the simulation from just discovering novel things about your current universe.
Is a black hole a bug or a feature? If you find a way to instantly observe or manipulate things at Alpha Centauri by patterning memory in a computer on Earth a special way, is that an exploit or is it just a new law of nature?
Science is a descriptive endeavor.
I guess that some extreme cases would be obvious - if a god-admin shows up and says "cut that out or we'll shut your universe down", that's a better indication of simulation than the examples I gave. But even so, it could be a power bluff, someone pretending to be a god. Or it could be comparable to aliens visiting Earth rather than gods revealing themselves - i.e. some entity of a larger system visiting another entity of the same system, not someone outside it poking inside.
anthk
Also that Universe could use entities similar to hard and soft links (quantum entanglement), memory deduplication and so on.
How many people did we met in the world with similar face appearances and even personalities, almost like you are finding copycats everywhere? Also, it happens as if some kind of face/shape would just have a single personality with minimal differences spread over thousands of lookalikes...
quantum_state
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.
mw67
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.
EdgeCaseExist
The author of the article on the site, is the author of the paper!
mg74
Which of him is simulating which?
boomskats
Zero cost abstractions! I'd almost be interested in Bostrom's inevitable physics-based counter (if he wasn't such a racist bellend).
nrhrjrjrjtntbt
Like running Kubernetes in a Docker container.
raverbashing
We can't even run docker inside docker without making things slower, the simulator hypotheses is frankly ridiculous
lioeters
That's what a simulated universe running inside Docker would say.
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.