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.
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"
Maybe I'm too out of this scope but if you want to simulate Universe X plus the computer Y that simulates X then you'd need at least 1 extra bit of memory (likely way more) to encompass the simulation plus the computation running the simulation (X+Y). The computer running the simulation by definition is not part of the simulation, so how can it be that it can truly simulate itself?
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?
It’s also a little silly for the same reasons discussions of theoretical computability 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.
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...
>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...
Isn't that 'just' the laws of nature + the 2nd law of thermodynamics? Life is the ultimate increaser of entropy, because for all the order we create we just create more disorder.
Conway's game of life has very simple rules (laws of nature) and it ends up very complex. The universe doing the same thing with much more complicated rules seems pretty natural.
Yeah, agreed. The actual real riddle is consciousness. Why does it seems some configurations of this matter and energy zap into existence something that actually (allegedly) did not exist in its prior configuration.
I'd argue that it's not that complicated. That if something meets the below five criteria, we must accept that it is conscious:
(1) It maintains a persisting internal model of an environment, updated from ongoing input.
(2) It maintains a persisting internal model of its own body or vehicle as bounded and situated in that environment.
(3) It possesses a memory that binds past and present into a single temporally extended self-model.
(4) It uses these models with self-derived agency to generate and evaluate counterfactuals: Predictions of alternative futures under alternative actions. (i.e. a general predictive function.)
(5) It has control channels through which those evaluations shape its future trajectories in ways that are not trivially reducible to a fixed reflex table.
This would also indicate that Boltzmann Brains are not conscious -- so it's no surprise that we're not Boltzmann Brains, which would otherwise be very surprising -- and that P-Zombies are impossible by definition. I've been working on a book about this for the past three years...
If you remove the terms "self", "agency", and "trivially reducible", it seems to me that a classical robot/game AI planning algorithm, which no one thinks is conscious, matches these criteria.
How do you define these terms without begging the question?
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.
The real universe might be different and far more complex than our simulated reality. Maybe a species that can freely move within 4 or 5 dimensions is simulating our 3D + uni directional time reality just like we „simulate“ reality with Sim City and Sims.
> 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.
Okay, here's the thing: this is creating revenue, this is fascinating literature for a huge class of armchair scientists that want to believe, want to play with these mental toys, and are willing to pay for the ability to fantasize with ideas they are incapable of developing on their own. This is ordinary capitalism, spinning revenues out of sellable stories.
The problem of computers is the problem of time : How to obtain a consistent causal chain !
The classical naive way of obtaining a consistent causal chain, is to put the links one after the other following the order defined by the simulation time.
The funnier question is : can it be done another way ? With the advance of generative AI, and things like diffusion model it's proven that it's possible theoretically (universal distribution approximation). It's not so much simulating a timeline, but more sampling the whole timeline while enforcing its physics-law self-consistency from both directions of the causal graph.
In toy models like game of life, we can even have recursivity of simulation : https://news.ycombinator.com/item?id=33978978 unlike section 7.3 of this paper where the computers of the lower simulations are started in ordered-time
In other toy model you can diffusion-model learn and map the chaotic distribution of all possible three-body problem trajectories.
Although sampling can be simulated, the efficient way of doing it necessitate to explore all the possible universes simultaneously like in QM (which we can do by only exploring a finite number of them while bounding the neighbor universe region according to the question we are trying to answer using the Lipschitz continuity property).
Sampling allows you to bound maximal computational usage and be sure to reach your end-time target, but at the risk of not being perfectly physically consistent. Whereas simulating present the risk of the lower simulations siphoning the computational resources and preventing the simulation time to reach its end-time target, but what you could compute is guaranteed consistent.
Sampled bottled universe are ideal for answering question like how many years must a universe have before life can emerge, while simulated bottled universe are like a box of chocolate, you never know what you are going to get.
The question being can you tell which bottle you are currently in, and which bottle would you rather get.
Konrad Zuse was a German pioneer in computing, best known for building the Z3 in 1941—the world's first functional programmable digital computer. Later in his career, he explored profound philosophical and theoretical ideas about the nature of the universe.
Rechnender Raum (literally "Computing Space" or "Calculating Space") is the title of his groundbreaking 1969 book (published in the series Schriften zur Datenverarbeitung). In it, Zuse proposed that the entire universe operates as a vast discrete computational process, akin to a giant cellular automaton. He argued that physical laws and reality itself emerge from digital, step-by-step computations on a grid of discrete "cells" in space, rather than from continuous analog processes as traditionally assumed in physics.
This idea challenged the prevailing view of continuous physical laws and laid the foundation for what we now call digital physics, pancomputationalism, or the simulation hypothesis (the notion that reality might be a computation, possibly running on some underlying "computer"). Zuse's work is widely regarded as the first formal proposal of digital physics, predating similar ideas by others like Edward Fredkin or Stephen Wolfram.
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.
Sorry, I don't understand what you are saying. What do you mean by "something reasonable, that reality is virtual"? In many ways, by definition, reality is what is real not virtual. I have other questions, but this is a good start :)
I think the underlying assumption is that we are “real”, meaning our existence is grounded in some undisputed “reality”. So if what we perceive as the universe isn’t real, then there has to be some other real universe that is simulating it in some way.
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.
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.
Trying to read the paper... I guess if you ignore the difference between finite and infinite tape Turing machine, and if all physical constraints are outside the scope of the paper, then it is easy to prove the universe can simulate itself.
I wonder if there’s a concept akin to Shannon Entropy that dictates the level of detail a simulation can provide given a ratio of bits to something. Although presumably any level of bits could be simulated given more time.
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.
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.
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.
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...
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.
Time and space aren't well defined, but current models indeed put a discrete limit on both: Planck-Length and Planck-Time (~1.9×10^−43s and ~5.7×10^−35m respectively).
Below these limits, physical descriptions of the world lose meaning, i.e. shorter time spans or distances don't result in measurable changes and our models break down. That doesn't mean these limits are "real" in the sense that space and time are indeed quantised, but experiments and observations end at these limits.
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.
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.
I would consider this if someone was able to demonstrate a way to distinguish these phenomena from altered states of mind (i.e. hallucinations). We know and can demonstrate that the human psyche can easily be manipulated in various ways (psychological manipulation, drugs, magnetic fields, sleep depravation, stress, etc.) to cause such experiences.
Some actual evidence for for "past life regressions" and "astral projection" would be nice...
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.
Maybe I'm too out of this scope but if you want to simulate Universe X plus the computer Y that simulates X then you'd need at least 1 extra bit of memory (likely way more) to encompass the simulation plus the computation running the simulation (X+Y). The computer running the simulation by definition is not part of the simulation, so how can it be that it can truly simulate itself?
Maybe the problem is axiomative deduction, we need a new inference-ology?
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...
Isn't that 'just' the laws of nature + the 2nd law of thermodynamics? Life is the ultimate increaser of entropy, because for all the order we create we just create more disorder.
Conway's game of life has very simple rules (laws of nature) and it ends up very complex. The universe doing the same thing with much more complicated rules seems pretty natural.
(1) It maintains a persisting internal model of an environment, updated from ongoing input.
(2) It maintains a persisting internal model of its own body or vehicle as bounded and situated in that environment.
(3) It possesses a memory that binds past and present into a single temporally extended self-model.
(4) It uses these models with self-derived agency to generate and evaluate counterfactuals: Predictions of alternative futures under alternative actions. (i.e. a general predictive function.)
(5) It has control channels through which those evaluations shape its future trajectories in ways that are not trivially reducible to a fixed reflex table.
This would also indicate that Boltzmann Brains are not conscious -- so it's no surprise that we're not Boltzmann Brains, which would otherwise be very surprising -- and that P-Zombies are impossible by definition. I've been working on a book about this for the past three years...
How do you define these terms without begging the question?
I think I agree you've excluded them from the definition, but I don't see why that has an impact on likelihood.
That's the question that prevent me from being atheist and shift me to agnosticism.
A lot of people are more interested in the Why of the Universe than the How, though.
How is an implementation detail, Why is "profound". At least that's how I think most people look at it.
Ha
> 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.
The classical naive way of obtaining a consistent causal chain, is to put the links one after the other following the order defined by the simulation time.
The funnier question is : can it be done another way ? With the advance of generative AI, and things like diffusion model it's proven that it's possible theoretically (universal distribution approximation). It's not so much simulating a timeline, but more sampling the whole timeline while enforcing its physics-law self-consistency from both directions of the causal graph.
In toy models like game of life, we can even have recursivity of simulation : https://news.ycombinator.com/item?id=33978978 unlike section 7.3 of this paper where the computers of the lower simulations are started in ordered-time
In other toy model you can diffusion-model learn and map the chaotic distribution of all possible three-body problem trajectories.
Although sampling can be simulated, the efficient way of doing it necessitate to explore all the possible universes simultaneously like in QM (which we can do by only exploring a finite number of them while bounding the neighbor universe region according to the question we are trying to answer using the Lipschitz continuity property).
Sampling allows you to bound maximal computational usage and be sure to reach your end-time target, but at the risk of not being perfectly physically consistent. Whereas simulating present the risk of the lower simulations siphoning the computational resources and preventing the simulation time to reach its end-time target, but what you could compute is guaranteed consistent.
Sampled bottled universe are ideal for answering question like how many years must a universe have before life can emerge, while simulated bottled universe are like a box of chocolate, you never know what you are going to get.
The question being can you tell which bottle you are currently in, and which bottle would you rather get.
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.
So, as long as one believes in continuum, this is just toying around?
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.
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.
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...
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.
Below these limits, physical descriptions of the world lose meaning, i.e. shorter time spans or distances don't result in measurable changes and our models break down. That doesn't mean these limits are "real" in the sense that space and time are indeed quantised, but experiments and observations end at these limits.
https://arxiv.org/pdf/2404.16050
bad bad not good.
> Consequences of Undecidability in Physics on the Theory of Everything
https://news.ycombinator.com/item?id=45770754
An emergent simulation, nature borne out of nature, may not have those same defects.
Some actual evidence for for "past life regressions" and "astral projection" would be nice...