Thanks, I think that is a useful observation. I agree in that I wouldn't necessarily say it is a problem for the validity of the proof itself, but I do like the extra scrutiny.

This is fun, I appreciate it. I've only made it as far down this rabbit hole to the part of building AGI on current architecture. Had no idea how much deeper this thing goes. This is the reason I was engaged in the first place, thanks for leading me down here.

Tbf, I personally don’t think consciousness is necessarily non-algorithmic but that’s a different debate.

I'm looking forward to that one when it comes up!

Thank you, this is helping. However, I am still not following your logic here, I do not know what you are referring to when you say I am missing the initial step?

1. Assume that these proposals are correct.

Is this the initial step? And if so, what are the proposals that are being assumed?

There are many situations where we just have to agree to assume. If you read 14 and 36, you’ll find some of the core assumptions that go into this letter (both interesting ideas and the same authors so you can understand why they’d continue).

I have read through the abstracts and fail to see a connection regarding assumptions in those papers and the assumptions in this proof. Can you please clarify further for me? What are the specific assumptions being made in these papers that are also being made in the proof?

An assumption Faisal makes is the rejection of objective observability which is one of those things you either believe or don’t believe

There are several different interpretations of quantum mechanics. There are very valid arguments in favor of and against every one of them. If you accept one interpretation over an other, would that not just imply you believe that the arguments in favor of that particular interpretation are more logically valid than the other arguments? And so, it follows that you would continue that line of logical reasoning in further interpretations of theory?

I don't understand how favoring objective collapse theory over objective observability is in any way making assumptions about how formal computational systems are logically constructed.

Thanks for responding! I never meant to claim that I am right. The whole purpose I am engaged in here is that I do not understand the proof at all and am trying to understand it better.

Here is where F_QG is introduced in the proof:

As we do not have a fully consistent theory of quantum gravity, several different axiomatic systems have been proposed to model quantum gravity [26–32]. In all these programs, it is assumed a candidate theory of quantum gravity is encoded as a computational formal system FQG = {LQG, ΣQG, Ralg}

Here, LQG a first-order language whose non-logical symbols denote quantum states, fields, curvature, causal relations, etc. ΣQG = {A1, A2, . . . } is a finite (or at least recursively- enumerable) set of closed LQG-sentences embodying the fundamental physical principles. Ralg the standard, effective rules of inference used for computations

Is this not just saying that it is the existing theories (string theory, LQG, etc.) that are assuming gravity takes the form of a formal computational system? And so, F_QG as it is defined above is how any formal computational system is logically constructed, as in it has to have those three components in order to logically be a formal computational system?

I am not a logician and do not understand what a first-order language is, or closed sentences or all those logic terms in the definition of notation. However, is F_QG in this case not just logically how any theory would need to be constructed in order to logically be a formal computational system? Is there an assumption being made here with regard to those three components in how formal systems are logically constructed?

Thank you for this. My recent hyper fixation has lead me down the rabbit hole of non-algorithmic theories of consciousness with a specific focus on the theory mentioned in this proof. Would I be interpreting this proof correctly in asserting that if consciousness is non-algorithmic, this proof means AGI is impossible?

Thank you!

This is the third time I have seen this story come up from three different science journalism websites recently.

Here is the actual published proof.

It seems a lot of commenters on these threads have a lot of skepticism about the authors claims, as we should with such a bold claim. Are there any mathematicians or logicians here that can actually unpack the proof with scrutiny and explain it to me in lay terms?

However, their argument rely on that ”quantum gravity” is what makes the universe uncomputable. I’m not sure how valid this statement is.

Here is the assumption the authors use that brings quantum gravity into the proof:

As we do not have a fully consistent theory of quantum gravity, several different axiomatic systems have been proposed to model quantum gravity [26–32]. In all these programs, it is assumed a candidate theory of quantum gravity is encoded as a computational formal system F_QG = {L_QG, ΣQG, R_alg} .

I interpret their assumption to mean that describing quantum gravity in this way is how it would be defined as a formal computational system. This is the approach that all of the other leading theories (String Theory, Loop Quantum Gravity) have taken, which have failed to provide a fully consistent and complete description of gravity. I think the proof is saying that non-computational components can be incorporated into a fully consistent and complete formal system and so taking a non-computational approach to quantum gravity would then incorporate gravity into the formal system thereby completing the theory of everything.

Does that make sense? I am not a logician by any extent and I have no idea how robust this proof really is. I do think the bold claims the authors are making deserve heavy scrutiny, but I am not the one to provide that scrutiny.

Disproving the 'matrix theory' is just the catchy headline to garner clicks. The results of the research are beyond just the matrix. For example, this proof means that non-algorithmic determinism isn't something that represents a lack of deeper theoretical understanding. There are theories that consciousness is non-algorithmic. In that case, this proof means that AGI is also impossible.

I genuinely was not intending to 'bait' you. You presented an argument saying your knowledge of the subject is more robust than the experts who refereed the paper. Since I am not an expert in the subject and am curious about learning more, I was asking you to guide me in that process with your experience.

I felt that your arguments suggesting that the author is presenting an inconsistent logical proof were not well defended and so I asked for clarification on the points you raised. I am still unclear what you are saying in this statement:

No, these are four criteria the authors assertion F_QG must satisfy.

These are the four criteria that establish how a computational theory is logically defined as a formal system, not an argument. The author makes this clear in addressing the notation being used:

For clarity of notation: ΣQG is the computable axiom set; Ralg comprises the stan- dard, effective inference rules; Rnonalg is the non-effective external truth predicate rule that certifies T -truths; FQG = {LQG, ΣQG, Ralg} denotes the computational core; and MToE = {LQG ∪ {T }, ΣQG ∪ ΣT , Ralg ∪ Rnonalg} denotes the full meta-theory that weds algorithmic deduction to an external truth predicate.

After that paragraph the author uses several very specific examples in modern physics theory describing how the findings apply starting with the paragraph:

Crucially, the appearance of undecidable phenomena in physics already offers empirical backing for MToE. Whenever an experiment or exact model realises a property whose truth value provably eludes every recursive procedure, that property functions as a concrete wit- ness to the truth predicate T (x) operating within the fabric of the universe itself. Far from being a purely philosophical embellishment, MToE thus emerges as a structural necessity forced upon us by the physics of undecidable observables. Working at the deepest layer of description, MToE fuses algorithmic and non-algorithmic modes of reasoning into a sin- gle coherent architecture, providing the semantic closure that a purely formal system FQG cannot reach on its own.

Again, I am trying to approach the authors bold claims with skepticism and scrutiny, not argue with you. But you have to be a little more humble, the paper wasn't published in order to convince you. Just because you weren't convinced doesn't mean that the proof is invalid.

We don't understand gravity to the point where we have a consistent algorithmic explanation for it. As suggested, there are competing theories, all of which are algorithmically based. The holy grail of modern physics is to find the algorithm that explains gravity as that is the last missing piece to finalize the theory of everything.

The results of this research are implying that it is not possible to prove, algorithmically, that gravity is quantum but rather that quantum gravity as the foundation of the universe is non-algorithmic and therefore non-computational. And so a theory of everything is impossible, implying that the universe cannot be simulated by computing the theory of everything.

This research builds on a lot of the work that Roger Penrose did in the 90s in exploring the potential non-algorithmic nature of consciousness (https://en.wikipedia.org/wiki/Roger_Penrose#Consciousness). If you read his book "Shadows of the Mind" published in 1993 you will find a prediction of future computational abilities that is a shockingly accurate description of AI deep fakes and the AI slop we see today with LLMs.

The no-simulated universe idea is one interesting conclusion of this research, but in my opinion, a more interesting conclusion of this research is that if you believe Penrose's argument for consciousness being non-algorithmic, than this research is implying that AGI is also impossible.

That does help. Thanks.