CeffTheCeph

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?

Good unpopular opinion!

The goal of capitalism is maximizing capital. What happens in society then is that human well-being comes second after capital maximizing. Yes, it is uncontested that capitalism has improved global human well-being. GDP growth is very obviously correlated with increase in human well-being. But correlation does not imply causation. If the goal were to maximize human well-being first and have capital come second, the outcomes would be different.

One criticism of capitalism that is ignored is that it was the 19th-20th century discovery of super-low entropy energy sources that were incorporated into production that has lead to such rapid growth in technological advances and efficiency. Within neoclassical economic models oil is considered a substitute for capital (which is infinite), not as a limited natural resource that provides energy that allows production to take place.

And so, as capitalism chugs on and on in society, burning more and more oil will continue to generate more and more capital, growth will go up and up and finally after all of that human well-being will go up and up. There is no endgame there, what happens when oil runs out? Or when there is too much CO2 in the atmosphere for human well-being to be sustained on earth?

If the goal changes from capital maximizing to human well-being maximizing then there is an endgame, to ensure ~~sure~~ that human well-being (infinite?) is always sustained on earth. Increasing capital can come after that instead.

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.

https://en.wikipedia.org/wiki/Journal_ranking

It isn't a perfect system, but it is a place to start.

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.

Any viable F_QG must meet four intertwined criteria:

This statement is simply defining the fundamental structure of how a full theory of everything would be composed. A consistent and complete theory must meet all four criteria.

Also the core concept of F_QG is defined in a very hand-wavy way. I'd like to see a concrete example of an existing theory formalized in the way they proposed in the paper.

The above four criteria are how F_QG is defined. The author, in presenting these four criteria, provides two very specific, concrete examples of theories (String Theory and Loop Quantum Gravity) while introducing the premise of his argument. He clearly affirms that these theories do meet three of these four criteria but fail on the fourth. If there were an example of a theory that meets all four criteria than that theory would be the theory of everything and the whole issue would be resolved.

It's unclear to me how mathematical derivability from the formal system correspond to how laws of physics apply. Specifically mathematical logic is a discrete process, yet the world described by physics is generally contiguous.

The rest of the paper explains exactly this. Mainly that the only way to satisfy all four criteria is to include non-algorithmic components that bridge the discreteness of math with the observable continuity of physics. The author goes on to describe several examples where this process can apply in modern physics theory.

I do agree that the author is making a dramatic and bold statement regarding a proof of a theory of everything (that being that the theory of everything can never be computational) which requires heavy scrutiny. However, I am in no way an expert in these fields and so I have accept that the journal that published the proof can provide that scrutiny. It is easy to check on the reliability of that journal as a lay person, and in doing so doesn't seem to raise any flags about the validity of the arguments the author is presenting.

I am also not a physicist nor a logician, just interested in the subject matter.

full of assertions not backed up by arguments

Can you provide some examples from the paper of assertions that aren't being backed up by arguments so I might try and look further into it? Thanks!

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.

These are all great questions we should be asking policy makers who cite 'economic growth' as justification for policy. In this context, 'economic growth' refers specifically to GDP growth. Who benefits most from GDP growth? Tobacco companies provide billions to GDP annually but also contribute to increased public health costs that everyone has to pay for in one way or an other. Growth for the sake of growth doesn't necessarily lead to the best outcomes for all of society.

The rate of return on capital is a macroeconomic aggregate of the overall rate of return that capital generates. Capital is any asset, so the rate of return on capital is the average rate of return on all of the machines in factories, all of the money in government bonds, all investments in the stock market, literally all capital of any form in an economy that is used for production or savings.

Western economies operate in a form of capitalism, which by definition means to maximize capital. So realistically, all producers in capitalist economies are incentivized to maximizing returns on capital, that's the goal.

But if we change the goal from maximizing capital to something else, like maximizing human well-being for example, than there would be less incentive for producers to constantly try to earn greater returns on capital and the growth rate of the economy could then surpass the rate of return on capital and inequality could decrease.

So in this case, investing money in libraries, schools, hospitals, transit, infrastructure etc. would generate growth without the expected rate of return on capital associated with that growth.

This is an other option to reduce the wealth gap, as was asked by OP.