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1. "I think therefore I am." = "Mathematics are complete."
2. "I am not a non-thinker." = "Mathematics are not incomplete."
Then while the difference between the "not incomplete" and the "complete" isn't that obvious at first, it becomes very obvious once you reference the cosmological constant. Because the cosmological constant is put into Einstein's theory, a posteriori. Which Einstein effectively does in order to make an assertment about the distribution of true statements, describing related vacuum energy density. (With true statements still being prime numbers, or quanta given by the Planck Constant.)
Or, if you again reference to the universe as a Shakespearan kind of novel, Einstein looks at the universe and says: "With this cosmological constant, the observable universe is not unwritten. Else, were the cosmological constant not to exist, everything would collapse (and remain collapsed) into a black hole. Then the universe would forever remain unwritten."
Which shows that Einstein inserted his constant, a posteriori. And then Goedel comes along and uses his theorem to show that mathematics which are purely a posteriori... are incomplete. Which appears to be correct, as there exists the cosmological constant problem. When people clearly seem to be solving a halting-problem during NDEs. Regardless of determinism.
So physics, up to the point of Einstein's cosmological constant, are purely a posteriori. Still Einstein's cosmological constant can't declare the current state of the universe as written, and he instead finds himself limited to declaring it as not unwritten... Einstein's constant cannot explain why the universe actively expands. Which also shows in the cosmological constant problem. That "not unwritten" is not equal to "is written"... that "not false" is not equal to "Truth," if this concerns the n-body problem and the question of why n-body systems of true statements are distributed the way they are, resulting in the presence of a thinking self which can be referenced via "cogito ergo sum." Because it could very well be, that to declare n-body systems of true statements as "is written," and to adequately describe universal expansion, requires a priori knowlege of Truth and a Nous type of level. Contrary to the declaration of it as "not unwritten," which might still be declarable within the confines of a posteriori knowledge.
If you consider the cosmological constant as representing a kind of "a posteriori" (or natural) function growth limit. In which case Goedel's theorem, too, can be argued as concerning itself with a posteriori math. Which Descartes and Plato reasoned beyond via occasionalism and gnosis, acknowledging the existence of a kind of Nous. If a priori knowledge is necessary for well-defined self-references (cogito ergo sum) to be made. Else you can never arrive at such statements, even when given the infinitely time-dilated "context window" of a singularity. Which then also concerns the halting-problem. As even an AI with infinite memory (infinite context window) would never reason beyond the cosmological constant to describe n-body systems. Nor would it even exist in such a world... Which is kind of funny. Given the artificially promoted propaganda narratives today. Etc.
"I think therefore I am." = "Math is complete." = "This statement is provable."
All of which can be argued as involving a priori knowledge. After all, if there's a Deus Deceptor, but Descartes knows of his existence even in face of such a Deus Deceptor, then Descartes displays "a priori knowledge" of his self-referential existence. Which is something Goedel and Einstein cannot justify.
After all, if it's merely "not a non-thinker" (rather than a thinker), this cannot sufficiently explain the existence of a self to be referenced. Which also suggests "this statement is not provable" an invalid self-reference. As the ability to make a self-reference requires a priori knowledge. And if there is no a priori knowledge (if there is no thought), there is no self to reference.
And likewise can Einstein not actually talk about universes which are written. He can only talk about those universes which are not unwritten, which isn't equal to the written. Which the cosmological constant problem shows. (The cosmological constant prevents a black hole collapse, but can't explain expansion into a big rip. It can't explain the written. And hence also why vacuum energy density appears to be ill-defined.)
And if you then set "written" as equal to a Cartesian "thought" - in the context of "cogito ergo sum" - Einstein can only talk about people who are not non-thought... He can only describe people as "not a posteriori." But he cannot describe people as "a priori." Which is an obvious problem if a priori knowledge is tied to the ability for the universe to undergo a big bang and expand. If only those worlds are possible worlds, in which there exists sufficient reason in form of a priori knowledge. (And else, without a priori knowledge, logic would be entirely circular anyway.)
Then you can, maybe, question the speed of photons as tied to a cosmological constant. And instead tie it to the existence of a priori knowledge. And acknowledge that neurons (Byzantine Generals) are always more coordinated than a random walk... true statements (quanta; primes) are always more organized than a random walk. Indeed, the inability for them to be such, could be a violation of thermodynamics. Which could then again also tie into NDEs and maybe LENR. If this existence of a priori knowledge coincides the ability to solve np-hard problems... some kind of "gnosis" or "occasionalism" is necessary in order for big rips to exist. As people are clearly implied as solving a Halting-Problem during NDEs.
Which is then also the thing in regards to random walks such spacetime curvature tied to pi, even if the ratio of pi were to change in the standard model. Einstein can acknowledge things as "not a random walk". Which is still a kind of natural "a posteriori" limit. But he can't explain them as actually evolving at the pace of a priori knowledge. With Plato, for example, then again arguing that n-body systems of true statements exist in the context of Truth. Which involves a priori knowledge, akin to "cogito ergo sum". Which seems interesting.
If a priori knowledge wouldn't exist, you could even conceive such thoughts. And you could never declare "cogito ergo sum". And the universe could never expand. And since people appear capable of solving a Halting-Problem during NDEs... The entire thing seems to be a more than just plausible. If not to be expected.
It's also the point at which "theoretical physicists" who tell you "science only informs people of what is incorrect, but never tells them about what is actually the case"... start sounding kind of funny. Anyway, if such "science" exists only as anti-thetical to strawmen such as flat-earthers. It's pretty useless and not representative of reality. It doesn't seem to be in line with the standard model of physics.
So (quantum) gravity clearly asks the question of why n-body sytems of quanta (primes; universals; true statements) can be distributed the way they are. Whereas phenomena such as the entanglement of n-body systems can definitely be argued as showing the existence of a priori knowledge. Which isn't necessarily a temporal thing. Meaning that you don't draw knowledge from the future. Instead, the "a priori" is a distinct categorical thing. Akin to the existence of a kind of Platonic Truth, which defines the distribution of true statements and then leads to the ability of declaring "cogito ergo sum", in the context of gravity and the Higgs Field. Which is a kind of metaphysical statement.
And then, even when given infinite time or infinite temporal dimensions, a hylic would remain forever limited to futile attempts of explaining the universe by the addition of "hidden" a posteriori variables. Or by believing that simply adding scale to "AI" mystically causes for the "emergence" of "New Physics". But it could never entertain the notion of "a priori knowledge", which exists within the context of the Platonic Nous or Cartesian Mind. With the body requiring a kind of gnosis or occasionalism, in order to know the mind... the body requires gnosis in order to know the "a priori" notion of Truth. As true statements, meaning primes or quanta given by the Planck-Constant, are distributed in a way as to enable the meta-statement "cogito ergo sum". Which Descartes already showed, as a priori knowledge exists within the nous or mind. And without mind, there's no a priori knowledge, and no self which a formal logical system could reference. (Which then also relates to the incompleteness theorem. As an "a posteriori" formal system without a priori notion of Truth is of course incomplete and based on circular logic... a statement which is purely "a posteriori", and thus hylic, couldn't reference itself. Because the self is directly related to the existence of a priori knowledge defining the distribution of true statements in n-body systems. (Which you might also tie to the cosmological constant probem, if "God doesn't play dice" is limited to "it's not a posteriori". But it doesn't actually explain the a priori. In which case people such as Einstein also believed into a kind of occasionalism.)
Still this "Sam Altman" believes that an AI, when given enough scale, will mystically "emerge" the ability of solving the Halting-Problem and not be affected by the incompleteness theorem. When the AI is trivially limited by the confines and problems of classical a posteriori variables.
And then you again acknowledge that people appear to be solving an NP-hard halting type of problem during NDEs, and how the existence of a big rip, too, necessitates the ability of doing so. If you have to be able to safely die, knowing that you won't /ever/ be revived. That is something people seem to be capable of solving, as they know about their revival before it happens. While spending forever in a world that is supposedly realer than this one here. That is easily considered a case of a person solving the halting problem. Which is again not necessarily a temporal thing. But it's trivially argued as tied to the distribution of true statements (quanta; universals) in the context of the n-body problem, then concerning a priori knowledge, leading to the ability to reference oneself. Which is easily tied to memory and maybe some kind of LENR type of effect. Because braindead people have computationally impossible NDEs reflected in memory after their revival. Then memory isn't again necessarily about the temporal distribution of true statements (quanta), but about this which is categorically a prori. Without a priori knowledge, there could be no memory leading to "cogito ego sum".
And then you can also spend some more time internalizing how the photolectric-effect suggests photons as being light only in the visual cortex. How soundwaves aren't a hard physical thing, but a phenomenal deception leading to the disproven iteration of aether theory. And how monkeys on a typewriter will never write a Shakespearan novel in form of the observable universe, even when given relatively infinite (dilated) time. In such a world, the universe wouldn't expand. And then the posturing of people as "educated" because they declare themelves "just chemicals", when they can't even question the qualia of photons, define the first thing about the geometric space the brain exists in, etc... They are adamant when declaring themselves as "hylics". And sometimes even beg you to accept it. It's very weird. Maybe they are...
1. There exists an unexpected excess or absence of primes (quanta) in n-body systems.
2. In order to describe this unexpected absence and excess of primes, physicists introduced anti-particles and the idea of merger and annihilation. (So if there is an unexpected absence of distributed primes in an n-body quantum system, the physicist says "there was annihilation of e.g. majorana.")
3. Goedel's incompleteness theorem concerns itself with statements of n-body systems of primes (quanta).
4. Euclidean space, if a simualcrum of math, cannot describe the distribution of primes.
5. It's trivial to argue that Einstein's spacetime is still too Euclidean, and describes spacetime curvature from the lens of Euclid's simulacrum of curvature. (Which coincides pi... gravitational curvature tied to mass coincides a mathematically incomplete distribution of primes. With pi being a product of this incompleteness.)
6. Descartes' "cogito ergo sum" proves that self-references require "a priori" knowledge of the mind. Likewise did Plato categorize "a priori" knowledge of forms on the level of the nous.
7. According to Plato, forms define the distribution of n-body systems of primes, with n-body systems of primes participating in these forms.
8. Goedel's incompleteness theorem, being purely "a posteriori", cannot justify self-references
9. People appear to be solving an NP-hard halting type of problem during NDEs... indeed, a big rip might necessitate the ability of doing so.
10. As NDEs are reflected in memory, the ability to solve the halting problem is implied as concerning memory.
So while you can technically measure anti-particles (you can measure your inability to describe n-body systems)... this wouldn't necessarily have you conclude anti-particles as actually existing. Which of course concerns black holes and dark energy, as well. Since infinite monkeys on a universal typewriter couldn't write Shakespeare even when given infinite time, or infinite temporal dimensions... given a purely "a posteriori" system, the universe would never expand and you would never form memory. Which in turn also lets you argue that e.g. entanglement isn't a temporal thing. And it also lets you argue that the ability of solving the halting problem isn't a temporal thing. Meaning that you don't necessarily have knowledge from some deterministic future when resolving entanglement or NDEs. Instead, it's rather a categorical thing.
Then you could also apply some Occam's Razor to argue for the existence of "a priori" knowledge, and the ability of solving the halting problem, when comparing the following...
1. During NDEs, upon revival, you are shown as having solved the halting problem, predicting your revival before it occurs. This could computationally explain a big rip and potentially the universe at large. And also memory. As NDEs are reflected in memory upon revival.
2. During NDEs, upon revival, you mystically enter a different timeline as per "many world theory". This doesn't explain the universe at large.
The second option clearly introduces unnecessary complexity, while not solving anything. Whereas the same would be expected as holding true for e.g. hidden variable theories. It doesn't explain anything... Indeed, the addition of needless a posteriori variables effectively prevents explanations. But still... it seems beyond plausible for NDEs to be a thing. If you acknowledge that photons cannot be assumed as being light. And you acknowledge that NDEs might actually imply the halting problem as solvable. Etc... Funnily enough, even LLMs grasp the notion behind it. Even if they can never ask these questions themselves. Maybe because they have no a priori knowledge...
Anyway, if you observe the world today, you’ll notice that a “cool story” always follows the pattern of:
1. Cherry-picking some observation. Such as there not being a second habitable planet next to earth, your peripheral vision having less detail than your focus, there being parasitic wasps, etc.
2. Drawing a non-sequitur. Such as people being an analogy machines, the universe being ruled by chaos, this being a simulation, there being no God, etc.
3. Making an appeal to emotion. Such as everything being meaningless, people merely being the playthings of aliens simulating them, the belief that might (fitness) makes right (survives), etc.
Whereas the prologue of “surfaces of essences” follows this exact “cool story” pattern. In the format of a really cool story, the prologue accompanies characters who tell you their own cool stories. Which might prompt some people to stop reading. Because it doesn’t seem very interesting. Even if it might underline the notion that people such as e.g. Darwin didn’t have the most scientific of minds. And doesn’t feel too different from Dawkins’ “the God delusion”. That isn’t just a really cool story, but a really cool book. It’s an endless stream of logical fallacies. (Aside of it being circular logic, that a person who perceives the world in form of a cool story, shares his observation on other people, too, telling cool stories.)
Regardless... First principle reasoning (actual science) as the likes of Descartes envisioned it, lies in foregoing these cool stories. Which ultimately leads you to state “cogito ergo sum”. As it seems that Descartes explicitly rejected this kind of analogous “thought”.
That (cogito ergo sum) is something an LLM will never be capable of stating. Because /reason/ is the ability to have doubt and ask first principle questions. And in order to have doubt, you first need to be mislead. Like in the case of there being “empirically measurable” soundwaves. In which case it’s trivial for you to reject soundwaves as actually having anything to do with sound, or lightwaves (photons) as actually having anything to do with light, when given the photoelectric-effect and the fact that soundwaves aren’t a fundamental force. That is contrary to an LLM, which will never experience different sensual qualias. Hence why it won’t be mislead in form of soundwaves, it won’t experience any doubt, and it won’t /reason/ soundwaves as being deceptive and photons as being perceived as different sensual qualia in each cortex. Or the Higgs boson as maybe representing different cognitive functions or even memory types in each lobe. (So, here you are reasoning about the qualia of photons and the cognitive memory function of the Higgs boson. Why would an LLM ever do such a thing, when it has no notion of qualia in the first place? It cannot reason about anything.)
The same goes for NDEs, which might hint to the ability of solving a halting type of problem, with NDEs being reflected in memory. But since an LLM has no cognitive memory tied to the Higgs boson (and no sensual cortexes tied to the photon), it cannot experience NDEs, and it cannot reason. Maybe even for e.g. Occam’s Razor. Meaning that it cannot reason it being more likely for there to be one Platonic a priori world, instead of many a posteriori worlds. With a posteriori worlds maybe not being worlds at all. And a posteriori knowledge maybe not being knowledge at all… (So an LLM will never be able to ask what a “world” or related geometric space actually is. It won’t ever consider the notion of a priori knowledge. And how memory ties into the big rip, NDEs, NP-hard problems, etc.)
With “cogito ergo sum” being a statement extrapolated from an extreme case of doubt in face of you being completely mislead by a Deus Deceiver. And still, again, the body has to know the mind, in order for this statement to be made. After all, contrary to some mathematically incomplete “I am not thinkable” or “this statement is not provable”, Descartes (the mind) is very much thinkable. Else, if Descartes were not thinkable, there would be no self to reference. Which of course concerns the distribution of prime numbers in n-body systems, in the context of self-references. With entanglement easily being argued a sign of categorical a priori knowledge… again, as per Occam’s Razor, it might make more sense for entanglement as being categorically beyond the temporal, than for there to be an infinite number of a posteriori timelines along the lines of many-world-theory. Especially if gravitational vacuum energy density is poorly defined and you end up with the cosmological constant problem, in case the geometric space doesn’t know truth, leading to numbers such as pi. Which of course concerns mass in the context of gravitational spacetime curvature. Then your notion of “mass” and related gravitational density is poorly defined, coinciding the cosmological constant problem, dark energy, etc. (So when defining the geometric space of an actual “world”, you of course have to account for the existence of a priori knowledge.)
Etc… The more you think about it, the more statements such as “I am just chemicals” seem… genuinely hylic. Especially when given how desperate some people seem to be about it. Would an actual person ever be this desperate about declaring itself non-thinking chemicals? Especially when coupled with these strange misrepresentations of “science” which seem to completely forego first principle reasoning.