Talk:Theory of everything/Archive 3

Archive 1

Archive 2

Archive 3

Possibility of a TOE

Also, I can inform you that TOE (physics) actually is about a combination of QM and general relativity, so the fact that Alexander is a phenomenologist and instrumentalist is of no metaphysical meaning to this TOE page. But it might in fact be because of the lack of this TOE especially , that Mr. Gieg has developed these theories. —Preceding unsigned comment added by 83.134.84.140 (talk) 00:52, 2 June 2008 (UTC)

The problem with the name "Theory of Everything", at least as far as it's referring to a physical theory, is that it's imprecise. A more appropriate name would be, say "General Theory of All Physical Phenomena", or something like that. That's because Physics doesn't study "everything", only a subset of it. It doesn't study, for example, where Mathematics or Logics come from. For Physics, Mathematics and Logics are "givens", something that simply "is there", available for physicists to use.

As for a philosophical (metaphysical) "Theory of Everything", it's just impossible. The reason is simple: a "Theory of Everything", to really be "of everything", would have to be able to explain itself under its own terms. Now, a theory is, by definition, a formal construct. Being formal, it's dependent on a formal language. But Gödel has proved that no formal language can express itself. Thus, any "Theory of Everything" would necessarily lack at least its own explanation (and probably more), meaning it's not "of everything", but only, again, a theory describing a subset of "everything".

As for instrumentalism and phenomenology, those two aren't needed in the above argumentation, but I'll talk a little about both for the sake of completeness. They'd apply to the meaning of an hypothetical "General Theory of All Physical Phenomena". If such a theory came to exist, an instrumentalist would look at it and say: "It's cool indeed, but this doesn't change the fact that you don't know at all whether those beautiful mathematical entities the theory talks about, be them strings, aether, space-time distortions, quanta etc., are something that exists in reality, or whether they are just a clever way to describe with high precision, by way of unobservable fantasies that aid our reasoning but have no reality in and of themselves, all the macroscopic phenomena we actually observe."

A phenomenologist would add to this: "Not only what the instrumentalist says, but also no one can affirm there's a real world 'out there'. We have access only to sensory perceptions recombined by our minds into conceptual wholes we ordinarily call 'things', but are better called 'phenomena', to make it clear we're talking about things as perceptions, not things-in-themselves. Sure, we can study phenomena 'out there' as if they were real entities in themselves, but that's imprecise. In fact, what we're studying are our own perceptions, or as happens in the sciences, arbitrary formal constructs in correlation with these perceptions. As for the 'out there', meaning a space-time outside our perception, we cannot say anything about it, not even that it 'exists' in any meaningful sense of the word, except as the phenomenal background in which distinct phenomena develop. What's outside our perception or outside a formal system cannot be known. Only perceiveds, perception itself, and formality are known. And from these, only what's formal is scientific."

All sciences are de facto instrumentalist and phenomenological. It's lack of philosophical rigor that leads both scientists and common people to believe (and this is a pure belief) that science talks about concrete realities, not about formal systems built upon purely perceptual phenomena. Such a naive belief is a jump to conclusions, and jumping to conclusions is never scientific. -- alexgieg (talk)

Thank you for the clear insight. I think we both agree this pertains to TOE (philosophy). As such, that indeed has deep metaphysical issues. The only thing I can add to that is a quote from Albert E. himself;

"The eternal mystery of the world is it's comprehensibility", where one could in fact ask the question as to why, if it's not "REAL", why it all works out so beautifully? ( Not including any non-local theory ofcourse, this not being determinism)

So if Albert E. can't answer this question, I'm not even gonna try :)

But the objection still stands, that instrumentalism and phenemologism are only metaphysically prefferred, if science can't explain everything. But as SR states, a new macroscopic theory should indeed help with many such problems, maybe all problems, and for sure with problems imagined unexplainable such as 'immediatism' and 'over-unity', and how there are shapes and sizes ( info on how matter relates to energy )

Why the link of logic and mathmatics with 'realness' is not found is perhaps then more a problem of neuro-science, where conciousness and abstractability are closely related?

—Preceding unsigned comment added by 83.134.83.20 (talk) 21:37, 2 June 2008 (UTC)

More to the point even is one of the last sentences on this TOE (physics) page, if physicalism is true, a physical TOE would coincide with a philosophical theory of everything

Next to the fact that the author of SR is a software model engineer, and self-taught theorethical physicist, he is also a philosopher. One of the main physical implications of SR's correct metaphysical and mathmatical thought, is the non-existence of a vacuum. You know, a physical/metaphysical vacuum is where there is literally nothing there. One of the more famous metaphysically/mathmatically correct quotes of Mark Fiorentino is

"You cannot put something into nothing".

Think about that for a minute..

Thought about it?

This in itself implies a 5th dimension. It implies this dimension is solid (From What is outer space?) Preceding unsigned comment added by 83.134.83.20 (talk) 01:35, 3 June 2008 (UTC)

Journalism

A continuation of TOE science communcication, leaving from wiki/Talk:Theory_of_everything#TOE_science_communication where whe have left off

From Journalism Wikipedia:NOT#OR

Journalism. Wikipedia should not offer first-hand news reports on breaking stories. Wikipedia is not a primary source. However, our sister project Wikinews does exactly that, and is intended to be a primary source. Wikipedia does have many encyclopedia articles on topics of historical significance that are currently in the news, and can be updated with recent verified information.

Adding this primary reliable source as a reference would make wikipedia a secondary source not a primary source. Please get your facts straight.

So it's still about either adding an "invariant laws" piece as only a metaphysical piece, with either one of these references

• Relativity / General Relativity
• Objections against relativity / Lorentz (A.Einstein)

Einstein letter to Felix Klein (A. Einstein)

---

or with this reference as to the current status in invariant laws

these would be then added to the recent addition

---

an addition with only a 'new laws' reference, without the current status reference would be outdated but still correct. —Preceding unsigned comment added by 83.134.83.20 (talk) 18:26, 3 June 2008 (UTC)

There's a difference between a news piece about the discovery of a new law, accepted as such by the scientific community, and a news piece about the opinion of an individual who believes he discovered a new law. I myself could invent a "new law" and manage to get some scientifically illiterate journalist publish a news piece about it in some secondary or tertiary generic and scientifically illiterate online news source.

Can you show some reliable scientific journal, say, Nature or PNAS, reporting on the discovery of this new law? If no, why not? -- alexgieg (talk) 19:50, 3 June 2008 (UTC)

You are wrong in your premise. This is not about the new law, but all about the possibility thereof.

This should indeed be the question. Should it stand in between determinism and approximations?

For completeness sake; of course...

But indeed there would be a problem linking this kind of subtractive approach, which is in itself very referencable, to this news about a subtractive approach, as where there is no verifibility as to wether this is the subtractive approach mentioned in relativity. The only clue here available that it does abide to relativity laws, is that it's called

• Super (SR) Relativity; where there is clear direction as to the extension within and to relativity, following "Lorentz",

In the "car fuel" article, a physicist reading invariance mechanics, would immediately think about Lorentz, within relativity

• Objections against / "Lorentz" (A.Einstein); which says relativity is wide open to unite with "Lorentz". this for sure meaning the subtractive approach, because of the importance of Lorentz invariance in such a possibility, and the subsequent possibility of a 'new law' on it's own.

So these references would indeed have to be both included —Preceding unsigned comment added by 83.134.83.20 (talk) 00:57, 4 June 2008 (UTC)

For other references also see these googlepages --83.134.75.215 (talk) 01:51, 7 July 2008 (UTC)

A cookie

I will give a cookie to the first person who can point a mistake(-><-) on this phrase:

A theory of everything (TOE) is a hypothetical theory of theoretical physics

—Preceding unsigned comment added by 200.104.185.223 (talk) 01:03, 2 July 2008 (UTC)

Well it's theory, so theoretical physics is a given! You can't mix hypothesis, which is proposed answer about something, as theory is much closer to a given answer, a solid guess!

It's a tautology —Preceding unsigned comment added by 99.238.142.12 (talk) 15:29, 21 August 2008 (UTC)

I thought it was saying that the theory of everything was just a theory. I chuckled when I read that. Hopefully I wasn't being silly and laughing at the wrong thing. :< —Preceding unsigned comment added by 208.190.25.220 (talk) 20:25, 3 November 2008 (UTC)

Theory of Everything is a name, a folder perhaps that contains all note able scientific contributions. every theory since man began to write. Theory of Everything should be call the Super Teacher, anyhow are everybodies theories correct? The scientific communities do not always agree, but will concurr on specific laws, and there applied sciences. Scientists have accumulated an atlas of experimentation since the early days of commercial and governmental development projects. That information is todays subject matter by a broader audience, as the interest and new discovery employs further quest to identify better with an experience life forms have come to cheerish honor and analyse to its foundations, It is the respect of posterities that we keep these special records and gifted contributions, for advancement. In the TOE multiple tables are availible to use as tools and guages like applied mathamatics one formula introduced with others to confirm or result. within this folder of applied mathimatics reside fundimental basic knowledge, revolutionary discover and unique insite BENEFITED by ageless curiosity driven by a sensation in the human apparatus to evolve. TOE is not the theory its the blackboard of our intuitions and what knowledge in our possesion available to confirm our hypothosis that will directly respond with predictions. Predictions require result, yet the scale of our predictions are no longer simple experimentation, When Einstien, predicted the bending of light, that prediction could only be observed outside our Planet. This was a monumental experiment, never been done before, His predictions needed multiple scientific disciplines in order to confirm and his prdiction eventually was cornfirmede with the help of photography and a solor eclipse in addition with some good nautical navagation, vuala, light was observed bending and confirmed by the community! So a theory of everything simply implies under this asumed name all related field of study are malgamated to support another potentially monumental prediction, That will be the theory. Also included are the very possibilities that a unifying theory will even exist, when and whats it's purpose. —Preceding unsigned comment added by 24.161.43.109 (talk) 18:32, 12 August 2009 (UTC)

• Well, for one, that phrase should end in a period. Also, when defining a phrase, one should not use a word in that phrase to define it.24.243.103.249 (talk) 05:56, 12 October 2009 (UTC)

Combining the theories

Combining the elements, forces of the universe is impossible, even Einstein knew that...but did not say it publicly, he worked on it until the end of his life.

Theory of everything was possible when all the forces were held together at the beginning of time, since they split (after big bang, within our universe, not within multiverse where light did not reach us yet), atoms split and went their different aways, changed or combined into other forms, structures. I think theory of everything, something close to it is possible but not fully, mathematical formula would be complicated! {{{ BoxingWear - BWear - Miranda }}} (talk) 23:04, 4 September 2008 (UTC)

Theory of everything is yet to be found. So, Wikipedia should use this page for allowing scientists to express their views freely; every view should be available for everyone to read; there should not be any deletions. And readers should give their feedback encouraging every attempt if it is correct. One such theory has been formulated by me, but peer-reviewed journals are afraid of their prestige,learned referees lack courage to take risk; and so the scientific community is being deprived of the right theory. —Preceding unsigned comment added by 219.90.99.11 (talk) 08:51, 22 April 2009 (UTC)

Nuclear Force

Shouldn't the nuclear force be on the breakdown chart below Strong Force ? 76.66.198.171 (talk) 08:02, 10 January 2009 (UTC)

The nuclear force is the strong force (aka the strong nuclear force). PaddyLeahy (talk) 19:46, 10 January 2009 (UTC)

I cannot get my head around how all the sciences are intrarelated in there language of communicating, intuitivly I imagine the theory of everything will have too bring together the reletive formulation in overlay of data,they would in that case require symatrial metre, this would require more intelectual resorces than i have too bring too bear on this topic,but considering history ,the tower of baael comes too mind. —Preceding unsigned comment added by Munkey corpse (talk • contribs) 16:43, 13 January 2009 (UTC)

Four radical routes to a theory of everything. New Scientist.

Here is an interesting article:

"Four radical routes to a theory of everything." 02 May 2008 by Amanda Gefter. New Scientist. Magazine issue 2654.

• http://www.newscientist.com/article/mg19826542.300-four-radical-routes-to-a-theory-of-everything.html

Full article:

• http://www.tmcnet.com/usubmit/2008/05/02/3423660.htm

Here is another article:

"Our world may be a giant hologram." 15 January 2009 by Marcus Chown. New Scientist. Magazine issue 2691. Full article:

• http://www.newscientist.com/article/mg20126911.300-our-world-may-be-a-giant-hologram.html?full=true

I don't pretend to understand either article. :) --Timeshifter (talk) 08:35, 30 April 2009 (UTC)

Here is another related article:

"How to map the multiverse". May 4, 2009 by Anil Ananthaswamy. New Scientist. --Timeshifter (talk) 15:18, 6 May 2009 (UTC)

теория ЭМР (Электромагнитного резонанса) вращающихся масс на примере планета Земля.

Теория единого поля как частный случай теории ЭМР ,расчет частотного спектра геомагнитного поля ядра земли и его строение.

  ядро земли и мониторинг землетрясений
 http://forum.web.ru/viewtopic.php?f=29&t=2605&start=195
 http://live.cnews.ru/forum/index.php?showtopic=49543&st=0

cтроение земли

 http://forum.web.ru/viewtopic.php?f=29&t=2599

Или альтернативная физика ,от автора ,имеющая перспективу : - при освоении дальнего космоса(передвижение со скоростями , близкими к скоростям света). - генерции энергии - мониторинг ЗМТ. - создание ЧД(пространства , невидимым локаторами). - управление сознанием и т.д. и т.п. авторский алгоритм , советую просмотреть. от автора Арсеньева А.А. Россия Приморский край г.Арсеньев —Preceding unsigned comment added by 86.102.37.96 (talk) on 13:53, 12 April 2010 (UTC)

As far as translation utilities can tell me, this appears to be a personal fringe theory based on an analogy with electromagnetism, and the supporting links provided are discussion forums. Material in this article should be based on sources that satisfy WP:RS, and should already be recognized to some degree by the scientific community (per WP:FRINGE and WP:UNDUE). --Christopher Thomas (talk) 23:14, 28 December 2010 (UTC)

Godel's Theorem

Godel's Theorem makes use of the fact that an infinite series of steps or statements cannot be formally proven within a formal logic, as the practicality of independent verification is sadly wanting. Thus, its fundamental relationship to Cantor's Diaganol slash, in which it seems intuitive to conclude that the suggested conclusion is true, because the premises are so straight-forward, but a formal proof would require not only a) the soundness of the start, and b) the soundness of the recursive step by itself, but further c) that the recursive step be applied infinitely, until a qualitative transformation results from the infinite quantity.

(A. a finite list of numbers, arranged in a grid, B. a sample taken at a diagonal through the grid, and added as a new number to the list, or tacking on additional digits as necessary, C. that a new number can be generated in all finite samples until the list created is an infinite list of numbers each with infinite digits)

Thus, one solution that presents itself is to decide if this and other infinite-regress arguments can be accepted as true, by the introduction of a new principle, without rendering obviously (and not-so-obviously) false statements to be so "proven" as valid within the resulting system. --65.37.105.102 (talk) 21:41, 16 April 2010 (UTC) TheLastWordSword--65.37.105.102 (talk) 21:42, 16 April 2010 (UTC)

Even such a solution would not invalidate the proof in the larger sense, that a formal system can, and must, fail to prove its own validity. Why this might imply that human beings cannot ultimately understand the physical universe, however, seems unclear to me. It means only that human beings can never prove the "validity" of human reasoning in total, which is far different from proving the validity of human reasoning concerning the laws of physics. If I ask you "What do you know of physics?", the answer can be valid or invalid. If I ask you "Why do you bother to study such an esoteric and useless subject as physics at all?" the nature of the answer is likely to be far different (!!!) but ultimately, there is no formally valid answer to offer. (Much to our shared dismay.) --TheLastWordSword (talk) 16:21, 17 April 2010 (UTC)

Godel's Theorem applies not to 'underlying rules' or axioms but rather to formulae derived many iterations down the line. Of course the initial axioms would be consistent. Thus there is no 'definitional' explanation for the difference of opinion among physicists on TOE and Godel. —Preceding unsigned comment added by 76.22.58.46 (talk) 02:59, 26 January 2011 (UTC)

Origin of the Phrase "Theory of Everything"

The article states that the term "Theory of Everything" was coined by John Ellis in 1986. If you look at that letter in Nature, John Ellis says: "Less seriously, I plead guilty to coining TOE as a non-anatomical acronym for Theory of Everything in an article that appeared in Nature (323, 595–598; 1986)." He is claiming responsibility for the acronym, not the phrase itself, and he's not very serious. mahaabaala (talk) 08:58, 4 December 2010 (UTC)

Move

The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

The result of the move request was: page not moved per discussion below. - GTBacchus^(talk) 21:39, 28 December 2010 (UTC)

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Theory of everything → Theory of Everything — Relisted. Vegaswikian (talk) 20:46, 16 December 2010 (UTC) ToE is almost universally capitalized in any physics textbooks and publications (plus the usual abbreviation is ToE, and not TOE). Headbomb {talk / contribs / physics / books} 02:40, 9 December 2010 (UTC)

• Support per nom 64.229.101.17 (talk) 05:55, 9 December 2010 (UTC)
• Oppose though I don't feel terribly strongly about it. I don't see how it's a proper noun (there could in principle be more than one such theory, that made the same predictions) and the general Wikipedia style is to be spare with upper case. I suspect the capitals in the literature relate to the tongue-in-cheek origins of the phrase. --Trovatore (talk) 06:59, 9 December 2010 (UTC)
  • Not really. It's like "Grand Unified/Unification Theory" or "Theory of Evolution" etc... It does not refer to a theory of everything, but rather the "theory of everything", hence "Theory of Everything" and not "theory of everything", in exactly the same way GUT does not refer to a grand unified theory, but the "grand unified theory" hence "Grand Unified Theory". Headbomb {talk / contribs / physics / books} 07:12, 9 December 2010 (UTC)
    • I'm fairly sure I'm used to seeing theory of evolution in minuscule rather than caps. I think caps would look a bit strange, frankly. --Trovatore (talk) 07:22, 9 December 2010 (UTC)
      • It depends on whether you are referring to evolutionary theory "i.e. the theory of evolution" or the "Theory of Evolution". Headbomb {talk / contribs / physics / books} 07:46, 9 December 2010 (UTC)
        • Well, no, actually it doesn't. I would find Theory of Evolution strange-looking for either meaning. --Trovatore (talk) 07:47, 9 December 2010 (UTC)
          • Well, yes, actually it does. Ask any biologist worth their salt out there. Alternatively, you can check out some books about the language of science, such as this. Lowercase "theory" means the details of it, uppercase "Theory" refers to the whole framework. (P.S., no point in me asking this to them again, I already did.)Headbomb {talk / contribs / physics / books} 07:49, 9 December 2010 (UTC)
            • You ask 'em. I think you're wrong. The first couple pages of Google hits confirms. --Trovatore (talk) 07:56, 9 December 2010 (UTC)
• Oppose. Compare General relativity and Special relativity, both of which also refer to specific models and are occasionally, but not usually, capitalized. --Christopher Thomas (talk) 21:26, 16 December 2010 (UTC)

The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

Core ideas of a TOE

For the infinite divisibility of everything, the concept of elementary particle in recent physics should be eliminated and repalced with the concept of "material point". Similarly, in mathematics, we use "point" to define everything like line and plane. As for physical process, the elementary unit should be the encounter of two material points. Thus, the fundamental principle is: When two objects can be treated as two material points, they will combine to a single material point when encountered, and its velocity will be

${\vec {V}}={\frac {E_{1}{\vec {v_{1}}}+E_{2}{\vec {v_{2}}}}{E_{1}+E_{2}}}$

With this principle, everything could be described in infinite precision, in theory. Nightingale.zj (talk) 10:35, 23 March 2011 (UTC)

Another Cookie

The following sentence doesn't make sense.

Many candidate theories of everything have been proposed by theoretical physicists during the twentieth century, but none have been confirmed experimentally.

You can never confirm a theory experimentally. You can only disprove it.

So, I would suggest something like

Many candidate theories of everything have been proposed by theoretical physicists during the twentieth century, but all of them have been have been disproven.

The problem is that I don't know if this is true. — Preceding unsigned comment added by 193.136.138.62 (talk) 17:14, 16 June 2011 (UTC)

Foundation of Theory of Everything

A research article has been published in the journal Indian Journal of Science & Technology & is available on www.indjst.org. The theory presents a different perspective of existence of matter, time, space & radiation besides almost proves the existence of aether. — Preceding unsigned comment added by 59.94.190.171 (talk) 09:50, 2 September 2011 (UTC)

This page is not about the latest paper on TOE

It's about well established approaches that have been discussed by the scientific community, not about everyone who writes a paper or a book somewhere, especially if it isn't even published. 98.244.54.152 (talk) 17:11, 19 May 2012 (UTC)

Foundation of Theory of Everything (Only written material without mathematical formulae & figures)

Sorry for the new post above previous one. This write up while having merit, sets a definite tone as Philosophy. And by nature is to complex for inclusion in this article as content. I appreciate the time and effort it took, yet, I did not take the time to read it in its' entirety. The text cites too many conjectural authorities as references, for demonstrations. This provides a lack of focus. Demonstration must be valid in the argument itself, without requiring the reader to brush up with Aristotle, Descartes, or any other researchers ideas. It needs to stand up on its' own merit in other words. Please don't be offended, the content is well written and may be of value, I wish the writer well and hope he can find a vehicle to present his ideas to interested parties. Jeffrey mcmahan (talk) 12:43, 13 March 2013 (UTC)

It was a copyvio of the paper at this URL, there's no need to quote it in full on this talk page. I've removed it. --McGeddon (talk) 12:58, 13 March 2013 (UTC)

Candidate Theories

I'm somehow missing a list of current approaches towards a ToE. I found a recent overview in these slides:

• String Theory
• Canonical quantization in metric formalism
• Path integrals: Euclidean, Lorentzian, matrix models,...
• Loop Quantum Gravity (LQG)
• Discrete Quantum Gravity: Regge calculus
• Discrete Quantum Gravity: Causal dynamical triangulations
• Discrete Quantum Gravity: spin foams, group field theory
• Non-commutative geometry and non-commutative space-time
• Asymptotic Safety and RG Fixed Points
• Emergent (Quantum) Gravity
• Causal sets
• Cellular Automata

If someone with a little more background could incorporate this list into the article, I'd find that a significant improvement, even though these approaches surely have very different ambitions regarding their explanatory power. I'm not even sure though if my links are always pointing to the right article and even though there is the article Physics beyond the Standard Model, I could not find any list such as the above anywhere on Wikipedia. --Mudd1 (talk) 11:00, 24 September 2012 (UTC)

/* Alternate Mathematics */ — Preceding unsigned comment added by Beercandyman (talk • contribs) 21:26, 1 December 2014 (UTC) I'd like to point out that Gödel had the incompleteness theorem and the completeness theorem. I believe that most of the problems in reconciling QM and GR is using the wrong number system. We currently use Real numbers but Real number have infinity embedded in their definition. Real number are continuous and yet continuity is not needed compactness is. I define "C" (capital C) equal to the largest number you will need not equal to infinity. For example if you talk about all the undividable quanta in the universe it does not make sense to speak of all the quanta plus one. The rational numbers seem a better choice. If you pick a finite number set to describe the mathematics of physics then Gödel's completeness says you can have a theory of everything.

Another interesting thought is that there could be only 3 1/2 dimensions. Since no one has ever seen or measured anything going backwards in time, time would be a half dimension. I note that string theory only uses integer dimensions and yet if you imagine a compact universe instead of a continuous one fractional dimensions would seem natural. — Preceding unsigned comment added by Beercandyman (talk • contribs) 21:22, 1 December 2014 (UTC)

Too much attention to Godel arguments

The Godel arguments against the potential existence of a Theory of Everything aren't taken seriously by modern physicists or mathematicians. It's fine to show both sides of the debate, but together they encompass something like 10% of the article. By analogy, we wouldn't want 10% of the article on The Origin of Species to be misapplications of the second law of thermodynamics to disprove evolution, even though we could find lots of literature on both sides of this "debate." — Preceding unsigned comment added by 128.179.153.19 (talk) 12:59, 2 February 2015 (UTC)

"Fundamental theory of physics"

I see this expression "a fundamental theory of physics" in Google Books. Is this a reference to the ToE? If yes, are there any refs towards this (ie. the ones that directly say that FToP == ToE)? If somebody finds one, please add into the intro and into Fundamental theory (disambiguation). Staszek Lem (talk) 17:44, 24 July 2015 (UTC)

I think that:

Solving the theory of everything using Euler's formula and category theory results in a 3 dimensional universe. (simulation by any Turing complete computer provides bridge between lisp machine using recent topological and set theory related proofs. — Preceding unsigned comment added by 74.206.96.92 (talk) 14:38, 17 August 2015 (UTC)

Basically all I'm saying is that it takes two turing machines, only pentagon, triangle and square blocks, to equal an infinitely powerful lisp machine and 3d universe printer. It's basically cause of the new "ceiling" of the proof tower linking exponentials and functional programming to "boolean anylitical geometry" within and without of the rectangular prism physical building (like a skyskraper as wide as math as we know it.) — Preceding unsigned comment added by 74.206.96.92 (talk) 14:58, 17 August 2015 (UTC)

What the heck is going on? Someone just came up with a theory of everything solving for the cosmological constant and quantum entanglement and no one has disproved it yet?!!! Are Conway, Mira and the topology and set theory logic users going to disprove it? Where the **** are the Boolean geometry experts? The cult of Pythagoras and Euclid are probably keeping us from turning into a black hole right now... — Preceding unsigned comment added by 72.208.57.4 (talk) 11:00, 18 August 2015 (UTC)

Basically, with the recent shape configurations composed of rhombuses that aren't technically patterns because they are individually distinctive, the octagon composed of 10 right triangles making squares and four more not making squares, the regular pentagon, the "golden" rhombus that has a golden ratio of side lengths and a certain angle, it's pretty darn easy to combine Boolean algebra, Euclidian geometry, and Euler's identity to make a 2d model of a unique universe containing universes of pure quantum entanglement of a certain shape. Instead of strings, basically the entire universes shape and quantum entanglement contents take the strings place. Relativity is provided by distorted the plane. It states on the relevant article about the relevant patterns that it is a 2d geometric topic that is quite a recent revolution. It was thought impossible to come up with a collection of shapes like this that was not a repeating pattern. It can be used to create any turing computable encoding given enough space. — Preceding unsigned comment added by 74.206.96.92 (talk) 14:46, 10 September 2015 (UTC)

penrose tiling is the quadralateral arrangement I'm refering to. I might be mistaken about the rhombus part actually. — Preceding unsigned comment added by 74.206.96.92 (talk) 14:59, 10 September 2015 (UTC)

TOE vs. ToE

This article uses the acronym of ToE when practically everyone else uses TOE for theory of everything. I tweaked the article to use the BIG TOE, but someone but it back to the small ToE. 2601:589:4705:C7C0:1C96:2508:525A:2F69 (talk) 16:03, 1 January 2016 (UTC)

2601:589:4705:C7C0:1C96:2508:525A:2F69: I have made your changes per [1]. Dreamy Jazz ^{talk | contribs} 11:23, 3 July 2018 (UTC)

Theory of Local Universes

We have to renormalize the first cause, and the fundamental forces themselves at the maximum energy (there is a limitation due to causality breaking; that's an issue because that limit can be outreached but with some rules).

The terms "theory of everything" is wrong, except if we prove that any universe is of a single group of mathematically similar universes, which is wrong.

We should use the term "Theory of Local Universes". — Preceding unsigned comment added by 2A02:587:410E:2B59:A072:6C41:4B28:5761 (talk) 07:35, 11 August 2020 (UTC)

there may be ohter multiverses out there, but its light did not reach us yet, as far as theory of everything, no, all powers of the universe including dark matter, dark energy, gravitation field, electricy and megnetism only existed at the moment of big bang as one unit. also, energy can not be killed or created (thermodynamix) but that is only on earth but since universe expands energy has to create it, so there is no energy and since energy does not die, universe does not die or shrink but it expands but not at the speed of light!!!

Regarding the incompleteness argument against attempting a TOE

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I understand that the section Theory of everything#Arguments against is only meant to give a flavor and references to the topic. But i will here make my own criticisms of some of those criticisms, because i feel it is the right place, where some readers will find them interesting. First of all the statement « any "theory of everything" will certainly be a consistent non-trivial mathematical theory » is dubious: a physical theory is not a mathematical theory. There are actually several notions of a mathematical theory, the most commonly used being a 1st-order classical theory with equality, but we could well consider alternatives, like intuitionistic logic, or other non-classical logics. Beyond this, when modeling some physics we only attribute a physical interpretation to very few mathematical variables and well-formed mathematical formulas, clear from the context. When we work in ZF set theory we will construct real numbers, vector spaces,... many mathematical objects and then apply them intuitively to some physical situation, assuming a certain level of accuracy, limitations on how faithful our mathematical description is. But there is of course plenty in our ZF theory that we can express that is not supposed to model anything physical, whatever the context, whatever the physicists or mathematicians doing the modeling. In fact much weaker theories than ZF probably suffice to prove all rigorous results of current physics -though of course there are many concepts which are not yet rigorous, like solutions of equations of fluid mechanics, or the quantum field theories of high-energy physics. It seems unrealistic to expect any nontrivial mathematical theory to be a physical theory -in particular a TOE. After all, how could we expect a simple intellectual construct to exactly match some set of physical phenomena ? And there is little point in attempting that: it is enough to have a flexible mathematical framework where to easily model physics of all kinds, which is what usual set theory provides. Next it seems to me that one difficulty with the existence of a TOE is not mentioned in that section: proving existence of some mathematical objects satisfying what we observe in reality may be impossible in usual mathematics, in ZF(C) set theory. For instance it may be that the standard model of particle physics cannot be proved to exist in ZF -proving existence of quantum Yang-Mills theory with the expected properties is one of CMI's millenium problems. It would make sense then to add to our mathematical theory the desired existence as axiom, or some other axioms which imply it. Especially if we can prove that those axioms are consistent with ZF. I should mention here that the standard model is known to only be an effective theory, only an approximation of a more accurate theory, like the Navier-Stokes equations are only an approximation of the evolution of newtonian fluids; and in both cases it is conceivable that the more accurate models have regularizing effects which allow existence for all (initial or boundary or otherwise) conditions, while the effective theory provably does not have solutions in some cases. So even though a TOE might be a good framework to study small scale/large energy phenomena it may not provide the nice expected existence results for effective theories, which may be consistent with a given TOE without being provable in the TOE, so we would have useful physical models in ZF or some extension thereof not strictly consequences of our TOE -this does not seem to be mentioned in the various critiques cited in the page. Gödel's incompleteness theorem is really a theorem about computability, in particular about self-reference. So eventually, the question of its applicability to a physical theory depends on what we mean to use our physical theory for. Perhaps the very concept of a TOE implies that we want to do "everything" with that physical theory: we would use it to model any kind of computer. We could actually do the same with a theory of psychology: after all it is always humans who think about such issues, so a theory describing all their mental processes must describe all the theories they come up with; so perhaps psychology is a TOE. Research, reflection is an inherently circular process, which is well embodied by our brains: with recursive connections, and rythmic looping activation of its diverse pathways. We may consider psychology as part of chemistry (so perhaps chemistry is a TOE), chemistry as part of quantum physics (...), and quantum physics as part of a TOE, and this as part of set theory, and set theory as part of psychology. But most mathematicians would recognize set theory as a theory of everything, mathematical or not: except for some logicians, set theorists, and "foundationalists" (who may consider higher-order logic or some axiomatization of category theory as alternative to ZF), sets are more than enough for mathematicians, and for physicists. So arguing that logical incompleteness is a limitation to the existence of a TOE seems to imply that we want to apply our TOE to problems of logic and computability, which are already well understood within logic and computability. This does not make much practical sense, and we know already the conclusion. It is like expecting our TOE to explain to us why planes fly, or water boils at 100ºC: those questions belong in theories which are accurate enough where they apply, and have well understood answers -though some may argue that water is very complicated and still poorly understood, with papers published in Nature and Science every year. :) The issue of limits on accuracy, observed in the text, is very interesting; i do not know how far it has been explored in the literature, but to the comments and citations in this wiki page i would add considerations of complexity: there may be tradeoffs between accuracy of a theory and its computational complexity. For instance theory X may be in theory more accurate than theory Y, but the computations in X may be so complex as to make theory X unwieldy and yielding poorer results than theory Y. This is related to the above. If we try to describe chemical reactions or psychological phenomena with the standard model of particle physics we won't get very far. Such tradeoffs can be observed in a finer situations, for instance in video games we may use ray-tracing or lightmaps to render a scene, and although the former is more accurate, it will yield poorer results on a slow machine -not in a given image once rendered, but in the whole animated result being unbearably slow. In conclusion i would say that the "incompleteness critique" is (given present knowledge) either trivially right, or trivially wrong, depending on what we mean our TOE for: if we mean to use it as a mathematical theory to decide all mathematical statements (say the continuum hypothesis) then the critique is right, but if we mean, as seems to be the intention of high-energy physicists, to be a physical theory modelling all fundamental physical phenomena leaving place to other theories at large scales, low energies, or high complexity (low entropy), thus most probably to be a theory of quantum gravity, then Gödel's incompleteness is irrelevant as we would just prove the necessary existence results in ZF, or add them as axioms -and all known mathematical undecidability results would surely be unaffected. Given the remarks above i guess that the name "theory of everything" itself makes little sense: it would be more descriptive and less polemical to call that kind of theory a "fundamental theory of physics", "theory of fundamental phenomena", "theory of fundamental forces", "foundation of physics". Note also that there would actually be infinitely many such theories, as we could add random axioms which are untestable, for instance large cardinal axioms in set theory -though i think some set theorists believe that some large cardinal axioms could somehow imply down-to-earth existence results in analysis, or more plausibly in computability theory, but anyway... PS: I hope wiki's editors will not be annoyed by this lengthy entry. I feel that the wiki discussion page is the ideal place to make such comments, as for now the subject is not difficult, serious, well-defined, or useful enough for physics journals. Yet it is good to have a somewhat centralized discussion, where to gather comments, some of which will turn out useful. Plm203 (talk) 19:02, 11 August 2023 (UTC) Addenda: First note that what is discussed above and in the wiki article is only a mathematical notion of incompleteness of a putative TOE. This is because Gödel's theorem is a theorem about a formal mathematical system, extended to other mathematical systems -it is mostly applied to recursively axiomatizable 1st-order theories. The undecidable statements within a formal system are mathematical. For instance those constructed by Gödel are: 1 a fixpoint of $\neg {\text{Prov}}_{\text{PA}}(|\phi |)$, where $|\phi |$ is the Gödel number of $\phi$, and ${\text{Prov}}_{\text{PA}}(n)$ is a formula in PA modeling provability in PA and 2 in his "second incompleteness theorem" the metatheory formula ${\text{PA}}+{\text{Con}}_{\text{PA}}\not \vdash {\text{Prov}}_{PA}(\neg 0=1)$. Remark that Gödel's theorem, and indeed the whole field of logic (and computability), involves modeling of a physical or psychological nature: PA is expressed in a metatheory with symbols that as humans we connect to one another, and within our metatheory we prove eg that the PA-formula ${\text{Prov}}_{\text{PA}}(|\phi |)$ is equivalent to ${\text{PA}}\vdash \phi$. The metatheory is usually taken ZF set theory for comfort but it can be much weaker: for instance Gödel's theorem can be proved within PA itself, as can be the independence of the continuum hypothesis or the axiom of choice from ZF. One can also model recursively axiomatizable 1st-order theories in PA and construct a PA-formula ${\text{Prov}}_{\text{ZF}}(n)$ which models provability in ZF, ie such that ${\text{Prov}}_{\text{ZF}}(|\phi |)$ is equivalent in PA to ${\text{ZF}}\vdash \phi$. We can thus prove in PA that ${\text{ZF}}\vdash {\text{Con}}_{\text{PA}}$ -the formula ${\text{Con}}_{\text{PA}}$ will be different from that in the 1st paragraph, as we were in the meta language of informal set theory, while here the formula is a formal ZF-formula expressed in the meta language of PA. But of course we cannot prove in PA that ${\text{ZF}}\vdash \phi$ implies ${\text{PA}}\vdash \phi$, nor just that ${\text{ZF}}\vdash {\text{Con}}_{\text{PA}}$ implies that ${\text{PA}}\vdash {\text{Con}}_{\text{PA}}$. And this is general: when proving things in mathematics (ie set theory) we use finitistic means (in the sense of Hilbert, included recursion), so any theory like PA (i think it is enough that our theory can decide the "value formula" for a universal Turing machine, $U(n)=m$) is enough to reason rigorously about proof. In other words, one can study within PA all rigorous demonstrations: that is prove that the demonstration gives the desired result. But that does not prevent us from being interested in more powerful theories than PA, and to usually work with a language and axioms stronger than the minimum required: in the practice of mathematics we make decisions as a community, we get interested in some theories and settle for some language, and we usually reason within set theory, or some kind of type theory, or just some theory even closer to the subject of study -before set theory of course people would reason only this way. We even usually only formulate some very partial axiom system, or not even that much, just some vague idea of the things that hold and of the results we derive, and then writing down our thoughts for others is nontrivial, it takes some time, or we may not even be able to achieve it. Coming back to incompleteness: the mathematical statements which are undecidable within PA or any mathematical theory will a priori only have mathematical interest. In particular in any mathematical theory where we have expressed a physical TOE (or fundamental theory of physics, FTP, or FOP, foundations of physics) it is plausible that no physical statement is undecidable. Up to the present time no physical statement (the definition of what is "physical" is to be agreed upon by "the community" as a matter epistemology) has ever been proved independent of set theory. It is conceivable that the well-posedness of some "physical" PDE could be independent of set theory, or that "P=NP" is independent of set theory, but it seems reasonable to assume that physical statements can be decided within a simple and reasonable theory such as ZF. It is a very interesting problem at the crossroads of logic, psychology, and physics to define some kind of measure of "physicality" of a statement, and determine some kind of probability for a statement with a given level of physicality to be decidable in a "natural" formal system (as ZF). At any rate there is a more straightforward and physical notion of incompleteness in physics: consider the state of physics at the end of the 19th, when researchers expected nothing new in physics would be discovered. Yet theoretical and experimental progress showed that there were many phenomena that were up-till-then poorly modeled or entirely ignored. It is not impossible that humans in one thousand years discover some hitherto totally ignored phenomenon that does not fit in any previous fundamental theory. Beyond this: perhaps the universe observable to present humans does not even display some phenomenon that will be observable to future humans, or that is observable to other intelligent beings, or simply that exists. The anthropic principle implies a strong such limitation, that there are parts of the universe unobservable to humans because humans cannot exist in them. After those remarks it looks quite probable that any fundamental theory is physically incomplete, that it is only a foundation for local physics (a FLOP :). I've read that some physicists deplore the existence of such an idea as the (or an) anthropic principle, arguing that it demotivates researchers, but 1 i see no evidence of that, 2 motivation to do research in any field of science seems to me to rely on many other factors, 3 the anthropic principle says a priori nothing of the complexity of humanity-local physics, they can be very complicated, 4 there are plenty of fields of research other than fundamental physics, which are arbitrarily complicated, and actually even if at some point some anthropic principle is seen as justified humans may always try to falsify it, or research as pure mathematics (pure thought) the physics of an imaginary universe where no anthropic principle holds. The second addendum is to the 4th section in my entry. So we have a circular chain of theories with fundamental physics expressed within psychology (as mental dynamics) and psychology expressed as the dynamics of brains (made up of fundamental particles described by our FOP). But i should have made an important observation: when we theorize and describe psychology we assume that is only an approximation, a coarse description of more complicated phenomena (dynamics of many neurons); but when we describe fundamental particles within the standard model of particle physics we assume it is very accurate, and a requirement for a FOP would be that it would be ideally "exact", that is its theoretical results would exactly match "ideally prepared" real experiments, and with it we could do numerical computations to an arbitrary level of precision which would also match any real phenomenon to an arbitrary level of precision. Several observations: First on psychology, on why it is limited in accuracy. We would usually not model all interactions of the brain with the physical world, or indeed with the rest of the human body, which may eg fail due to a heart attack -this does not prevent us from describing a human researcher thinking about fundamental physics within psychology. Next on physics, limits on accuracy are mentioned in the article: matching to reality is itself a poorly controlled process, which will usually be extremely difficult to analyze. In general there are many uncertainties that are irreducible, or course we have the quantum mechanical uncertainty principle, but even with a hypothetically perfect classical model of measurement/experimentation (like a wind tunnel and a theory of fluid mechanics that would be perfect/fundamental) we can easily prove that a human+digital computer system cannot match the experimental apparatus -under reasonable assumptions and almost surely. A further difficulty is that current models of particle physics are only perturbatively defined, from an effective lagrangian whose couplings and masses are running. Of course we expect the theory does exist mathematically (exactly, in particular nonperturbatively), and the idea of a TOE/FOP implies that we can make exact theoretical computations, and numerical to arbitrary accuracy. I note here that the issue of complexity is too easily overlooked. For instance does it not make sense to consider that an analogue computer like a wind-tunnel is a counterexample to the Church-Turing thesis ? The answer would surely be yes if we take into account complexity and social limitations, as there will be analogue computers that cannot which can obtain better results than any digital computer mankind can build. I think this kind of question is well tackled in some articles on "hypercomputation" -i only know the field exists, i've never read any article. There is one field where complexity is taken seriously: quantum complexity, with the question of quantum supremacy. However i would like to end with a plea for the Church-Turing thesis, in fact a "moral proof" of it: i should have remarked that the very idea of a FOP (or TOE) and the observation of a circular chain of theories/models (from physics to psychology) implies the Church-Turing thesis; it is clear that any theory of psychology should be computable, that is its results should be recursively enumerable (it is already clear from our practice of mathematics and modeling, all being done in ZF, a recursively enumerable theory), but would have to be proved in detail in a given theory of psychology -in all this text when i use "psychology" it should probably be read as "human reasoning" or "cognition", here we don't need emotions, dreams,...-; thus if we can as humans formulate a FOP, it will be necessarily be describable and interpretable (in the sense intuitive sense, or the rigorous sense of logic, originally investigated by Tarski) within psychology, but then all its results, "theoretical or numerical", would be recursively enumerable, thus our fundamental theory would be Church-Turing computable, but given sufficient computational power it also approximates any possible theory of real phenomena, in particular any real computation -we can limit what we call "computation" or just call "computation" any real (observable or not) phenomenon, and it does not present additional difficulty for a Church-Turing computer with unlimited power. Thus bar complexity limitations the Church-Turing thesis holds. PS: I hope again that wiki will forgive my lengthy comment -which seems to be at its home. Plm203 (talk) 20:16, 13 August 2023 (UTC) Third instalment, a couple of addenda: First i think that what i called a "circular chain of theories" had perhaps better be called "cyclic chain/sequence of theories", or "cycle of theories", as "cyclic" is used in category theory and algebra -as in "cyclic order", or "cyclic set/object". And it is certainly interesting and natural to consider generally, for the sake of it, the complexity theory aspects of sequences of theories, beyond just the practical examples mentioned above and in common science. For instance in research one derives theorems, or makes further assumptions (adds axioms), which simplify greatly the proofs of further results. In logic and simple mathematics this is a domain of proof theory, where questions of speedup are investigated; i'm not familiar with it, butt could be interesting to look at the subject beyond pure mathematics, to connect with more applied issues, and with theoretical physics. In my two previous entries there is an important point which i did not make explicit: in logic there are several cognate notions of comparing or modeling one theory in another, or one computational system in one theory. There is the notion of extension of theories, where one adds axioms, or formulas, even quantifiers, or deduction rules. There is also the notion of interpretability (not usually related to the notion of interpretation in model theory, but of course they can be related to one another), where one defines (ie translates) the terms of a theory S in a theory T in such a way that T proves the results of S -that is T with the definitions is an extension of S. And finally there is the notion which i used in my discussions above, and which is implicit in discussions of TOEs, of description or a theory in another. In traditional logic there is the notion of representation of functions in arithmetic. $f$ is representable in theory T (in the language of arithmetic) if there is a formula $\phi (n,m)$ that is true in T if $f(n)=m$ (there are further refinements of the notion), and with this notion one shows in a metatheory modeling both PA and Turing machine computations that Turing-computable functions are representable in PA -and there are weaker arithmetical theories where (partial) recursive functions are computable. The notion of describable extends this to theories. Roughly (and i have only thought about this at the intuitive level) all theories which can represent recursive functions should be able to describe one-another. This is related to my remarks on descrbing ZF proofs/provability in PA. Now description is what scientists do most naturally: using mathematics to describe the world, to do physics, should correspond rather closely to the notion of description i evoke here, and describing psychology within chemistry, or chemistry withing quantum mechanics, or all of those within a FOP, would be formalized as descriptions in this sense. But now the remark on computability indicates that to describe a FOP/TOE we only need a theory which can represent Turing computation/recursive functions. So from a mathematical perspective and if we only require being able to reason about a theory (without asking feasibility/practicality) we already have plenty TOEs, and they are all mathematically incomplete. We may consider theories where we manipulate physical objects directly, where we only axiomatize physical phenomena, but this seems extremely awkward: even the purest of physicists finds very practical to manipulate numbers, like natural numbers, and we can roughly describe numbers in terms of elementary particles or physical objects like beads made of zillions of elementary particles, but the description would be very complicated, approximate, and require a very heavy formalism, to basically do just common arithmetic. So the notion of description, and a practical theory of mathematics where we describe physics is what we want, and we are back to my original observations on incompleteness(es). One observation may make the foregoing clearer: we always have computers at hand and as a community formalize much of our science on computers nowadays, and see with experience that we can always work out such formalism, and we often do bits of that and of programming so as to have our ideas yield rigorous theoretical results or more often computations -ie working out large but relatively straightforward/repetitive particular cases. So all the theorizing we do is realized in (Turing) computations, and we do not conceive otherwise, because we intuitively know we can model our brains and even compute them with a powerful enough computer -some thinkers like to sometimes claim not but... In physics nowadays we clearly expect computers to participate in all our large computations, in high-energy physics in particular for a FOP as it will be a primary field of application; in mathematics nowadays we have theorem provers used to prove nontrivial results, and we can (with time) feed them any mathematical theory we use as humans. This does not exhaust though the discussion on restricted/weak theories to do physics. In mathematics there is the subject of reverse mathematics: we seek the weakest theories (in terms of quantification allowed and axiom sets) which prove a given common mathematical result. This tells us about the strength of theories and mathematical results and also of their difficulty. One can add complexity to this but i think usually researchers in the field don't do it. Now i am not aware of highly "physical" results which have been "reverse-mathematized" but it would be interesting to figure what minimal axioms can prove that Lipschitz ODEs or some classes of PDEs are well-posed, or results in quantum mechanics like the uncertainty principle. Or to construct the full quantum gauge theory of the standard model of particles. I should briefly mention the issue of defining "physical": it would be quite complicated, there is a psychological aspect in the sense of closeness to physical phenomena observed and reflected upon by a human brain. This would be reflected in a mathematical theory describing physics. In the previous post i said that questions of computability were somewhat physical, but then we quickly derived that everything is physical, so we should introduce quantified nuance to this. There would be social aspects to take into accound, as research is highly dependent on and structured by society. I can also mention the notion of decider: a Turing machine which halts on every input. This is related to strength and consistency strength of a theory: a typical such Turing machine is one which halts after n deductions in a given theory if it has not found a contradiction, and loops indefinitely otherwise; a decider for ${\text{Con}}_{\text{PA}}$ can be proved to be a decider in ZF but not in PA -of course both theories can represent the function corresponding to this decider machine. Another standard example, of similar flavor is the Goodstein decider, which halts if the Goodstein sequence terminates (at 0) on input n, therefore can be proved to be a decider in ZF but not in PA. Yedidia and Aaronson have constructed a 7918 states-Turing machine (with 1 tape and 2 symbols) whose non-haltingness implies that ZFC is consistent and thus which cannot be proved not to halt, though they prove it halts in a consistency-stronger theory. All TM can be run in simple theories but there are small computers whose behavior we cannot predict although we can make reasonable guesses. This leads to the issue of what makes a mathematical theory "natural" and (partially in particular) trustworthy. Pondering the issue it becomes clear that the main reason is psychological: humans are used to considering sets of things, this is a very sensory experience, we visualize, verbalize, or "auditivize" several similar objects, and we pick one within them. We have cognitive structures, hardwired in our brains, well-designed to carry out such tasks, to realize such neural dynamics. Thus it is natural, easiest for us to abstract from such "real" mechanisms. We build up our mathematical and mathematical modeling abilities throughout life in introspection/reflection and in interaction with sensory experience (a little) and mostly with society in particular with its scientific output and discussing science with other humans. Society will search for an optimal presentation of its scientific theories, through various processes. And so far the first-order theory of sets has settled as the most efficient way to do mathematics/computations. As remarked previously most mathematics do not require the full power of ZFC, and set theorists would like to reject choice as standard axiom, but the mathematical community likes to have it (in Zorn's lemma, algebraic closures, maximal ideals,...). It is practical, it makes some results simpler to prove too. And there is a sense that it is consistent, which we could reformulate in the form "it is infinitely counterintuitive that ZFC is consistent". When reformulated this way we see that consistency should really be considered from a quantitative perspective: imagine a theory that is inconsistent but whose shortest proof of a contradiction is $10^{1}00$-deductions long, then two things 1 humans would never find any inconsistency and all the results they would obtain would be "essentially" consistent and as useful as if working in a consistent theory and 2 actually it is probable that such a theory would have to have a rather complicated axiom system and that the contradiction would rely on some tricky, interesting mathematics. Now i don't know if the question has been researched, but i think that inconsistencies in a given "size n" theory can with high probability be reached in "few steps" relative to n. Thus having as a community explored set theory quite thoroughly without finding any inconsistency we can (could) be highly confident that it is consistent -of course this raises the issue of how representative or exhaustive human exploration is, but i think it would not be too "nonuniform". But to be honest, even this is overkill: as humans we make innumerable mistakes, but through education we learn to correct, to check better when necessary, to make-do with approximate results; so if ZFC was inconsistent we would instantly work around it, it would surely be in an interesting way, and the inconsistency would obviously bear very little relevance to building bridges or sending rockets -whose theories rely on much weaker mathematical theories than ZFC as hinted above. Of course the consistency any mathematical theory that will be used to formulate a FOP will never be fully explored; but this is somewhat misleading: we can actually make sure to a very high-degree that it is consistent, by normal mathematical research, but also in a more systematic way, and we could probably quantify in a nice way how consistent we have made sure it is -by the hypothesized results on the complexity of inconsistencies as function of the size of a theory. PS: I'm pretty sure i'm forgetting things i thought i would write, but that will be it for now. A big thank you to the admins who allow my commenting here, which i think is still relevant to the page's topic. Plm203 (talk) 05:04, 16 August 2023 (UTC)