Essay Abstract

ABSTRACT: In this paper we show that the term 'fundamental', as used in physics, can generally be defined from two different points of view. Firstly by looking at this term from the frog's perspective within our limited world and secondly by looking at it from a bird's perspective above and beyond our limited world. One of our main results is that what seems to be fundamental from a viewpoint within a certain system can be fundamentally meaningless from a viewpoint outside this system and vice versa. We further demonstrate that unequivocally answering the question "what is 'fundamental'?" is an instant of the so called 'Boolean satisfiability problem' (SAT-problem). We solve this SAT-problem by a modus operandi which transcends these extrinsic and intrinsic viewpoints by introducing a fundamental concept that is capable of being universally valid inside as well as outside our limited world. Our approach is able to explain the origins of mathematics as well as those of antivalent logic. It further shows that the problem to assign any truth value 'true' to the 'possibility' that absolutely nothing instead of something could have existed in the past is an unsatisfiable SAT-problem. By the very reason that our framework spans the bridge between the extrinsic and the intrinsic, it finally establishes a bird's view on certain aspects of ultimate reality.

Author Bio

The author's main scientific interests are mathematical undecidability, algorithmic information theory, questions concerning consciousness, human free will and logics. Additionally he is interested in various interpretational questions about quantum mechanics.

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Hi Stefan - I enjoyed reading your paper - You sound very philosophical in this presentation. I gather from your conclusions that it is not possible to start with nothing. You must start with "F" and accept it as a fundamental truth from which everything else can be logically (and mathematically) derived. That leaves us with one important question... (which in essence is the same question I posed to another similar philosophical essay)... Who gets to figure out "F"?

    Scott, thank you for the comment. My opinion on this is that one cannot completely 'figure out' F, in our limited world this is impossible. Every F can simply be doubted. If you mean by 'figure out' a kind of formal proof, one cannot prove by means of a formalized procedure that ultimate reality is *not* entirely only a formal system. Only a formal system can prove itself to be formal, what gives us no new information. 'F', in my opinion, is not fully formalizable and therefore not provable, similar to every nuance of our emotions. Surely, one may believe that consciousness and emotions can one day be formalized completely as kinds of special mathematical patterns (in the brain). I doubt this. This led me to conclude that - due to my conviction that one has to start with 'F' - one either ends with 'F', or with the deduction that 'F' must exist - but cannot be fully formalized. The latter not due to practical impossibilities, but due to a *fundamental* principle. This 'principle' says, in my opinion, that ultimate reality is not exclusively only composed of formal systems but necessarily must be more than that. Because since mathematics as the prime formal system cannot prove its own consistency and completeness, the assumption that formal systems are fundamentally capable of encompassing the real 'F' seems to be absurd to me. Especially if this 'F' should be mathematics itself.

    I agree - "F" cannot be provable - but "F" can be physical with a mathematical description. If the initial conditions involving "F" sets off an inevitable chain of events that also follows a mathematically derivative course, and in doing so leads to every known law of physics and property of particles... then we may have something!

    Yes, then we have at least a logically consistent scheme. But it would not automatically be a scheme that necessarily must be realized by nature. I think - due to Moore's theorem mentioned in my essay - that what you describe is indifferent to the status quo of fundamental physics today. Cause there are a multitude of different interpretations of quantum mechanics, all matching the 'known' laws of physics, means the observational output these laws generate. In all these interpretations, 'initial conditions' are interpreted differently.

    I love your essay. This is my turf.

    A truth is an absence of choice, a fact.

    A truth is only valid in the truth system that created it.

    Nothingness is the necessary logical opposite to existence.

    Existence-being is not possible from nothingness.

    But existence as "happening" is possible. Happening is not being...

    We must understand the universe as such a logical system, born from nothingness via a loophole in the primitive rule of non-contradiction...

    My essay is coming up. You might like it.

    Marcel,

      Marcel, thanks for your comment. Happy that you like what i exemplified in my essay. I am looking forward to your essay contribution to be published!

      Hi Stefan, In your last response to my statement (Scott S Gordon) :

      "If the initial conditions involving "F" sets off an inevitable chain of events that also follows a mathematically derivative course"

      You stated,

      "Yes, then we have at least a logically consistent scheme. But it would not automatically be a scheme that necessarily must be realized by nature.

      Actually if the initial condition is so basic with only one ingredient (and the energy associated with it), and it derives every law of physics, the manner in which each particle exists and came to exist, every force, every energy field.. - It would have to be the ONLY scheme possible - And afterall, are we not looking for the solution to the theory of everything? Do you think there are multiple solutions?

      Once the laws of physics are known and the manner in which they came into existence is known - there should only be ONE solution. So again the question becomes - Who finds the initial ingredient (and its associated energy) and their mathematical representations?

      Scott, you make some very strong claims.

      I have a question: how can you know that

      "...it would have to be the only scheme possible"?

      As I outlined in my essay, the criterion for every TOE must be Truth, not simplicity. This somewhat simple statement may hit you, but even your own approach has to obey a simple scientific rule for being able to claim to be the one and only TOE: it must make a testable prediction that could be falsified. Even for the case that such a 'TOE' incorporates 'all the known laws of physics' (what I seriously doubt in case of your approach) - it must be able to derive from within itself a prediction of a phenomenon that has not yet been observed. Or do you think that mankind has already observed ALL natural phenomena that are observable according to our hitherto known physical laws? Do you really think that physics is theoretically and practically a finished job? Wouldn't claiming such things have at least a little bit of hybris within it and for the more serious case even the inability to discriminate between what has factually been achieved by physics (or by the own approach) and what one wishes to have achieved by one's own approach?

      For the case you want to talk me into your approach to be indeed THE TOE..., I would recommend you to go again to the drawing board and find a testable prediction your approach is able to make from within itself.

        Yes - I AM making a huge claim - and of course people will question it... like when you say you serious doubt that my theory explains everything. You asked what my theory predicts... My theory predicts that the experiment planned for neutrino/anti-neutrino annihilation that there will be no annihilation despite the "fact" that neutrinos were "proven" to have mass.

        By definition the math of the theory of everything must begin very simple since it starts with one ingredient. It has to be more simple than any equation we have because it starts before ANY particles were created to exist in spacetime (and all we know is the physics and math of particle that exist in spacetime). The math of the theory of everything has to built to the math that derives the postulates used to create GR and QM. If the postulates used to derive these two theory can be derived by one model, then they will automatically be united under one theory.

        Physicists do not seem to understand that it is not possible to unite these theories using the math of the theories because you will never be able to derive why their initial postulates are true and why they should exist in the first place.

        I suggest you learn exactly what the ruby slipper conundrum and the concept of infinite scales are and how my model increases in complexity through the hierarchy of energy before you automatically dismiss it. AND YES - If a theory that starts with one building block ingredient (and energy) does explain everything and also explains what is not possible, then it is the one and only scheme possible for the theory of everything.

        Scott, i read your essay. Even in the papers you cited on your essay page, you mention your 'ruby slipper conundrum' only for the purpose that for understanding it one has to buy and read your 300 page book available on amazon.

        In your essay, this presupposed important concept is not exemplified, not referred to a single time. You have to understand that for your strong claims, you can't simply refer to a 300 page book (one has to buy for 40-90 Dollars) in an essay contest like this. You missed the chance to give the reader an access to the 'ruby slipper conundrum' (if it at all exists) by outlining it in your essay. Everyone of us has the problem of limited space and characters for accurately writing down one's own ideas. Compressing these ideas into a 9 page, 25000 character body is difficult, but a challenge.

        Your essay is in large parts a copy of your papers published on academia.ru. Why you didn't use the 9 pages to explain the 'ruby slipper conundrum' a bit closer is a hint for me that this conundrum doesn't play the important role you claim. Anyways, you can't expect that the reader buys your book (350 pages for 89 Dollar hardcover), when you can't convince him with what is the sole purpose of this essay contest - namely with a well composed essay on the essay's theme.

        What is a conundrum for me, is that you are in my opinion one of many people who think they found THE TOE, people who want the appropriate merits and credit for what they think to be THE TOE, but different from most of this people, you deny the access to the claimed understanding of your TOE by trying to SELL it, instead of publishing it for free. Therefore I recommend you to give away your book's content for free, so that everybody can prove for himself whether or not your claims are justified.

        "Yes - I AM making a huge claim - and of course people will question it... like when you say you serious doubt that my theory explains everything."

        Remember that the one who makes huge claims has to justify them. I will not buy your book to refute your claims, simply make it available for free and we can further discuss it.

        https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

        quote

        Completeness[edit]

        A set of axioms is (syntactically, or negation-) complete if, for any statement in the axioms' language, that statement or its negation is provable from the axioms (Smith 2007, p. 24). This is the notion relevant for Gödel's first Incompleteness theorem. It is not to be confused with semantic completeness, which means that the set of axioms proves all the semantic tautologies of the given language. In his completeness theorem, Gödel proved that first order logic is semantically complete. But it is not syntactically complete, since there are sentences expressible in the language of first order logic that can be neither proved nor disproved from the axioms of logic alone: for example, "the flower is pretty".

        In a mere system of logic it would be absurd to expect syntactic completeness. But in a system of mathematics, thinkers such as Hilbert had believed that it is just a matter of time to find such an axiomatization that would allow one to either prove or disprove (by proving its negation) each and every mathematical formula.

        A formal system might be syntactically incomplete by design, such as logics generally are. Or it may be incomplete simply because not all the necessary axioms have been discovered or included. For example, Euclidean geometry without the parallel postulate is incomplete, because it is not possible to prove or disprove the parallel postulate from the remaining axioms. Similarly, the theory of dense linear orders is not complete, but becomes complete with an extra axiom stating that there are no endpoints in the order. The continuum hypothesis is a statement in the language of ZFC that is not provable within ZFC, so ZFC is not complete. In this case, there is no obvious candidate for a new axiom that resolves the issue.

        The theory of first-order Peano arithmetic is consistent, has an infinite but recursively enumerable set of axioms, and can encode enough arithmetic for the hypotheses of the incompleteness theorem. Thus, by the first incompleteness theorem, Peano Arithmetic is not complete. The theorem gives an explicit example of a statement of arithmetic that is neither provable nor disprovable in Peano's arithmetics. Moreover, this statement is true in the usual model. Moreover, no effectively axiomatized, consistent extension of Peano arithmetic can be complete.

        Consistency[edit]

        Andrew, what is the main point you refer to? Let's have real discussions here at the Essay contest, with arguments from yourself instead of citing chapters from wikipedia. I cannot conclude from your citings what your main point is and if there is any point at all you want to make.

        Exelent essay

        In my opinion, Newton's theory of gravity holds:

        - 1.聽聽聽聽聽 The theory is not wrong, but at the same time also not necessarily a complete description of what is going on.

        Do you think so?

        Regars,

        Brfanko Zivlak

        meteorologist

          Branko, thanks for your comment, your question and that you cherish what you read.

          As to your question, you cited a case where a prediction of a theory has been confirmed. Let's say this is the precession of Mercury's perihelion, what comes about in GR to be approximately the value of observation. Since GR was not designed to a posteriori fit these observational data (as far as I can know!:), I would say that GR predicted it.

          I cannot exclude that there are different theories possible which also can predict this phenomenon, theories that rest on different postulates than GR does.

          For the case of Newton's theory of gravity, I cannot see how it can hold to explain the precission of Mercury's perihelion. But that I cannot see it does not mean that you necessarily must be wrong. Tell me more about your view on Newton's theory of gravity if you like.

          No doubt Anstein's contribution to the understanding of nature is huge.

          But I do not believe that the explanation of Merkur's problem with the GR is essential.

          According to RuÄ'er BoÅ¡ković, 2 in the square of the distance of Newton's gravitational formula is not exact 2.

          I believe, the essential is the surface, not the distance in Newton formula.

          I do not know how to prove it.

          Regards,

          Branko

            stepan

            your point was far better made by Godel, and you still do not get it. I am not castigating you, but until you read the Godel incompleteness proof and understand it, then there is not a lot more I can bring up

            To whit, what you wrote is a tautology and until you actually read the PROOF of what Godel wrote, and understand it, I have little to discuss with you.

            https://plato.stanford.edu/entries/goedel-incompleteness/

            Just read it, please, and if you do not, I will abstain from any further comments.

            Good luck

              stepan

              your point was far better made by Godel, and you still do not get it. I am not castigating you, but until you read the Godel incompleteness proof and understand it, then there is not a lot more I can bring up

              To whit, what you wrote is a tautology and until you actually read the PROOF of what Godel wrote, and understand it, I have little to discuss with you.

              https://plato.stanford.edu/entries/goedel-incompleteness

              /

              Just read it, please, and if you do not, I will abstain from any further comments.

              Good luck

              bluntly put, Godel did a far better job than you did, and all I am asking you to do , is to read the source of the idea.

              If you cannot bother doing that, I have nothing further to say.

              Your demands for a "real discussion" do not get to the point.

              The point is, that your essay is a loose paraphrase of what Godel was bringing up, and until you accept that, and actually get some mathematical rigour to your exposition, there is little to discuss.

              I.e. Godel nailed it.

              Paraphrasing Godel as you have done, is not exactly a strategy to break new ground.