Essay Abstract

Decidability, provability, computability and predictability are all instances of *algorithmic determinism*. The crux with the latter is that it a-priori assumes for every mathematically well-posed question that either an answer exists or a proof that the question has no answer or a proof that there is no proof etc. But all of the just listed assumptions are by no means guaranteed to be constructible or to be at all mathematically existent for each and every case. Moreover, since algorithmic determinism is equivalent with the process of deductive reasoning, consequently deciding, proving, computing and predicting arrive at their natural limit when the deductive method arrives at its natural limit. Furthermore the method of deduction is often limited in its reliability by the unprovability of its starting premises. Much worse, for many unprovable false starting premises - for example about some unknown physical circumstances - the resulting conclusions cannot be proven to be false by any algorithmic procedure or physical experiment. Nonetheless, algorithmic determinism rigidly suggests that everything in nature has to be considered as being completely formalizable, despite the fact that this claim already fails when it comes to predict single quantum events. By revisiting Gödel's incompleteness results we argue that the above mentioned failure has its roots in the incompleteness of physicalism, because if physical reality would exclusively only behave due to algorithmic determinism, the latter would determine itself to be forever non-detectable. We further argue that this non-detectability is an instance of Gödel-undecidability, because just as with the latter it demonstrates that only something *outside the system* can distinguish causal-algorithmic incompleteness from causal-algorithmic inconsistency: the latter would render Quantum Theory impossible to at all being predictive whereas the former is merely incomplete due to a filtering-process from outside space-time.

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.

Download Essay PDF File

Hi Stefan,

very interesting and well-argued essay! I do, however, disagree with your use of the term 'abstraction'. Latin 'abstrahere' means as much as 'to draw' or 'pull away from something'. We can observe nature as long as we like, but we will find neither impuls, EM-waves nor gravitation in it. These entities of classical physics have not been 'drawn away' from observations but put into them; they are a priori, which means they make observable in the first place.

On the other hand much of thermodynamics and the discrete nature of atomic energy in particular have been discovered experimentally (empirically). The particle nature of e.g. light has thus been ABSTRACTED from measurements. It is merely an a posteriori model over measurements.

So, while classical physics can be regarded to be PART of the world, 'modern' physics is just an explanatory model.

Heinz

    Hello Mr Weckbach,

    I congratulate you for a relevant general essay. You have well detailed and extrapolated the works of Godel also. The incompleteness theorems of Godel and the axiomatic system for basis arythmetic are indeed essential and can be correlated with our physics in fact because we have a kind of convergence between the partitions in physics and maths. That implies a kind of unpredictability indeed and uncomputability just because we are simply limited in knowledges, we don t know mainly the mathematical and physical objects nor the main philosophical cause of our universe and this is trua at all scales , quant or cosmol. That implies a kind of humility when we study our physics and maths, and that implies also a kind of prudence when we extrapolate this general philosophy , we cannot affirm simply in resume when we are not sure or that we have not proved generally speaking. It d be very vanitious even to pretend that we have all understood and that a TOE exists, we have so many things to add at this universal puzzle.

    If I can like I am curious, could you tell me more about what do you consider like foundamental physical and mathematical objects ? strings or points or others and what is the main philosphy correlated ? is it a 1D main field of a geonetrodynamics and why ? and do you consider an infinite eternal consciousness beyond this physicality or do you Think that we come from the hasard like a mathematical accident from a lind of energy?

    I have liked your essay and I wish you all the best in this Contest.

      Hi Heinz,

      thanks for your comment! When using the term 'abstraction' i refer to something other i do abstract from in the first place. Would i not conclude that there has to be a metaphysical realm beyond physicalism and determinism, i couldn't refer to our world as being an abstraction of that metaphysical realm. But as you read, by assuming the existence of such a realm, the physical world becomes a kind of abstraction for me and i tried to justify this induction with several examples in the essay.

      Anyways, thanks for your feedback which is always appreciated!

      Best wishes,

      Stefan

      Hi Steve,

      thanks for your comment and your questions. Firstly i agree to all of what you wrote and that a 100% certain knowledge about all these issues is not possible - except as a kind of 'belief'.

      Honestly, i have no idea what the building blocks of physical reality are, how and why they work (to the expense that the 'how' can be modelled to a certain extend by mathematics). Since i assume these questions to be not answerable in a satisfying and objective manner, i tried to search for other general patterns that could link logics, mathematics and metaphysics (aka philosophical questions).

      I think we are in a similar position as every system would be that tries to explain its own origins. Although a mathematical system isn't conscious but we are, i nonetheless assume - for several reasons - that we, too, are unconscious of many things between heaven and earth and that the fundamental questions you pose cannot be answered by any algorithmic or deductive means (at least not completely). A certain amount of belief will always remain. I conclude that answers to such fundamental questions must be searched for *outside the system* - as was demonstrated by Gödel. So if we want to have more certainty about these questions we must look for some answers outside the system. Since we are practically 'caught' within space-time, the outside of space-time becomes interesting at least for me.

      As i already have wrote in another essay, i also take near-death experiences and certain (well-examined) supernatural experiences into account. These experiences are not taken serious by many people and / or scientists, but i think they could open the door for a realm beyond space-time that i mentioned above.

      And yes, i believe in a higher entity, traditionally called 'God'. But i excluded such considerations from my essay, because it makes matters much more complicated. One can only begin to include it when one has realized the limits of the hitherto known tools for answering all this fundamental questions. My essay is supposed to show these limits and how they eventually could be linked.

      Concerning the 'infinite' part of the consciousness you mentioned, i would say that we really do not know what 'infinite' really means or could mean ontologically. As for now i take this term as a shortcut for the term 'unknown until eventually revealed by God' and i think that fits well into the ancient scriptures, at last the Abrahamitian ones, since one should not facilitate a picture of God - it simply would be false or at least hopefully incomplete - and therefore misleading.

      All the best,

      Stefan

      Respected Professor Stefan Weckbach,

      Wonderfully argued essay please. I just quoted some of your words............Let us now assume that we have a complete list of all things at hand that are impossible to exist. Let us further assume that this list is not infinite and that we have enough time to completely go through it...............

      Now the question arises whether is possible form a complete list of all the things impossible to exist? How to do it?

      Of-course I made a list of impossible things! in my essay ("A properly deciding, Computing and Predicting new theory's Philosophy")!!! Hope you will look make your comments please.....

      Best Regards

      =snp

      5 days later

      Dear Stefan,

      A very important essay, topic and deep ideas that you give to comprehend, especially in the direction of the deepest metaphysics. I believe that the crisis of understanding in the philosophical basis of fundamental science, its metology, is caused precisely by the crisis of metaphysics and ontology. Gödel sought metaphysics in tune with Leibniz's philosophy. He described his views as "rationalistic, idealistic, optimistic and theological. [Wang Hao. A Logical Journey: From Gödel to Philosophy. Cambridge, 1996.].

      Gödel believed that in metaphysics there existed such fundamental primitive concepts, the discovery of which would be a genuine breakthrough in philosophy. Godel argues that philosophy has not yet been developed sufficiently to assert something with the necessary certainty. He even speaks more harshly about "the underdevelopment of philosophy at the present stage". [Gödel 1995 - Gödel K. Collected Works. V. III. Unpublished Essays and Lectures. Ed. S. Feferman. NY, Oxford, 1995.]

      I believe that a breakthrough in search of a stronger ontological basis of science, knowledge in general, its boundaries, carcass and foundation will help the dialectic, which for some unknown reason is ignored by modern philosophy of science.

      Respectfully, Vladimir

        Hello Mr Weckbach,

        I like how you see the generality of our universe. Thanks for developing and sharing your thoughts. I know that the sciences Community is divided about God.

        Personally I consider an infinite eternal consciousness beyond this physicality , a Little bit like Einstein, a God of Spinoza with determinism respecting our rational laws. In studying the philosphy of our best thinkers, I have remarked that all they considered a creator , Planck, Einstein, Newton, Tesla, Galilei, Poincare, Godel, Cantor, Maxwell, Lorentz, Fermi, Lie and so more. I beleive strongly even that it is essential to well understand the transformations matters energy and the informations but I respect also the thinkers thinking the opposite witha kind of mathematical causes and Hazard if I can say.

        In my model of spherisation, an optimisation evolution of the universal sphere or future sphere with 3D coded quantum spheres, I consider a central main cosmological sphere and it is there that this infinite eternal consciousness codes and tranforms the energy in particles. So I have considered this generality.

        Imagine this with humility, take 3 main systems, series finite of quantum 3d spheres where this space disappears due to a specific serie having the same finite number than our cosmological 3D spheres. so one for the vacuum space , they are coded, one for the photonic fuel, they are coded differently and one for the other fuel a cold dark matter and so when they fuse they create our geometries, topologies, matters ann properties because they are coded simply ,now consider this at this planck scale and utilise these series and superimpose 3 E8 for the geometrisations, utilise the Ricci flow, the poicare conjecture, the Topological and euclidian spaces, an assymetric Ricci flow for the unique things, and the lie derivatives.....all will be easier to explain all our unknowns than just a E8 and geonetrodynamics. E8xE8xE8 in fact with finite series of 3D spheres instead of points or strings. the main codes are in this space , the two others are fuel permitting the gravitation and the electromagnetism simply, see the combinations possible , we can create all Shapes, geometries, topologies and the unique things ....

        Best Regards

        Stefan Thanks for your essay. I agree with he the conclusions of your essay even though our methods to attain those conclusions are very different. In my essay " Clarification Of Physics: A Derivation Of A Complete, Computable, Predictive Mode Of "Our" Multiverse", I present the Creation of your ..metaphysical realm" and the reasons for it to work. Successful Self Creation is the processing that becomes the metaphysical result and the reasons for it to work is that it has to overcome entropy in order to emerge from chaos and exist. Also the SSC processing produces and "uses" its own mathematics which "maps" to its processing and results. Hopefully, the mathematical model and its narrative can be of some help in your thinking. Also, I would appreciate your comments on my essay. JohnCrowell

          Hi Mr Weckbach, see this for the quantum gravitation,

          take a serie of quantum BHs farer than the nuclear forces,, take their mass , now consider particles of DM cold encoded in nuclei and encircling this standard model and particles, now consider the distances between a relative sphere of quantum BHs and the electrons encircled by this DM and now apply the equation of newton about the force of this gravitation between mass.....see the result .....quantum gravitation reached because the standard model is just emergent and we must take into account others distances and mass .

          All this is due to fact that the main codes are farer than our actual standard model, now consider for the formalisation 3 E8 , and consider the finite series of 3D coded spheres, one for the space, vacuum, one for the photons, a fuel and one for the DM, an other fuel cold. Now consider the space and these finite series like the main codes and so see the finite series of quantum BHs......do you see what it appears in making the fusion of these 3 E8 and their 3D spheres instead of points or strings ?

          Regards

          6 days later

          Dear Stefan Weckbach,

          Your essays are always fundamental and always enjoyable. Your first statement that grabbed me was concerning systems or machines and the "profound limit of their own abilities to deduce something to be ontologically true or false."

          Guthry's essay; "no amount of computation will lead you to discovery of a pattern that wasn't in the data in the first place."

          This seems to relate to your: "neither machine nor humans can reliably deduce that certain things exist or do not exist."

          I fully support your conclusion that "the naked act of deduction is really only a deterministic, mechanical process."

          You and I treat ontology from quite different directions. I hope you will enjoy my take on a specific problem of ontology: Deciding on the nature of time and space

          My best regards to you,

          Edwin Eugene Klingman

            9 days later

            Dear Stefan,

            Thanks for this stimulating essay, which, like every good essay, raises more questions than it answers. The link between deductibility and finite information has also been raised by Nicolas Gisin, and is the topic of the essay by his collaborator Flavio Del Santo in this very competition, perhaps you can read each other's essays and comment. My overall view on this, shared by Gisin and Del Santo, is that intuitionistic mathematics should be incorporated into physics to really deal with these issues. Concerning your own essay I would also make this point: to make your claims rigorous (apart from the ones that are already well argued) you would also need some of the ideas of L.E.J. Brouwer, especially about choice sequences. Otherwise, I agree with everything you write, and you write it very well!

            Best wishes, Klaas

              5 days later

              Dear Stefan,

              For some reason, Lawrence Crowell cannot post on the FQXi and has not been able to do so for several days. FQXi is fixing the problem. In the meantime, Lawrence asked me to post here his comments on your Essay. I past them below. I profit by this email to inform you that I will also read comment and score your Essay soon.

              Good luck in the Contest and best wishes,

              Ch.

              From Lawrence Crowell

              This is a bit late, for some reason I can't post to FQXi. I meant to post this several days ago.

              I just read your informal essay and there are points I agree with. Thanks for the kind words with respect to my essay. I finally just now got to reading yours, as this illness came roaring back yesterday and I am still feeling not too well. I am coming up on a month with this thing. I have not been horribly ill, but it is rather debilitating and leads to deep levels of fatigue.

              You are making issues with what I see as the continuum. The continuum hypothesis Чђ_0 < C < 2^{Чђ_0} is something that haunts all of this. I am not an expert on this, though I have Cohen's book on the proof he worked on that it is consistent with ZF set theory, but not provable. From a physics perspective it seems almost absurd to worry about this. Though with Robinson's numbers and related matters this does impact the ideas behind calculus. With large N entanglements of states a continuum though should exist. The Raamsdonk idea that spacetime is an epiphenomenology of quantum entanglement should imply that a smooth continuum will emerge from a finite, or with N в†'П‰,using ordinal notation instead of в€ћ, discrete system of states. This can never be observed completely with physics, but it would give a theoretical reason to think there are no granular disruptions to spacetime, at least for IR (E в†' 0) measurements such as across cosmological distances. The NASA and ESA Fermi and Integral measurements bear this out. At UV measurements spacetime should I think appear very bubbly or granular with discreteness, where what are measured are just discrete states and not even what we could call space or spacetime.

              You wrote, "Hence, our axiom that the world is an informationally closed (void) system must be erroneous, since the fact that Gödel-incompleteness is factually constructible contradicts this axiom." This is a part of what I advocate on several fronts. A black hole with mass m = GM/c^2 has a temperature T = 1/8πm in natural units. If this black hole were placed in a spacetime region with a background temperature equal to its Bekenstein temperature the black hole will emit and absorb photons in a stochastic way. This will mean the temperature and mass of the black hole will drift away from this condition of equality in a Langevin manner. The result is there is no equilibrium. This then points to an open world perspective instead of a closed world.

              The halting issue also impact spacetime. Suppose there is a binary state on a Turing machine that we read out. We set this machine to make its first step in 1 second, the next in ½ of a second, the next in ¼ of a second, it is not hard to see that after 2 seconds we should have an answer. If this machine halts it will finish before 2 seconds. If not something odd happens, for the energy required to fun this machine diverges in an asymptote and even it if is "unbreakable" the energy involved will generate a black hole. If this machine does not halt, we have a black hole, and even if it halts but takes a huge amount of time it could be in a black hole. Thus, if we generate a black hole, we have no information about the halting state of the machine. We must go into the black hole to find out. A Kerr black hole has an inner event horizon, and we could instead have the Turing machine send a regular interval of binary pulses into the black hole. An observer who goes into the black hole could then in principle read off this binary stream and determine completely if a black hole halts or does not halt. This is because the inner horizon is continuous with I^∞ and the infalling observer would reach this in a finite time in an eternal black hole. However, the Planck unit of distance muddles this up, and further Hawking radiation breaks the connection between r_- and I^∞. In fact, as the observer reaches r_- it is a singularity at the end point in the black hole explosion into Hawking radiation. So, either spacetime physics or quantum mechanics enforces a condition whereby the Gödel-Turing result can't be overruled by physical means.

              These are interesting matters to ponder and think about. Your essay does provide food for thought along these lines.

              Cheers LC

                Dear Stefan

                Congrats for you essay which is well argued and illuminating, you gave some details on Godel and Turing theorems that are quite interesting for me. In my essay I argue that science is about truth, in yours you seem to imply that truth is an illusion. In my view, as science progresses we are reaching a metastable truth. The understanding of electromagnetic phenomena, light, gravity, biology, condensed matter and nuclear energy are some of the clear examples where we can see some truth.

                Good luck in the contest!

                Israel

                  Dear Israel,

                  i am happy that you found something interesting in my essay. Contrary to your assumption that my essay argues for truth to be an illusion, it argues for truth being something that is real, together with logics. The world is ordered in a mindful manner via patterns and other meaningful connections, and this is reflected by "The understanding of electromagnetic phenomena, light, gravity, biology, condensed matter and nuclear energy are some of the clear examples where we can see some truth.".

                  Logically, truth can't be an illusion because if it would, this would be a truth too! Every "illusion" - if indeed existent - is a truth (means the existence of an illusion would be a truth). When i speak about "the world as an abstraction" i do not claim that the world has no truths in it, but i differentiate between eternal truths and truths that come and go. If the universe is not eternal, then its truths haven't been around for eternity, but had to come from somehting prior to its birth (big bang etc.).

                  I will read your essay and if i have something constructively to say will comment on it.

                  Best wishes

                  Stefan

                  Dear Christian and Lawrence,

                  thank you for your comments! I am glad that you Lawrence haven't been attacked by that virus as much as i thought on first sight - keep on regenerating.

                  I appreciate your deep knowledge on mathematical relations and how you adopt that knowledge to big questions like black holes and the continuum. Although i am not an expert on all of this, i intuitively like your ideas, as mentioned in my comment on your essay page. Yes, i too think that Gödel's and Turing's findings are that deep that even black hole physics can't circumvent them. Therefore i argue that the logical possibility to always extent Gödel-incomplete logical systems - but they never will reach a state where they are completely complete is a hint to something beyond what we know today about the universe, spacetime and how logics is linked to physics and mathematics. My take is that if we do not want to end up with infinities in all directions - mathematical as well as physically - we should consider Gödel's results as a hint that points beyond algorithmic determinism. The problem with this route is that it would then point towards a transcendental realm that could well be defined as something "spiritually" or "religious" and this wouldn't be opportune for the physics community (as far as i can guess). But i think we can't circumvent some "spiritual" component because consciousness simply seems to be of that "spiritual" kind - in my opinion it can't be defined or understood exclusively only be the method of algorithmic determinism and there are many other essays here that assume the same.

                  Dear Lawrence (and Christian), i wish you a safe and healthy time and all the best in the current essay contest!

                  Stefan

                  Hi Claas,

                  thank you very much for your comment and the appreciation for my essay. I am happy if it could stimulate a bit. I already read Flavio's essay and rated it, good contribution to the contest indeed. I do not remember wether or not i also left a comment on the page, but i will soon check that to also give my appreciation about what i read in the essay.

                  Unfortunately i am not into intuitionistic mathematics, i googled choice sequences and the point seems to be to me that Brouwer aimed to limit or redefine the use and definition of infinities in maths. This surely would be along with my own lines of reasoning.

                  Wish you best of luck in the contest and stay healthy!

                  Stefan

                  Dear Vladimir,

                  thank you for your comment and your appreciation of what i wrote. Thank you also for your citation of Gödel, this is very interesting. I soon will read your essay and if i have something to say, leave a comment.

                  Best wishes and stay healthy!

                  Stefan

                  Dear John,

                  thank you for your comment. Honestly i do not think that something can "self-create" into existence - unless something other already existed (entropy, physical laws, mathematics etc.). I nonetheless will read your essay and look what you concluded.

                  Best wishes and stay healthy!

                  Stefan

                  Hi Edwin,

                  thanks for your comment, happy that you could enjoy what i wrote.

                  I will read your essay and if i have to say something constructive will comment on it.

                  Best wishes and stay healthy!

                  Stefan