Essay Abstract

In this paper I posit that if our universe is mathematical in nature, we should come across undecidable features in various places. These are synonymous with strong emergent properties, which I suggest should also be taken as fundamental. Doing so would require a restructuring of our view of reality to something that appears more interrelated than the view seen through reductionism.

Author Bio

Ernesto Vaca has a Bachelors in Physics, and is currently pursuing a second Bachelors in Mathematics. Currently living in Oregon City, Oregon.

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Ernesto. Your intuitions are right on. If you read my essay you will see justifications for many of your ideas. In the essay I introduce a new theory and a new fundamental level. The combination overcomes entropy, emerges from/converts chaos to order and progresses to create "all of the order in existence". I call the theory Successful Self Creation(SSC).. SSC emerges with the most fundamental processing/results and "creates/becomes" math, physical, chemical, biological and psychological existence. The emergent composition of the original SSCU (read the essay to find out what that is) was the initial processing/result that made it possible. The SSCU emergence can be explained from the creation and progression of its constituent parts. Also the loop of fundamentality you mention is a result that enables the process to be stable and overcome entropy. As I mention in the essay, the emergent conversion of C*s to the SSCU are also the emergent characteristics of solar systems, galaxies and universes. I would appreciate your comments on my essay and how it compare to your thoughts. John Crowell

    Dear Ernesto Vaca,

    wonderful out-of-the-box thinking! If I understand correctly, you devise an epistemology (the emergent reality of formally undecidable truths). Since one can not work out the truth of undecidables, you import a standard layered ontology and then claim that this ontology is what your epistemology speaks about. What's the relation between the two?

    Now, since I believe nescience (relations between knowledge elements not logically=affirmatively tractable) has a major role to play in human knowledge, I yet don't see what other kind of relation would prevail between the ontological elements of your system, for no relation at all would entirely separate epistemology and ontology, thus making your epistemology not referring to anything by virtue of its own.

    In my FQXI essays I have tried to argue for an epistemology that at the same is an ontology, which avoids the fairly weird idea that there could be a truth (ontology) independent of the way of knowing that truth (epistemology). Rather than a layered cake, I figure human knowledge as a multi-dimensional space with orthogonality (Absolute non-contradiction) playing the role of censorship.

    the best for your essay,

    Heinz

      Ernesto, I like your layer cake analogy. Especially when you talked about mixing up the cake "Batter". As in nature the scales of things are not separated but all muddled up together. I don't think mathematics is the ground floor layer but rather it is existence. I feel you are too apologetic for expressing your ideas. We do not have to agree on everything. Kind regards, Georgina

        Hi Georgina,

        I think EXISTENCE hits the nail on the head! And since contradiction can not possibly exist, the prime job of science may well be to get rid of it.

        Heinz

        P.S. Non-contradiction does not wipe out difference, it makes it additive and even functional....whereas difference for the sake of difference is a dysfunctional concept inherited from postmodern arts.

        Hi Georgina,

        Thank you for the feedback. I will do my best to be less apologetic in the future. I believe it's in part because I am new to all this.

        When you say you think mathematics is existence, are you saying you agree with the Mathematical Universe Hypothesis, or are your views slightly different?

        All the best,

        Ernesto

        Hi John,

        Thank you for the encouraging remarks. I will check out your paper soon.

        Kindly,

        Ernesto

        Hello Heinz,

        I apologize if I'm not picking up everything you are putting down, I'm still quite the novice.

        So in my paper, I am trying to say that the standard layered ontology is incorrect or at least incomplete, and that a truer structure looks more mixed an chaotic than a layered regime. This is suggested by the existence of formally undecidable truths, which I suggest should be taken as fundamental.

        I'm not sure what you are asking in your second paragraph. What are you referring to as ontological elements?

        I will check out your paper soon.

        Best regards,

        Ernesto

        Hi Ernesto. Let me restate that. In my opinion, mathematics is notthe ground floor layer. Rather it is existence that is that ground floor layer.

        Thank you Heinz.

        Georgina, I see. I like that take, it resonates with me well.

        6 days later

        Dear Ernesto Vaca,

        I read your wonderful essay, take my congratulations for that.... Your words .........Is there any evidence for this? This is no rigorous proof, but if and only if an example of Gödel's undecidability is found within nature, can we claim that there is something more fundamentally mathematical about reality, than the math simply being a useful tool..............say that you are searching some proof...

        I have few questions about it. This law is applicable to Quantum Mechanics, but will this law be applicable to COSMOLOGY.......?????.........

        I never encountered any such a problem in Dynamic Universe Model in the Last 40 years, all the the other conditions mentioned in that statement are applicable ok

        I hope you will have CRITICAL examination of my essay in this contest(" https://fqxi.org/community/forum/topic/3416 ")... "A properly deciding, Computing and Predicting new theory's Philosophy".....

        Best Regards

        =snp

          8 days later

          An enjoyable read Ernesto...

          I agree with all of your premises and the conclusions up to a point. I prefer an interpretation that the universe is maximally mathematical. My sticking point is your statement that the lowest level, Math, does not have emergent properties, and this is a common misconception, but untrue.

          I would start by looking at page 8 of Alain Connes "Noncommutative Geometry Year 2000" arXiv:math/0011193, where he makes the curious observation "noncommutative measure spaces evolve with time!" and 'explains' there is a 'god-given' one parameter group of automorphisms (his emphases).

          This gets more involved when working with the octonions, for example. So when one ventures into non-commutative and non-associative spaces, one does encounter evolutive and then sequentially evolutive properties unavoidably, and this is precisely a kind of seed for emergence in pure Maths. However; I very much liked your paper.

          I especially like the way you mix the layers up, or assert there is no topmost or bottom-most level. And I have just submitted for review a paper entitled "Painting, Baking, and non-associative Algebra" that expands on my comments above, which may interest you. I will have more to say here when there is time.

          All the Best,

          Jonathan

            Dear Ernesto,

            I enjoyed reading your essay, and I think that, while you modestly declare it "a play in speculation", you make some excellent points.

            > To create a mapping onto reality beyond a simple model would require something else. Not to mention the 'true' nature of reality is up for debate, which is why I take as an assumption in this paper that "reality is mathematics".

            These and other mathematical universe statements you make make sense to me, and I wrote about such things, for example here. You mention Tegmark, I believe that he proposes to take into account only computable mathematical structure, which I think makes his ideas digital philosophy rather than mathematical monistm as it seems. While I think both you and I find more appealing to go beyond this limitation. Which leads to the following.

            > if and only if an example of Gödel's undecidability is found within nature, can we claim that there is something more fundamentally mathematical about reality, than the math simply being a useful tool. This is because a truly undecidable result would only be possible if there existed a true mathematical structure underlying reality. In fact there are a few instances of undecidable results being found within quantum mechanics (Cubitt, Moore).

            I think this is idea that "a truly undecidable result would only be possible if there existed a true mathematical structure underlying reality" deserves more serious consideration. Usually people misuse Gödel's undecidability theorem in the complete opposite sense, which makes no sense. Too many still understand it as being proof of the limits of mathematics, not of the fact that it goes beyond the limits of logically consistent language.

            > in this view, certain fundamental properties would also be high level properties.

            This is another claim with which I agree, and it seems to me that a good example is the micro, quantum level of reality fails to determine the macro level, which makes me think that there's something fundamental at the macro level, although I don't consider it to be extra stuff than the wavefunction, just constraints of it. I wrote about this here sec. |7>, and here, example 10.

            I also liked this one

            > Because certain emergent properties cannot be explained from their constituent parts, from the point of view I am taking in this paper, they must be examples of Gödel truths [...] strong emergence.

            which is something I think too, cf. my longer essay, def. 11. In fact, because "emergent" is sometimes used in completely opposite way by philosophers compared to physicists, I removed it everywhere in that essay and replaced the part about "emergence" in terms of "reducible", so "strongly emergent" became "weakly reducible" :). But the way I understand it is in terms of Gödel undecidability like yours.

            Now, a good question I think may be whether for something to have Gödelian truths, it necessarily has to be a mathematical structure with no other ontology.

            Cheers,

            Cristi

              Hello snp,

              Sorry for the late reply, this has been a busy time for me. Thank you for your kind comments. I like what you said about saying that I am searching for a proof. that is a much better way to phrase that, so thank you.

              I believe it would have applicability to cosmology, though I can't say for certain, at this point its is mostly conjecture/speculation.

              Thank you for telling me of your essay. I will do my best to get to it soon.

              Sincerely,

              Ernesto

              Hi Jonathan,

              Thank you for reading my paper, and for your encouraging comments.

              I don't think I meant to say that Mathematics doesn't have any emergent properties, but maybe my wording could be improved. I honestly hadn't even thought of whether it could be or not. I'll check out the paper you referenced me to, it sounds interesting. I will try to get to your paper as soon as possible.

              Sincerely,

              Ernesto

              Dear Cristi,

              Thank you for your very detailed feedback, i really appreciate it. You've given me a lot to look through. I do think we have a lot in common in the way we think about these ideas.

              I actually found your paper from the mathematical universe essay contest, and having been digesting it slowly. I will do my best to get through all the material you linked me to, though this time has been quite hectic for me.

              Thank you again, and I think you make a great point with your final question: "for something to have Gödelian truths, it necessarily has to be a mathematical structure with no other ontology." Something to definitely give further thought.

              Kind regards,

              Ernesto

              8 days later

              Thank you Ernesto...

              I am getting to offer my rating now. I enjoyed your paper a lot. I thought it was a delight how you changed things up from the ordinary. I think you will appreciate what Connes has to say over time. It took me several readings and much thinking to fully grasp the opening sections, but it is worth checking out. FWIW; Connes also has some thoughts for aspiring mathematicians. One of the things he advises is to read until you are full up, and then recline while musing about what you just read. Works wonders!

              Best,

              Jonathan

              I think you will like my essay Ernesto...

              Like you; I believe in the MUH, and there are a few other common points as well. You bring to mind the story of Jaime Keller, who began by studying Chemistry, then found that to fully understand it he needed to know Physics better, and finally he decided what he really needed to know was Math - and he became an expert in Clifford algebras before his demise.

              Bye for now,

              Jonathan

              I hope some others return to rate you favorably...

              I see only positive remarks and I gave you a good grade, but your essay has not fared so well. Nor has mine, so far. There must be some people who are not courageous enough to criticize, or articulate at stating what they don't like, but want to take others down anyway. That is so sad.

              Regards,

              Jonathan