Essay Abstract

There are many layers to our understanding of the world. There are things that are immediate to our senses, which we know (or think we know). There are models we construct to explain, and which correspond with, the physical world that we sense, observe and measure. There are mathematical concepts we imagine that can be seen to be true in-and-of-themselves. But, over the last century, advances in science and mathematics have revealed many things we would like to know that we do not. Some have been proven to be impossible to know. FQXi has asked us to explore these limits in our ability to understand the world. How are these limits related and what do they mean? This essay addresses that challenge by exploring features that the physical world and mathematics share with consciousness. Self-reference, entanglement and purposeful agency are key features of autonoetic (self-knowing) consciousness. They are also found in physical and mathematical systems and are manifest at the limits of knowledge that FQXi is exploring. These autonoetic features serve as gatekeepers limiting our understanding of the world we live in, but they also make living in this world so marvelously interesting and beautiful.

Author Bio

George Gantz is a retired business executive with a life-long passion for mathematics, science, philosophy and theology. He has a Bachelor of Science degree with Honors Humanities from Stanford University, and in 2017 he created Spiral Inquiry, An Exploration of Science, Faith, and Philosophy. George is a Fellow of the RSA and Board Member of Long Now Boston. His FQXi essays include: The Tip of the Spear (2014, 4th place), The Hole at the Center of Creation (2015), The How and the Why of Emergence and Intention (2016) and Faith is Fundamental (2017).

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"... How does the physical world give rise to consciousness minds ... How can minds perceive mathematical truth ..." Consider 3 beliefs: (1) Milgrom is the Kepler of contemporary cosmology -- on the basis of overwhelming empirical evidence. (2) Nature is finite and digital. (3) Infinity is a semi-theological concept. Now consider 3 questions: (a) Can mathematical beliefs be entirely divorced from theological beliefs? (b) Can empirical beliefs be entirely independent of ethical beliefs? (c) Are Peano Arithmetic and Zermelo-Fraenkel set theory relevant to theology?

Gödel's ontological proof, Wikipedia

Religious view of Isaac Newton

Consider a minimalist definition of a monotheistic God: God is the unique Supreme Being with an infinite mind. If the hypothetical God had a finite mind then why would such a God be different in principle from mammals and birds?

    Hi David - I would say all yes! All yes!

    I read your essay and had a struggle with it. Here's where I ended up:

    For "Is" and "Is-not" though with Rule and Line

    And "UP-AND-DOWN" by Logic I define,

    Of all that one should care to fathom, I

    was never deep in anything but--Wine.

    It's COVID cocktail hour. Cheers! - George

    Dear George Gantz.

    Thank you for giving a beautiful essay explaining the fundamental views of Godel Turing etc., with a smooth nice flow. Well you are a retired person like me, thinking of Science Philosophy............

    I am working on Dynamic Universe Model for the last 40 years and got many results many predictions came true. I have few questions about Godel. 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 a CRITICAL examination of my essay... "A properly deciding, Computing and Predicting new theory's Philosophy".....

    Best Regards

    =snp

      Hi George, I particularly like your introduced the "three worlds" and your comparison with lines from a verse of the Rubaiyat of Omar Khayyam. I think that worked very well and revived my interest, that carried me 'effortlessly' to the end. A satisfying read.

        M. Gupta -

        Thanks for your comment. Yes, Godel apples to any consistent theory that has sufficient complexity to express arithmetic, which a cosmological model would have to be.

        I have read your essay and found it offers some good advice but no explanation I could follow for what the "Dynamic Universe Model" actually is. In English, the acronym is somewhat unfortunate.

        This comes to mind:

        Would you that spangle of Existence spend

        About THE SECRET--quick about it, Friend!

        A Hair perhaps divides the False from True--

        And upon what, prithee, may life depend?

        Regards - George

        Thanks, Georgina -

        I also enjoyed reading your essay and found the elephant allusions to be quite hilarious. I also found it quite unpredictable, which will stand it in good stead in this contest.

        I was unable to find any elephants in the Rubaiyat for you, but I did find a lion:

        They say the Lion and the Lizard keep

        The courts where Jamshyd gloried and drank deep:

        And Bahram, that great Hunter--the Wild Ass

        Stamps o'er his Head, but cannot break his Sleep.

        Peace - George

        11 days later

        Dear George Gantz

        Continued from my forum.

        I appreciate the optimism in your essay.

        (1) - "Why do mathematical laws apply to the physical world;"

        My short answer is -discovered mathematics.

        (2) How does the physical world give rise to conscious minds;

        My short answer is - like everything else through mathematics and closer through the driving forces of attraction and repulsion.

        (3) How can those minds perceive mathematical truths.

        My short answer is - Using your time to understand the greats of 18th and 19th century philosophy of nature.

        Mathematics is "unreasonably effective in the natural sciences ..

        I disagree, math is reasonably effective in the natural sciences ..

        I appreciate your conclusions and I can add that I see the universe in three frames:

        1 - Exp (i * pi) - which is a known quantum physics

        2 - Exp (2 * pi) - which is my original discovery and expresses matter and radiation

        3 - I do not know so far.

        "Yet they are fundamentally interconnected and behave as a whole."

        I call my theory: The unity of the whole and the parts.

        Regards,

        Branko

          Branko -

          Thanks for your comment. I appreciate your enthusiasm.

          I did enjoy your essay and its commitment to the standardization of dimensionless units as a solution to much of the confusion in the understanding of science. At the same time, you assiduously avoid dealing with the confounding issues at the heart of this essay contest - incompleteness, undecidability and non computability. All of which, by the way, do relate to the tangles you allude to regarding infinity.

          XXIX. Into this Universe, and Why not knowing

          Nor Whence, like Water willy-nilly flowing;

          And out of it, as Wind along the Waste,

          I know not Whither, willy-nilly blowing.

          Best - George

          Dear George

          If we have 100% of the problem and we can solve 95% with 5% power and rest 5% with 95% power we first choose to solve the more productive part.

          So - incompleteness, undecidability and non computability didn't bother me to come up with predictive formulas at the end of my essay.

          Regards,

          Branko

            Branko -

            There are problems worth solving to the 90% level, and the 95% level, etc - particularly the challenges of prediction or estimation. And then there are problems for which and answer must be 100% or it is no answer at all. This contest is, I think, focused on these.

            Best - George

            7 days later

            George,

            An essay full of wisdom that does justice to the ambiguities and challenges of the topic imposed on us. The many challenges and mysteries we face have the time limit of humankind's existence on this planet, the period of consciousness we have to solve these problems. I also speak of the capabilities of the autonoetic consciousness you speak of regarding the thought experiments of Einstein and how such cognitive abilities, coupled with quantum computing could enable us to solve our problems if there is no limit set by our early demise. I'm surprised so few ratings for a superior essay. Mine is your 4th. Hope you have time to read mine: https://fqxi.org/community/forum/topic/3396.

            Jim Hoover

            Thanks, Jim. I will do so. I appreciate your kind remarks and a new score!

            For you -

            Come fill the cup, and in the fires of Spring,

            The Winter garment of repentance fling,

            The bird of time has but a little way

            To flutter, and lo, the bird is on the wing.

            Cheers - George

              George,

              Someone bombed you with a 5th rating. My 4th rating left you with a 6.8.

              Jim

              Hi Jim - I try not to pay attention to the ratings and simply tell it like it is. The scores I give are consistent with how I read the relative merits of each essay in responding to the FQXi challenge.

              Regards - George

              Dear Mr. Gantz,

              Your essay is clear and interesting. You focus on the role of human consciousness as a self-recognizing agent, using a term "autonoetic" that I was not familiar with.

              In my own essay, "The Uncertain Future of Physics and Computing", I take the novel view that consciousness is due to specific computational architectures in the brain, and that the internal sense of consciousness provides direct clues to the structure of these architectures. The key aspect is that neural networks may be configured to match patterns not only in space, but also in time. Recognition of temporal correlations provides the basis for recognizing agency and the self, which is the core of consciousness.

              I further argue that these can be emulated by artificial neural networks of the not-too-distant future. I might envision an autonomous vehicle with a level of consciousness comparable to a horse, for example.

              Alan Kadin

                Alan - Thanks for the kind words. I agree conscious states are likely to exhibit a sophisticated computational architecture in the brain (both space and time), but I also think this will fail to answer the philosophical questions - including the Penrose mysteries and the tangled conundrums of Turing and Godel - these will remain unanswered until the end of time (so to speak).

                I will read your essay next!

                -George

                What, without asking, hither hurried whence.

                And, without asking, whither hurried hence?

                Ah, contrite heaven endowed us with the vine

                To drug the memory of that insolence!

                Dear George,

                Glad to read your work again.

                I greatly appreciated your work and discussion. I am very glad that you are not thinking in abstract patterns.

                "This essay addresses that challenge by exploring features that the physical world and mathematics share with consciousness. Self-reference, entanglement and purposeful agency are key features of autonoetic (self-knowing) consciousness. They are also found in physical and mathematical systems and are manifest at the limits of knowledge that FQXi is exploring. These autonoetic features serve as gatekeepers limiting our understanding of the world we live in, but they also make living in this world so marvelously interesting and beautiful".

                While the discussion lasted, I wrote an article: "Practical guidance on calculating resonant frequencies at four levels of diagnosis and inactivation of COVID-19 coronavirus", due to the high relevance of this topic. The work is based on the practical solution of problems in quantum mechanics, presented in the essay FQXi 2019-2020 "Universal quantum laws of the universe to solve the problems of unsolvability, computability and unpredictability".

                I hope that my modest results of work will provide you with information for thought.

                Warm Regards, `

                Vladimir

                  Thank you Vladimir - nice to see you again, as well!

                  I will head over to read your essay - yes COVID is certainly a preoccupation for us right now. I believe that an entangled, purposeful and self-referential world argues for greater compassion, empathy and action to alleviate suffering than fear, anger and selfishness.

                  Cheers - George