Essay Abstract

This discussion of the powerful and mysterious connection between physics and mathematics begins with a look at the relationship between mathematics and cognition itself. Mathematics' deep, biological source associates it with a searching, instinctual will. To build this perspective, the paper surveys observations in cognitive science, physics, and mathematics, developing the idea that mathematics both characterizes what we see and how we see it. In this light mathematics can be viewed as a manifestation of the structural coupling of an organism with its environment, providing, perhaps, new insight into both.

Author Bio

Joselle DiNunzio Kehoe is a writer and Lecturer of Mathematics at the University of Texas at Dallas. She earned a Master of Science degree in mathematics from NYU's Courant Institute of Mathematical Sciences and has been teaching mathematics at the university level for more than 25 years. She has been published in the journal Isotope, +Plus Magazine, and has provided guest blogs for Scientific American. She is currently most involved in a book project that considers a biological view of mathematics. It is this pursuit that also guides her choice of subject matter in her blogs at mathrising.com.

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Joselle,

Are we speaking of a mathematical enactivism, where we, through interaction, selectively create our environment and manifest it through math? That defines the relationship of math to physics?

My view in "Connections..." seems more mundane.

Jim

    Dear Joselle DiNunzio Kehoe,

    We begin with essentially the same observation, that mathematical representation, in the form of "vectors" based on numerical "magnitude" is natural to mammals and insects, and "counting" goes on even below this level (think telomeres) as logical operations (NOT and AND) exist at the RNA-DNA-protein levels and below. This is evidence for the belief that logical structure is embodied in physical reality, supporting counting (hence integers) and, per Kronecker, "all the rest" of math.

    I show in my essay how numbers can be statistically massaged in a way to produce "feature vectors", and, as you state in your essay,

    "Statistics is not only intuitive, but part of our intuition. Biologically, the brain seems to be good it a kind of statistical calculation."

    Thus, the basis of natural integers from natural physical phenomena, leading through statistical feature extraction from the real world provides Rav's

    "Rational explanation for the usefulness of mathematics", required of epistemology.

    And while I do not at all buy Giulio Tononi's specific theory of consciousness, my own theory of consciousness, introduced in an earlier FQXi essay, leads to an identification of mind with matter, and hence most of the same general conclusions can be drawn.

    I very much enjoyed your well thought out and well-written essay and invite you to read my essay and comment.

    Best regards,

    Edwin Eugene Klingman

      Enactivism is probably the right word, but I'm not meaning to say that we "selectively create our environment and manifest it through math." What I mean to say is more that mathematics, even its most abstract sense, is an action, an enhancement of the senses. And this enhancement is possible because we have somehow managed to willfully direct formalizations that may be reflecting unconscious cognitive mechanisms.

      Thanks for the question. I like trying to answer them.

      6 days later

      Dear Ms. Dinunzio,

      You wrote: "As I see it, this universe, defined by the brightness of integrated

      information or consciousness, is more than a poetic metaphor. It proposes a

      significant change in ones point of view, making an unexpected equivalence

      between mind and matter."

      This is my single unified theorem of how the real Universe is occurring: Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of abstract NOTHING. Proof exists that every real astronomer looking through a real telescope has failed to notice that each of the real galaxies he has observed is unique as to its structure and its perceived distance from all other real galaxies. Each real star is unique as to its structure and its perceived distance apart from all other real stars. Every real scientist who has peered at real snowflakes through a real microscope has concluded that each real snowflake is unique as to its structure. Real structure is unique, once. Unique, once does not consist of abstract amounts of abstract quanta. Based on one's normal observation, one must conclude that all of the stars, all of the planets, all of the asteroids, all of the comets, all of the meteors, all of the specks of astral dust and all real objects have only one real thing in common. Each real object has a real material surface that seems to be attached to a material sub-surface. All surfaces, no matter the apparent degree of separation, must travel at the same constant speed. No matter in which direction one looks, one will only ever see a plethora of real surfaces and those surfaces must all be traveling at the same constant speed or else it would be physically impossible for one to observe them instantly and simultaneously. Real surfaces are easy to spot because they are well lighted. Real light does not travel far from its source as can be confirmed by looking at the real stars, or a real lightning bolt. Reflected light needs to adhere to a surface in order for it to be observed, which means that real light cannot have a surface of its own. Real light must be the only stationary substance in the real Universe. The stars remain in place due to astral radiation. The planets orbit because of atmospheric accumulation. There is no space.

      Warm regards,

      Joe Fisher

        Thank you very much for your comment. I apologize for not responding sooner. I just now read your essay, and will leave a comment for you.

        Joselle

        Thanks for responding with this. I can only say that I've thought for a long time that the way we have conceptualized light, the speed of light, even the arrow of time, may yet be getting in our way.

        11 days later

        Dear Joselle DiNunzio Kehoe,

        Very interesting essay and ideas that are close to me in spirit.

        The most important thought: "The representations are vectors, in that they contain both magnitude and direction."

        I started my studies 25 years ago with the concept of "consciousness - a vector value", "vector of consciousness."

        I fully agree with you that you do focus on the idea of the relationship of "matter" and "memory". About this Bergson wrote in "Matter and Memory". Unfortunately, he is not absorbed in the ontology of the relationship of "matter" and "memory".

        It is also very important concepts "beauty", "information". "Form"- the root of the word. Here lies the relationship with the "matter" and its absolute (unconditional, limit) forms of existence (absolute, limit states).

        Most important is your last words to guide your research and find an answer to the fundamental question of the ontological knowledge base, connection of mathematics and reality:

        "If we become accustomed to this idea, that consciousness has structure as valid as the structure of material, the physical sciences will likely find more commonality with the cognitive sciences. This calls to mind something I heard Deutsch say in a talk he gave - that our awareness contains "with ever increasing precision the structure of everything." Mathematics characterizes both what we see and how we see it. It is both a source and a target. Its deep biological source associates it with a searching, instinctual will. And, if we agree that an effective body/brain would have a structure that matches its world, then the really interesting question is how are we matched? Perhaps mathematics is in the unique position to help us begin to answer that question. "

        I believe that only the deepest ontological turn of the fundamental science will provide an opportunity to get out of the "crisis of understanding", "crisis of interpretation and representation" to the new heuristics.

        I invite you to see my analysis of the philosophical foundations of mathematics and physics, the method of ontological constructing of the primordial generating structure, "La Structure mère" as the ontological framework, carcass and foundation of knowledge, the core of which - the ontological (structural, cosmic) memory and information - polyvalent phenomenon of the ontological (structural) memory of Universum as a whole. I believe that the scientific picture of the world should be the same rich senses of the "LifeWorld» (E.Husserl), as a picture of the world lyricists , poets and philosophers.

        Kind regards,

        Vladimir

        11 days later

        Dear Dinunzio,

        I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

        All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

        Joe Fisher

        Joselle,

        Looking at your bio, I wonder about your view of math in biology. My essay speaks of physic's role via quantum physics in quantum biology as well as in DNA and the LHC.

        Jim

        14 days later

        Joselle,

        Shark time, so I am revisiting essays I've read to assure I've rated them. I find that I did not rate yours, so I am rectifying. I hope you get a chance to look at mine: http://fqxi.org/community/forum/topic/2345

        Jim

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