Essay Abstract

I argue that mathematics are generated by computation, specifically the lambda calculus. I further argue that mathematics cannot exist without dimensions, and that those dimensions are only manifest once they have been engendered by computation. The first of these dimensions gives us the number line, which encapsulates all of number theory. I draw on a number of famous insights to build up a picture of a universe in which each point in space is enumerated by a dedicated computation. The ensuing calculation of space engenders the mathematics we use to model the macroscopic behaviour of the universe, mathematics that are idealized approximations to the discrete machinations at the basis of reality. The model I present naturally lends itself to an accelerating expansion of space, and offers to merge the concepts of singularity and superposition, the two great mathematical pillars of last century's physics. The essay addresses the theme "Trick or Truth? The Mysterious Connection between Physics and Mathematics" by drawing the reader into pondering whether or not I'm being serious about my conclusions.

Author Bio

I am a computer systems engineer, living and working in Canberra, the bush capital. My wife and I are almost empty nesters - we are ever so slightly crazy about our Russian blue, who still lives at home (when it suits him...)

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Dear Rowan Grigg,

Thanks for your very interesting essay. You begin by stating that "mathematics are generated by computation", and I fully agree with this. In my essay I view the inherent logical structure of reality as that which enables AND and NOT 'gates' to exist at many scales (from RNA-DNA-protein to telomeres to neurons to silicon, etc.) and hence to compare and compute. Further, you state that, as a systems engineer, "we of course understand that there is ultimately some real hardware behind all this virtualization." It is the "real hardware", that is, "physical reality" that most concerns me.

If I understand you correctly, you then suppress the real hardware in favor of recursive or otherwise iterated virtual architectures in which, of course, fascinating structures may be constructed and overlaid on reality, but you seem to recognize this as artificial. When you end with "one massively parallel computer ... engendering reality", it is not clear whether you have forgotten the requisite underlying hardware in favor of sleight-of-hand or whether this "reality" is simply some perceived reality at a virtual level. You might wish to clarify this point.

Finally, for a new take on "action-at-a-distance" I invite you to read my essay.

Best regards,

Edwin Eugene Klingman

    Dear Rowan,

    I really enjoyed reading your essay.

    You wrote "In 1990, John A. Wheeler saw a clear opportunity to break this cycle, mounting an argument that the world consists entirely in information enacting the laws of physics - delivering 'it' from 'bit' - and that our consciousness creates the very reality from which it has emerged, in a self-referential loop".

    I propose a model of the Universe that follows the above description. I thought that you might want to take a look at it if you have a spare moment, you can find it here.

    You can also take a look at my essay althought it is mainly a list of equations.

    All the best,

    Patrick

      Dear Edwin,

      Thanks for your kind feedback. I'm a bit of a 'hardware' man, and reading Massimiliano Di Ventra and Yuriy V. Persin speak in the February edition of Scientific American about the building blocks of 'Memcomputers' reminded me just how special this hardware we're lucky enough to be made of really is. In his famous paper, Alan Turing used the wonderful word 'desultory' to describe the way the read/write head of his machine moves tirelessly back and forth along the tape without a single word of complaint. Nature has this same agnosticism in her slavish adherence to her laws, and that is where I saw the opportunity to map nature's consistency onto the consistency of computation.

      I don't presume to fully understand the virtual architecture engendering (simulating) the perceived hardware of the universe, but I do posit its existence, and furthermore posit that it is NOT subject to the laws of nature. Indeed, the entirely virtual entity I borrowed from Gottfried, the 'monad', must exist outside the physics it engenders, for I posit that it holds itself up by its own boot straps in a kind of perpetual motion, a condition very clearly outlawed by the laws of thermodynamics (without which life as we know it would, sadly, not exist).

      I accept this appears to be a sleight-of-hand, but so too does the single surface of a mobius strip seem as such - but there it is.

      regards

      Rowan

      Dear Dr. Grigg,

      You wrote: "But of course many a foundational thinker (including Weinberg himself) is just so inclined - for example in 2008, Max Tegmark, a mathematical physicist, argued that the universe is literally 'made out of mathematics.'iii"

      Professor Max Tegmark was comprehensively wrong.

      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

        Dear Joe,

        I think we all agree this world we live in is real (except when it is unreal). So then what we're all trying to do in this forum is figure out what on earth this stuff actually is. To this end, like it or not, the current fashion is to attempt to merge idealism and realism. It was once thought that the world was either a dream inside someone's head, or genuinely material. It's now looking likely that it is both,

        kind regards

        Rowan

        Hi Patrick,

        Thanks for reading my essay.

        Please see my response on your essay thread,

        regards

        Rowan

        9 days later

        Hi Rowan,

        Thank you for your comment on my blog. I posted a response.

        Since I wrote my essay, I have released a new list of equations that seem to indicate that the Universe is purely mathematical and just pure information.

        You can download it on www.vixra.org/abs/1503.0184

        Cheers,

        Patrick

        13 days later

        Dear Rowan,

        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

        Dear Rowan,

        Very interesting ideas and important conclusions for search of a ontological basis of fundamental knowledge:

        "If the monad is an abstraction, having no intrinsic dimension, then it is perhaps fair to suppose that all the numerous (but countable) monads generating this virtual reality 'exist' at a single dimensionless point. "

        "However, it is just as valid to think of this point as a superposition of the monads, a place where one massively parallel computer, burgeoning in capacity, engenders reality. When researching and developing 'quantum computing', we should bear in mind that we may be accessing precisely this superposition of the universe. If the entire machinery of reality exists in one place, concurrent action at a distance no longer seems "spooky".

        These thoughts and conclusion is consonant with the thought Henry David Thoreau:

        It is by a mathematical point only that we are wise,

        as the sailor or the fugitive slave keeps the polestar in his eye;

        but that is sufficient guidance for all our life.

        We may not arrive at our port within a calculable period,

        but we would preserve the true course.

        I also fully agree with these inferences:

        "At the deep basis of reality, we should be looking for the most primitive computation, rather than the most primitive equation, to emblazon our T-shirts."

        "Every age establishes a paradigm informed by the dominant technology of their era - Isaac Newton's clockwork universe has become today's computational universe."

        Now is the Information age, which requires a new conceptual paradigm to overcome the crisis of understanding in fundamental science. My appreciation for your original ideas on representation of dialectics ideal that is very important for understanding of the nature of information and time. I also with interest read your previous essay "On the Origin of Time" and noted your ideas of "quantum of space" and " quantum of time".

        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 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 poets , artists and philosophers.

        Kind regards,

        Vladimir

        10 days later

        Rowan

        Great essay, speaking as a fan of both Jackson Pollock and jigsaw puzzles. Does physics not too often try to solve puzzles by studying and numerically describing one piece at a time/

        Very original and thought provoking. I was indeed left wondering if I was serious about my own conclusions. I must go and look up the definition of 'real'!

        best wishes.

        Peter

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