Essay Abstract

Some hints concerning the Mathematics effectiveness from the evolutionary biology are proposed, and the unexpected fecundity of ideal concepts is handled with qualitative clues form Category theory. Then, the question of the ontological status of Mathematical entities is investigated, comparing the main philosophical approaches about it, with emphasis on their epistemological aspects. Plus, one tries to show that the concept of intrinsic qualities is misleading, and that for both physical fundamental quantities and methodological assessments, a relational view is inescapable. This leads to a radical position according to which stating the existence of physical and mathematical entities is ultimately the same process. Eventually, some very interesting consequences about information, complexity and mathematical descriptions are illustrated.

Author Bio

Former researcher active in the field of particle physics, now physics and math teacher and independent scholar with interests in applied mathematics, fundamental questions and philosophical issues.

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5 days later

Hi Paolo

Our systems show some similarity at fundamental level but not in detail. Please see if my statement is correct.

Essay

Thanks and good luck.

Dear Mr. Bellan,

You wrote: "If the Universe is a purely mathematical structures, the incompleteness theorems ensure that there will be undecidable statements

around; so we may wonder what they would represent in physical terms; perhaps, aspects of reality not addressable in mathematical terms."

This is my single unified theorem of how the real Universe is occurring: Accurate writing has enabled me to perfect a valid description of untangled unified reality: 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'm afraid I don't get your point, neither what should be the link with the quotation; if it's supposed to be funny, I'm sure you can do better than that.

    Dear Mr. Bellan,

    Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of abstract NOTHING. My comment proved it. If you did not understand it that is too bad. If you thought that I was joking I pity you.

    Joe Fisher

    8 days later

    Dear James,

    A wonderful essay like a chessboard with all the players and ideas.

    But, one must admit that a universe that "existed" or "lasted"13 billion years has 'substance / process' to support this existence, long before we ever started playing SA.

    The main problem is that we keep the SA point of view when we know exactly the point of view of the universe. For example, for the universe to effect a contact between any two points on the Moon, even at the speed of light, it requires time. Then, from the point of view of the universe those two points are not at the same time. The "Moon" is in fact just an aggregate of matter across time. We make it "Moon" when we perceive or conceive it as being all at the same moment; a moment of perception, a snapshot! We make the Moon as an object when it is not.

    Philosophers using scientists tools was no more fruitful than scientists trying to use philosopher's tools.

    It is all very "Wheeler" simple. The mathematically friendly universe means that it simply follows rules of logic, and the requirements for a logically operational universe are extremely simple...

    Please see my essay http://fqxi.org/community/forum/topic/2488 , with details in previous essays.

    Good luck,

    Marcel,

      • [deleted]

      • Post #7

      Paolo,

      Of course, in my post above I meant Paolo..... Where did I get this James name from anyway ????

      Marcel,

      Dear Marcel

      thank you for having read and commented my essay!

      Don't worry for having called me James.. it sounds good actually! :)

      I'm absolutely not committed to deny physical existence, rather I'm arguing about the meaning of assessing existence of something without any sentient agent that ever had relation or access at it at all. That statement is a plausible extrapolation only about something that's already been assessed, as the Universe indeed. Hard to conceive a sound meaning for something to exist if not any relation or access to it has ever occurred; in short, the existence is a relational feature, as Physics is showing for all basic qualities as well.

      The point you mention about the human process of building 'object' out of out perception is very interesting, even though a slightly different one IMO: the question of the relational nature of qualities holds up even for features not related to a structure or an object; and indeed, we can make sense and set the boundaries of structures and 'aggregates' in physical term, somehow independently from SA, through the persistence of their patterns, basically.

      Cheers

      P

      11 days later

      Dear Paolo,

      Your research, concepts, ideas and the direction of search is extremely important. I particularly liked the concept of "ontological par":

      "Ontological par", on the other hand is a bit harder to swallow".

      Today, mathematicians and physicists continue to fear the ontology, and especially dialectic, at least in the spirit of Cusa - "coincidence of opposites." Outcome: mathematics and physics lost existential certainty.

      Mathematics and Physics- sciences without ontological justification (basification), as well as all the "fundamental knowledge". Requires the deeper ontology and dialectic in the spirit of Heraclitus - Plato - Cusa - Hegel as well as the deepest synthesis of all the accumulated knowledge, including Tradition. At the same time "Occam's razor" should be extremely sharp.

      E.Husserl gave good tips in "Origin of Geometry": "Only to the extent, to which in case of idealization, the general content of spatio-temporal sphere is apodictically taken into account, which is invariant in all imaginable variations, ideal formation may arise, that will be clear in any future for all generations and in such form will be transferable by the tradition and reproducible in identical intersubjective sense."

      I believe that only the deepest dialectic-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 poets and philosophers.

      Kind regards,

      Vladimir

        4 days later

        Dear Paolo,

        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 Paolo,

        I see some similarities of your ideas with mine (see my essay A Mind/Mathematics Dualistic Foundation of Physical Reality): you wrote "The obvious answer is that existence is a quality relationally attributed to entities by Sentient Agents", and it pertains only to their current status or informational content. We are forced to say that something exists if an only if a SA is aware of it. The quality of existence comes out to be, firstly, deeply relational, and secondly, inseparably related to the awareness and knowledge one has about entities".

        In my view, there are 2 different concepts of existence that need to be distinguished: one is the mathematical existence, which is a purely abstract, mathematical concept independent of all contingencies (independent of the whole physical universe). The other is this contingent form of existence that you mention, that is for an object (be it mathematical or not) to be either created or pointed out (distinguished) here and now by conscious perception. I have explained in my essay how the laws of quantum physics can be explained from an interplay between these 2 forms of existence.

        You talk about "Nominalist approaches" that "deny an independent ontology to the mathematical objects". I think, the main reason why philosophers of mathematics keep talking about nominalism, is that they failed to update their discourse to the consequences of the Completeness theorem. Indeed, this theorem shows that the existence of the objects of any consitent theory can be directly produced by its formalism itself as soon as we admit an actually infinite set of natural numbers. In these conditions (and just if we admit the existence of an infinity of natural numbers), there is no fundamental difference of nature between the objects of a theory and its formalism, and there is no sense trying to oppose them. We need not wonder if we allow or deny an independent ontology of mathematical objects if the objects do not need any independent ontogy, since the formalism is already sufficient to provide the ontology that is needed. With the only defect, of course, that building the whole system of objects requires to consider the whole infinite set of all possible expressions of a kind that can be written from the theory, while sentient agents can only explore a finite set of expressions at each time.

        You asked the question of "how mathematical entities could 'exist', and having causal impact on reality, without being physical. A possible way out could be forcing their stance of 'being real', equating the physical reality to a mathematical structure.". Indeed, a possible way for 2 things to be related is to consider them identical, but there is quite a margin of possibilities in details. In particular, in the idea of "physical reality" I distinguish between the things that are real, and their quality of being real. So, I see the things that are "physically real" as particular cases of mathematical structures, while I attribute their quality of being physically real, to conscious perception.

        However I would diverge on the following: you wrote about "...phenomena potentially not addressable in mathematical terms. In fact, rephrasing it as 'if there could ever exist aspects of reality non describable abstractly', and sticking to the conscious, relational meaning of existence, we may conclude that it cannot be the case". Maybe your use of the word "abstract" is ambiguous : while I would agree that things have to be consciously perceived for being "real" (beyond a mere mathematical existence), I think that "being perceived" does not imply being mathematical, as we are also able to perceive some non-mathematical stuff (feelings, etc: not everything we can understand is a mathematical structure, especially for people who are not mathematicians).

        You may also be interested to see my review of essays, with a list of those I found most interesting (unfortunately I'm still far from finishing to read all I wish... the link to your essay will appear in the next update).

          Dear Vladi,

          many thank for your interest and your nice words! Surely I'm gonna have a look to your work.

          I've tried to refrain myself from going too deep into the cracks of philosophical foundation of the today's physics in my essay, focussing rather onto the true essence that 'things', either physical or mathematical, share... as to say, speaking of ontology but without saying it too loud; but this didn't prevent you from getting the point I see :)

          Best wishes,

          Paolo

          Thank you, Paolo. for your kind words. I once gave you a happy nine (邃-9), but some "sniper" then lowered rating. Waiting for you on my forum. Today it is important for the understanding of the deepest meanings of being.

          Sincerely, Vladimir

          9 days later

          Dear Paolo

          Poirier sorted essays and gives he, you and me in the same box, named ''Spiritualism: Consciousness is fundamental''. I need to read you more precisely, but it is already seen that we agree a lot.

          I do not understand your opinion about MUH, but in my opinion it is not necessay some anthropic principle, but only very simple axioms for all physics, or even without axioms. What is your opinion?

          My essay

          Best regards

          Janko Kokosar

            7 days later

            Hi Janko,

            thanks for your words and interest; sure I'm gonna have a look to your work asap.

            Concerning what you ask me about MUH, well.... there is a lot to say; honestly, I had to cut out quite some stuff related to it I put in my essay in the draft versions.

            I found that the core idea of MUH is a very interesting one, as I've written in my essay: equating the necessity of mathematical structures to the one of physical reality actually solves a number of philosophical issues, and sheds light to the nature of the possible ultimate fabric of the universe (in a sense). Also, MUH main idea is deeply rooted in something that I found myself a key point in physics, namely the relational nature of all quantities and entities... imo, a well proved fact.

            Nevertheless, it seems to me that MUH is definitely an unverifiable statement (and hence, a kind of metaphysical statement), as all the empirical tests purported by the Author are preposterous; also, it is prone to a number of heavy objections, raised from different Authors and still pending, and it lets unanswered many questions. Overall, I deem no more than a thoughtful exercise, with a number of innovating hints for further speculations.

            All my best,

            P

            Dear Sylvain,

            thanks for your interest and your rewarding opinion; it is a relief indeed: I'm a bit afraid that my sake of conciseness ended up to deliver a messy tangle :)

            Let me also acknowledging your work in reviewing the essays... really wonderful !

            Your ideas about the two kinds of existence are keen, and I'm eager to read your paper; at first glance I would only say that I'm not sure is it necessary, or convenient, call into the matter of what 'existence' really mean the concept of contingency/necessity. Indeed, this would require to assess how much our physical universe is contingent, an open and very intricate issue, far to be fully understood.

            Your observation about the survival of nominalist approaches and their ontological status are definitely thoughtful: indeed, one may alight on what's the role of 'admitting' the (mathematical) existence of something... but I'd rather say 'accept an axiom': again, the role of a SA conceiving something is what lays at the ground.

            I found the distinction you made about something being real and having the quality of being real (if I got it correctly) quite subtle... maybe a bit slippery: once you state a larger superset of reality made by the conceived object, you end up with something a bit hard to handle.

            Eventually, let me try to answer to your last point. I can agree on the vagueness of my use of 'abstract' there.. in fact, I would have liked to insert at that point a deeper discussion on what is, or we mean with 'mathematical description', but there was no room left :) What I've tried to sketch there is indeed a key point of my view, namely that thoughts themselves are ultimately of the same nature of what we mean by 'mathematical description': neuronal potentials act as hidden 'symbols' in the dashboard of our head, and they carry semantic content, as usual mathematical symbols do. Only the interpreter is different: either our full awareness, or some neural district of the brain acting as 'decoding function'.

            Thus I definitely agree that as you say , but I've tried, in stead, only to put forward an argument supporting that 'being mathematical implies being conceived'.

            All my best,

            cheers

            P

            a month later

            I agree that the distinction between something being real and having the quality of being real, is paradoxical, and even absurd at a fundamental level, since, to consider the attribution of a quality of reality to an object as something different from the object itself, the object would have to somehow exist independently of that reality that may be optionally attributed to it. But my point is that there are different possible degrees of reality for the same mathematical objects: all mathematical objects have the quality of mathematical existence (to be mathematical objects at all) but not the quality of physical reality (which depends on conscious perception).

            "being mathematical implies being conceived" : I disagree.

            Let's take a concrete example: consider the set of all numbers between 0 and 10101000. They all mathematically exist. They are all mathematical objects. Still they cannot all be conceived, at least by human beings, since most of them (the "random" ones) are too complex to be pointed out : each of the random ones would require about 101000 digits of information to be specified. The same goes for the physical universe: it is a choice of a mathematical object in a landscape of mathematical objects that all mathematically exist but are not all consciously pointed out.

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