Some great questions throughout. Sometimes I feel certain assumptions are allowed to pass by uncritically, due to your beguiling prose, and this leaves me with questions regarding their purpose in the context of the essay. By asking the questions, I would want clarity on your conclusions to posing them. If this entails saying they are unanswerable, so be it.

You ask, "In what way do the values of cognition and creativity, often being at odds with life's comforts and necessities, could have entered the world? The remainder of this text is devoted to that question."

I don't get how the remainder of the text tackles your question. (The word creativity is to be found only once in the whole essay...)

My impression is that you suggest, in effect, that we bow to the intangible depths of certain questions, proposing instead, (in a manner reminiscent of the vitalists), that we look no further than to the beauty in such things. "The world was created for its beauty, and man--as one who may hear that and respond." That there is no evolution of value, nor a direction from which our individual freedoms have arisen nor a direction to which future individual freedoms will evolve, seems to be skirting the question and all such questions posed. Maybe I misinterpret...

You say, "To see in mathematics nothing but a collection of all possible, value-neutral, formal systems is no better than to view the art of sculpture as a collection of all possible articles made of stone, or defining man, according to the old anecdote, as a two-legged creature without feathers."

The profound beauty in a theorem may be in the conceptual freedoms it allows, namely, in granting us the ability, through its principles, to qualify the diversity of our experiences and/or understandings, and therefore, grant us the tempting potential to further explain things we are yet to experience and/or even dare to understand. Such conceptual freedoms thereby formalise the individual's subjective viewpoint as one that relates to the objective world and in so doing, adds substance and meaning to the individual's existence. So in my view beauty does not breath freedom.

    Alexey and Lev Burov,

    I liked reading your essay but think you rely on asking questions as a form of argument far too much.

    You are, in my pinion, too dismissive of the connection of mind to matter as you only consider the movement of atoms ( did you mean ions?). You completely miss out on arguments about emergence of characteristics at higher levels of organisation.

    Though i don't agree with all of your arguments, you present your points of view in an enjoyable essay. Thanks, Georgina

      Dear Mark,

      Thank you for your interest in our essay. I'll try to respond to your critical remarks.

      1. You write: "I don't get how the remainder of the text tackles your question." [about values].

      I think, the last paragraph of our essay gives an answer to that very question. In a sense, there is no evolution of value: beauty is the eternal one. From another perspective, however, our conclusion assumes this evolution resulting from permanent efforts to respond: "Eternal beauty calls to new manifestations; by evincing the contemplation of itself, it beckons birth, never promising but sometimes giving hope, always deciding the fate."

      2. You write: "The profound beauty in a theorem may be in the conceptual freedoms it allows". In our text, we did not dare to suggest our own formulation of mathematical beauty; we grounded our consideration on the hints given by great mathematicians, trying to understand them. I do not know any great mathematician who would agree with your formulation of the mathematical beauty, and do not think it is possible.

      Best regards,

      Alexey Burov.

      Dear Georgina,

      I am glad you enjoyed reading our essay.

      We did not use the word "emergence" in our text because we did not think it would be reasonable to sacrifice other ideas for that. As to the "atoms of a brain", this image of Haldane certainly includes ions as well.

      Thank you and all the best,

      Alexey Burov.

      Dear Professors Alexey and Lev Burov

      Please excuse me for I have no intention of disparaging in any way any part of your essay.

      I merely wish to point out that "Everything should be made as simple as possible, but not simpler." Albert Einstein (1879 - 1955) Physicist & Nobel Laureate.

      Only nature could produce a reality so simple, a single cell amoeba could deal with it.

      The real Universe must consist only of one unified visible infinite physical surface occurring in one infinite dimension, that am always illuminated by infinite non-surface light.

      A more detailed explanation of natural reality can be found in my essay, SCORE ONE FOR SIMPLICITY. I do hope that you will read my essay and perhaps comment on its merit.

      Joe Fisher, Realist

      Seeing beauty in mathematics is so often lost on folks who don't do mathematics. It's seen simply as very complicated arithmetic. Your equating the excitement, creativity, joy, and spirtuality of "serious" mathematics with sculpture and poetry rings so true to me. I have a hard time explaining it to others, and you have been very successful--of course to another mathematical physicist!

      I think the idea of "seriousness" is most true--it provides linkage of ideas to some sense of the whole, the one. Maybe it's this sense of unity that drives us to seek a deeper explanation of what we experience and provides the purpose that this "contest" wants us to address.

        Dear Joe,

        I am happy to see that one of my senior colleagues shares with me these noble ideas about mathematics, which I found in books of great mathematicians and tried to understand. Many thanks for your compliments!

        Dear Burov,

        Zdrassti

        Thank you for the nice essay on " Development of science vs Cognition "

        I congratulate on Good flow of English you wrote; instead of usual translations from Russian....

        Your observations are excellent like,

        1. Rene Descartes came to a necessity to separate all knowable into two parts, one of which encompasses all material and the other all mental.

        2. Cartesian dualism represented, before anything else, a methodological principle, a boundary condition, stating the problem at first approximation as a necessary step of the beginning of cognition.

        3. the birth and development of thought and comprehension of the laws already

        discovered by sheer power of chance seems utterly impossible

        4. Third, we have to accept that even in those cases, when the fundamental cognition in no way benefits the improvement of life conditions--in fact, it often

        being the opposite--the motion forward is not prevented. These assumptions are quite far reaching, and natural selection demands all of them without any arguments or a possibility of a scientific check.

        5. "I f my mental processes are determined wholly by the motions of atoms in my brain I have no reason to suppose that my beliefs are true. They may be sound chemically, but that does not make them sound logically. And hence I have no reason for supposing my brain to be composed of atoms."

        .................... Probably here I will put a little remark that the Brain is hardware, food we eat is the Electrical power supplied to computer, and the Mind is the software.... So software is required then the atoms will work and the cognition will develop....

        My essay is not on your subject....But I request to have look...

        For your information Dynamic Universe model is totally based on experimental results. Here in Dynamic Universe Model Space is Space and time is time in cosmology level or in any level. In the classical general relativity, space and time are convertible in to each other

        Many papers and books on Dynamic Universe Model were published by the author on unsolved problems of present day Physics, for example 'Absolute Rest frame of reference is not necessary' (1994) , 'Multiple bending of light ray can create many images for one Galaxy: in our dynamic universe', About "SITA" simulations, 'Missing mass in Galaxy is NOT required', "New mathematics tensors without Differential and Integral equations", "Information, Reality and Relics of Cosmic Microwave Background", "Dynamic Universe Model explains the Discrepancies of Very-Long-Baseline Interferometry Observations.", in 2015 'Explaining Formation of Astronomical Jets Using Dynamic Universe Model, 'Explaining Pioneer anomaly', 'Explaining Near luminal velocities in Astronomical jets', 'Observation of super luminal neutrinos', 'Process of quenching in Galaxies due to formation of hole at the center of Galaxy, as its central densemass dries up', "Dynamic Universe Model Predicts the Trajectory of New Horizons Satellite Going to Pluto" etc., are some more papers from the Dynamic Universe model. Four Books also were published. Book1 shows Dynamic Universe Model is singularity free and body to collision free, Book 2, and Book 3 are explanation of equations of Dynamic Universe model. Book 4 deals about prediction and finding of Blue shifted Galaxies in the universe.

        With axioms like... No Isotropy; No Homogeneity; No Space-time continuum; Non-uniform density of matter(Universe is lumpy); No singularities; No collisions between bodies; No Blackholes; No warm holes; No Bigbang; No repulsion between distant Galaxies; Non-empty Universe; No imaginary or negative time axis; No imaginary X, Y, Z axes; No differential and Integral Equations mathematically; No General Relativity and Model does not reduce to General Relativity on any condition; No Creation of matter like Bigbang or steady-state models; No many mini Bigbangs; No Missing Mass; No Dark matter; No Dark energy; No Bigbang generated CMB detected; No Multi-verses etc.

        Many predictions of Dynamic Universe Model came true, like Blue shifted Galaxies and no dark matter. Dynamic Universe Model gave many results otherwise difficult to explain

        Have a look at my essay on Dynamic Universe Model and its blog also where all my books and papers are available for free downloading...

        http://vaksdynamicuniversemodel.blogspot.in/

        Best wishes to your essay.

        For your blessings please................

        =snp. gupta

          Dear Mr. Gupta,

          Thank you so much for your good words in the address of our text.

          I already looked through your essay, and I do not see how its cosmological content relates to problems of mentality. Maybe, it does on a deeper level which I do not see yet.

          Best regards and good luck!

          Alexey Burov.

          Dear Steve,

          Thanks a lot for your compliments and good wishes!

          All the best,

          Alexey Burov.

          Hello Alexey and Lev,

          There is much in your essay with which I agree, and even where I think I might disagree I find your ideas challenging and original. One important point with which I agree is your belief that "ethics, which answers the question about that which should be, is inseparable from metaphysics, which answers the question about that which is." However, when you discuss values, you bring in primarily aesthetic values, such as elegance, seriousness, and of course beauty generally. What metaphysical role do you see for ethical values, good and evil, right and wrong, as more particularly understood? In any case, I agree that we shall not attain the truth about reality unless we include an understanding of value, including the value of reality and the value of truth itself.

          Thank you.

          Laurence Hitterdale

            Dear Laurence,

            Your response is more than encouraging; it is inspiring. Thank you so much! We are glad to know that you share our belief in the deep entanglement between ethics and metaphysics, which is a cornerstone for us. Your question about relation of ethics and aesthetics requires at least a special essay (maybe for the next contest :^)). However, I would not like to weasel out of your question like that. The most important thing which I can briefly note is that at its depth morality takes power from the beauty of the soul and its profound feeling of beautiful, which is tragic at the same time. Without this feed from the beautiful, the good would be much weaker than it is. Thus, in the depth, beauty is more fundamental than morality. Somebody might object to that, recollecting the legend about Nero enjoying the view of the burning Rome. Well, even if the burning Rome contained some harrowing beauty, Nero was not beautiful in that act; he was abominable. One more support to primacy of the beautiful is suggested by the Book of Job: it was the beauty of the world that atoned for its tragedy in his eyes.

            One day we should talk more on many issues.

            Yours, Alexey.

            Two Burov(s)

            Excellent essay. Sufficiently excellent to inspire the following ramble:

            I had a different interpretation of "cogito ergo sum" as no mention of any physical (external) reality. Thinking and being resolved into separate entities. But this just goes to show how many ways the investigation can unfold. The "blind spot" metaphor is an insightful one. Some of us are (perhaps dimly) aware of this feature as something we can't see directly but yet, on some level, we are aware of it. Do we understanding that this "blind spot" is obfuscated by "logical self-refutation"?

            Somehow natural selection cannot be an intentional search for its own cognizance and this is opined as fact. As if fishing (a random search) should have nothing to do with any intention to catch fish. The spontaneous emergence of self-organizing entities from stochastic particle interaction manifests intention (may be subject to interpretation). To think otherwise belies our curiosity as something outside of this process and relegates us to an inconsequential side effect of entropy. From my frame of reference, most obvious to me, is the observation that the stochastic universe is weighted in such a way, to provide me with time to sit here, and receive the honor of your acquaintance, and discuss such matters, while the necessities of my survival run in the background. Or else our interaction is accidental and I am simply lucky and in no way loved by that from which I have emerged. We imagine many things are so. That physical reality exists aside from our imagination is unimaginable to my experience. Instead we have a correlation between experience and mathematical relationships. I fall into my self-referential pit of 'no understanding without interpretation and creativity'. (Is this statement an interpretation? fact? creation?) I have not encountered Epimenides Paradox before. It looks like Russel's paradox. You must have been amused by my cognitive suicide at the end of my essay. Actually I died during a religious experience in 1976, and have understood nothing universal since. So I imagine.

            You point out a most fundamental feature of cognition central to my own pet theory; "For each correct solution to a problem competes a myriad of possible errors". The truth floats in a sea of falsity. I note further the resolution of any object, identification, symbol, attention, relation ... as singling out a particular perception from the background i.e. resolution of superposition (my pet theory). This is so basic that it escapes our notice. The "swarm of everything else" is an allusion to what I call the Superposition, which has connotations to quantum mechanics, wave theory, mechanics, electromagnetism, and everything else, and especially the nature of self (ego, God...)

            My impression of your essay is the objectivity of mathematics and the subjectivity of its application to observables as two sides of the same coin. If you agree then we have both arrived at the same place from different approaches. Such a coincidence validates us as parallel expressions of the universal intention we recognize. That would be a beautiful thing.

            If beauty is in the eye of the beholder, and the proliferation of life (change) manifests intention, then beauty is made for us and we are made for beauty. A significant step towards the unspoken Unity neither of us mentioned yet.

            This essay, especially the closing paragraph, will live in my study from now on.

            Vik

            P.S. I don't get the Title

              Vik,

              Thank you for such generous compliments.

              One can imagine a philosophical axis, with utter logicists at its one extreme and ultimate irrationalists at the other. I imagine you in the company of the mystical latter, while most of the contest's participants are concentrated at the opposite end. This makes your acquaintance particularly pleasant. We are somewhere in between, I think, with our high appreciation of both reason and its mother, mystery. The title of our essay refers to Diotima's vision on who helped that birth and who decided the fate of the wonderful baby.

              All the best,

              Alexey.

              • [deleted]

              Hi Alexey and Lev,

              Wonderful essay. I particularly liked "Only those moved mathematics ahead who loved it not for some other aim, however good and important, but for its own sake, for its eternal, super-human beauty."

              For my own pleasure I would change it just a bit: "Only those moved humanity ahead who loved it not for some other aim, however good and important, but for its own sake, for its eternal, super-human radiant beauty."

              Esthetics and a bit of emotion go a long way toward a goal. Appreciate your work.

              Don Limuti

                Hi, Alexey and Lev.

                Congratulations on wonderful work! The beauty of mathematics and the unity of deep emotional reactions of multiple mathematicians in all the times and countries reveal the objective connection between the impersonal mathematical ideas and "mathematical needs" of personal human intelligence.

                Like knows like. Like loves and enjoys like. Like consumes like. Thus, mathematics is the "food" for the mathematical, logical, rational nature of the humans. Human nature is not just biological and material, it is logical and mathematical. Mathematics show us the immaterial intentions of this immaterial part of the human being, of the human mind.

                The beauty of mathematics attracts human consciousness like voice of Moira and pulls it out of animal existence like Eileithyia to the birth of pure human mindfulness and happiness. Your essay shows this with indisputable clarity!

                  Hi Don,

                  It's a pleasure to see our statement played with in a new way. I will read your essay and leave my comments on your page tomorrow.

                  Thank you!

                  Alexey.

                  Hello Andrew,

                  We enjoyed reading your poetic response; many thanks!

                  We fully agree: mathematics is indeed a wonderful, delightful food cooked by and prepared for human rationality.

                  Yours, Alexey and Lev.