Dear Gavin,

Thank you so much for your compliments and support. I just finished reading your essay; it is one of the best at this contest, I think. Perhaps, you have already read my comments on your page.

All the best,

Alexey.

Dear Alexey and Lev,

I was really pleased to see this angle in the batch. With some collaborators, I've been doing work on mathematics as a cultural process, driven by taste and aesthetics and group norms as much (or even more than) by utility. Michael Harris has written a lovely book on the question, an autobiography as well as a response to Hardy, called "Mathematics without apologies", and it was intriguing to see such a high-level mathematician talk so frankly about the aesthetic (and social) prejudices that drive him.

It's a value-laiden process, in other words, and it is just really weird that it ends up producing the raw material for physics. The "Unreasonable Effectiveness" that Eugene Wigner wrote about seems even more mysterious. And I think it provides either a challenge, or a bizarre next step, for someone who signs on to the standard Platonism that most physicists walk around with (or the hypertrophic version in Max Tegmark!) You're forced either to say that it's doubly weird that mathematics works so well despite the "contamination" by values, or, conversely, that of course value-laiden mathematicians do so well: the universe is values through and through.

Yours,

Simon

    Hi Ted,

    I think all your 'quibbles' are important, giving me a chance to focus on some of our key issues.

    1.

    "One quibble with your essay was with regards to the claim about the mystical nature of many great mathematicians and physicists. My sense of being a mystic is that it mostly entails a sustained inward commitment or awareness, and that tends to place the intellect in the backseat."

    The historical fact is that essentially all those great people who deserve to be called 'fathers of physics' were mystics. This is true not only for Pythagoras and Plato, but also for Galileo, Kepler, Descartes, Leibniz, Newton, Euler, Gauss, Faraday, Maxwell, Planck, Einstein, Schrodinger, Heisenberg, Pauli, older Dirac, Wigner... You may read about that, for instance, in a wonderful recent historical treatise of Wagner and Briggs, "The Penultimate Curiosity", or enjoy "Quantum Questions: Mystical Writings of the World's Great Physicists", collected by Ken Wilber, or in "The Music of Pythagoras" by Kitty Ferguson, to name just a few.

    2.

    "You talk a lot about the significance of intellectual beauty. On the hand I suggest that a lot of progress (intellectual/spiritual/whatever) is derived from the obstacles and suffering we encounter. "

    The high importance of the intellectual beauty is not my arbitrary claim; I am finding that in writings of those highest rank mathematicians and physicists who cared to express their worldview. Moreover, I think everybody with sufficient mathematical experience knows that in his/her heart. Mathematics is loved by many people, and it is loved for its beauty. Obstacles and suffering may play an important role in ways that beauty is revealed to us, as, for example, one may read in the book of Job.

    3.

    "I think that the underlying reality is that religions were on to something real and science should be open to that possibility."

    I do not think that science, as a special mode of cognition, can be open to religious reality. Science is limited by its strict exclusion of all subjective, which makes it so effective. I would rather say that scientists should not be as closed to the religious, as science is.

    4.

    I am not sure that I fully understand your last paragraph. I would say that the God-soul relation is extremely subtle both bottom-up and top-down.

    Thanks again for your extensive and thoughtful comments. Stay warm and please do not forget to rate our essay.

    Good luck, Alexey.

    Hi Alexey,

    I thank you for your note. You can respond at your leisure to this if you wish.

    1. "Mystics" apparently has multiple meanings then. In a philosophical sense you (and those authors) might be right. In what I would term a meditational sense I don't think those individuals were mystics (very few people are). Books like "And There Was Light" or "I AM THAT" were written my individuals who somehow got a deeper perspective on things (i.e., a mystical perspective) and that is exceptional and I don't think intellectual in nature (the latter author was completely uneducated).

    3. The deeper point of my book is that you can get coherent objective traction across a number of life mysteries from a premodern religious perspective. In any case in the pending wake of DNA's failure people are going to want to comprehend individual innateness and the associated challenges. I doubt scientific approaches will find traction.

    Thanks again,

    Ted

    Dear Simon,

    Thank you for the good words in our address. We are glad to see a rare person who shares with us understanding of a necessity for ontological conclusions from the 'unreasonable effectiveness of mathematics', and the problem of values in that respect. Many thanks also for the info about Harris' book; I already ordered it. The ending of your post "You're forced either to say that it's doubly weird that mathematics works so well despite the "contamination" by values, or, conversely, that of course value-laiden mathematicians do so well: the universe is values through and through" looks as a possible epigraph to our previous fqxi paper :) I am going to respond to your captivating essay on your page.

    Good luck at the contest,

    Alexey.

    Alexey and Lev,

    A nice purposeful combination of prose and poetry, uniting the material and the mental with the bridge of mathematical beauty, which almost poetically describes the natural world.

    I try to display the birth of hypothesis with a speculation regarding dark matter in my essay, bringing together thoughts of others, mathematical laws, and an intensely perturbed material world. I hope you have time to read it and provide your thoughts.

    Jim Hoover

      Jim,

      We are specially flattered by your truthful compliments to our blend of the romantic prose and rational poetry (now imagine my artistic bow and :)). Thank you! Your essay is in my short list; you will see me soon on your page.

      Best,

      Alexey.

      5 days later

      Dear Alexey and Lev

      I read with great interest your beautiful essay. It was a real pleasure, there is a kind of luminosity that emerges from it - I think you understand what I mean.

      The res cogitans of Descartes corresponds to mind but now we know that most of mind functions depend on matter - for instance, memory: a damage in the brain can cause a lost of memory. If we compare what can be achieved by Artificial Intelligence with ourselves, it seems that our sole characteristic that we cannot, by now, consider that depends on matter is consciousness. It may depend but by now, we do not know how.

      In my essay, I exclude consciousness from my analysis; but I give a contribution to explain everything else, i.e., how, from the simple properties of matter, can the universe evolves as if guided by an intelligence towards a goal (a surprising contribution of my essay is to explain "intelligence" from matter properties).

      Note that in the above phrase I excluded "mathematics"; because mathematics is just a tool, a language. When I was young, I was marveled with mathematics, but along my life I learned to consider it as a tool - a powerful one, essential, but a tool; like language is a tool for communication. Of course that it can be a source of the feeling of beauty - like it happens with language. And, like language, it can be it in two ways, the formal one and through the ideas it represents. Nowadays, I don't use an equation that I cannot replace by plain text (excluding the quantifying aspect). The reason is that mathematics has no goal, we cannot let be driven by it, we have to always understand the road in which we are because mathematics can follow any road. Like language.

      As you seem to have an open mind, I dare to say that along my life I had a set of personal experiences that I cannot explain by coincidences or hazard; although I try to explain everything from matter properties, and to some extend I feel that I do it better than anyone else (my essay is just a minimum demonstration of it), I know that there is a level on the universe that in no way can be explained by our present conception of it at the Physical level.

      All the best!

      Alfredo Gouveia Oliveira

        Dear Alfredo,

        Thank you for your kind words in our address. Beauty is in the focus of our essay, and this obliges. We are glad to know that some of our readers appreciate aesthetic side of our text.

        Certainly, it is true that mathematics is a language. However, it would not be correct to attribute it solely to humanity, as we tried to show. Galileo stressed that it is the language of the "book of nature" itself, and the same idea was expressed by Wigner: mathematics is "the correct language", that is why it is "unreasonably effective" in physics. The discoverability of the laws of nature (in the meaning of our essay) can not be attributed solely to the inventiveness of the human mind; it also has its objective counter-part, related to the nature itself.

        Your post above sounds both intelligent and friendly, convincing me to read your essay attentively. I will do this soon, leaving my comments on your page.

        All the best,

        Alexey Burov.

        Dear Alexei

        I thank your very kind words! I can see that "beauty" is something in which you live in... and it emerges in anything you do or think.. I will try to follow your example!

        You know, mathematics is a logic language, strictly logic; however, to where it leads depends on the hypothesis and assumptions on which it is applied. Because it is logical, it leads to "understandable" models provided that the hypotheses and assumptions are "understandable"; however, if those hypotheses and assumptions are not understandable or incorrect, mathematics leads to models of reality that are not understandable.

        If we accept that the universe is as simple as it can be, than hypotheses and assumptions must be understandable, no "magic" in them; and also the models mathematically obtained.

        From this point of view, a model that is not understandable implies that the hypotheses/assumptions made are not correct.

        Mathematics has also the possibility of fitting whatever set of data - it is just a matter of considering enough parameters. This is very important and is the first phase of discovery process because it allows having control over phenomena and organizing data. These mathematical models are usually "not-understandable", they present logical inconsistency and parameters that obviously cannot represent a physical entity. However, many consider that these models of data are correct models of reality; and so they consider that the universe is "not-understandable". That seems to be the case of Wigner, as expressed in the statement you cited: "mathematics is "the correct language", that is why it is "unreasonably effective" in physics".

        Therefore, while some (the mainstream) consider that the unreasonably effectiveness of mathematics in physics is the proof that it is "the correct language", for others, like me, it is the proof that the hypotheses and assumptions made are wrong because mathematics can only lead to "reasonable" models.

        Now, how do you know which approach is correct?

        If you take just a quick look to my essay, you will probably suspect that I may know unexpected things about the universe. How is that possible? By looking for understandable models of the universe. That is the ultimate beauty of mathematics, the fact that it allows us to go finding the nature of the universe by looking for models that are understandable. And one does one step in the correct direction, one feels the amazing beauty of it.

        All the best!

        Alfredo Gouveia Oliveira

          Dear Alfredo,

          You caught me in pondering over your essay. Before commenting it on your page, I'll try to answer briefly here. You are right, that mathematics allows to describe any process. However, if your formulas has nothing to do with reality, like in the Ptolemy model, the number of fitting constants increases with required accuracy and the span of parameters. The effectiveness of mathematics in physics is "unreasonable", because very simple formulas, with clear reasonable principles behind them, with very small number of fitting constants describe physical reality at huge range of parameters and with extreme accuracy. I cannot go into details here, you may read about that in the classical Wigner's essay "Unreasonable effectiveness of mathematics", or in the reference to R. Penrose in our essay. This was also one of the main points of Einstein's cosmic religion, which is brilliantly described in Max Jammer's "Einstein and Religion".

          Thank you,

          Alexey Burov.

          Dear Alexei

          Thank you very much for your comments and your vote. Your doubts are certainly the ones of others and your comments give me the possibility of clarifying important aspects. A Portuguese writer said "Do not affirm the error of a truth before changing its context. Unless it gives you joy to be stoned." Unhappily, the short size of this essay has limited my capacity of changing current context. So, allow me to try to do it now.

          The classic definition of Intelligence is just a useless description of human mind, grounded in the belief of our exclusive nature.

          Do you think your computer is "Intelligent"? I think your answer is "no". But why? A personal computer has memory, it can play music, make calculations, answer questions by finding the answers in the net - some can even talk with you. So why is not the computer "Intelligent"? The reason is that it cannot answer a question like: What killed the dinosaurs? (it can present current hypotheses, but that is not the answer, just hypotheses); or "does dark energy really exist or is just an ad hoc parameter?"; or "how to do a non-polluting and inexpensive car"?; or "how life was created?"; etc. That is the capacity computers do not have (yet).

          Now, lets see your questions

          About my definition of Intelligence you say:

          1 - It looks as a circular logic to me, since not only "mind" and "problem", but "database" already imply "intelligence".

          From the above I think that now you understand that what you say is wrong. Database is the content of memory; your computer has databases, a book can have databases. Intelligence uses them but they are not Intelligence, in the same that you use the computer but the computer is not you. And also a problem is not Intelligence, of course.

          2- about your mention of Poincare, of course that Poincare has influenced me. As it happened with Einstein, by the way. I read it more than 30 years ago. It is not only with Poincaré or Compton that you can find resemblances - also with Darwin, as I detailed explain. In this case, it is Darwin that has inspired me the most.

          3 - ""Is nature able to generate by itself something with new properties? The answer is yes, of course."

          This I do not understand. How can you know that with certainty? If you said that you believe in that, I would understand; however, if you wanted to claim it obvious, I would disagree. "

          I explain: take an electron and a proton; they immediately converge and form a Hydrogen atom. This atom is something new with new properties, is not so? And these atoms then can merge and form other atoms, with new properties. Therefore, the answer to the question is obviously yes, of course. I explained in the essay why I say that.

          4 - "The problem is that these long molecules are not just long, but they are specially ordered, and the order is important. They are like long meaningful texts, not just like long arbitrary sequence of letters."

          Again you are not correct and in two ways. One is that I don't claim to explain the creation of life, just the appearance of the long organic molecules it requires - molecules of the kind of DNA and with the capacity of auto-replication. The other is that the order is not so important as you seem to think because there are (or were) many thousands of different types of bacteria, presenting a huge diversity of DNA, and these are just the survivors of a still much larger set of previous cells. Now you have to consider the huge number of those large molecules that were produced in the described Earth early environment during near one gigayear - it's an astronomical number, making the possibility of obtaining specific sequences a reasonable value.

          When we see something different of what we are used to think, the first reaction is to consider that the author is wrong; the possibility that he/her is correct is so low that we do not consider that possibility. But it can happen.

          Once again, I thank you very much for your comments. I hope that I was able to clarify your questions, which are consequence of the short size of a text that had to analyze such a complex subject.

          I hope to ear from you again, this is a fruitful discussion.

          Alfredo Gouveia de Oliveira

          Dear Alfredo,

          1.

          Database is not intelligence, of course, but, as I said, it implies intelligence. That is why it seems circular to define intelligence through databases. The same is true for "problems", "solutions", etc.

          3,4.

          I would not consider a Hydrogen atom as something new compared to proton and electron, since at certain condition there must be a lot of these atoms as soon as you have enough electrons and positrons. This is not true for life: apparently probability for life origin, with all the required atoms provided, is so low, that it cannot be explained by the physical laws. Life can be considered as really new, and it is a big question if nature could produce it itself.

          Cheers,

          Alexey.

            Dear Alfredo,

            I wanted to add to Alexey's reply by noticing a very powerful assumption you make. "If we accept that the universe is as simple as it can be..." While working out scientific ideas, assumptions are one of the primary methods. There is no need to question them if they turn out to be supported by the results. Once the science is done though, and we step back to reflect on what it is that we've learned, assumptions themselves become the focus of explanation. This reflective thinking is the domain of philosophy.

            I know of no philosophical position that would allow for the extreme assumption that you make. Even the luminous theologies of the fathers of physics don't venture so far. Even Einstein used it only a sort of working philosophical hypothesis. Physics does make the assumption that the laws are simple (not simplest), and this assumption is justified with its success, but looking back, this is an incredible miracle that is not at all necessitated by any purely logical conclusion -- that's Wigner's point. It is, perhaps, the greatest contribution of physics to humanity's vision of the world, its greatest discovery. Don't you think that glossing it over as a mere assumption is the least appropriate way to treat it? Or did I misunderstand you?

            Our essay Genesis of a Pythagorean Universe is devoted to the philosophical consequences of this particular discovery.

            Thank you very much for your plentiful compliments and appreciation. Alexey and I will discuss your ponderous essay.

            Lev

            Dear Alexey & Lev Burov,

            Thank you very much for your enjoyable essay. Your perspective of beauty in what we perceive around us, including "mathematical beauty" is key consideration that many people ignore or choose to ignore when building abstractions to formulate problems to solve analytically. In many cases in the past, it seems they may not have been all that successful in this separation, being silently seduced by the beauty of mathematics in the first place. (For example the Copernican system insisting planets orbit in perfect circles.) I also love how you so eloquently put it in your conclusion that, "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". Wonderful!

            Thank you again and I have in the meantime rated your essay too.

            Regards,

            Robert

              Dear Robert,

              Your compliments to our essay are especially pleasant, since you see the core of our text on the background of that strange blindness of the spirit of time. Thank you!

              I've learned something new from your composition and left my comments and a couple of questions on your page.

              All the best,

              Alexey.

              Dear Alexey and Lev,

              Congratulations for another strong essay! The subject of this year's contest truly called for an examination of the connection between thought and matter. In your view, thought is "cosmic, even super-cosmic", and you defend the need for a non-deceiving (Descartes), non-malicious (Einstein) God to make sense of our Universe and of the truthfulness of our thought processes. I too struggle with the search for a first principle that would ensure, among other things, the "lawfulness" of the Universe. I am willing to accept that, in the space of all possibilities, there are local domains that are shaped by god-like super-intelligences, but I cannot see how this explanation can be scaled to encompass all of reality. So I am still searching for a way to have All-that-Exists be a self-existing ensemble that is overall devoid of characteristics and information, and to have local minds and ordered worlds "co-emerge" within it. We do not share the same hypotheses about fundamental metaphysical axioms, but we do share the same yearning that made Schrodinger say that knowledge truly has value when it contributes to the synthesis toward answering the demand, "Who are we?".

              By the way, in my current essay, I refer to your "Pythagorean Universe" essay from the last contest, specifically about the difficulty in accounting for the stability of the universal constants of physics by simply invoking the Anthropic Principle. It's always a pleasure to read your essays, and I am already looking forward to the next contest. In the meantime, I wish you good luck in this one!

              Marc

                Dear Edwin,

                Thank you for the compliments and the detailed comment.

                Before Alexey and I respond to your interesting ideas, could I ask you to take another look at the way you quote me, namely, "Physics does not make the assumption that the laws are simple?"

                The original statement, I think, was exactly opposite, without the "not". Would you please confirm or correct your post in this regard?

                - Lev

                Dear Lev,

                I apologize for misquoting you. I read the several comments several times, and still managed to get it wrong. I do not know how to edit posted messages, but I apologize again for the inaccurate quote.

                We are therefore in even more agreement than I thought.

                Thank you for correcting my mistake, and thanks again for a most fascinating set of comments on your page. You seem to inspire more insight on your page than most of us can manage.

                My best regards,

                Edwin Eugene Klingman

                Dear Marc,

                Many thanks for your encouraging words and very clear reference to one of the most important ideas of our Pythagorean Universe. I just left my comments on your current essay at your page, with a hope that our compliments, supported by the score, will not be overshadowed by some criticism there.

                We wish you good luck too!

                Alexey Burov.