Dear Alexey,

Your essay is something of a mystery. You spent 80% proving that there is one universe. Then telling us the obvious that the laws of nature is mathematical. Then you suddenly switch and say it is all mysterious. In what way it clarifies the relation between mathematics and reality.

Thanks

Without an engineer, any feedback is a part of the laws of nature. With or without them, the question of the fine tuning remains the same, John.

Dear Efthimios, thanks for your good words.

As we are showing in the essay, the laws of nature, described by beautiful mathematical forms, do exist objectively, as a logical structure of the universe. They are comprehensible only as elements of the mathematical world, or, at least, a sufficiently big part of it. It means that the mathematical world do exist as a special reality, the Platonic world. That's it.

Dear Joe, thanks for your attention and compliments.

The observations, taken in general, show both universal/reproducible and uniq aspects. The former constitutes the domain of science, the latter belongs to art. We say nothing about art in our essay.

Dear Demond, thanks for your attention to our essay.

A part of it is to show that "self-evident, self-explanatory, and independent of any other supportive methods" unified theory (taking "theory" in scientific sense) cannot exist.

Regards,

Alexey Burov.

Dear Sujatha,

In a sense, this is true :)

I am taking the fundamental science as the most fundamental fact.

Thanks for your wit remark!

Alexey.

Dear Alexey and Lev,

I read with great interest your essay. I think we are going in the same direction. You write and bring important conclusion A.Vilenkin: "Because the logical structure of our universe can not be explained by chaos, and because it can not explain itself, we are left with only one possible explanation remaining, that it was conceived and realized by a mind. A. Vilenkin prefers to formulate this apparently inevitable conclusion about the cosmic Mind as a question: "... the laws should be" there "even prior to the universe itself. Does this mean that the laws are not mere descriptions of reality and can have an independent existence of their own? In the absence of space, time and matter, what tablets could they be written upon? The laws are expressed in the form of mathematical equations. If the medium of mathematics is the mind, does this mean that mind should predate the universe? "

As for the "Penrose triangle", I believe that his model of "three worlds" - a splitting of the triune world. Cosmogony of Pythagoras as the unity of the "limit" and "infinite" (thesis and antithesis) give access to the three-pronged synthetic structure, based on the absolute state of matter. The concept of "structure" in Russian - a structure that is «s-troe-nie», give a direct hint to build generating structure of the Universe as a "three in one", the measure of being whole, primordial structure of harmony generating "unity" and "plurality".

Kind regards,

Vladimir

    Dear Vladimir,

    thank you for your interest and good words in the address of our essay.

    In fact, Vilenkin expressed the old Platonic vision, the realism. Then Linde questioned about a possibility for the laws, with all their simplicity/elegance, still to be anthropically selected. What we tried to show in our essay, is that this Linde hypothesis by no means can be true. For that, we counted those orders of magnitude gap between the anthropic requirements and the accuracy of the elegant laws of nature.

    The Penrose Triunity is a good idea to contemplate about possibility of burbakian "La Structure mere". Apparently, they are not compatible, are they?

    Dear Dr. Burov,

    your philosophical essay is so full of good ideas that it is easy to loose track of them. It would have helped if you added some examples where math has led physics astray.

    Your descriptions of Pythagorean truth are excellent. No wonder that the Pythagoreans were for hundreds of years a secret society that had to meet in lonely caves.

    Please continue your quest for truth

    Best

    Lutz

      Dear Lutz,

      Thank you for your encouraging words in our address! Your suggestion to "add some examples where math has led physics astray" could give a new extremely interesting essay. At the moment, I'd like to mention just one important case in this respect. Perhaps, you know this story, but still I wish to mention it here for the sake of your wonderful question.

      Copernicus was convinced that the planet orbits must be nothing but circles, as the most perfect, most symmetric among figures, corresponding to the symmetry of the Sun's attraction. The idea was beautiful, reasonable,--and still wrong. As a result, Copernicus was forced to introduce his own epicycles, and his heliocentric system was not as beautiful as he expected. Most likely that was why he held over with the publication. It required a genius of Kepler to solve this problem and to prove the heliocentric idea is correct. This was one of the most dramatic moments in the history of science, I am sure. Seeing the failure of Copernicus, Kepler still believed in the beautiful mathematics underlying the world. As well as Copernicus, he was Pythagorean/Platonic, but his field of search of the mathematical beauty in the sky was wider, and he was heavenly rewarded!

      Many thanks and all the best,

      Alexey Burov.

      Okkam's razor has to be very sharp. But I am sure that the unified basis of knowledge can be constructed only on the simplest triangle is "a heavenly triangle" of Plato which sum of invariants represent both structures of the physical world and mathematical structures ("les stuctures mere"), modern and future, still the unknown.

      Dear Alexey,

      You avoid mentioning anything about reality as well.

      Regards,

      Joe Fisher

      Dear Alexey and Lev,

      As I noted in a reply to a statement about my essay, The Geometric Core of Spacetime, various mathematical types were created to solve a problem. We do not know which problem many of them were originally developed to solve, but this is not mysterious, we simply have incomplete information.

      My essay is about simple geometry and how it can be used to identify specific characteristics of a physical law. You were much bolder in your title stating we have a Pythagorean Universe. I cannot prove that we have a Pythagorean Universe, but I did demonstrate a Pythagorean link to one of the physical laws of the universe.

      What is mysterious is that our essays are juxtapositioned next to each other, as though they were meant to support each other.

        Alexey and Lev -

        Thanks for the excellent essay! I was delighted to read a strong defense against the prevailing metaphysical winds of physicalism and reductionism so evident in most essays. I, too, find mathematical order to be a fundamental organizing principle quite apart from the action of the physical world itself. Moreover, those positions cannot address what I refer to as "The Hole at the Center of Creation" - only consciousness and purpose can provide the answer. As you say: "Since the laws of our universe are not picked randomly, they can only be purposefully chosen."

        Thanks for a great essay and good luck in the contest. - George Gantz

          4 days later

          Dear George,

          It's delightful to get so inspirational response as yours! Scientism, a deadly shadow of science, is indeed so prevalent in this contest, that it makes a special pleasure to be recognized by a likeminded thinker. Good luck to you too, dear friend!

          Alexey.

          Dear Frank,

          Thank you for your comment. I have read your essay. What we mean by our universe being Pythagorean is reflected in "Starting with Pythagoras, it was a matter of faith for sparse groups of few people and lonely individuals that 'fundamental laws of nature are described by beautiful equations.'"

          It's not the fact that the laws of nature are expressed by mathematics that's most mysterious, but that they're "rather simple in presentation and extremely rich in consequences," and that the Pythagoreans somehow knew that!

          I do not see what would be a thought, the mental world, in that sort of basis of knowledge, Vladimir. Don't you consider a creative thought as a mathematical structure or physical phenomenon, do you?

          Alexey! When you build a primordial generating structure, then the question arises: what it holds? This ontological (structural, cosmic) memory. Matter is that from which everything is born, and the ontological (structural) memory is what gives rise to all. Ontological (structural) memory - the measure of being of the whole, "the soul of matter", qualitative quality of the absolute forms of existence of matter (absolute states). Ontological (structural, cosmic) memory - the core of the world picture of Information age.

          Vladimir, if I understand you correctly, you are following Plato's vision that the new knowledge is in fact nothing else but reproduction of what atemporally is in the "ontological (structural, cosmic) memory." Is it correct?