Dear Cristi

I really enjoyed reading your beautiful essay.

Here some considerations.

(1)" A universe in a dot". This is a lovely peace of writing. It reinforces my conviction that the principle of finite information density must hold, as Feynman himself believed (see his 1982 Int. J. Th. Phys.) The continuum is paradoxical: you can write the whole history of the universe on a single atom. This is also related to the following point (3)

(2) I totally disagree with Smolin on many things, even if I enjoyed reading most of his books, in particular Time Reborn where he already expresses his new ideas that you can also find in his current essay taken from his last book. The two main things I disagree on are: (2a) the physical laws are not constant; (2b) mathematics cannot describe "particularities". I think that both assertions are unscientific according to Popper.

(2a) Imagine a physical law that changes every minute, and you don't know how it does. It is not a law anymore, right? What about if it is valid for a year, or a billion of year, or not valid e.g. two billions light-years from our planet. What should be the validity time (and space) of the law? If we state a law, it is supposedly eternal. This, however, does not protect the law from possible falsification, which will ask for another law, yet supposedly eternal. In particular, the new law maybe a "meta-law" which regulates the change of the falsified law.

(2b) A theory cannot describe "reality as it is". It can describe/predict only connections between known conditions/preparations/events and observed facts. Inferring initial conditions in the past needs an increasingly larger knowledge of the current state, the more distant is the past from the now. We can only connects known facts with known facts, or predict facts from known facts: the theory cannot provide the initial conditions. If we want to predict what will happen, we need information about the past. Accounting for the Smolin's "particularities" requires the knowledge of the initial conditions, otherwise it is not science: it is magic.

I love your ideas about "Is everything isomorphic to a mathematical structure?". I agree with you that the answer is positive, and I enjoyed very much this part of your essay. I think that the point, however, is another one, and again it is about "what is theory". A theory is a reduction of complexity of connections between events/observations. Transforming a set of observations (a peace of "reality") into a list of propositions does not necessarily entail a complexity compression, it is not a theory. Suppose I give you the observation made of the following digits:

3.1415926535897932384626433832795028841971693993751058209749445923078164062862...

A good theory would be the Plouffe formula that fits in few bits.

Also, as Poincaré says, the power of mathematics stays in the induction method, which produces an infinite compression of true statements. This is also the case of a physical law.

It would be too long to write everything I would like to say ..,

I hope to meet you again very soon and have a long discussion of philosophy of physics at a dinner table.

My best regards

and compliments again

Mauro

    Dear Mauro,

    Thank you very much for reading the essay and for the interesting comments. I find myself in agreement with what you say. The continuum seems to allow much more information than it actually uses, so seems to be a waste :). So perhaps the continuum is rather an ordering principle for discrete information. With respect to Smolin's recent philosophy, I think you and I agree again, and your points 2a and 2b are right on the spot. And yes, you are definitely right about a theory being an efficient way to compress information. Indeed, we would have a lot to discuss, and I look forward to see you again at a conference, to discuss in more detail.

    Best wishes,

    Cristi

    Daer Cristinel

    I find your essay very interesting, indeed, I consider mine an extension to it. I agree on almost everything.

    I believe, that the universe is "an hyper-equation". "A mathematical structure inside an other, and depends on another external"

    "Mathematics and physics are two sides of the same thing. numbers and physical entities in motion".

    Now, I think we need concrete things from which we can start. For this. I proposed The Paradigm Bi-iterative: a concept that goes beyond quantum mechanics and general relativity.

    Quantum mechanics is not enough, General Relativity is not correct. Maybe, that's why it was impossible to combine the two branches of modern physics. Therefore, it was necessary to introduce the mechanics iterative, as the source, to justify the origin of acceleration, force and time. In addition, the rhythm and the polarization.Two mechanics seemingly separate, connected with a constant, only in this way, we can unify them.

    I am convinced that reality is made up of thin numbers and geometric shapes. For this, I have proposed a Theorem and various mathematical structures (see Annex), which in my opinion, could be the true universe's mathematics.

    The Bi-iterative system's calculation considers reality multi-directional and multi-dimensional. with (1) we mean (1 * 1 * 1). while, the recursive computation and the Fibonacci series uses only the first, the fractal uses the first and the second. So, are wrongly linear, interprets reality on a bi-dimensional sheet. Instead, the system Bi-iterative uses all three.

    Let's take an example:

    (1 + 5 + 7 + 12) =

    聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽= 1 + 5 + 7 + (6 + 8 + 10)

    聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽= 1 + 5 + 7 + (3 + 4 + 5) + 8 +10)

    聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽= 1 + 5 + 7 + (3 +4 +5) + (1 + 6 - 9) + 10

    聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽= 1 + 5 + 7 + (3 +4 +5) + (1 + 6 - 9) + 10

    聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽= 1 + 5 + 7 + (3 +4 +5) + (1 + (3 + 4 + 5) - 9) + 10

    聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽

    聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽= 13

    = 2197

    This structure is compact, inside it could coexist other structures indipendent.

    which can be expressed also in a linear fashion:

    (1 + 5 + 7 + 12) = 13 = 2197

    聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽= (6,5) + (6,5) + (6,5) + (6,5) + (6,5) + (6,5) + (6,5) + (6,5): A straight line.

    "A complex and varied reality , can be described only with a structure capable of transforming".

    This sequence is like a clock going always forward, or rather, reflecting itself, coping itself.

    ( a + b + c + d ) + K

    (1 + 5 + 7 + 12) + K

    In agreement with the concept of light propagation and the distribution of mass and energy, fairly, K is a constant equivalent to (1) ....... + 1, + 1, + 1, + 1, + 1 ........

    "The universe was born so, one bit after another, and continues to do it today."

    Sincerly yours

    BannouriAttachment #1: Theorem_1.jpgAttachment #2: Theorem_345.jpg

      Christi,

      Congratulations on another fine essay, and on hitting the top. Not only do I agree with most of your propositions (I axiomise that maths CAN describe all) but more importantly you set them out and describe them succinctly. I was also pleased to read you agree that a TOE IS possible and that Godel does NOT preclude a mathematical description. Do you agree that recursive higher orders should be able to model that formalism asymptotically?

      One thing perhaps 'missing' was any reminder that a mathematical structure may not necessarily precisely model any physical process for which it's developed, though giving apparently correct outcomes. Do you agree this is possible? I assign this 'false proof' issue to much anomaly and paradox in physics and identify an important example in my own essay, confounding logic in QM. My suggestion is that if we say ALL maths must ALL be right if the bottom line proves right then we can be misguided about how nature actually evolves in time (which I agree is 'physical'). I hope you'll read and give your views.

      You don't suggest a direction for any new formalism pointing towards a TOE, which is not a criticism as very few do, but again I hope you'll analyse the hierarchical 'rules of brackets' which i suggest does so consistently with your analysis (as far as I can see, but your view?)

      I'm not surprised you're in the top group again and hope my score will help keep you there.

      Very best of luck in the final judgements.

      Peter

        Hi Cristinel,

        Your excellent essay makes a compelling case for mapping the universe to mathematical structure, and you presented it in an upbeat and enjoyable narrative. Your demonstration of how pivotal topics from relativity and incompleteness do not limit this isomorphism, provides a very persuasive argument. I like that you explained there is no conflict between mathematics and causality, and your discussion on physical explanation and mathematical description was very pertinent. My essay also discusses the strong connection between physics and mathematics, and for example how changing the mathematical representation affects physical explanation. I also show what was considered a limitation on computation due to (Gödel) incompleteness, can in fact be an expansion when attempting to physically model the mathematical structure of indecidability. This may address or at least support points raised in your essay.

        Also, I appreciated the wide variety of examples encompassed in your essay, and am motivated to check out your work on the Weyl curvature hypothesis, singularities, and free will.

        A very interesting contribution that thoroughly addresses this topic, I give it the highest rating.

        Please take a moment to read my essay and rate it as well. Thanks again,

        Steve Sax

          Dear Bannouri,

          Thank you for the kind and interesting comments. Indeed, in order to advance toward the understanding of the foundations, we have to go beyond what separates quantum mechanics and general relativity.

          Best regards,

          Cristi

          Peter,

          Thank you for the interesting remarks. Let me congratulate you as well for your place. Regarding your question "Do you agree that recursive higher orders should be able to model that formalism asymptotically?", I would say maybe.

          > "One thing perhaps 'missing' was any reminder that a mathematical structure may not necessarily precisely model any physical process for which it's developed, though giving apparently correct outcomes. Do you agree this is possible?"

          I think I addressed the question of models that are not "true" in a section of my essay named "Is mathematics merely a tool in physics?". If you refer to models that give all the correct outcomes, and can't be distinguished by other models by no matter what experiment, I think it is possible. But I think that if these can be related to anomalies and paradoxes, then they can be distinguished and falsified. Regarding "if we say ALL maths must ALL be right if the bottom line proves right then we can be misguided about how nature actually evolves in time", well, correct maths is right, but being right doesn't make it true about our physical world.

          "You don't suggest a direction for any new formalism pointing towards a TOE". I think it is too early for such a suggestion.

          I look forward to read your essay, which is on my todo list.

          Best wishes,

          Cristi

          Hi Steve,

          Thanks for the interesting comments and kind remarks. Indeed, some may qualify my essay as (too) optimistic, and I don't really think there are limitations that should stop us from trying to learn more. By the same criteria, any attempt to understand the universe has to be optimistic. In the same time, I advocate an agnostic and skeptical position regarding the belief in the absolute validity of our theories. And as you said, I indeed see no conflict between mathematics and causality. I think you have a keen eye and understood well my points. Your remarks about how changing the mathematical representation affects physical explanation, and the idea to take advantage from Gödel's incompleteness theorem seem to me very interesting. I look forward to read your essay. Good luck in the contest!

          Best regards,

          Cristi

          Cristi,

          Thanks for being engaged in my essay and for your kind words.

          Jim

          Christi,

          I don't know how I missed your essay.

          Your essay is delightful, like you have the essence of Socrates on your shoulder, distilling with questions and answers his method of inquiry and discussion. I think the potion you create works. It helps to clarify the mind-numbing. You also throw in helpful progressions of studies, GR beyond Newton, singularities.

          Impressive essay.

          Jim

            Thank you Jim, for reading and commenting my essay.

            Best regards,

            Cristi

            Dear Cristi,

            Since this comment relates to both yours and our essays, I am reproducing it here, in your blog, with a slight abbreviation.

            Thank you so much for your compliments; it is a true pleasure to be highly appreciated by one of the experts!

            You underline that your main take away from our essay "is the uniqueness of the laws." Maybe, our laws of nature are not exactly unique, but they definitely belong to a very special and narrow set of mathematical structures, much more narrow than Tegmark's multiverse suggests. In other words, our laws are truly beautiful in that deep meaning of mathematical beauty which was professed by Pythagoreans of all times, from Pythagoras and Euclid to Kepler and Newton and to Einstein and Dirac.

            In that light the statement of your essay that,

            "Mathematics is already there, eternal and unchanging. What we invent is the discovery of mathematics,"

            is revealed as having an even deeper meaning than it may at first seem.

            Cheers and good luck!

            Alexey and Lev

            I enjoyed your exploratory approach to the essay question, Cristi.

            You parse it into many questions. But I get the impression that you are not dogmatically attached to any of your answers. Rather you enjoy the dialectic struggle between opposing ideas.

            I would enjoy a joust over a beer with you sometime!

            ......David

              Thank you, David. I loved very much your essay. I am very pleased and honored that you liked mine. I have the feeling that you understand so well my position. I would be very happy to have a beer with you!

              Warm regards,

              Cristi

              Dear Christi Stoica,

              I enjoyed reading your essay. In particular, I liked your approach to include many questions. Most of the competitors (including me) are too eager to give answers, but I think it is an important goal to get the reader to wonder about these questions first.

              In addition, I would like to discuss two points.

              The idea of illustrating how you can code various texts as numbers in the [0,1] interval seems well chosen for the intended audience. On the other hand, I worry that you may have stretched it a bit too far when you write: "That line contains your entire life". After all, my life is not a text. ;-) And even if it would be narrated, a lot would depend on the wording - in particular: the first word! (If the narrater always starts with "Well,..." then all our lives end up close to 1.)

              You write at some that "the fact that mathematics is useful doesn't mean that the universe is mathematical". At a later point, you say that a full isomorphism (unknown so far) between the universe and a mathematical structure would mean that there is no difference between the two. This second part is not so clear to me: could there really be an isomorphism between the universe and a mathematical structure? In my opinion, at best we can find an isomorphism between _the structure of_ the universe and a mathematical structure. This makes all the difference: ascribing a structure to the universe leaves a lot of degrees of freedom, but more importantly, it would leave out the 'substance' of the universe, and it would avoid the conclusion that the universe is mathematical.

              Still, my general impression of your essay is a positive one. And the fact that it leaves topics for discussion is a sign of its quality, not a criticism.

              Best wishes,

              Sylvia Wenmackers - Essay Children of the Cosmos

                Dear Sylvia,

                Thank you for the comments. You raise interesting questions.

                One point you make is about my words "That line contains your entire life". You thoughtfully reply "After all, my life is not a text". Well, could you please tell me the part of your life which is not a text? I don't intend to be too curious, rather to ask you a trick question, since if you can tell this, you will make it into a text :) A quick reading of my essay may leave the reader with the feeling that I choose to ignore consciousness for example, but as I wrote, "I don't claim we can explain consciousness, with or without mathematics." What I wrote about this may clarify what I mean: "However, any feeling we may have, there are neural correlates associated to it, and hence, physical correlates. And these physical correlates are in the domain of known physics, which is strongly mathematized." About your excellent remark that you can choose to narrate the same life differently, and make it closer to one number or another, I fully agree, but I can't see why would this be a problem. As you know, there is a bijection between the points on a segment and those in a square, or the entire space, but that bijection can't be continuous. I understand that your remark reveals that representing everything on a segment is counterintuitive, and I like it. I just wanted to make a point regarding whether math is discovered or invented.

                Another point you make is "could there really be an isomorphism between the universe and a mathematical structure? In my opinion, at best we can find an isomorphism between _the structure of_ the universe and a mathematical structure." I agree, isomorphism is between structures. For example, there are more isomorphisms between the set of real numbers and other structures. The real line is isomorphic with a square, if we refer to the category of sets, with a line if we refer to the category of topological spaces, with a totally ordered set if we refer to the order, with a vector space, with a metric space, with a group, semigroup, ring, field, etc., it all depends on the structure we are interested in. As I explained in the essay, the structure is captured in the relations, all relations that can be described by propositions. So there's nothing that can be left outside the structure, if we take into account all the true propositions about the world. Saying "ascribing a structure to the universe leaves a lot of degrees of freedom" is not necessarily true, I mean, of course it is true if we leave outside some of the truths. About the substance, I don't know what you mean by this. Is it something that has effects? Then its properties are captured in the structure. If you think that there are properties of the substance that don't have effects to the structure, then I have nothing to say about it, and anything we would say would be out of our possibilities of verifications. I think the text in a book is what makes a book, and not the paper or the electronic memory used to keep a copy of that text.

                It was a deep pleasure to talk with you, and I wish your essay will do well, since I loved it.

                Best wishes,

                Cristi

                Dear Christi,

                Thank you for your (fast!) response.

                If I tell you an episode of my life, my life itself will not turn into words. To keep it simpler, let's talk about colours: mentioning a colour does not produce that colour (at best, it may trigger a memory of it). Even if I would be able to say everything about a particular colour (not just 'red', but the spectrum, possibly partial translucence, etc.) I would still not have reproduced the colour. Sure, I could use the information, in computer graphics for instance, to reproduce it. But I would need some hardware to run it on (part of the universe). With the universe as a whole, I don't see how a full description (for simplicity, let's rely on an outdated materialistic view: some mass here and some mass there) is enough (in the materialistic example: you would still need to get some mass in addition to a mere description thereof).

                On your view, can you destroy all copies of a book (including our memories of reading it etc.) without destroying the text?

                Best wishes,

                Sylvia

                Dear Sylvia,

                Thank you for the answer. I think I understand what you mean, but I don't think I made you understand what I mean.

                "If I tell you an episode of my life, my life itself will not turn into words." Sure it will not. And even if you give me the complete list of episodes, your life will not turn into words. What I mean is that its structure will be captured in those words. So, going back to my words "That line contains your entire life", I should have said perhaps "That line contains a complete description of your entire life". The main subject of my essay was about the relation between mathematics and physics, and I was careful to mention that I don't aim to explain unphysical stuff, perhaps consciousness being an example.

                You give a good example, that of a color. But you answer it yourself, you can reproduce it on a computer (and that information can be expressed if we wish as words, or as a point on a segment). Your worry that there will be not enough room for hardware in the universe to simulate the color is a new element you add. But the proof of principle remains: the possibility to describe that particular color exists. I am talking about the possibility of a description, not a real implementation of it, not of a hardware. I don't think that, in order to prove it, one should effectively build that description. For instance, the number π exists even if its decimals are nowhere written completely, and even if the entire universe is not enough to write it.

                "On your view, can you destroy all copies of a book (including our memories of reading it etc.) without destroying the text?" If you destroy all writings containing Pythagora's thereom, you will not destroy it, you will destroy the information about it that we have. It will be soon rediscovered. But if you destroy all books by Shakespeare, I don't expect that we will rewrite them soon. They will still be in that segment, but we will lose the address to retrieve them. Think for example at a computer. When you normally delete a file, you delete a reference to it, but the information remains on the hard drive, and can be recovered by special software, until you overwrite it with other information. When you lose the address, the file is not lost. A home is not lost when you lose the address. But you lose your access to it. In the case of a book, the address is the book.

                But when we talk about life, the things are different... I don't think that a complete description of your life values at least 0.000...01% of your life. You may think that this is a contradiction: on the one hand I claim that everything is isomorphic to a mathematical structure, on the other hand, I don't reject the possibility that consciousness or life is more than this. Maybe this is not obvious in my essay of this year (where I focused on the relation between mathematics and the physical world), but perhaps the one for last year is more on this topic.

                Best wishes,

                Cristi

                Dear Christi,

                Yes, it is easier for me to agree with the new formulation "That line contains a complete description of your entire life".

                Just a clarification: my point with the color example was not that there isn't enough room in the universe for the hardware. Simply that we need hardware, which presupposes that we already have the universe at our disposal* - and exactly this does not work when it is the entire universe we want to describe. If we have that mathematical description and delete the physical universe, it does not become reality. Our description will at best be isomorphic to the structure of the universe, but still something is missing to be able to bridge the gap from a mere description to reality.

                Thanks for your reply to my question about the book text! It was really nice to have this exchange with you.

                Best wishes and good luck,

                Sylvia

                *: It's a bit like the Sagan quote: "If you wish to make an apple pie from scratch, you must first invent the universe" ;-)

                Dear Cristi,

                A very enjoyable and easy to read essay, with interesting thoughts and observations. Especially noteworthy for us were your remarks on Godel's theorem.

                The duck: for us, a description of the duck is different from the duck; thus we said that mathematics lacks in material substance. Would you agree?

                And if pushed, what stance would you take: Platonism, or non-Platonism? :-)

                Our best wishes,

                Anshu, Tejinder