Dear Sylvain,

your essay contains a number of stimulating ideas, although after a first reading they are still poorly ordered in my mind, leaving me still doubtful about your main intended message. In particular, I find the closing part as more related to the topic of the 2014 Essay Contest (on the future of humanity). I hope I'll have the time to read it again anyway, to better grasp the flow of your reasoning.

I like very much the idea to start by asking how a non-mathematical world would look like. In this respect, I have a remark on your attributing a low mathematical content to an algorithmic world . My view is that an algorithmic world may well have islands of (deterministic) randomness, mixed with islands of complex but mathematically accessible phenomena (e.g. particle interactions), mixed with very regular structures, easily described in math. So, imaginative tips may help shortcut a non trivial portion of the computation, I believe.

Another point I found very interesting is the responsibility you assign to consciousness to give substance to a part of the mathematical world - I point I also tackle in my essay, although under a totally different, humorous narrative key. Consciousness illuminates a portion of the mathematical world, making it 'real'. Then, I wonder what is your take on the three interconnected spheres (platonic ideas, material world, consciousness-thought) in the opening chapter of Penrose's Road to Reality - did you see that? Maybe you could have yourself provided a drawing of that sort, that would have helped summarising your view?

(Penrose presents actually two variants of that figure - I can't point to the page number unfortunately, since I do not have a copy of the book at hand.)

Best regards

Tommaso

    "Is very, very, very high probability the same as certainty?" : it all depends on context and how accurately we need to discuss. For example in a star, colliding atoms have every time a very low probability of undergoing some nuclear reaction, however there are so many collisions and each reaction releases so much energy that it suffices to provide the power of stars. Similarly, the chance of winning at Lotto is very low, but so many people are playing that the chances of existence of a winner becomes significant. Also, as free will operates by deviations from physical probabilities, it can make happen some possibilities that had very low "probability" as defined by quantum physics.

    "Is it very, very, very probable that 2 3 = 5 or is it a certainty? When adding 2 and 3 apples together, can any of the apples perish as you go about doing your summation to see what you get?"

    Of course, the formula 2 3 = 5 is a certainty but what is uncertain is whether its correspondence with apples is a valid one, in case an apple might perish.

    "When adding 2 quantum particles to 3 of same, is it more or less likely the results you will get will be same as for apples?" Again, it all depends on the specific kind of particles you work with; and on the time passing between when you introduce the particles and when you count how many are still there. We cannot seriously go anywhere with such childish pseudo-examples. It is of course very easy to "prove that science isn't valid" by introducing some ridiculously naive way of pretending to do some experiment and apply a mathematical model, and victoriously failing to do so properly. The validity of mathematical theories to describe physics has been verified with an amazing degree of accuracy, but of course this requires to have done the very hard and professional work of finding out which theories are applicable and in which conditions. And generally I don't buy any "argument against reason" such as "it is possible to victoriously fail to reason (or experiment something) correctly, thus all reasonings (or experiments) must be incorrect as well". More comments on this topic here.

    "Give this a thought." Do you think I waited for your invitation to do so ?

    Hello. By "lowly mathematical" I meant "of a low mathematical kind" though it remains 100% mathematical. Moreover, not all algorithmic worlds are equal. Some, like Conway's Game of Life, have a low density of interesting possible behaviors lost in an ocean of chaotic ones, as I once verified by systematically testing hundreds of initial configurations, so that imaginative tips are most often impossible.

    Indeed I concentrated here lots of ideas, so it may be hard to follow. It may look clearer reading the longer exposition of my interpretation of quantum physics from which the main ideas here are extracted, and maybe other texts on other aspects (introduction to quantum physics, problems with other interpretations, foundations of maths)

    The last part touches last year's contest that I missed as I was busy trying to get people implement my project (but I actually failed to do so). But I stayed here at such a level of generality that I still see it on-topic: rather cosmological and related with the rest of ideas of the essay, without entering the details of how things can work. But for last year I am not sure what I could have explained in 9 pages. Maybe just a few key ideas and cases of functions, longer explained in my site. As a substitute, I undertook in the last few weeks to write a much longer comment on many ideas found in other essays of that contest.

    About the relation between the "spheres" of the mathematical, the physical and the conscious, I think I was clear already in the title, and more details are expressed for example by the diagram on page 7.

    "Time and tide waits for none"

    is exceptionally perceived and written by you in this work.

    Yet the probabilities and questions still remains unanswered.

    Sincerely,

    Miss. Sujatha Jagannathan

    11 days later

    My title, "Duality, the War for Existence:" identifies the "mysterious connection" as panpsychism. My expertise in swimming, geometry, and thermodynamics are merged to construct a model to guide "all wars". It focuses the chaos of my 2012 submission, "To Seek Unknown Shores".

    Sorry, meant to compliment you on considering "panpsychism". Therein is the mysterious connection between "all things" , hidden centrally and only viewed distally.

      Sorry, while my view may be considered not far from panpsychism, it is different.

      I may admit the idea of panpsychism as an a priori possibility, maybe true in other universes, but I do not see it compatible with the facts of our universe, namely the data of quantum physics which admits the presence of material systems that keep quantum superpositions as they are not observed, and are thus totally unconscious. As I explained, I consider the deep nature of such systems as not "material" but mathematical ; still they "are something", in the sense that they occupy space as we usually conceive it, they have mass, undergo physical reactions, etc.

      Dear Sylvain Poirier,

      I suggest three main candidates for the mathematical concept , which seem naturally suited to describe features of the physical world:

      bit (it was the subject of the competition FQXi 2013);

      exp(x) (You know the unique features of this function);

      Euler's identity.

      There are other useful functions, but of less importance.

      Suitable use of pervious can to describe features of the physical World.

      What are your main candidates? If you agree with me, part of the solution can be found in my essay.

      Best Regards,

      Branko Zivlak

        The mathematical systems best suited to describe the physical world are well-known. There is no wonder what they are. Much of the competition is already past and now over. Possible candidates were already reviewed, and the ones that best fit were selected and very well verified. They are of course the established theories of physics : as far as we can tell now, they are the theories of General Relativity (with the Least Action Principle), Quantum Field Theory with the Standard Model, and the concept of density operator. Or, to take the main effective theories respectively resulting from them that more directly appear in practice : Newtonian gravitation, electromagnetism and thermodynamics. For more details on these lists, see in my essay, and in my site.

        15 days later

        Dear Sylvain Poirier,

        I have replied to your questions on my essay over at my post page. I will read your essay opportunely. Thanks.

        Regards,

        Christine Cordula Dantas

        Dear Sylvain,

        Very deep analytical essay in the spirit of Cartesian doubt and interesting thoughts about "consciousness" and "law". I think that in order to overcome the "crisis of understanding" in basic science must be a deeper ontology and dialectic in the spirit of Nicholas of Cusa - "coincidence of opposites" and dialectics of "eidos" and "logos". Fundamental knowledge, mathematics and physics, requires a deep ontological justification (basification). In fundamental physics is necessary to introduce an ontological standard justification (basification) along with the empirical standard.

        I invite you to see and appreciate my analysis of the philosophical foundations of mathematics and physics, the method of ontological constructing a new basis of knowledge and new unifying paradigm - the basic generating structure, "La Structure mère" as the ontological framework, carcass and foundation of knowledge, the core of which - the ontological (structural, cosmic) memory... I began to read your site.

        Kind regards,

        Vladimir

        Dear Sylvain

        You have interesting approach toward physics. You do not look all with some physical laws, but every correlation, every information is like a physical law. Thus, all lack of information about uncertainty principle or about chaos, or about entropy are very similar, according to you.

        You have a huge web page about quantum consciousness, I will read it more precisely, when it will be enough time.

        We agree about panpsychism and about quantum consciousness. Although many scientists think that this is crackpot, Tononi and Koch also agree with this.

        We disagree about entangelment at quantum consciousness. As I understand, by you, time arrows are causes of wave function collapse and not entagelment? I need to read you more, but by me, entangelment time means time of decision. What is your motivation for this claim, maybe because entagelment times are very short?

        I like your statement, that checking by measurement is necessary, where mathematics is not enough.

        My statement that »QG will also tell more about quantum randomness, what can be connected with free will« is not very confirmed intuitively, others are more.

        You have very interestiong argumentation of FQXi points with a blog and I hope that this will happen more often by other contestants. A year before I also gave some proposals for more fair estimations.

        My new statement in this essay is that consciousness and free will are connected, consciousness does not exist without free will. In prolonged version and in 2013 essay I described also thought Turing experiment on this topic.

        We both also find Peter Woit's as an interestiong essay.

        I gave comment about U(1) symmetry. Peter Woit.

        What is your opinion about U(1) symmetry?

        My essay.

        Best regards Janko Kokosar

          9 days later

          Dear Professor Poirier,

          I thought that your engrossing essay was exceptionally well written and I do hope that it fares well in the competition.

          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

          The word "entanglement" may be ambiguous. The formalism of quantum physics makes no fundamental distinction between entanglement and classical correlations. Usually, classical correlations are entanglements that macroscopically behave as mere classical correlations due to decoherence (that destroy the practical ability to measure observables not commuting with a specific one). And decoherence is an emergent phenonenon.

          In my opinion, wave function collapse is caused by conscious observation (a non-physical condition) which requires decoherence (an emergent condition from physics). And time arrow is a property of consciousness, which causes the time arrow of thermodynamics.

          Yes, not only entanglement times (i.e. before decoherence) are very short, but I see the idea of letting decoherence a precondition for observation (or free choice) a more logical way to articulate physics with metaphysics, for the reasons I explained in my site.

          See my reply about U(1) symmetry in comment to Peter Woit's essay.

          Best regards

          Sylvain

          Dear Joe Fisher,

          Sorry for you but I have several reasons to consider the review of other essays a higher priority than yours, and one of them is your ridiculous claim to think that all essays in this competition are exceptionally well written, and that you do hope that they all fare well in the competition.

          Dear Sylvain,

          Due to the fact that I think I had a relapse of my Asperger's Disorder, a comment I posted on some of the esteemed essayists sites was woefully contemptuous. The recipients rightfully complained about the inappropriate nature of the comment and the Moderator removed some of them. Unfortunately, the Moderator classified the useful part of the comment as Obnoxious Spam. I have proven that Newton was wrong about abstract gravity, Einstein was wrong about abstract space/time, and Hawking was wrong about then explosive capability of NOTHING.

          You hate that proof. That is your option.

          Admirably

          Joe Fisher

            You cannot have proven anything, since you don't even have a clue about logic.

            I don't hate any proof, I just don't have time to waste with pure nonsense.

            I cannot take seriously a "proof" that 2+2=5 and I do not consider it worth looking at the details because I have good reasons to know it must be false and worthless, no matter what the details may be. Where is the hate ? Just a reasonable time management. It is clear that you cannot be having a clue at the things you claim to refute. You are trying to make up claims of problems where there is no problem except the problem of your own failures to grasp things that were successfully discovered. That's only your personal problem and science is not concerned. Now that's enough.

            Asperger? Haha. To be called so, people ought to be intelligent, which you are not, or maybe a little more than average (yeah I often forget where the average is) but nowhere close to what is need to discuss physics. You already proved quite enough that all your thoughts are nonsense, by the absurdity of you first comments to me. You insulted me and treated me like idiot right from the start, and now you would like me to dedicate work to examine your... nonsense ? And argue with you until when ? Until your majesty is satisfied and convinced that my replies are good enough and that you are convinced ? Are you crazy or what ? Now please go play elsewhere and don't disturb those who have serious stuff to discuss, thanks.

            Dear Sylvain,

            Following the conversation we already had on my essay's page, I am now going to comment your essay in detail.

            The way I understand it, your system is based on the twin entries at the bottom of your table on page 7: Mathematics and "The Matrix", which encompasses all relevant aspects of "reality" that are not mathematical. That's why you begin your essay by arguing for the existence of laws that are not mathematical. You give the example of "artistic laws" and "psychological laws" as being impossible to define in an algorithmic fashion. I agree that those type of laws can certainly seem non-algorithmic and un-mathematical, but could it be that it is just due to our failure to be able to consider complex enough algorithms and mathematical entities? You claim that the behaviors that result from these laws would require algorithms that are "too big to be stored in a computer", but do we really know what is the theoretical limit that a computer can achieve? Even if we could show that the physics of our universe prohibits such a computer, how can we be sure that our universe is not being "run" on a computer in a higher-level reality where the physical laws do allow for such complex algorithms? I know, from reading your website, that you firmly believe that artificial intelligence will forever remain impossible, because of the classic "computers have no soul" argument. We certainly do not agree on this issue: I think we will see true general artificial intelligence within the next 20 or 30 years, and I am convinced that this technological breakthrough will have a profound impact on philosophy and on the way we see reality. I guess we will just have to wait and see!

            On page 2, your discussion of "Time and unpredictability in mathematics" is very intriguing. I will have to dig deeper and explore what you wrote on your website about the "time order" of mathematical reality. Since, in my view, there is a way to understand the totality of what exists as a a mathematical structure, I believe that, although mathematics as a whole is "atemporal" and "eternal", it is possible to define mathematical structures that evolve and change relative to other mathematical structures that play the role of "time counters".

            On the issue of the relationship between mathematical and conscious existence, I agree with you that "the conscious perception of mathematical structures can explain and constitute their physical existence". In my view, mathematical structures that do not contain "self-aware substructures" are not physical, since there is no one to "feel" their "physicality". Where our views diverge (but maybe not that much), is on the question of the need to "add" something to brain computation (what you call an "immaterial soul") to explain consciousness and feelings (qualia). I think that the mathematical computation, the biophysical reactions, and the conscious experience are three different levels of description of the same structure --- a structure that can be seen, from one point of view, as purely mathematical (all is computation), but at the same time, from another point of view, as purely mental (all is thought). Of course, I think most physicists, and most authors in this contest, would say that it is the middle ground, the biophysical reactions, that is the true fundamental level... which make essays such as ours terribly counter-intuitive and almost nonsensical to many!

            Let's assume for a moment that you're right and that there is a non-mathematical Matrix, a set of minds united in a coherent whole, that uses the mathematical (and sometimes physical) Maxiverse as a "playground". You claim it is the Matrix that "selects" which universes truly exist: as you say on page 4,

            "To create the Universe, Consciousness first chose a mathematical law as "theory of everything" of physics [...] The physical Universe is the trajectory of this exploration of the Hilbert space by consciousness."

            It is an intriguing hypothesis, but to entertain it, we need to postulate an entire, separate level of reality, "The Matrix", that has remarkable capabilities and complex behavior, such as the ability to "choose" and "explore". Everything that current scientific understanding has trouble with (the hard problem of consciousness, the flow of time) gets conveniently explained and taken care of by The Matrix. The Matrix even allows us to have "real" free will, while making sure that we do not have too much liberty to individually select which part of the Hilbert space gets explored, by enforcing global coherence across all physical perceptions... But the fundamental nature of the Matrix remains a mystery, and it seems to me that we are back to square one: instead of having no idea what the fundamental nature of the Universe is, we've separated the Universe in two: one part is what we understand (math/physics), and all the rest is The Matrix, but we have no idea what it truly is, where it comes from... As Morpheus says in the movie, "No one can be told what the Matrix is... You have to see it for yourself!"

            Although we do not agree on many issues, I find your essay and your website fascinating, and I will certainly be going back to what you wrote (and continue to write, as I see your process as a work in progress) when I have the time. Meanwhile, I've given your essay a boost that, I hope, will make it more visible: with so many essays, the essays at the top of the community ratings have a better chance to get more attention and more votes, while many good essays remain buried and forgotten in the middle of the heap...

            Oh, I almost forgot one specific question I have: in your essay's abstract, you talk about the mathematical world being a "Platonic mathematical realm slightly less than infinite". Why "slightly less than infinite"? To avoid the paradoxes associated with infinity and incompleteness? I find the concept of "slightly less than infinite" intriguing, so I would like to know more about how you think about this.

            Best regards,

            Marc

              Thanks. I just added your essay in the top list of my general review of essays in this contest. Despite our efforts, it seems the ratings (both community and public) remain nonsense as I explained. About "too big to be stored in a computer - do we really know what is the theoretical limit that a computer can achieve ?", I think I already explained. Reminds me of "the unit of distance (meters, m) is specified strictly for decorative purposes" in William T. Parsons essay. But the main point here was, more than an exact measure of this complexity, the fact that the source of this complexity is non-mathematical (unlike anything that this universe can produce, which logically results from its relatively simple physical laws).

              The "slightly less than infinite" is explained in p.5 as concerns the physical observation that it goes so (it is a character of quantum physics). Or are you asking for a philosophical motivation why it should be so ?

              Dear Sylvain,

              One significant feature of your essay is the fact that the two poles of your dualism are mind and mathematics. This is unusual, because, as you are well aware, the two poles for an ontological dualism are generally stated to be physical and mental existence. Without trying to enter into the mind-body problem, I can say that your positioning of mathematics as fundamental is well worth considering.

              I find it also important that you bring issues of good and evil into the picture. In your discussion of the problem of evil, you state clearly and concisely a relevant fact when you say, "It is very strange indeed that psychological laws (free will) only physically operate at the level of individual minds." We are so used to the individuation of consciousness that we do not notice that it is at least logically possible that consciousness in the cosmos might have been organized differently. Moreover, as you say, the world would be a different and better place with either superordinate co-ordination or effective application to smaller-scale details. Nonetheless, as you also indicate, people have to start with the world as it is, not with the world as people might have wished it to be. Probably the main thing for readers to retain from your essay is this emphasis on values, and the call to action to make the world a better place.

              Best wishes,

              Laurence Hitterdale