I'll pick up the thread here...

I want it to be clear that I don't think the Platonic view is the last word on everything in Physics. Instead; I feel that the idea of a mathematical universe is an essential piece of the puzzle to understand. It is fruitless to debate the notion of the pre-existence of the orderly form that appears in Math. The point is instead the unvarying nature of some aspects of mathematical reasoning, or persistent objects and principles within Math - which come out the same regardless of how you get there.

These patterns appear in nature, as well as in abstract studies like Mathematics. It is freely admitted that some attempts at a constructivist formulation for Math have been disappointing, but I see nothing wrong with the basic mechanics of that approach. My guess is that there is a constructive proof possible for any mathematical statement that is generally proved in other ways, but I could be wrong. The nice thing about constructive proofs is that they can be turned into computing algorithms with great ease.

But as many have pointed out; Physics is all about how natural law and the universe unfold whatever underlying principles exist into observable form. I think the underlying principles are identical however, and it's a matter of whether concrete or abstract information is desired. I may talk more about this idea in the page Zeeya Merali and FQXi have opened up for discussing Dimensional Reduction in the Sky, because of its relevance to the topic of that paper.

Have Fun!

Jonathan

    To clarify further;

    I think that following the emergence of natural principles which inspire Math, and assuming there are pre-existing mathematical archetypes which shape physical form, takes you to the same place, ultimately. The act of determination in a constructivist sense is both measurement and construction. That is; observation is creation, just as with Quantum Mechanics.

    What I am proposing is that the way we learn about the universe is a model or simulation of how the universe gives rise to form - through a dynamic process of determination, which serves both to make things observable or measurable, but also makes them actual. I'll have more to say on this later.

    Have Fun!

    Jonathan

    Jonathan,

    I think we are probably in general agreement there. It unfolds according to principle, but the more complex, the more interactive and subjective. It is a fundamentally dynamic process, not static principles. They appear static "in principle" only because they repeat.

    The only absolute is zero.

    Dear Jonathan,

    Very beautiful and well written essay. Indeed, there is much agreement between us, and also a complementarity in the approaches. You were able to present the interplay (dance) between it and bit also from psychological and evolutionary viewpoints, and also to analyze with an impartial eye the relation between them.

    Best regards,

    Cristi Stoica

      Thanks so much Cristi!

      I appreciate the high regard. As I recall, you and I did agree on a number of points, and I liked your essay a lot this time around. A compliment from you is esteemed highly.

      All the Best,

      Jonathan

      Thanks for the thoughtful accommodation John,

      I'll not belabor things here, but I'll take the time to read your essay instead, and take you to task on your own page - if I think you have gone too far afield this time. I generally enjoy your writing a lot, and I appreciate your perspective. Thank you for sharing here.

      Have Fun!

      Jonathan

      I liked the essay, but find these essays hard to rate. While this and others explore the area, they don't really seem to come to grips with the core aspects, in the same way that brought Hume to say 'Consign it then to the flames: For it can contain nothing but sophistry and illusion.'

      This is a general comment, not specific to this essay. This was one of the better essays, I felt.

      The connection between minds and worlds, under the GPE (see my essay) is that the Harmony Set may have several equivalent interpretations in the same way that a top hat functions can be replaced by a Fourier series, or redistributed values in higher dimensions. Which interpretation is the 'right' one? None. Which has priority, or is the foundational space? None. But these spaces are ontologically locked together. One might propose that one of these interpretations gives rise to mind.

      Stephen Anastasi.

        Thank you Stephen,

        I appreciate the thoughtful remarks. I agree that with a more philosophical entry it is harder to say 'it is right or wrong.' I'll have a go at your essay soon, and comment there.

        All the Best,

        Jonathan

        Dear Jonathan,

        "certain regularities of Math have a life of their own, and influence or shape the laws of physics", I fully agree but the unknowable is that it works.

        In my essay the Riemann sphere rigidified at three points is a very regular mathematical object, introduced by Grothendieck, that plays the role of measurement space for multiple qubits. To use your language the form is the 'dessin' on the rigidified sphere (or may be the stabilized geometry of observables) and the information is encoded at the extremities of its edges.

        "The acquisition of object constancy, which takes place in early childhood...", may be you implicitely refer, and without knowing it, to Grothendieck's 'dessins d'enfants'.

        Good luck,

        Michel

          Dear Jonathan,

          Another excellent essay! Not only do I agree with your previous conclusion of analogue and digital, but that reality and information are also too intertwined to separate. My essay also concludes not to have either more fundamental. The child like thinking is a good reminder that we need to keep things simple and reach conclusions based on the simplest explanations.

          Nice read too!

          Very well done.

          Best wishes,

          Antony

            Thank you Michel,

            Grothendieck was a master at discovering the roots of things, where others would spot only the flowers. And of course; his insight that it was children's play with forms that would reveal those roots is priceless. Too often, adults forget the intelligence of play, or the wisdom of the very young, in their hubris to believe adult understanding is better, but sometimes the drawings of children reveal things most adults cannot understand.

            I shall examine some of the material I just found on the 'dessins d'enfants' and also take the time to read your essay Michel. I appreciate your thoughtful comments.

            All the Best,

            Jonathan

            Thank you Antony!

            Your kind remarks and high regard are appreciated. Of course; some things are only apparent to a child like mind, and others can't grasp them because their understanding is too sophisticated or developed in a particular groove. Alison Gopnik suggests as a metaphor that children use a lantern to learn, while adults prefer a spotlight. There is a lot us older folks miss that way.

            Your essay is still on my list of papers to read, but I hope to get there soon.

            Have Fun!

            Jonathan

            Hi Jonathan,

            I always appreciate that you don't dodge the biggest questions: "Does life descend to play in or with form, bestowing consciousness and creativity? Or does form rise and evolve to acquire these attributes, so it may play in the heavens?"

            You allow that science takes the latter course. Things are changing, though -- in complex systems models of laterally integrated information, those upper and lower bounds of agent awareness and action are not so clear. What is becoming clear, through high tech data analysis of interacting systems, is that hubs of activity that control the system's output through negative feedback constantly shift position.* Most remarkably, the most drastic changes are on the shortest intervals of observation, while the system shows little change on the longer scale. Hence, your dance of creation.

            "In considering the question 'It from Bit, or Bit from It?' one must always ask 'With respect to what?' The question is undecidable otherwise, as it is essential to understand that entities or systems can have a dual role, and can in fact be a blend of It/Bit flavors ..."

            Nice. I am reminded of a recent U.S. president who assigned to himself the role of "decider," in vain. He should have taken a lesson from King Canute, standing in the surf and commanding the ocean waves to roll back. I expect the next chapter of human history will be one of cooperation, the only decision that really needs to be consciously made.

            All best,

            Tom

            *See, e..g., Braha & Bar-Yam, "From Centrality to Temporary Fame: Dynamic Centrality in Complex Networks." Complexity vol 12, no 2, pp 59-63. [2006]

              Dear Jonathan,

              I have down loaded your essay and soon post my comments on it. Meanwhile, please, go through my essay and post your comments.

              Regards and good luck in the contest.

              Sreenath BN.

              http://fqxi.org/community/forum/topic/1827

                Thanks greatly Tom,

                Astute observations about the short scale vs long scale activity within a system. This appears to be more or less universal. As you say, the most drastic changes often happen on a short interval, and go unnoticed if one's observation considers only longer time scale phenomena.

                Non-linear entropy is observed mostly when you take things that appear to happen instantaneously, and re-examine that behavior in terms of reciprocal exchanges. It's not instant at all, and involves a lot of back and forth activity, but it does happen very fast. Decoherence happens quicker still, but a closer examination shows us that is a dance as well.

                However one would never know it is a complex phenomenon, without examining large excursions that happen in a short time more closely.

                All the Best,

                Jonathan

                Thank you Sreenath,

                I have downloaded all of the essays at this point. I look forward to reading your essay, and I will post a few comments on your page once I do so.

                Have Fun!

                Jonathan

                I had a delightful excursion into your Mandelbrot slides. And then I surfed over to Joselle Kehoe's blog (my first exposure), where an archived article on Gregory Chaitin's new book (*Proving Darwin*) caught my eye. After noting Chaitin's wonderfully phrased philosophy: "Each time mathematics faces a significantly new challenge, it transforms itself." Joselle follows up with her view:

                "The idea that life itself is creativity, and that our knowledge of it is always incomplete, is a view of things that I believe mathematics easily inspires. My own experience with mathematics has always led me in this direction, both within the confines of my very personal experience as well as when I explore ideas in science, philosophy and art. It's a provocative and optimistic view. Mathematics seems to be coming from us, yet it keeps giving us images of the larger thing of which we are a part, to the point of showing us that we can never fully know that larger thing. We are seeing something about us and the world."

                I so agree. Some say the Mandelbrot set is the most complicated object in mathematics. Actually, my vote for that honor is Chaitin's Omega number. Both objects, though, inform us that everything we are certain about is history -- a history that continuously creates infinite bifurcating trajectories. Only the hidden patterns of self similarity gives us even a hint of the global reality.

                All best,

                Tom

                Wow! Thanks Tom..

                I appreciate affirmation of value in the insights offered, and the hearty 'Hi Ho' that your comments indicate and inspire.

                Have Fun!

                Jonathan

                Jonathan,

                You provide a generalist's perspective to a bunch of specialists. As I like to rib Tom, Generals run armies. Specialists are somewhere between corporal and private.

                Regards,

                John

                Jonathan,

                I have received word that although it was unfortunate that there was a delay in conducting the ratings, no extensions to the final deadline will be made. I will keep this in mind when I get a chance to review your essay later this week.

                Best wishes,

                Manuel