A lot to think about John...

The designation of base or apex is a matter of perspective. It's the same structure, really, only inverted or reversed. Is the upright cone of more value; or is it the inverted cone greater - because its emptiness will hold a fluid like water? Actually; the cone extends to encompass both upright and inverted sections, though we normally see one or the other depicted. Was the cone always there, in the realm of possibilities, and does that constitute a Platonic archetype or ideal?

My object of contemplation was, for a number of years, the Mandelbrot Set. And I played endless tricks with the algorithm and rendering, to reveal faces of that figure most people have never seen. It was more than 25 years ago now, that I had a few phone conversations with Professor M, to discuss the relevance of the mapping of form at the periphery to the cosmological epochs. I was slated to give a talk about this at FFP12, but unfortunately I didn't make it to Udine. However; this topic got me to wondering about how something mathematical might exist apart from our derivation or discovery of it - for obvious reasons.

Slides for FFP12 talk

More later,

Jonathan

Hello again John,

I just wanted to say that in my view, the archetypal and emergent existence of ideal forms are identical. This comes about because of the dual nature of determination in constructivism. That is to say; the process of learning about or creating anything are two sides of the same coin. But in some measure; the role of theoretical Physics is to correctly intuit what some of the ideal forms are, that emergent forms in nature are approaching.

Using iterated function systems, a wide variety of fern-like forms can be created, and the Math is simplicity itself. The collage theorem of Barnsley is basically a 'copy and paste' formula, where an image can be stretched or rotated. If one notes where the self-similar forms within the fern shape reside, and creates a map of how fern maps to branch, which maps to frond, which maps to leaf, then this becomes your formula. Amazingly, the shape of the fern emerges from the copy and paste algorithm itself. And we are left to wonder if a fern has a mathematical ideal it is reaching toward.

Have Fun!

Jonathan

Thank you for your insights Hai Caohoàng

Much of what you say in your comment makes sense, but I imagine I will better understand your intent by reading your essay. This I will attempt to do. Indeed; I do favor 'It from Bit' and then 'Bit from It' - because I feel that the relationship between the two defines each outlook, rather than giving either one supremacy.

All the Best,

Jonathan

Jonathan,

I have to say one of my earlier influences was complexity theory, but lost track of it, as it became something of a business mantra, so I was quite excited to read Nature and Nonlinear Logic by William C. McHarris.

I think people like he, who have spent their careers on the subject, are better able to explain how the development of patterns really does depend on dynamic randomness. We logically assume the causal link of effect is effectively predetermined, but patterns create their own instability. They rise up and crumble. The belief in deterministic outcomes is in fact part of the pattern prevalent in human action, as stability leads to stagnation. So yes, in a linear sense, I can understand how bottom up dynamic processes follow all possibilities and top down ordering self selects sustainable patterns, but I know that thread will eventually fray and fade. The cone of prior cause is ultimately random, as is the cone of consequent effect.

An ideal form is still contextual.

That said, I do believe in emerging ideals. I think life on this planet is building a central nervous system, with humanity as the medium, but it will require a phase transition we care not to imagine.

Ah Yes..

The butterfly emerges not by transforming, but by consuming its prior form. The butterfly's genome is distinct from that of the creature it emerges from. Little by little, the imaginal discs link up, until the caterpillar becomes a soup and the butterfly continues to develop its winged form.

All the Best,

Jonathan

Jonathan,

And that goes to the point I keep making about time; That it is the changing configuration of what is, rather than a vector of duration from past forms to future forms. This change being a thermodynamic, non-linear process, with the measure of duration is only an effect, like the scalar of temperature. The present doesn't move, only changes shape.

Regards,

John

"The butterfly emerges not by transforming, but by consuming its prior form."

Pushing the reset button. Part of the pattern is erasing pattern.

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