Dear Stephen,

It seems that I am still far from understanding philosophical categories. But it is unimportant here.

I am preparing a response to your questions and later, if you wish, we can continue our exchange by email.

I am very glad that you are enthusiastic.

All the best,

Michel

Dear Stephen,

As you gave a perfect summary of what I did, I don't have much to say.

You write

1. "not only does the universe collapse to a single minimally simple omnet, all of mathematics went down the tube with it.",

The translation of this sentence would be the Belyi theorem (see the step 3 in my Sec. 2 giving the definition of a child's drawing) and the property that the child's drawing D itself is the preimage of the segment [0,1], that is D=f^-1([0,1]), where the Belyi function f corresponding to D is a rational function. All black vertices of D are the roots of the equation f(x)=0, the multiplicity of each root being equal to the degree of the corresponding vertex. Similarly, all white vertices are the roots of the quation f(x)=1. Inside each face, there exits a single pole, that is a root of the equation f(x)=\infty. Besides 0, 1 and \infty, there are no other critical value of f.

Sorry about the technicalities.

2. "the thought that a compatibility (i. e., commutativity) diagram of observables has a kind of engine that drives it: a dessin d'enfant (a child's drawing). "

Yes, exactly. I leave you free to translate it in the GPE language. The point is that you can have many 'engines' for a given compatibility diagram, a kind of redundancy. For your example of the 3-simplex, e.g. the tetrahedron, I just checked that there are 6 distinct dessins/engines, for the 4-simplex, e.g. the 5-cell, there are 13 distinct dessins/engines that can be built with the cartographic group C2+ as the constructor [my equation(1)]. It would be interesting to understant what means this non-bijection in your approach.

3. Orientabilty: we need an oriented surface like the Riemann sphere, or a torus, not a Möbius strip (that is not oriented). Thus the dessin is more than a graph and corresponds to a permutation group P with two generators, as given in my step 2 of Sec. 2.

One needs to develop some familiarity with these concepts, then they become natural.

I anticipate an unexpected and fascinating complementarity between your approach an the one based on Grothendieck's concepts.

Thank you for your enthusiasm about this work.

Michel

Hello Stephan

Richard Feynman in his Nobel Acceptance Speech (http://www.nobelprize.org/nobel_prizes/physics/laureates/1965/feynman-lecture.html)

said: "It always seems odd to me that the fundamental laws of physics, when discovered, can appear in so many different forms that are not apparently identical at first, but with a little mathematical fiddling you can show the relationship. And example of this is the Schrodinger equation and the Heisenberg formulation of quantum mechanics. I don't know why that is - it remains a mystery, but it was something I learned from experience. There is always another way to say the same thing that doesn't look at all like the way you said it before. I don't know what the reason for this is. I think it is somehow a representation of the simplicity of nature."

I too believe in the simplicity of nature, and I am glad that Richard Feynman, a Nobel-winning famous physicist, also believe in the same thing I do, but I had come to my belief long before I knew about that particular statement.

The belief that "Nature is simple" is however being expressed differently in my essay "Analogical Engine" linked to http://fqxi.org/community/forum/topic/1865 .

Specifically though, I said "Planck constant is the Mother of All Dualities" and I put it schematically as: wave-particle ~ quantum-classical ~ gene-protein ~ analogy- reasoning ~ linear-nonlinear ~ connected-notconnected ~ computable-notcomputable ~ mind-body ~ Bit-It ~ variation-selection ~ freedom-determinism ... and so on.

Taken two at a time, it can be read as "what quantum is to classical" is similar to (~) "what wave is to particle." You can choose any two from among the multitudes that can be found in our discourses.

I could have put Schrodinger wave ontology-Heisenberg particle ontology duality in the list had it comes to my mind!

Since "Nature is Analogical", we are free to probe nature in so many different ways. And you have touched some corners of it.

Best,

Than Tin

    Dear Stephen -

    I agree with your approach - you rigorously re-evaluate our fundamental assumptions, and force the reader to do so - and I like your coining of new terminology so as to avoid 'putting the new wine into old bottles' as one might say.

    As someone wrote on my page - 'The Universe doesn't explain itself, it presents itself to us.' And you take this all the way and define a non-anthropocentric model, which is a bold and unique undertaking.

    I'd be curious to see how you'd apply this imaginary universe to my paradigm, where the Cosmos is described in terms of the correlation existing between Inorganic, Organic, and Sensory-cognitive phenomena.

    I'll certainly re-read your paper - it's a little difficult to absorb all at once - and hope you have time to look at mine soon.

    I also wish you all the best in the competition -

    John

    Hi Stephen,

    to let you know I have replied to your questions on my essay thread.

    Hope to read your essay soon

    I have not understood the relation without Causal Dynamical Triangulations. Can you day more about it. carlo

    Thank you Carlo

    As is pretty obvious, the Harmony Set as shown is a one-space interpretation. Simply, because this model has to be a proper world model (for reasons shown) it remains for the investigator to find how the system gives us our world, as opposed to 'a' world.

    After a long, long period of thought (which of course doesn't make me right) I tried to interpret the system by maintaining equivalence (under the GPE) and distributing the values into three dimensions, assuming that the formulas of mathematics applied to this distribution as much as it does in our present models (this is not strictly allowable for the endpoint rationalist because first one must show how Pi comes to be, but I have no really big concerns there for the moment).

    Doing this redistribution is allowable because of Kant's argument about our never being able to say that a particular world model is reality, meaning 'the' world model (I know this seems to be the antithesis of Kant, but it has the opposite effect for an endpoint rationalist--I can explain in more detail if needed). All models that add up to the values of the Harmony Set are valid.

    Doing this redistribution brings the number i into existence, as the square root of a negative pointing vector, which, combined with the exponential nature of the Harmony Set suggests a possible connection to Schrodinger's equation, and hence Feynman's Path Integral, but in a summation form (as in CDT). The redistribution however, provides an almost flat universe in all but the center, in a region that might be around the Planck scale (one would have to show equivalence between the scale of the Harmony Set and that of the real world, but there are ways to work with this). This flat system applied to the real part of the solution. The imaginary part could be doing anything -- I don't know how to work with this second part in this very different context. While the real part suggests that space is essentially flat except locally, I'm looking for an interpretation that implies more interesting structure.

    One way to achieve this is to begin the development probabilistically. That is, consider the boundaries to be point like structures, and ask oneself where the next point must go, given the boundary condition of maintaining equivalence. In two dimensions, one gets into bothers quite early. In three dimensions placing the first four points is easy, and, with the digraph connections they produce first a line, then a triangle (implied 2-space, not embedded in higher spaces) then a tetragon, and all forms are equivalent under the GPE (e.g. any interaction can be swapped with any other and the same form results). The form of CDT has it that triangles are 'glued' together along their lines, but in the Harmony Set these lines are necessarily glued, because they are ontologically dependent, so if this is a valid world model one might expect CDT to be an expectation. The difference of course is that CDT, if I understand it correctly, assumes a much larger world model initially, where mine brings the world into existence a step at a time (literally).

    To continue adding points and their interactions starts to get more challenging after this. Equivalence can be maintained by assuming extra spacelike dimensions, but doing so leads to another tetragon in 4-space, then another set of these in 5-space and so on. I don't know what to do with these, but this seems to be a bit like CDT's idea of 4-simplices. Another way is to simply add the point to the outside of the initial tetragon, which under equivalence might go in any of four places, but, in the absence of an oriented space, all four places are the same place (meaning the same form arises). The same applies as one adds the next three points. My concern here, as endpoint rationalist, is that I'm not completely convinced of this approach because the bi-vectors have to be 'stretched' to make it fit. But such stretching seems to be the same form as CDT's simplices, as best I can tell.

    Lastly, one interesting thing for me is that CDT hits a wall when it aims to reduce its length scales to zero. They can't do it, and I don't think they should be able to do it, if the tenets of my armchair universe stand (which, under endpoint skepticism leading to endpoint rationalism, they ought, which is a stronger argument than that of empiricism).

    Of course, there is a long way to go with this development. I need someone with a strong knowledge in philosophy (metaphysics), mathematics and physics to talk to about it, but, as this is so far away from present science, finding such a person is likely to be difficult.

    Thank you for your question. Feel free to ask other questions.

    Stephen Anastasi

    Stephen,

    This "ontology" does not even mention any substance? There is an infinite number of truth systems that may describe the universe from a specific point of view. Each truth system requires at least one rule of impossibility that defines it along with the mother of all impossibility, the rule of non-contradiction, required for the system to be internally consistent or "logical". I think, that all points of view require two or more impossibilities while the universe could require two rule of impossibility, that of the non-contradiction and the rule of existence. This is because beyond the question of the logical consistency, there is the question of "existence" and substance. So, the universe needs this other rule, either of impossibility or one boundary rule on the possibilities of existence. This last one would give direction to the whole thing; evolution, time, future ...

    [12] is missing. I have Lowe's possibilities of metaphysics... I did not give him good reviews...

    Marcel,

      Hi, Stephen,

      Wow, what an impressive, well-written and literate essay! I wrote more details after your comments and questions on my essay, "It from Bit from It from Bit..." This seems a good way of tying feedback and nonlinearity into the picture. Also, as I noted there, I'm looking forward to your book when it becomes available.

      Best wishes,

      Bill McHarris

      Thank you Marcel

      Thanks for your very valid questions. You said:

      'This "ontology" does not even mention any substance?'

      There is no need for the use of 'substance' in this development. You will see that the meaning of substance is dependent on one's idea of equivalence anyway.

      You said:

      'There is an infinite number of truth systems that may describe the universe from a specific point of view.'

      I see your point, but there are not an infinite number of perspectives that conform to the general principle of equivalence, and initially all perspectives collapse to a minimally simple omnet, under the GPE. All well-founded models must 'add up to' the evolving one dimensional values in the Harmony Set in one way or another, and one cannot apply contemporary mathematics to the set without an understanding of the foundations of the mathematics being used (for it went down the tube with the world, at the first step). Truth systems must first be well-founded, if they are not actually just belief systems. That is perhaps the key point. This system is well-founded, being immune to Cartesian doubt.

      The Law of Non-contradiction is obvious and true, but is founded upon the General Principle of Equivalence, and epistemologically dependent upon it, not the other way around, for the LNC is accepted as self-evident, while the GPE is accepted because it is immune to doubt. Let me derive the LNC from the GPE to make it clear. Simply, the LNC is necessarily true because to suppose that an omnet can both have, yet not have a particular asset, would violate the GPE. This remains true independent of the nature of an asset.

      This 'rule of existence' is unnecessary, so can be dropped under Occam's razor, replaced by the recognition that what is implied to be by the GPE exists. It's purely nominal. Also, there is a problem in trying to have a universe that comes from more than one principle because more than one principle implies that there are differences between them, and this difference drops one back into the bundling problem.

      You said:

      'So, the universe needs this other rule, either of impossibility or one boundary rule on the possibilities of existence. This last one would give direction to the whole thing; evolution, time, future ...'

      I wonder if you are describing the evolution of the Harmony Set here, which is good. My initial derivation was for a particular situation which I found was a form of Zeno's paradox. Then someone asked me what I meant by 'a boundary'. Ouch. It took me a while to realize that the 'boundary' is a word covering an omnet that exists due to an ontological condition, and from there I generalized the whole argument to find that it all reduces to one's idea of equivalence, as captured by the GPE.

      You said:

      '[12] is missing. ' My apologies: Lowe, EJ 2005, 'Ontological Dependence', in EN Zalta (ed.), The Stanford Encyclopedia of Philosophy Summer 2005 edn, http://plato.stanford.edu/archives/sum2005/entries/dependence-ontological/.

      'I have Lowe's possibilities of metaphysics... I did not give him good reviews...'

      I hope you can see my development toward providing me a good review, so we can together work out the very great challenge of interpreting the Harmony Set in higher dimensions. Please recognize that this is a work of foundation that starts from a single principle and produces a mathematical world model. This was thought not possible.

      Feel free to ask more questions or provide ideas on how to work with the one-space Harmony Set.

      Best wishes

      Stephen Anastasi

      Yay Bill!

      Your encouragement made me feel great. My aim is just to get into the top 40 papers so that the experts read it. To get there I need some big numbers.

      It's so abstract! What I love is that it implies that the world will be kind of non-linear, being sets of similar but not exactly the same sets.

      Stephen

      Hi Stephen,

      I read your essay and helpful replies in this discussion thread but I'm afraid I am not "someone with a strong knowledge in philosophy (metaphysics), mathematics and physics to talk to about it". I don't think I have the necessary background to fully appreciate what I have jut read. Sorry.

      Are you talking about a process of elimination from all possible model universes ? Would this accomodate the possibility of universe within universe? In the way that a fantasy world can exist within a book. The world being constructed by the reader from the information contained in the book itself. Sorry if that seems obscure and irrelevant it relates to the framework I mentioned in reply to your question on my essay thread. Regards, Georgina

      PS I've replied again to your reply in my essay thread

        Hello Georgina

        Firstly, I hope that my comment on the 'knowledge of philosophy...' statement didn't seem to put you down. If so, my apologies. Because of your interest, I am attaching a copy of a portion of a chapter of my book, The Armchair Universe, which is written in a way that most people can engage with it. I hope you like it, and find it interesting.

        You said:

        'Are you talking about a process of elimination from all possible model universes?'

        Yes. The GPE then implies that all universes that we might suppose to be are degenerate to a single simple initially, then this evolves into a complex entity. It happens to also provide a new foundation for mathematics (some mathematicians might choke on this claim) free of Godel's Incompleteness Theorems (oops, there I go again. These theorems imply that contemporary mathematics can never be proven to be complete - one can never be completely sure one will not bump into an inconsistency).

        You said:

        'Would this accommodate the possibility of universe within universe? In the way that a fantasy world can exist within a book. The world being constructed by the reader from the information contained in the book itself. Sorry if that seems obscure and irrelevant it relates to the framework I mentioned in reply to your question on my essay thread.'

        Um. What a marvelous idea. As a writer of alternative world fiction, but not here (!) (Amazon me!) I appreciate the concept, and one ought to recognize that this crowds the mind-body problem. Under the GPE, it is not that there are universes inside a universe, but that there seems to be different interpretations of the Harmony Set, any one of which is a proper world model. Which is 'our' universe? I think there are layers of universes. Under the GPE none has ontological priority, meaning none can be said to be 'the top layer'. But the 1-space interpretation has many interesting properties that, if carried into higher dimensions seem to answer fundamental questions, such as why there is a minimum length and time.Attachment #1: The_fireside_armchair_universe.pdf

        Stephen,

        A quite unique essay that I found uncannily analogous, in terms of many concepts and descriptions, to the fundamental discrete field model (DFM) underlying my own and previous two essays. I think we may find we might have many points in common!

        I loved your most fundamental approach and interesting use of logic. How nice to be able to build an ontology (which I do in mine) free of all doctrine, preconditioning and hidden assumptions.

        I agree "Aristotle's idea of place, in which everything has its place, and place too has its place." (I derived an almost infinite hierarchy last year) As also in; "If a boundary exists, it too has an end; it too has a boundary."

        Also your perceptive; "such difference implies the existence of some kind of dimensionality, a space in which the boundaries exist, and exist separately. The causal dependence relation between boundaries prescribes an interaction, and that interaction has a value."

        Your 'harmony sets' also mirror DFM frame domain transitions, but again mostly in the basic model not the particular 'Intelligent Bit' I discuss from a very practical standpoint this year. Which you may not at first recognise as I describe. I think I do however show the power of extending your approach to some logical conclusions.

        Anyway, I suspect we may both have heaps of points to apply. I look forward to your comments, and think I'll also look forward to your book.

        Very best of luck

        Peter

          Dear Stephen,

          You are correct, Thank you for your comments.

          I am sorry in the delay in replying you. I did not check the replies. FQXi should have issued a notification that you have replied....

          It was my proposition / question, that can we produce matter from our thinking it was not an inference to your essay. What I mean is that we should be more close experimental results for our propositions.

          I think we form a picture of anything in our mind, and keep them in our memories. We communicate about that picture to others, which we call information. When we die we loose all these pictures and memories.

          Now in this context, can we create material from information...?

          You can discuss with me later after this contest closes also.

          Best

          =snp

          snp.gupta@gmail.com

          Dear Stephen,

          Contests FQXi - is primarily a new radical idea. "The trouble with physics" push ... In your essay deep original ontological analysis in the basic strategy of Descartes's method of doubt, given new ideas, new concepts, new images and conclusions.

          Constructive ways to the truth may be different. One of them said Alexander Zenkin in the article "Science counterrevolution in mathematics":

          «The truth should be drawn with the help of the cognitive computer visualization technology and should be presented to" an unlimited circle "of spectators in the form of color-musical cognitive images of its immanent essence.»

          http://www.ccas.ru/alexzen/papers/ng-02/contr_rev.htm

          In the russian version of a article: «The truth should be drawn and should be presented to" an unlimited circle "of spectators.»

          Do you agree with Alexander Zenkin?

          Please look also my essay and essay FQXi 2012 related to the ontological justification of "Absolute generating structure"

          http://fqxi.org/community/forum/topic/1796

          http://www.fqxi.org/community/forum/topic/1362

          We have the spirit of close reserch. We have a common reference "point" and "vector" the road to the truth. Is this the right way - time will tell and others. My mail ideabank@yandex.ru

          Best regards,

          Vladimir

          Stephen,

          I found your approach to the topic at hand fascinating and would like to rate your essay highly. However, before I do may I run some questions by you via email? Please let me know at: msm@physicsofdestiny.com

          I look forward to hearing from you.

          Regards,

          Manuel

          Stephen,

          Thanks for your post on my blog. I responded in both places but both have been lost with others in the server change (along with some scores, including from mine it seems!) Brendan seems to think we may get the posts back so I won't repeat it yet.

          I hope you've read my essay now and that it lived up to it's promise (I need the points!) If you have scored it please check again, I note I'm also down as not having scored yours yet, so a nice lift on the way now. I look forward to discussing the areas of commonality, which may appear more directly from my previous two essays (domain boundaries with boundaries etc.)

          Very best wishes

          Peter