Dear Lev

I have enjoyed your essay very much. You point a very interesting fact and is how our conception of the continuum through points is based on the notion of limit. On my essay I try to explain how this conception of limit and others are just the tools that allow classical logic work on our conception of reality. Once we remove the excluded middle from our logic, concepts like limits, closed sets etc. loose their meaning and our continuum recover its relational character. We can keep then a lot of the richness of our classical formalism but getting the powerful relational character that you propose. I wonder what kind of logic governs the models you proposed, I think my ideas can be useful to you, I find particularly interesting your new conception of the Peano axioms I think it could have a closed relation with the models I propose. I would like to hear your opinions about it.

Regards,

J. Benavides

    Hi John,

    Thank you for your interst in the essay!

    First, I should mention that I believe in the priority of (object or data) representation in science over any logical considerations: the latter should follow the "logic" of the chosen representation, i.e.logic should emerge during our "manipulation" of data.

    Regrettably, the concept of representation emerged basically outside natural sciences (and was driven by CS applications), mainly because mathematics has not yet addressed it (and that is why it has been developed properly).

    It took me some time to gradually realize that when replacing "point" representation by a structural representation, you get a much richer "geometry", because of the much richer variety of various path between two entities (just look at the variety of paths between two strings over a finite alphabet under deletion, insertion, and substitution operations).

    I am familiar with category theory, but I felt that the concept of category is useful under the conventional mathematical (point) representation. What would be necessary in the "structural" mathematics is not yet clear to me: in the conventional math one has to seek (and build) various math. structure "outside" the (point) representation itself, since such numeric representations are too "simple". So the "structural" math. in view of very rich natural data structure, there is much less pressure to seek it in a manner similar to the conventional math.

    I will comment on your essay shortly, in your essay's page.

    Dear Lev,

    Your essay offers a fascinating analysis of why science has historically viewed nature as spatial and continuous. I very much enjoyed your methodical account of how spatial measurement has served as a core of mathematics, and how we may need to re-examine our assumptions. Well written and developed!

    Best wishes,

    Paul

    Paul Halpern, The Discreet Charm of the Discrete

      5 days later

      Dear Lev,

      Congratulations on your dedication to the competition and your much deserved top 35 placing. I have a bugging question for you, which I've also posed to all the potential prize winners btw:

      Q: Coulomb's Law of electrostatics was modelled by Maxwell by mechanical means after his mathematical deductions as an added verification (thanks for that bit of info Edwin), which I highly admire. To me, this gives his equation some substance. I have a problem with the laws of gravity though, especially the mathematical representation that "every object attracts every other object equally in all directions." The 'fabric' of spacetime model of gravity doesn't lend itself to explain the law of electrostatics. Coulomb's law denotes two types of matter, one 'charged' positive and the opposite type 'charged' negative. An Archimedes screw model for the graviton can explain -both- the gravity law and the electrostatic law, whilst the 'fabric' of spacetime can't. Doesn't this by definition make the helical screw model better than than anything else that has been suggested for the mechanism of the gravity force?? Otherwise the unification of all the forces is an impossiblity imo. Do you have an opinion on my analysis at all?

      Best wishes,

      Alan

      Dear Alan,

      I'm sorry, I'm by far not the best person to address your question.

      My best wishes to you!

        Lev

        You have found a solution I've spent some years looking for. I've tried many words but they have normally failed me and been inadequate. I have to congratulate you on your inspired use of the word 'cataclysmic'. Well done for finally pinning the right word down so precisely.

        I've recently added a couple more analogies and explanations to my string which, if you have time, I'd greatly appreciate your looking over. The last in in response to a tome by Basudeba.

        The solution has come through departure from the abstractions of points and lines and reversion to simply the 3D 'body' Einstein originally specified. This is so close to your own thesis I do hope you can perceive the enormous result, well able to extract us from cataclysm. You will need all your dynamic visualisation skills and a tiny bit more. An earlier post breaks the variables down and deals with each observer and path 'condition'.

        Very best wishes

        Peter

        Lev

        Thank for message on mine. Shame, but it seems we're all different for good reason.

        The problem with the DFM is the construct has to be in motion. Did I post you this video, with two observer frames involved.; http://fqxi.org/data/forum-attachments/1_YouTube__Dilation.htm

        It still takes a lot of thought and imagination!

        Best of luck.

        Peter

        7 days later

        • [deleted]

        • Post #33

        Gentlemens

        I wonder why you did not notice or do not want to notice the radical view that an independent investigator.Remember this name: name,Friedwardt Winterberg

        http://bourabai.narod.ru/winter/relativ.htm

        http://bourabai.narod.ru/winter/clouds.htm

        Yuri Danoyan

          Hi Yuri,

          I don't see his view as "radical", just not typical. ;-)

          2 months later

          Dear Lev

          I am honored to be your neighbor on this week's top essays web-page. I have read your interesting essay twice, and cannot honestly say I fully understand your concepts completely yet, but I did get the general idea that we need to use a new conceptual language when dealing with nature. The reason for this is due more to my own rather too-focused ideas on my own specific approach to reconstructing physics, rather than to any lack in your lucid and learned presentation. Your graphics rather reminded me of Penrose's suggestion to represent tensor operations in what he called diagrammatic notation (Roger Penrose "The Road to Reality" Figs 12.17 and 12.18) but of course the specifics and intentions of the diagrams are quite different.

          From your obviously well-defined point of view and set of ideas I wonder what you would think of my scheme to reconstruct physics in my 2005 Beautiful Universe paper on which my present fqxi paper is based?

          The only way to go forward for me now seems to be by computer simulation. Any ideas how I can start?

          With best wishes from Vladimir

            • [deleted]

            • Post #36

            One of the fundamental problems in continuous and discrete revolves around what actually happens in reality vrs the limitations of the information medium that conveys it to us. The problem is as follows:

            Everything that constitutes reality is undergoing a process of change. Every sequence of change has its own intrinsic rate of change. [This is time, incidentally, but not the point I am making here].

            Logically, both the maximum number of states and the fastest rate of change potentially experienceable, is a function of the maximum frequency with which the medium conveying the information is able to differentiate them. This could differ from what actually exists, which should be inferable.

            So, the attributes of the medium (the obvious one being light) needs to be disentangled from the resulting experience of reality, in order to extrapolate what was reality.

            © Paul Reed

            April 2011

            Extracted from Theory of Reality and Time posted on Re Ality (Facebook, look for the boy with his cat)

            Dear Vladimir,

            Thank you for your interest in my essay!

            I am, by far, not the best person to judge about or comment on your attempt "to reconstruct physics".

            You see, I am coming to physics from the point of view *quite* different from a physicist (see my latest book proposal). The reason for the latter is that I came to a tentative but very radical conclusion for the necessity to rethink the entire science of physics as it exists today (as a science of "motion in space").

            So, I'm afraid I cannot be of much help to you.

            My best wishes to you!

            5 months later

            • [deleted]

            • Post #38

            Hi Lev,

            I would like to help you understand my views on the problem continuous vs. discrete. Please take a look at these papers:

            http://www.psiquadrat.de/downloads/schroedinger52_jumps1.pdf

            http://www.psiquadrat.de/downloads/schroedinger52_jumps2.pdf

            I will quote some paragraphs:

            "I believe one is allowed to regard microscopic interaction as a continuous phenomenon without losing either the precious results of Planck and Einstein on the equilibrium of (macroscopic) energy between radiation and matter, or any other understanding of phenomena that the parcel-theory affords."

            "I wish to consider some typical experiments that ostensibly force the energy parcel view upon us, and I wish to show that this is an illusion."

              4 days later

              Thank you for the references!

              In light of his views expressed in the book "Science and Humanism" (published one year prior), I find his views expressed in this 2-part paper a bit puzzling. In that paper, it appears, he is leaning towards a less radical solution than he was advocating in the book. One can appreciate this: no one, at that time, could think of a fundamentally new, non-continuous, formalism.

              3 months later
              12 days later

              Thank you very much!!

              However, although I find it interesting, it appears that, on the formal (and partly on the informal) side, this work is still in a relatively hazy state. ;-)

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