• [deleted]

Dear Paul Halpern,

Twenty years ago, when I heard for the first time of CA, they were used almost like FEM by those who model plasma, heat conduction and the like. Since then I did not get aware of reported convincing benefits. Your essay makes understandable to me chains of more or less speculative hope for foundational insight that might be confirmed in the very far future.

Let me frankly admit that I am ready to accept the big bang as an exiting hypothesis but not yet as proven for good. What about the attribute foundational, I prefer to judge it as did you from experience over centuries. I appreciate that you avoided technicalities that would perhaps anyway not be convincing.

Most appealing to me was your question for upper and lower frequencies of in particular electromagnetic waves. You will certainly not need reading my essay in order to understand that discrete frequencies correspond via cosine transform with continuous functions of temporal or spatial distance and nice versa. Cosine transform differs from Fourier transform in that performing it twice yields the original function. In other words, it is its own inverse.

Not just in CA the notion neighbor plays a role. Hausdorff topology does also consider a neighbor each to the left and to the right. I found out that this is based on a non-Euclidean notion of number and at odds with a lot. For instance, it is to be blame for trouble at zero, for the unwillingness to accept R as sufficient in case of non negative spatial or temporal distance, and even with the usual unilateral attribution of the increment dx to the direction of x.

Regards,

Eckard

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    Hi Paul,

    interesting essay!

    You write:

    'One measuring of entropy in network theory is the growth of complexity in link structure.'

    Are you referring to a specific definition of entropy for networks? Any pointers? Would this be something like the log of the number of graph automorphisms?

    You also write:

    'Given the promise of simple, discrete algorithms, it is interesting to consider a dynamic digital model of fundamental interactions based on holon states. Because holons would have the minimal wavelength of all fields, they might be thought of as 'cells' in a dynamic grid. It is possible that simple digital rules, akin to SDCA algorithms, could transform both the values (quantum states, such as polarization) and linkage of sites. This would render this stratum geometrically dynamic, offering a digital basis for distortions in spacetime'.

    I am interested in SDCA type of models, where interconnection patterns evolve, although I claim that having a dynamic interconnection pattern should suffice for building everything, without need of an additional layer of labels, or cell states. The interconnection pattern could indeed code for local states. In the planar case, for example, one has polygonal faces, each with its size, and this generalizes to simplices in higher dimensions. Depending on whether or not these 'atoms' have and preserve their own identity, one can conceive two different types of field/particle (I see analogies with fermion vs. boson behaviour here).

    Did you run computer experiments in which both the background cell structure and the additional layer of state information you place on top of it give rise, separately, to the emergence of solitons or other patterns?

    Thanks and good luck!

    Tommaso

      Dear Eckard,

      Glad you found my essay understandable. Yes, CA offer a great deal of flexibility in modelling a wide range of physical systems. Interesting about Hausdorff topology and the role of neighbors.

      I look forward to reading your essay.

      Best regards,

      Paul

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      Paul,

      From my perspective you have successfully moved a "holon" from the list of zeroes (could exist but don't exist) to the list of ones (exists). Also from the list of fuzziness to the list of clarity. Now, I am interested in more movement from zero to one. If I pointed to some point in space with my finger...would a holon exist at the end of my point? If not, what would increase the possibility of a holon being there? Expansion of the space pointed to...and what about expansion of the time allowed for observation at the intitial point at the end of my finger? Would expansion of space searched and time observed increase my chances of locating a holon? Why is the possibility increasing with a change in either condition? Or, is there actually only holons everywhere which make my questions mute?

      Irvon

        Hi Irvon,

        Glad my essay clarified things! The holons would represent the maximum energy fields, and therefore could not be directly detected at present. They would manifest themselves only through their indirect consequences (such as placing an upper limit on the vacuum energy density).

        Best wishes,

        Paul

        Dear Tommaso,

        Thanks for your kind comments and detailed message!

        In terms of a type of 'topological entropy' measuring network complexity, a quantity related to the Hausdorff dimension (and defined in the SDCA papers listed in the references of my essay) serves as an effective measure. The ratio of next-nearest neighbors to nearest neighbors tends to rise as the system becomes more complex. The parameter you mentioned, 'log of the number of graph automorphisms,' would be another measure.

        We did indeed run experiments looking for a type of 'topological soliton' that could potentially represent particle states.

        Your ideas sound very interesting. It would certainly be an important achievement to find evidence of 'fermion'- and 'boson'-like states developing from pure networks.

        Best wishes,

        Paul

        Dear Eckard,

        Glad you found my essay understandable. Yes, CA offer a great deal of flexibility in modelling a wide range of physical systems. Interesting about Hausdorff topology and the role of neighbors.

        I look forward to reading your essay.

        Best regards,

        Paul

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        Paul,

        So, are we willing to attach the fuzziness of nothingness to create meaningfulness in the sensory world (sensed objects, forces and relationships that we actually can point to and even get close enough to touch)?

        Here I would suggest what I think is an appropriate poem:

        V

        I don't know which came first

        After the chicken

        And sex

        And the egg

        And the empty can of soup

        There's no need for

        An opinion

        Based on observed facts

        Not in this day of

        Revealing ignorance

        What's left for modern man

        Isn't even a bone

        There's just the opportunity

        To scavenge

        To catch a glimpse of

        A suggestive piece of evidence

        An imprint exists

        Where it once was

        Substance

        And now

        Even

        Ideas are Art

        --------------------------

        Paul, you have created a great piece of art!

        Respectfully,

        Irvon Clear

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        Paul,

        I was looking forward to your entry in this contest, and I was not disappointed. You are so very expert at drawing a picture of abstract models in sensuous terms. I especially appreciate your comparison of an office tower to the possibility of a finite field theory (in itself a concept to launch a thousand dissertations). I was reminded of Jorge Luis Borges's short story, "The Library of Babel."

        Interesting, informative and original. Just excellent.

        Good luck in the contest, and I hope you get a chance to visit my essay, which shares in common with yours an emphasis on information theory.

        All best,

        Tom

          Dear Tom,

          Thanks so much for your kind comments! Glad you enjoyed it. Borges's "The Library of Babel" is one of my favorite stories. Looking forward to reading your essay!

          All the best,

          Paul

          Dean,

          Thanks for your comments. I would be indeed be interested in reading such evidence about when Planck became aware of Rayleigh's work. Yes it is interesting that the term "ultraviolet catastrophe" was coined by Ehrenfest, even though the concept was introduced beforehand.

          Best regards,

          Paul

          Dear Paul,

          Thank you for your very kind remarks on my essay. I had also read your essay, some days ago, and very much appreciated your holon idea.

          With my best wishes,

          Tejinder

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            Dear Paul,

            I liked very much the historical part of your essay, which is much more developed than mine. Also, I liked the analogy of the information contained in an envelope and the size of the characters.

            On the other hand, a minimal wavelength seems to me counternatural as this would mean an upper limit of the wavenumber. Intuitively both ends (linear and inverse linear) are unbound.

            Best wishes for this contest.

            Arjen

              Dear Tejinder,

              Many thanks! I am glad that you appreciated the idea.

              Best wishes,

              Paul

              Dear Arjen,

              Glad that you like the historical part of my essay! Thanks for sharing your thoughts about a minimal wavelength.

              Best wishes,

              Paul

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              Dear Paul Halpern,

              Thanks for your opinion.When I saw the heading of the essay contest 'Is it possible to reconcile digital and analog nature of reality' the idea of connecting it to Advaitha dawned on me.Because Advaitha in a literal sense means Non-dualism.If it is possible for us to reconcile both forms of reality,then it must be done only on the concept of Non-dualism (that is Advaitha).Combining digital with analog, in physics means combining QM with GR,leads to QG which is non-dual to both.

              Today itself I will go thro' your article and express my opinion.

              Good luck and best regards.

              Sreenath B N.

              Dear Sreenath B N.

              Great to hear from you. Yes your idea of connecting the notion of digital/analogue with the concept of Advaitha, or non-dualism, is fascinating.

              Hope you enjoy my essay.

              Best regards,

              Paul

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              Dear Paul Halpern,

              In your intriguing essay,you have argued for the existence of a fundamental particle called,Holon.It is really good if such a particle exists as all of our knowledge of elementary particles can based on it.But you have not mentioned holon's mass and wave-length.I hope you will soon do it as it gives limits to our understanding of the physics.

              Anyway your essay is enjoyable.

              Best regards and good luck.

              Sreenath B N.

                Dear Sreenath B N.

                Glad you enjoyed my essay. Thanks so much for your remarks. An excellent question about the value of the wavelength and mass (or, more precisely, energy) of the holon. Those values would be determined by a field theoretic calculation of the vacuum energy density that included an ultraviolet (high energy) cutoff, and a comparison of that vacuum energy density value to that needed to explain the observed acceleration of the cosmological expansion. In other words, the wavelength cutoff would be adjusted to match the observations. I expect that the wavelength would have a value close to the order of the Planck length (approximately 1.6 x 10-35 m) and that the cutoff frequency would consequently be somewhat less than 1.8 x 1043 Hz. The energy would be that cutoff frequency value multiplied by Planck's constant h . Clearly, under the current low temperature conditions of the universe, such a massive state would be highly unstable. However, its existence would offer field theory a natural maximum energy cutoff.

                Best wishes,

                Paul