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

  • [deleted]

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

          Paul

          I've just re-read your essay carefully. As a non 'professional physicist' I appreciated your knowledge and the latest detail of some current ideas.

          I also fully understand the logic of the holon, May this perhaps be somewhat apparent in Cherenkov radiation? and do you consider there may also be any 'lowest' energy for a discrete particle?

          I've been studying; .. "the overwhelming discrepancy between the calculated and observed values of the cosmological.." {'constant' I assume}, and the many other discrepancies, anomalies and paradoxes, and appear to have found a logical model which removes them all. This provides a resolution to the 'dark energy enigma' and evaporates the 'murky clouds', where indeed it derives 'exciting times' as you predict. I do hope you'll be able to read my essay. http://fqxi.org/community/forum/topic/803

          It is difficult to see beyond the murky clouds using current understandings, so you'd have to temporarily step back from those, use pure logic and focus on improving conceptual dynamic visualisation skills.

          You may also wish to see the strings, in which much added explanation lies, and you may see that immediate conceptual understanding has now improved significantly to around 1 in 4 professional physicists and others. It also explains the issues, proofs and gives links. It is simply a fine tuning of SR with a Quantum Mechanism, removing all issues in SR and beyond. (see also the identification of the errors, the logic, and the many thought Gedankens).

          I'd be extremely grateful for your thoughts if you have time to read it.

          Best of luck in the competition.

          Peter Jackson

          Dear Peter,

          Thanks for your kind remarks. Cherenkov radiation applies to energetic charged particles, so if there were an effect it would only be very indirect. The theoretical lowest energy of photons would depend on the size of the universe (with a theoretical lower limit of zero for an infinite universe). In practice, because of thermal fluctuations and the Third Law's prohibition against reaching absolute zero, this lowest energy would never be realized.

          Looking forward to your essay.

          Best wishes,

          Paul

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          Dear Paul,

          Planck's own Nobel lecture is a good place to see the infrared issues that drove him to the idea of discreteness: http://nobelprize.org/nobel_prizes/physics/laureates/1918/planck-lecture.html. Still a very nice read, I think.

          Best,

          Dean

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          Dear Professor Halpern- I have downloaded, studied, and copied your essay: THE DISCREET CHARM OF THE DISCREET, to my folder of seminal manuscripts. It appears to me that you are very much the heir apparent to Abraham Pais.

          You may find my paper: IS REALITY DIGITAL OR ANALOG? somewhat outside of mainstream thinking. I confess that my work, is of a decidedely different 'style' from your work. But the justification for my approach is not that I am right and you or any formally trained physicist is wrong. The virtue of my paper is that my methods allow for a completely mechanical explanation of the process of cell duplication. Coming to point on the subject of how it is that cancer cells duplicate faster than healthy cells. I'm going to make a thorough study of your books and papers. I'm hoping you can find the time to glance at: NEOPLASIA MATHEMATICS.

            Dear Joel,

            Thanks so much for your kind words!

            I am greatly humbled by your comments, as Abraham Pais is one of my personal heroes, and was a dear friend of my research advisor, Max Dresden. Pais was a brilliant historian of physics, whose books I have very much enjoyed. So, he is a role model for anyone interested in the history of 20th century physics (the history of physics prize is named in his honor).

            I appreciate that you are aspiring to a different goal in your work, and that your focus is on cell duplication. I will take a look at your work NEOPLASIA MATHEMATICS. One of the exciting aspects of this contest is encountering a wide range of ideas about science.

            Best wishes,

            Paul