Dear Mr. Schneider

Being myself involved in model theory, I read your article with great interest. And I fully agree with you that the understanding of physics is not exclusively a question of math. On the contrary, here in France and in Europe, many of us are grateful especially to Richard Feynman for his way to revolutionize the pedagogy of physics.

However, if the understanding of physics is not exclusively question of math, the latter plays an essential role in the elucidation of physical reality, and at this level, there is a great mystery remaining until further notice.

You say in your essay that math is a language like English. It is true that math, like English, can describe things that do not match reality, and that only experience determines if mathematical or English proposals correspond to the part of reality we try to describe. But I think that math has "something" than English or Spanish or Nipponese etc. do not have, and that this "something" plays an essential role in the relationship between math and physics.

Let us consider cartography, a domain on the periphery of physics. Of course, we can try to replace a map by a description of the area in question in English, Spanish, Nipponese. But the semi-offshore amateur sailor I am - I do not like the term "yachtsman" - prefers a map. On a map, rather basic mathematical tools allow me to establish and correct my course, to determine my position etc. This would not be the case with an even meticulous English description of the waters where I am sailing. Being a projection of a spherical surface on a plane, a map always involves deformations. But mathematical tools depending from the adopted type of projection - in non-polar navigation it is usually the Mercator projection - allow to effectuate the necessary corrections. Here again, English or Spanish alone would not be of much help.

On the other hand, in order to establish not a simple picture but a real map, the cartographer in turn needs mathematical tools, including differential geometry beginning with the famous ds, even if this ds does not exist in the physical reality.Let us now a bit of science fiction and imagine space-time relativistic cards destined for future and hypothetical space vessel diameter pilots traveling at a speed close to c. The establishment of these maps, necessarily computerized to be quickly accessible, requires the use of the imaginary number i, i2 = - 1, although the latter, by definition, in turn has no real existence.

For all these reasons I think that math have "something" that other languages do not have. Regarding the nature of this "something", there is a great mystery, and this mystery is in my opinion the main motivation for the present contest.

In my own paper "A Defense of Scientific Platonism without Metaphysical Presuppositions" (posted Feb. 25), I try - among others - to show that modeling of mathematics and modeling of physics by mathematics meet in both cases objectively given constraints and that this issue differs math from any other language and any other modeling procedure. In this connection my own paper defends a Platonic perspectiveand therefore a metaphysical position. But I try to show that any form of anti-Platonism is neither less nor more metaphysical than Platonism and that the latter is finally simpler and needs less (metaphysical and other) assumptions than its challenging theories, especially regarding the difference between existence within material reality and mathematical existence.

Your paper and mine diametrically opposed positions express. But boths papers have a common denominator: they refer to the concept of modeling. Since the purpose of this contest is a constructive confrontation of ideas about a mystery where, in absolute terms, no one may be right, I would greatly appreciate to know your comments about my own essay.

I would also like that this discussion could be continued for further, even after the closing of this contest.

With best regards

Peter Punin

    Peter Martin Punin:

    After reading this post and your essay, here is a few words that jump out at me.

    "For all these reasons I think that math have "something" that other languages do not have. Regarding the nature of this "something", there is a great mystery, and this mystery is in my opinion the main motivation for the present contest."

    I can explain this mystery. The many believe that math is the great and perfect descriptor of the all. Since it clearly fails, the many are dismayed, perceive a mystery, and search for some deeper meaning. There is none.

    In all of history, great leaders have gathered thousands of men and gone to war. Thousands on both sides in many battles have died. The great declare themselves the winner. Have those that died on the right side also won? It all depends upon one's point of view.

    All I am saying is that dependence on math does not automatically yield a correct description of reality. I am not questioning how it does it. Whether it is good or bad depends upon one's point of view.

    I have read your response and attempted to read your essay several times. Your education is superior to mine. I cannot extract understanding from the sophisticated language you use.

    Al Schneider

    Dear Al,

    You have presented the theme for this year's essay in a very entertaining and very informative way. In fact, if the remaining of the essay was as interesting and factual as the first five and a half pages, your essay would have been one of those to beat in this year's competition.

    The way you started by pointing out the scenes as the drama has unfolded was really good. Following that, your use of the parable of the "The King's Roses" to illustrate why math formula must correspond to reality makes the point clearly. This will spare us the various negative mass and negative velocities plaguing our physics today, which are the aftermath of the spell cast on our physics from Copenhagen.

    However, the euphoria I had from reading the early pages, reduced somewhat when in my opinion you went too deep into speculation in the latter part of the essay. For example, some things to ponder, if photons travel at c and are never at rest, how can they form a particle? Do they have an attraction force between them to bind them into a stable form? Your assumption does not take into consideration that light may be more of wave than particle. I will not tackle you on special relativity, which in my opinion you tried unsuccessfully to model. Special relativity cannot be modeled because it is not real, but as that is not the main focus of your essay, let me spare you the facts proving this (unless you want to discuss it on another forum on this site).

    Finally, under your Caveats, points of zero dimension are not a certainty. Indeed, in my 2013 essay I discussed the historical arguments between the Pythagoreans, Proclus and Aristotle on the one hand who held that the point had some minimum irreducible dimension and Plato who held that it was of zero dimension but not a "geometrical fiction". I continue on the same path in my essay this year, where I show that an infinite number of points on a line results in the kind of absurdity you demonstrated with your tale of the roses. I am sure you will like it because it contains things you have yourself pondered over and discuss in your essay. As a teaser, how do you propose to cut the kind of line on Deepak Chopra's hand as you mentioned, if the number of points are infinite and points are not things that are 'cuttable' into parts by definition?

    All the best in the competition.

    Akinbo

      Mr. Ojo:

      Thank you for responding to my essay. I am honored. I think you have pointed out that the beginning of my essay is on track. In viewing the second half you have pointed out what you think are flaws. In reaction to that, I would like to point out that when I talk of the things that are not modeled correctly, one would be the wave theory of light. In writing the paper I had considered addressing special relativity or the travesty of present understanding of light. I chose special relativity. I expect responses like yours and value it. Incidentally, the criticism of zero point particles was shown me by the director of a physics department of a significant university when I presented my idea to him. He didn't like my idea either.

      I will go take a look at your essay.

      Thank You

      Al Schneider

      Before I go however, I must point out that I wrote a book titled "New Age Quantum Physics" available on amazon dot com. It addresses the questions you have posed.

      20 days later

      Some time has passed. I have reread your essay. I am even more impressed. I believe your comment, "But questioning the foundations in this way is considered heretical, and is unpublishable in physics journals." is true. Then I believe, when the truth is out, there will be an earthquake in the physics community.

      12 days later

      Dear Al,

      I think it is impossible to disagree with your conclusion :) I don't think though that there exists presently any reason to rule out that reality ultimately is mathematics and the model that you speak about is too, so that we are just looking at self-similarities. I really like the focus of your argument though, it is well done. I wish you good luck with the contest,

      -- Sophia

        Dear Al,

        Your essay makes several sensible points to which I'd like to give the following comments:

        I agree that mathematics is a language which can sometimes describe things which are not real. It seems to me though that already in everyday contexts which seem rather far removed from mathematics. If you do me a favor and I say that "I owe you one", this does not prima facie have anything to do with math, yet it could be modeled as me being in possession of -1 favors from you.

        I think the real difficulty is that mathematics obscures when we transition from aspects of models that represent real things to those representation that already incorporate some abstraction because the transition is entirely seamless. To me, it is kind of like a slippery slope, in which the first abstractions are easily reconciled with our intuitions but are then followed by transitions to abstractions which are not so easily reconciled thus, Quantum mechanics being a prime example.

        In my opinion, at least part of the problem has to do with the expressive power of mathematics. The more expressive, the more likely it would be to serve as a language by means of which one can express models of reality that closely correspond to our intuitions about it. My own entry to this contest is an effort in this direction which, as far as I know, had not previously been undertaken, and the goal is precisely to find a way of expressing the standard formalism of quantum mechanics in such a way that it no longer clashes (at least as violently) with our intuitions.

        You devoted a substantial portion of your paper to a discussion of special relativity. I do not quite agree that "There is no model used to explain it. The claim is that understanding depends totally upon the math behind it."

        A book that is excellent for understanding it and which uses hardly any equations but only pictures is "Visualizing Relativity" by Lewis Epstein. I highly recommend that you peruse it. In fact, it stimulated me to write a paper on the foundations of special relativity that addresses one problem that his book unfortunately does not discuss, you might find that one interesting as well. It was my entry to the first FQXi essay contest:

        http://fqxi.org/community/forum/topic/329

        A version with minor corrections can be found here:

        http://deepblue.lib.umich.edu/handle/2027.42/83152

        Finally, I would like to mention a couple of corrections:

        "Given that a particle in this photon universe is a cluster of photons, an observer in this

        universe could identify a particle as his frame of reference."

        In a universe in which there are only photons, there is nothing to which a rest frame can be attached i.e. there is no physical object that corresponds to an "observer" (The problem is that observers are associated with a non-zero spacetime intervals i.e. they "age" while photons do not, so you cannot consistently attach a spacetime observer frame to a photon frame). So, while you can argue about the ability to mathematically represent such frames ( which I think is what you mean by "stationary states") it is not physically realizable, just like -400 roses. Different physicists seem to interpret this fact differently (an indication that this is not yet settled science). My view is that a universe with only photons in it is not a 3+1 Minkowski spacetime. Regardless of how you interpret this, I think any argument based on rest frame observations in a universe in which there are only photons is highly suspect, to say the least.

        "Then, present science today does not contain the concept of colliding photons."

        No, it does. The higher the energy of a photon, the more particle-like its properties. For gamma rays, the energy is sufficient that you can model photon-photon collisions. See, for example,

        http://en.wikipedia.org/wiki/Two-photon_physics

        What I see in your work is a call for taking a common-sense approach to modeling reality, in the sense of the opposite of what might be called a "blindly mathematical" approach, and with that I wholeheartedly agree. I hope you found my comments useful.

        Best wishes,

        Armin

        PS. I am a fellow alum of WSU (pharmacy) but I graduated quite a bit later than you did, and now I'm at U of M, completely immersed in physics, philosophy and mathematics.

          Dear Armin,

          Sorry for the length of this. I wrote a letter that occurs at the end of this post. Then, I went over your post line by line. Here are my thoughts.

          I am rewarded by your initial comments.

          [If you do me a favor and I say that "I owe you one", this does not prima facie have anything to do with math, yet it could be modeled as me being in possession of -1 favors from you."]

          Are we keeping score?

          [You devoted a substantial portion of your paper to a discussion of special relativity. I do not quite agree that "There is no model used to explain it. The claim is that understanding depends totally upon the math behind it."]

          This is not my claim. It is the claim of the literature I have read. That may well be limited. It is also the opinion of the Ph. D. physicists I have talked to about this subject.

          [A book that is excellent for understanding it and which uses hardly any equations but only pictures is "Visualizing Relativity" by Lewis Epstein. I highly recommend that you peruse it.]

          I did a search on it. Lot of confusion on the web about it. Finally found it for sale on amazon. Now I need to decide if I want to buy it. New, it is pricy.

          [So, while you can argue about the ability to mathematically represent such frames ( which I think is what you mean by "stationary states") it is not physically realizable, just like -400 roses. Different physicists seem to interpret this fact differently (an indication that this is not yet settled science). My view is that a universe with only photons in it is not a 3+1 Minkowski spacetime. ]

          I object to this. Bad English using something the reader is probably not aware of. Good writing would require naming the source as you have but demonstrate how the material applies to the subject at hand. I have successfully written a hundred papers on a wide variety of subjects that have been accepted by the appropriate audiences around the world. I am renowned in those industries. I do not use ambiguities such as this to impress my audience.

          [Regardless of how you interpret this, I think any argument based on rest frame observations in a universe in which there are only photons is highly suspect, to say the least.]

          This subject depends on how you define observer. In the context you select, (note that you select the frame of discussion then say, regardless) the observer appears omniscient. This is a drastic error. Note that I propose that the only material in the universe is photons. That includes the observer as well. In that context I propose an observer would be a particle consisting of whirling photons. Then, observation consists of photons moving between whirling clouds of photons. One observes using photons only at the position where one resides. To be able to observe the motion of photons at a distance is to be an omniscient observer. Any desire to be omniscient blows it all apart. Understanding this took me years to understand. I don't expect you to grasp it in a moment.

          ["Then, present science today does not contain the concept of colliding photons."

          No, it does. The higher the energy of a photon, the more particle-like its properties. For gamma rays, the energy is sufficient that you can model photon-photon collisions. See, for example,

          http://en.wikipedia.org/wiki/Two-photon_physics]

          Here I believe you are right. I did not want to open the discussion about photon collisions in the little bit I presented in my essay. I did not believe that suggestion would be acceptable. I did not want to ruffle too many feathers. I expected my presentation to be a hard sell as it was. Perhaps I was wrong.

          And now my initial letter.

          Dear Sir:

          I truly appreciate your post. Time will be required to study it. I scanned one of your documents quickly and noticed a reference to general relativity. I hope that is not used heavily in your arguments for I find the theory wanting. I find the concept of spacetime confusing and cannot wrap my mind around it. I suspect it is one of the victims of misapplying math models. While I believe special relativity is one of the most solid theories in existence, I find a flaw in general relativity. I see this when applying Feynman's QED to the meaning of light as it passes through space. Understanding his concepts crushes the expansion of space and warped space. I have published a video on YouTube addressing this issue. https://youtu.be/p0E5AWnYjys "Space is not Warped." The point is that photons move in straight lines from electron to electron. While a photon is interacting with the electron, gravity affects the electron and thus the path of the photon through it. However, when the photon is not interacting with an electron of matter, it is unaffected by gravity. Hence, general relativity is not wrong but its interpretation is slightly off.

          I must add my feelings to the presentation of special relativity in my essay. It only touches the significance of its meaning. This was not an idle study. I spent about two years examining the bit presented in the essay. I spent about three years attempting to explain my conclusions about that. With what is offered there, the math of special relativity unfolds. I believe if one follows the thread one encounters an explanation of what time and distance are. Then, a definition of energy and mass follows. From that the equation E = mcc falls out with ninth grade math.

          At one point I got out my Modem Physics book from college days and, beginning with chapter one, I paged through the book. With the turn of each page, the concepts that unfolded in my mind explained what I saw on the pages. As mentioned elsewhere, I have produced a book titled, "New Age Quantum Physics." It sells on amazon dot com. It details my path through this subject.

          Well, I guess I got carried away.

          I sincerely appreciate what you have offered and promise to study it.

          All the best.

          Al Schneider

          Dear Sophia,

          Thank you very much for your kind comments. However, I do not expect to place in this contest. The material presented by those here is of such a caliber and from such distinguished individuals, I feel small by comparison. I am very happy to present my ideas with the simple idea that people like you will read it and contemplate it a bit. In this, I am very honored.

          Al Schneider

          11 days later

          Dear Al,

          Thanks for your refreshing essay which I found well structured, easy to read, right on topic and very agreeable in content. I entirely agree your postulates, (and indeed demonstrate how maths can be misused in my own essay on the great red/green sock switch con trick!). As with most essays in this ilk it will doubtless be overlooked by the judges. I'm pleased not to have overlooked it and will score it very well.

          I'm certain you'll also like mine, and once scoring is over (quite soon!) I hope you may look at my recent past essays (2011 on) which I think are consistent with and achieve your own objective of a logical model incorporating SR (and now QM).

          I must also say I was greatly relieved the 2nd truck didn't charge the gardener to remove the first lot of roses!

          Best of luck in the last few days.

          Peter

          PS If you like physical models and have 9 mins to spare do check this out;

          Proposed resolution of Cosmic Redshift, CP Violations, Unification etc.. yes I know we'll agree it sounds crazy at first but "is it crazy enough to be correct?" (Bohr).

          PPS ..and I think in context Bohr was saying; look, it aint' logical OK, but it happens and the maths work.' (check out my last 2 essays and Academia paper).

            Dear Sir:

            I began to read your paper. I got excited and scanned it to the end. Then I have this intense desire to write you. When I calm down later I will study your paper closely. First, your point of view rings true to my ears. Second, I think I have an important ability to address this issue. I hope you don't mind my sharing it with you. I happen to be one of the world's experts on magic deception. I have studied it for over 40 years. I have written several articles and books on the subject for magicians. I have also lectured on the subject at most magic conventions in the USA and a few in Europe. The reason I bring this up is that magic is an art in which observers are to observe some reality and the artist is to execute some action totally different from the observed reality. While the result may not be magic, the observers are often unable to "explain" the event. Of interest is that often the observers have explanations. They are so weird and off track, they often credit the artist with incredible powers. (Sounds like the hype with QM.) I also happen to be a computer programmer. This again requires a talent to see one side of an operation, the user point of view and what actually happens inside the machine. My point is that I have trained myself over the years to observe events from two points of view.

            I began studying SR at the age of eleven. I believe that the above training and my studies has yielded an understanding of what it is all about. So, I stand as an individual amongst a thousand people that have authority on their side. This is why I am so excited to read your paper.

            Perhaps I am bragging. I have the idea that perhaps I can convince someone of the idea that observation and reality might be two different things.

            About polarization. I am not sure how to package this so I will just place it on the table. After studying structure for some years, I have discovered that photons move through space in a helical pattern. The length of one helix is the wavelength of the photon. Consider a spiral hitting a slit. The phase of the helix determines if the helix will pass through the slit. It also offers an explanation of the dual slit experiment. Also note that the equation of a helix is similar to a wave equation. In addition, if we scientists assume a photon travels in a straight line, its position will always be uncertain. This really goes on and on.

            Now, on to your work.

            All the best.

            Al Schneider