Essay Abstract

The story of physics and mathematics is the same great myth that is classic in every culture. Their mysterious connection is a story about the quest for a unified truth that must be derived from a world of duality. Physics is a quest for truth. It is a synergy of philosophy and mathematics, built on a solid foundation of measurement. Mathematics is a faithful process that uses symbols, like a wizard uses magic words, to give physics life. A mathematical equation models the process of life by separating a unified concept (with a symbol) into at least two equivalent yet different symbols. Thus unity symbolically separates into duality. Correct manipulation of the symbols is the trick that reveals truth, which in-forms physics and creates more questions. A physicist must be noble, with the highest degree of honor and integrity. He must be bold to submit new theories that may clash with the current paradigm. Yet he must be humble to submit if his theories fail the tests that ensure a firm foundation of Truth. He must be skilled in the use of mathematical tools and scientific weapons and he must be courageous and competent to handle the highly complex monstrosities that fill the literary forest. There are traps along the way. He will be tangled in paradox and confusion if he lacks philosophical insight and fails to rise above the flat perspective of duality. He will be tempted to force complex theories beyond the frontier of science for the sake of material rewards but the fate of the world depends on his integrity. As in every myth, there is an unlikely character who finds himself with a simple key and a mission to unlock the mystery. This essay will take you into and behind the scenes of the myth.

Author Bio

Theodore St. John is a retired U. S. Navy Radiation Health Officer who holds a dual degree in physics and EE, an MS in physics and a Ph. D. in Medical Physics. His career in the navy included 3 years in a nuclear submarine. He got out of the navy and received his M.S. after which he got back in the navy as a Medical Physicist. His graduate research was on analysis of oxygen implanted by recoil collisions in metal using Rutherford Backscattering Spectrometry and his doctorate dissertation was on geometric optimization of radiation therapy treatment planning.

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Dear Theodore St. John,

Thank you for your essay. It is a difficult essay to summarize or even understand all your points, but there are many very nice statements in it, beginning with

"He assigns a symbol that represents a concept, the simple truth, which can then be combined with other symbols to reveal other truths that lead to much deeper meaning."

Magical, isn't it! I also like your discussion on page 3 about "the secret to performing math..." That is very well done, concluding that "truths can be represented simultaneously as different and the same."

But, despite the power of the process, on page 5 you observe that the injured Albert "became more and more tangled in the web of complex math." Amen. But it produces golden grants and special privileges so, as you note "disparages those who appeal to simplicity..."

Your essay is full of nuggets, and ends with a line that I can agree with.

I invite you to read my essay and comment on it.

Best regards,

Edwin Eugene Klingman

    I am terribly sorry. I meant to use Dear Dr. St. John and I missed seeing that I had used a capital F and not a capital D.

    Ruefully,

    Joe Fisher

    Dear Edwin,

    Thank you for reading my essay and posting comments. I understand that the essay is not an easy one to summarize, but I am happy that you seem to "get it". I expect that there will be plenty who won't get it, so it is very encouraging for me that you, as the first reviewer, had positive comments. Most of the concepts that I discussed came to me over years of contemplation and introspection, and I hope that readers who don't get it in the first read will allow the process to unfold in their minds rather than discard them due to the unconventional approach.

    Respectfully,

    Ted

    Dear Joe,

    Thank you for reading my essay and posting comments. I must admit that I was a little chagrin about your first sentence, "I thought that your abstractions-filled essay was utterly incomprehensible". I couldn't decide whether your comment was about the essay or about your view of reality, which naturally affects one's ability to comprehend other ideas. But the fact that you wished me well and only had one minor quibble was encouraging.

    You said that both physics and mathematics are incomprehensible to you because they are both unrealistic, which to me is similar to Einstein's comment that "all models are wrong, but some are useful." That too is in agreement with my point that equations trap one in a shallow perspective.

    My goal is to have as many readers as possible, so I hope that readers decide to read my story despite the connotation of "utterly incomprehensible". Perhaps they will take it as a challenge. Keep in mind that the guidelines for the contest emphasized "Original and Creative: Foremost, the intellectual content of the essay must push forward understanding of the topic in a fresh way or with new perspective." Also keep in mind that "pushing forward understanding" does not necessarily mean reinforcing the current perspective.

    Your comments about what you can prove to be real might also be interpreted either way. But a key point you make, that "Real structure is unique, once" makes me think that you are reiterating my abstract way of describing the subatomic microcosm.

    Also, I wouldn't say that "abstract mathematics confounds reality." Instead I'd say that the complexities that we find in reality (e.g. every element in the periodic table is more complex than the previous) can hide the underlying simplicity. Because math attempts to model that complexity, it too is subject to the confounding process. Math is not the problem; it's the interpretation of the results that can lead us to our demise.

    Respectfully,

    Ted

    5 days later

    Dear Sir,

    The narrative suggests your command over linguistic proficiency.

    In mathematics, "Moving a symbol to the other side of the equation requires it to be represented as its opposite: it's negative". However, physics is guided by causality, where the left hand side represents the initial state and the right hand side the final state mediated by the equality sign specifying special conditions to be met for the reaction to take place. For example, you cannot write ¤â(q)¤â(p) ÔëÑ h/4¤Ç as ¤â(q)¤â(p) - h/4¤Ç ÔëÑ 0. It is meaningless. Manipulation of mathematics without putting correct values leads to misguided results.

    Mathematical reality is the quantitative aspect of Nature, which is logically consistent - hence unchanging - and harmonizes with other aspects. But the problem arises when we try to manipulate them. In one of the essays here, the final equation is consistent with the figures given. But if the same sets of figures are applied to the initial equations, it shows 1200 = -1250. The author has not cared to reply to our comment. With such basic flaws, even if the final equation turns out to be right, the theories become questionable.

    There is a need to review and rewrite physics and un-mathematical mathematics. We have discussed these in our essay.

    Regards,

    basudeba

      Dear Basudeba,

      Thank you for reading my essay. I understand and agree that there are certain operations and reactions in physics and chemistry that occur in one direction and not the other. And there are symbols that convey that process. However, I was not addressing these in my essay. I also did not mention inequalities, which certainly have their own set of rules. I was strictly referring to the concept of equivalence.

      Respectfully,

      Ted

      Dear Sir,

      We have discussed relativity and equivalence principle in our essay. You are welcome to visit.

      Regards,

      basudeba

      Hi Ted,

      A simple, easy to read and hilarious way to paint the current sad situation that our physics has found itself. Well done.

      Among the memorable words, "Mathematics has given physics its great success but it is the very same thing that will lead to its demise". In the light of this, as you discussed Calculus was invented to sidetrack the curse of Zeno. I will therefore say that in a way, "Calculus has given the physics of Motion its great success but it is the very same Calculus that will lead to the demise of our fully understanding the phenomenon".

      You may wish to comment on my suggestion how the curses of Zeno and Parmenides that (in my opinion) still plague our physics may be resolved since you appear to be familiar with both the philosophical and mathematical arguments.

      Best regards,

      Akinbo

        Hello Akinbo,

        Thank you so much for reading and commenting on my essay. I am glad to know that you appreciate the way I presented. It certainly does seem sad that physics has come so far only to be caught up in its own web of complexity, but I honestly think that this is the way the natural process works. And fortunately, as foretold in mythology, (and noted by Thomas Kuhn) the crisis sets the stage and the mood for the right spark of information to set off a revolution in science. I think the crisis has to run its course because it gives humility to those extremely smart people who have the power to break the spell and save the world.

        According to Mythologist Joseph Campbell, those who know how to break the spells -- those who know that there is even a spell that needs to be broken -- don't have the power to break them. The more knowledge they gain, the more confident they grow, the less willing they are to open their minds to other wisdom, and the stronger the spell becomes.

        In fact, the line you mentioned is almost exactly what Merlin the Magician said in one of the King Arthur tales. As I interpret it, the story of Merlin's death represents the trap created by our magical ability to define opposites and illustrates how the two sides of reality can be pitted against each other. In that story, King Arthur's sister, Queen Morgana le Fay, who represents the shallow material world of measured reality, recruits a "damsel of bewitching beauty," named Vivien, which I see as science and technology. They provide the enchanting lure of physical pleasure and comfort. Vivien gets Merlin to teach her the magic which she eventually uses to paralyze him. Merlin said, "I grieve not for my own undoings so much as I grieve at the folly that hath turned mine own wisdom against me to my destruction."

        I have downloaded and will read your essay soon.

        Ted

        I left out a couple of sentences in my comment above. After the sentence:

        "According to Mythologist Joseph Campbell, those who know how to break the spells -- those who know that there is even a spell that needs to be broken -- don't have the power to break them." I should have said:

        Those who do have the power to break them (the renown physicists who define the "authorized version" or standard model) do not know or do not accept the notion that there is a spell to be broken. The more knowledge they gain, the more confident they grow, the less willing they are to open their minds to other wisdom, and the stronger the spell becomes.

        I fully agree to this view: Those who do have the power to break them (the renown physicists who define the "authorized version" or standard model) do not know or do not accept the notion that there is a spell to be broken..., and the stronger the spell becomes.

        However, history shows that it is the eventual fate of spells that sooner or later they are broken. We can only hope that it is sooner so that our physics can make more rapid progress.

        When you eventually read my essay and the contained hypothesis I would prefer you to show its impossibility rather than accept as possible, out of trying to be polite.

        Regards,

        Akinbo

        Thanks for your comments over at my essay thread/ blog.

        I agree fully that by removing zero length or displacement from your model, you create a near perfect alibi to escape at least one of Zeno's paradoxes. But alibi are not always perfect, so let me interrogate your alibi a little:

        - Is length infinitely divisible in your model? How many positions lie on a given length between Atalanta and his destination? In moving on that distance, must Atalanta traverse all or only some of the positions therein?

        - You rely a lot on Special relativity and Lorentz factor in your model. Is SR infallible? Do you really know what the postulates of SR mean? If so, can you state them and answer questions on them? Perhaps, the dialectic on this is better done on another forum like 'Faster than light', 'Real-Time physics' or 'Ripping Einstein Apart' instead of on your essay thread. Your choice?

        Regards,

        Akinbo

        12 days later

        Dear Theodore St. John.

        Thank you for taking time to decode my essay; it was only an experimental writing, like a Gedanken experiment in the writing, to show that a story is nothing more than transfer of ideas; and it is not important the temporal order of a speech.

        I am thinking that a speech is like a physical experiment, with a temporal order, if there is not much interaction between parts of speech, then it happen like in the fundamental physical processes (time symmetry).

        I had thought of something more elaborate, a random distribution of the proposition (that work like a cinematographic flashback), but somehow the writing form reinforces the idea that it is not necessary a teaching linked to the history of scientific discovery (temporal order), because alternatives are possible, and the meaning is not lost (civilization can exist in which scientific discovery has followed alternative ways).

        I read your essay, and I see the Pythagorean school more like a religion, if not a cult, mathematics so that there was historical heresies, and this does not happen in physics.

        Your writing is interesting, a good experiment, and Einstein has in the name the legend of King Arthur.

        The equal sign is a new symbol, invented in 1557 by Robert Recorde, the zeros was invented in the 628 by Brahmagupta, before was a chaotic life for mathemaricians, but mathematicians existed, then the current equations were not so necessary.

        It is interesting that we are free to choice a definition of time evolution, then every motion has instant velocity unitary

        Respectfully

        Domenico Oricchio

          Hi Domenico,

          I appreciate your response. And thank you for explaining your intent. It's an interesting idea and yes, I can see how points in a speech can be compared to physical points in terms of interactions and temporal symmetry. However, I think that this only applies to the most elementary points since interactions (processes) do occur and the processes have more meaning than the facts. Facts are simply facts, so temporal order is irrelevant, but facts are what people tend to hold onto with devotion. The historical order of scientific developments, on the other hand, reveals patterns (analogous to a puzzle, discussed by Thomas Kuhn in The Structure of Scientific Revolutions) and patterns themselves hold meaning. Many new discoveries are made by finding the pieces that fit the anomalies. Anomalies are the holes in the tapestry and without the previous steps, or with different previous steps, the hole may look different; so the interpretation of its meaning may be different. On the other hand, the differences may only be different parts of the tapestry and as long as the patterns are eventually found, we end up at the same place (the golden ring). One path may just be more or less painful than the other. That's what the mythological journey is all about.

          The fact that the equals sign was "invented" in 1557 is an interesting tid bit of history. That was about one generation before Isaac Barrow, Newton's predecessor, was born so it fits well with my story. And it is a good example of a simple fact that doesn't change the pattern I was trying to convey. The choice of symbol (or combination of symbols) used to represent a particular meaning doesn't alter the point of the story. Prior to defining the parallel line symbol, mathematicians used the combination of symbols, "is equal to", which even non-magicians could understand. The new symbol made it easier to write but also served as a metaphorical brick in the school of magic/mathematics.

          And I don't doubt that the Pythagorean school was like a religion. But then some will argue that science has become the same thing; they call it scientism. Physics is based on certain assumptions that stand firm as paradigms that well-established physicists will defend religiously. Anomalies that lead to crises bring out new ideas, which are often considered heresies (See http://www.scienceheresy.com/). In fact, I read an article about a year ago (I wish I could find it now) that was about how science has become a religion. The author referred to another article in which one physicist literally called another a heretic. But heresy is just "any provocative belief or theory that is strongly at variance with established beliefs or customs" (http://en.wikipedia.org/wiki/Heresy) Without it, science would not progress. I think the current crisis in physics is the result of the assumption that there was a beginning to the universe. If time is nothing more than a scale, then the universe is timeless and regardless of the measurements that have been interpreted as evidence of a beginning, a timeless universe does not have a beginning. That's my heresy.

          Ted

          9 days later

          Ted -

          Thanks for a great essay! It was a pleasure to see someone else look to mythology for some answers (or perhaps, should I say, non-answers). I took a more direct approach, ealing with creation mythology. For me the questions of paradox are quite central. I am not, however, sanguine about new magicians coming forth to break the spell.

          Cheers - George Gantz