Dear Roger Schlafly,

Your focus on the significant difference between math and physics is very well done, and your choice of examples, 'randomness' and 'infinity', is excellent. I do not believe infinity has meaning in the physical universe, so I've never worried about the 'rigorous' math of infinity.

I also like your "Randomness does not explain anything", and your summarizing physicist's different views about randomness.

But you state that "Bell's theorem showed that quantum randomness cannot be simply a random sample of deterministic local hidden variables." Yet, in my current essay I show a local model constructed by randomly generating 10,000 spins for each of 300 choices of field orientation by Bob and Alice and the model's deterministic treatment of these does produce the quantum correlation -a.b that Bell claimed to be impossible.

Bell used correct mathematics describing an incorrect (because oversimplified) physics. I very much hope you will read my essay and provide feedback to me. I do not deny "randomness" in the universe as I do believe in free will. And chaos and noise are effectively random, but the model I present (aside from Alice and Bob's freely willed choice of orientation) is deterministic.

Thanks also for your informative overview of positivism.

Finally you're not the only one in past essays to remark that mathematics and physical realities are different, (although I do not in any way accept that math is a Platonic-like 'separate' reality.) My 2013 essay "Gravity and the Nature of Information" focused on this theme. In fact, all my essays view math as "derived from" physical reality. And I do agree with you that fundamental physics is not perfectly describable by mathematics.

My best regards,

Edwin Eugene Klingman

    Thanks. Maybe you have a new or better interpretation of Bell. I'll read your paper. I was just summarizing Bell. He defined a model with local hidden variables and showed that it made predictions different from quantum mechanics. That is all I was saying with that sentence.

    This is the first time I have written an essay for one of these contests. As I approached it, I assumed most would believe math and physics are somewhat the same. In my essay "Modeling Reality with Mathematics" I express the idea that math is somewhat like English and is just a descriptive language. In that sense, the description can be in error although mathematically rigorous. In your paper I perceive that you describe math and physics as two different things. I am comforted by this. I find your other points interesting but will need time to absorb them.

    Al Schneider

    Dear Mr. Schlafly,

    What an interesting essay, you mentioned: "...In short scientists believe that they are finding truth, and philosophers deny that it is possible...", I agree to your argument, to understand something, one needs to see the broader picture not just some details. I also saw your book "How Einstein Ruined Physics" and I invite you to see my essay from 2013,

    http://fqxi.org/community/forum/topic/1769

    You are also welcome to read my current essay that also highlight some aspects that you mentioned.

    Warm regards

    Koorosh

    Dear Mr. Schlafly,

    Long back, I was reading an article discussing: Infinite set of Natural-Numbers is smaller than the infinite set of Real-Numbers......some 8-10 page article, which I stopped reading further, because in my opinion, infinite is not a number, rather it is an 'expression of our inability to count or measure further'!

    And 'random' means UN-describable using available theory! In my opinion even quantum mechanics can not be fundamentally in-deterministic.

    What is your opinion?

    With my best regards,

    Hasmukh K. Tank

    Dear Roger Schlafly,

    In your essay you write, "Mathematics and physics have one big thing in common. They both search for objective truths. Beyond that, they have little in common. Math uses the methodology of logic and proof. Physics uses observation and experiment. ...

    By mathematics, I mean rigorously proving theorems from axioms, as in typical math journals. By physics, I mean explaining the fundamental causes of nature, such as energy, motion, and force. ...

    Sam Harris writes: If determinism is true, the future is set -- and this includes all our future states of mind and our subsequent behavior. And to the extent that the law of cause and effect is subject to indeterminism -- quantum or otherwise -- we can take no credit for what happens. There is no combination of these truths that seems compatible with the popular notion of free will. [Harris] ...

    ... consider the use of infinite numbers. Mathematics uses them all the time, with the infinity of primes being one of the oldest theorems. But it is debatable whether any true infinities occur in science. Measurements always give finite values. Some physical entities are often thought to be infinite, such as the density of the center of a black hole, the unrenormalized charge of an electron, or the size of the universe. But none of these examples is very convincing, and many physicists are content to regard infinity as just some mathematical fiction.

    ...The 2011 FQXi essay contest asked, "Is Reality Digital or Analog?" The answers accepted the premise that reality had to be one or the other, and no one admitted the possibility that it might be neither because both are mathematical. [Schlafly] I could be wrong, of course, but I seem to be the only one to have seriously considered the possibility that fundamental physics is not perfectly describable by mathematics. I was influenced by a logical positivist philosophy that embraces a logical view of mathematics, and an empirical view of science. To me, these views are so different that it would be bizarre if one were completely reducible to the other."

    I object to your characterization of the essays by the 2011 FQXi essay contestants. In an interview Francis Crick admitted being a reductionist but denied being a "caricature of a reductionist." What do infinity and measurement really mean? According to Virginia Woolf, "Nowadays it is easy enough to invent new words -- they spring to the lips whenever we see a new sight or feel a new sensation -- but we cannot use them because the language is old. You cannot use a brand new word in an old language because of the very obvious yet mysterious fact that a word is not a single and separate entity, but part of other words. ... words do not live in dictionaries, they live in the mind." How can the human mind be accurately described? If it can be done, my guess is that accurate description of the human mind would require superhuman intelligence. Words and formal symbols cannot be satisfactorily described and therefore mathematics and physics cannot be satisfactorily described. Whatever an "empirical view of science" might be, I claim that Milgrom is the Kepler of contemporary cosmology based upon empirical evidence accumulated by Milgrom, McGaugh, Kroupa, and Pawlowski, -- D. Brown

      What is your objection? Do you have some quote from one of those other essays that is contrary to what I said?

      Your quest to circumvent mathematics and physics goes cycling on a very long road!

      Great luck!

      Kind regards,

      Miss. Sujatha Jagannathan

      Roger,

      I like the stance your essay attempts to consider in the opposed view that Mathematics and Physics are separate entities. Logically we may assume the correlation of Mathematics and Physics aren't unified concepts because we have not understood fully certain aspects, but then again, we must also consider at our "current state", regarding the appropriate interpretations and understandings of Physics, we simply did not discover the "proper model" of describing nature and perhaps this is fundamentally the reason why we have not found unison within these separate disciplines.

      It is my strong conviction and belief, once we find the appropriate laws describing nature we will also find these separate disciplines describe the same reality- the concepts and beautiful truths regarding the observable and detectable existence of nature itself.

      Best Regards,

      D.C. Adams

      Dear Roger Schlafly,

      While you wrote "How Einstein Ruined Physics", Thomas Phipps ruined Einstein's mystic theory. I acknowledge your effort to at least put together different opinions of philosophers, physicists, and mathematicians.

      For my taste, you are a bit too much reflecting the mainstream of the latter.

      You wrote: "The mathematics is air-tight [within Cantor's paradise of course], and not subject to debate" and "The Newton-Leibniz discovery [from the word discovery I infer you are a Platonist] of differential and integral calculus was simultaneously [sounds like just by chance] a huge advance for both fields." If things are so simple then you might judge my essay fundamentally wrong.

      I don't understand the word BUT in "Most philosophers ... agree that causality is crucial to all sciences except physics, BUT the big majority [of them?] say that causality has no role in fundamental physics.

      Perhaps, a reference could clarify.

      If I understood you correctly, you consider yourself a positivist while not an anti-realist.

      Maybe, I am not someone serious if I too don't exclude that fundamental physics may evade perfect mathematical solution to all imaginable questions.

      In so far, I support your main idea.

      Kind regards,

      Eckard

        I supplied one reference -- the book edited by Galavotti. I will try to post another.

        I have thought about things in your essay beyond the disconnect between math and physics. I find your explanations of infinity and randomness very valuable. I do not consider them your opinion but statements of fact. I am lost in the philosophy discussions. I offer some points because the above has become part of my knowledge base from which I view the universe.

        Thank You

        I found your 2013 essay, and I notice where you said: Korzybski, in Science and Sanity1, claimed the distinguishing feature of sanity is the recognition that "the map is not the territory".

        That could be construed as saying that math and physics are different.

        Very interesting. But, so what? How is the dilemma of any thing in the world to exist when it does or does not. I believe in Chaos where chance is supreme. In the 2012 contest, "To Seek Unknown Shores" I was criticized because there was no focus. In my thinking since, I realized a model would be helpful to resolve all the pluralities that exist. "Duality, The War for Existence", should be ready to submit by March 1 or 2. I am making it merge my expertise's, which includes swimming, geometry, and thermodynamics. ....and a big of Yoga from my roomie. It applies to the action of all things from photons to electrons, electrons to protons, ...molecules to animals, etc.So far so good. It is an attempt to define "panpsychism" as action(s) of all.

        Thanks for your essay. I follow these contests because there usually are 3-4 papers with something interesting to me. Yours is one such paper. I'm finishing a study about the double--slit experiment and am beginning to search for the next project.

        What do you think about the following for discussion?

        (1) Would you classify the group models of particle classification the same as you classify statistical analysis. The periodic table was developed first by noting common characteristics of elements. A few holes were filled (predicted) by where the hole was in the classification scheme. Later, the causal underlying structure of atoms explained the periodic table. Indeed, the position of an element indicated something about the atomic structure. The same type of classification is true for the group models. Can this be used to imply an underlying structure of particles? How would such a study proceed? Is anyone working on the structure of particles (papers I see seem to stop with the group description with no indication of an underlying structure)?

        (2) You stated the statistical approach like in thermodynamics could be used to measure and predict when an underlying causal model is lacking. But could the parameters in the statistics be used as causal physics? For example, the Schrodinger equation is viewed as a probabilistic (`shut up and calculate') version of quantum mechanics. My view of the double slit experiment started with the postulate that the wave function was a real wave in a `plenum'. It worked. The sticking point was what creates the wave in the postulated plenum. The answer is the same thing that causes waves in General Relativity - matter. This view has the advantage of providing correspondence to the Big Bang model and to Quantum Mechanics. The advantage of this causal model is that more is explained and predicted with less. Here, the big is linked with the same causes as the small.

        (3) We may not be able to define truth much less know when we have found it. But we can determine if a model predicts observations or not. Or better, we can determine if a model predicts an observation within some zone of applicability. I think physics and philosophy can unite with this view. They each are looking for some model to predict outcomes of decisions. A philosophy that is inconsistent with future events is soon discarded. The same is true for religions.

          On (1), quarks were discovered like you describe. Protons, neutrons, charmed particles, and others were arranged into patterns. Properties were deduced by where they were in the patterns. Quarks were introduced as an underlying explanation.

          I know that. It what I had in mind. What about the questions? What about any implications of structure?

          Dear Roger Schlafly,

          I agree with your view that physics and mathematics are two separate branches of knowledge - physics is physics and mathematics is mathematics. However you have not mentioned whether mathematics has any role in physics. Do you think mathematics has any special role in the domain of physics (other than for measurements)?

          Dear Roger,

          You have brewed a sweet mix of philosophy, mathematics and physics.

          In your conclusion, you said, "While they both (i.e. physics and mathematics) agree that 2+1=3,..."

          I argue that this statement while true most of the time is not always so. There is an underlying, unstated assumption present in the statement, that whatever exists cannot perish. This is what I called the Parmenidean curse afflicting our physics and mathematics. Let me illustrate this curse...

          If you want to demonstrate the truism of the statement 2+1 = ?, you put two apples in a bucket, then you add one more and finally count how many apples in the bucket. If you count three, then you write 2+1=3. If you count 4, then you write 2+1=4. If you count 2, then you write 2+1=2.

          Now if existing things can perish contrary to the Parmenidean theory, and after all as I argue in my essay, cosmology says our universe can perish, then 2+1 may not always equal 3, especially at the quantum scale. If an atom perishes from the apples we are putting in the bucket, 2+1 will still equal 3. One atom perishing out of the billions in an apple does not affect the existence and identity of the apple. However, if what we are putting in the bucket are atoms, i.e. 2 atoms plus 1 atom = 3 atoms, noting that you mentioned radioactive decay in your essay as well, we cannot be sure any longer that when we count 1+2 will equal 3. It could be less, or if there is quantum fluctuation it could be more.

          I don't know how to make myself clearer. But you are welcome to seek clarification, if necessary.

          All the best in the competition.

          Akinbo