Than, this is a very smoothly written essay that makes some nice points.

I like "What quantum is to classical ≈ what analogical is to rational" You use the idea of analogy to make a deeper analogy, very good.

I also take to heart your point about the central rolw of Planck's constant.

    Hi Than,

    I have just read your essay. I must admit that I don't think I understood it very well. It seems that your argument is that because the action associated with quantum systems is usually only a small multiple of Plancks's constant-as opposed to that associated with classical systems for which it is usually much, much larger-the kind of approach to understand what quantum mechanics tells us about reality is not to be based on reasoning but on "analogy" where the word in the sense that you are using it implies certain characteristics such as an automatic recognition of certain dualities that occur in QM as being similar to a multitude of other dualities that occur in our experience.

    This argument would make more sense to me if some of the mathematics of quantum mechanics were "fuzzy" or not amenable to the usual methods of mathematics. How do you arrive at, say, the Kochen-Specker or Bell's theorem in terms of an analogy *without already knowing that they are true?* Here I mean both realizing that they are true as well as being able to supply the proof that they are true without utilizing the methods of reasoning.

    Also, "analogy" as you presented it to me seems to imply a certain level of imprecision. Sure, I can immediately recognize a friend under bad lighting, but if I were presented with the same situation many times, I would probably make mistakes every once in a while. You could argue that this is analogous to the imprecision in our ability to predict, say, where a given particle lands on a screen. However that is an imprecision in the theoretical content of quantum mechanics, whereas I am referring to an imprecision in the structure of the theory itself. Quantum mechanics (possibly with the exception of the collapse postulate) is very precisely defined. If the structure of the theory was more naturally suited to an "analogical" view, shouldn't we expect it to be a lot less well-defined? I grant that analogies can sometimes help us grasp certain concepts in a way that is beyond reasoning, as you use that word. But to me, they seem complementary not mutually exclusive, even when it comes to understanding quantum mechanics. Besides, analogies usually don't map exactly to the things for which they are meant to be analogies, and to that extent they may be misleading or confusing.

    I don't think it is impossible to build a "calculus of analogy", but I think that you will need to have more to show for it. As it stands, most if not all the insights about nature at the small scale were derived by reasoning, and characterizing these in terms of analogies seems post-hoc.

    It would be interesting if you could construct a para-mathematical language based on analogy, but this sounds like a life-project to me, so I'm not sure you'd want to do that.

    I hope you found my honest feedback useful.

    All the best,

    Armin

      Dear Armin

      First and foremost, I want to thank you for taking the time to read my essay and making suggestions for improvements. I am grateful, and to tell you the truth I actually wish for someone to demolish or eviserate the thesis so that I can fight back with gusto!

      With that preamble, allow me to restate my thesis: The Planck constant as a Mother of All Dualities is a conclusion from my premise: "What quantum (wave) is to classical (particle) is similar to what analogy (fuzzy thinking to many people) is to reasoning (generally with math and logic in the sciences, especially so in physics). Here I may have jumped the gun by not explaining clearly that: (1) Fuzzy analogical thinking comes before rigorous, logical and mathematical reasoning, as quantum is to the classical, (2) Analogical thinking is complementary to reasoning as quantum(wave) is to classical (particle), (3) The analogy-reasoning duality face the same problem of "measurement" as in the case of wave-particle. When we use analogy, we make the supposition that two things that are different are the same, as in Schrodinger's thought-experiment of superposed alive and dead cats. (I believe that quantum measurement problem will dissolve itself once we accept Planck constant as the reason for being of wave-particle duality.)

      Concerning questions from para 1 of your Comment. I understand that in some quantum mechanical circles, small or low multiples of Planck constant is considered to be the regime where quantum rules apply, whereas its opposite the high multiples is the regimes where classical rules apply. I did not use that particular viewpoint. What I use was a thought-experiment in which I envisioned the image of cell division as a prelude to diversification requiring necessarily of energy consumption. In other words, I asked how does one thing becomes two. What is the theoretical minimum of energy to affect such separation or diversification? By interpolation of course, i.e. high becoming low and low becoming high. Having some knowledge of quantum theory, I say it must be the Planck constant. If I had no knowledge of quantum mechanics, I'll stop short with the notion of a theoretical minimum. In quantum mechanical context however, Planck constant was discovered when Planck made the interpolation between low- and high frequency regimes of black-body radiation. We all know how many years it take for quantum theory to come to terms with the idea of wave-particle duality that has its origin with discovery of the Planck constant. I do not have time to do the proper research, but I had a feeling that we have not fully understood the full meaning of the quantum, wave-particle duality, or the problem of quantum measurement.

      Concerning the question "How do you arrive at, say, the Kochen-Specker or Bell's theorem in terms of an analogy *without already knowing that they are true?*". Within the framework of analogical model that I described in the essay, I know there's a duality between connected (global) and not-connected (local), i.e. I will have known that there are analogical relations between connected-not-connected, wave-particle, same-difference, etc. etc. If any one of these dualities have issues, I will assume that the rest will have also. The new layers of mathematical sophistication as provided by Bell and later contributors have enriched our understanding of these theorems you mentioned, but the resolution of the real issues -- the nature of reality, the superluminal or not, the spooky or not spooky - have not come to accords. I've heard people say Bell had proved quantum global nature. Didn't we know this facet of quantum story from other means, such as by analogy with wave-particle.

      Concerning the question from para 3 of your Comment. I do not understand the full scope of your question from para 3, especially the statement "Quantum mechanics (possibly with the exception of the collapse postulate) is very precisely defined." As I understand it, QM is defined mathematically (precisely?) by a wave function or by vectors in Hilbert space, but its essence is superposition, which is another name for sameness in my book. Superposition now dressed in math still needs to be decomposed by measurement, although we have yet to get some kind of consensus on this topic. Even the derivation of Born's rule is in contention, although the formula works fine in practice.

      I agree with you that "analogies usually don't map exactly to the things for which they are meant to be analogies, and to that extent they may be misleading or confusing." To wit, analogies are efficient for first forays into the unknowns, and for a person with good solid experience, they are no more error prone than reasoning. After all, analogy and reason are not absolute strangers, but members united by a single constant of Nature. Like wave and particle!

      I like to argue with your assertion about analogy being post-hoc. I just happen to think it is ad hoc! I love your term "calculus of analogy", but it is a project of life-size dimensions! And most importantly, I do not have the talent or the inclination.

      Likewise All the Best

      Than Tin

      Dear Than,

      Thank you for you excellent, highly relevant and very original essay. A pleasure to read.

      I liked you 'White Cliffs' analogy (I live in Kent UK) as it's always the aspect we look or approach from that provides the limits to what we observe.

      Interestingly our essays deal with the same subjects from quite different approaches, but find some 'unity in hidden likenesses'; i.e; a "quantum theory without the sobriquet of weirdness", definitions of what a 'bit' is, then also 'detection' and 'measurement', which considers how the brain as a 'processor' arrives at 'outputs', and certainly 'duality', where I look at 3D physical forms right down to the Planck length offering a simple explanation.

      Our essays then consider precisely the same critical parts of nature, but while standing in different places, so when combined the truth of the whole may be greater than the parts. That alone certainly earns a high score from me, I hope you will find the same of mine. I explore a little further into that uncertain zone to find rationality, and show how the EPR paradox (Bell inequalities) may be resolved via rational duality without spookyness or FTL.

      I really do hope you can read my essay and will be interested in your comments.

      Well done and thank you for yours. Very best wishes.

      Peter

        Dear Vladimir

        Here are some of the places from your essay where we are on the same wavelengths:

        1. "Reality may be like that at fundamental scales where its physical and informational content can be regarded as one and the same thing."

        2. "This chicken-and-egg Question was asked because everything looks like a nail to a person holding a hammer. Surrounded by our computers in this Information Age, we are tempted, as Wheeler was in his It from Bit essay to regard the physical universe-IT- in terms of BITs - binary 0 and 1 answers to yes-no questions."

        3. "One that I already answered elsewhere is whether Reality is digital or analog ?- it may be a bit of both. The second topic making up the substance of this essay concerns the necessity of examining our philosophy of knowing. How do we know what we know about Nature?"

        5. "The human brain evolved over millions of years from primitive cells made of molecules that are identical to those making up the rest of the Universe."

        Because of differing life experiences, we put our thoughts in different styles. But the important thing is our essays are much alike. Nature is tolerant when it comes to styles, but stern when it comes to substance.

        Best Wishes to You Too!

        Than Tin

        Dear Peter

        I have downloaded many essays from the contest, yours being one of them. I tried to be dutiful by trying to read every essays, but I find it hard going when those essays contain concepts from advanced logic and maths. However, I promise I will struggle on until the dead line of July 31st.

        Very Best Wishes to You too.

        Than Tin

          6 days later

          Hi Than,

          Nice work and I rate it highly.

          I particularly like your ending paragraph:

          One can only marvel at what a small constant can do, creating an impersonal cosmos of unimaginable dimensions out of nothing as it were, while not forgetting to populate a corner of it with conscious human beings like us, brimming with desire to know what it is all about.

          I too have this notion, take a little time and space, then add a little h, shake it consciously and you can make anything!

          Thanks for visiting my blog,

          Don L.

          Thank you Than

          You left an interesting note on my page concerning Feynman and simplicity, and you also summarized by example your analogical argument. Yes it is amazing how we can express different ideas in physics in very different mathematical models. I have noted that independantly too long ago during my diffraction research - but I think it is important to hold on to the idea that some of these models are 'closer to nature' than others usually the simpler ones are the ones!

          Your analogical arguments are a sort of clever intellectual exercise to categorize various ideas in physics. I see nothing wrong in that per se. I am not against that - but when you do that it creates artificial divisions. Some of us are trying to unify physics to show, for example, that both classical and quantum ideas are causal, linear and local. If that is so, i.e. if quantum phenomena are not actually probabilistic at heart, and if there is no duality, then putting these ideas into an analogical mold becomes unhelpful.

          Of course it it all depends which aspect of physics one is working on. I wish you the best.

          Vladimir

          Dear Than Tin,

          Thank you for reading and commenting on my essay. I like your enthusiasm and your explanations reach out to a wide audience. I think the analogy approach is good, after all we use them to describe the quantum world all the time. I remember my Chemistry professor explain duality as throwing a ball at a wall - in the quantum world, half the ball passes through the wall, half bounces back. But once we observe which, then this is the single result.

          Anyway congratulations on a super essay - I think you deserve to be higher so I hope my high rating helps.

          Best wishes,

          Antony

            Dear Than,

            I am fully agree with Fenman's genius observation (and with you also) that everything must gone to one general principle, which may be not so complicated to comprehend. Einstein, Schrodinger and others luminaries also has came to analogical/similar conclusions. The same thing saying me also in my work, and not only because to much famous people saying this.

            There are a lot of weighty arguments on this direction, and anybody, who has the healthy brain, may to came to this idea. So, you and me can be happy - with correctness of our viewpoints and (with our healthy brains too!) I have rating your work on high core, and I thinking suggest it to my attherants also.

            Best wishes,

            George

              Dear Than,

              Following your post on my webpage

              I found an excellent link to your topic

              http://en.wikipedia.org/wiki/Analogy

              As a fun of group theory, the analogy/isomorphism is especially important.

              Also in category theory that starts tobe widely used in quantum mechanics

              "Category theory takes the idea of mathematical analogy much further with the concept of functors. Given two categories C and D, a functor F from C to D can be thought of as an analogy between C and D, because F has to map objects of C to objects of D and arrows of C to arrows of D in such a way that the compositional structure of the two categories is preserved."

              But your topics also touches the idea of dialectic

              http://en.wikipedia.org/wiki/Dialectic

              Your point is

              "Quantum is analogical, and classical is rational."

              that resonates with

              "Analogy is about sameness, while rationality is about difference."

              I don't know, on this matter the philosophical language may help.

              For sure, we are always making use of analogies in exploring the world.

              In my view, trichotomy makes sense as well

              http://en.wikipedia.org/wiki/Trichotomy

              I hope you will analyze my essay as well

              http://www.fqxi.org/community/forum/topic/1789

              All the best,

              Michel

                Than,

                thank you for leaving comments in my blog and inviting me to read you essay. I appreciated the quotes and the links in your essay, especially Jim Al-Khalili - Quantum Life: How Physics Can Revolutionise Biology. I should have incuded how birds use the earth magnetic field for navigation in my essay. The full lecture is here: https://www.youtube.com/watch?v=wwgQVZju1ZM

                You have an unusual, for modern times, scientific approach. Analogies are very useful in introducing novel concepts, but are difficult to apply in practice. I largely concur with Armin's comments above and have read your thorough response to him. I agree with you that "we have not fully understood the full meaning of the quantum, wave-particle duality, or the problem of quantum measurement" and that " To wit, analogies are efficient for first forays into the unknowns, and for a person with good solid experience, they are no more error prone than reasoning. After all, analogy and reason are not absolute strangers, but members united by a single constant of Nature. Like wave and particle!"

                Well said!