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

      Vladimir

      Sorry about the omission.

      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

        Dear Peter

        By forgetting to click the right response button, I have placed my reply to your comment in the wrong place on mine. Please forgive me.

        Than Tin

        6 days later

        Dear Than,

        I have down loaded your essay and soon post my comments on it. Meanwhile, please, go through my essay and post your comments.

        Regards and good luck in the contest,

        Sreenath BN.

        http://fqxi.org/community/forum/topic/1827

        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.

        • [deleted]

        • Post #32

        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

          Greetings Than,

          I shall be reading and commenting on your essay soon. Thanks for the kind remarks on my page.

          Have Fun!

          Jonathan

          Dear Than,

          Thanks for responding to my posting in your thread and I will shortly respond to you by posting in your thread my comments on your essay and also to your query.

          Best wishes,

          Sreenath

          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!

                Vladimir?

                You said "Your analogical arguments are a sort of clever intellectual exercise to categorize various ideas in physics."

                I chose physical ideas as a gold standard of accuracy and trust, but at no time do I consider other ways of knowing as being inferior, or less trustworthy.

                Actually, I first saw a pair of dualities, viz. mind-body from philosophy and wave-particle from quantum theory, and came to recognize that there is an analogy between the two dualities, like "what mind is to body" is similar to (~) "what wave is to particle." From then on as they say, the dam burst: gene-protein; freedom-determinism; same-difference; variation-selection, bit-it; etc. etc.

                You said "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."

                Well, I am sorry if I had created "artificial divisions", but I thought I was just reporting only what I saw, and recording what follows indubitably from the symmetry principles that is synonymous -- and at home -- in physics.

                I am not a physics major (and give me ropes here! ), and my understanding as such is that there is a thin line between noncausal and causal, between freedom and determinism, between linear and nonlinear, between connection and noconnection, between global and local, between etc. and etc.

                And I don't see the "thin line" as a barrier. I see that as the Nature's way of saying that we are free to choose the sides without incurring large penalties of losing lifes or limbs for either. I see the "thin line" as a blessing, an opportunity to exercise free will.

                I have left out this passage from the essay I submitted to FQXi Contest, but I should have included it for more clarity:

                'We have two fundamental laws of physics, the QUANTUM and the CLASSICAL. The quantum deals in chance and probability, in uncertainty and in freedom, while the classical revels in the power of its Laplacian determinism, demonically fixing the destinations of planets and the destinies of people from now to eternity, leaving nothing to chance or willfulness. There is no place for our humanity in this Laplacian cosmos of classical physics! But we know we are willful creatures, and the sense of freedom and the flexibility we obviously needed and enjoyed do conflict with the deterministic claims of classical physics.

                What is more, the determinism defined within classical physics is also not - I believe - compatible with automaticity characteristic of the analogical, mainly because the determinism of classical physics is parasitic on the precision of the input variables for it to work, while the strength of analogy is that it works from small hints and vague inputs.

                How does Nature deals with this dichotomous competing worldviews? By forcing both to work together simultaneously on one small thing!

                One can 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 the Bleep is all about.'

                I believe dualities are Nature's way of saying that there are two sides to the same coin. The coin is the Planck constant with light of low and high frequencies, or as I generalize it as the Mother of All Dualities.

                Vladimir, I hope to have more exchanges like this, and in the meantime, I wish you the best.

                Than Tin

                Dear George

                I appreciate your very kind observations, and thank you for saying it.

                I believe in simplicity, the kind of simplicity involved in walking for instance. When you put your left foot down, the weight is on it, and so you move with your right foot, and when the weight is on the right, you move with the left. All is done with feelings, and we cannot tell it to a robot to emulate us even with hundreds of thousands lines of code. A child does not need instructions to start walking!

                Feynman is famous for saying that what's in textbooks is not new, and therefore he must think for himself. There is another iconoclast named Bob who said/sang "Don't follow leaders, Watch the parkin' meters." (I wish to amend the parkin' meter to pocket meter!)

                Wish you the best,

                Than Tin

                Dear Antony

                First of all, I want to thank you for your very encouraging high praise and high score to a newbie like me.

                I can't say I knew the etiquetts or the proper ways to conduct Q&A and other housekeeping necessary for managing the demands of the contest such as this.

                However, thanks to the unexpected extension of a week for the contest and encouragements from persons like you, I breathe a little easier.

                Best wishes to you too!

                Than Tin