More on Feynman

It had been many years since I last read any books by or about Feynman.  Unfortunately, I never had the chance to hear him speak in person.  I also had never read the book version of “The character of physical law” before so there were several things that struck me after watching some of the lectures.  The first was that Feynman was extremely philosophical and cultured.  This was somewhat surprising because the mythology surrounding Feynman, promoted by his own autobiographies, is that he was the no-nonsense street-smart kid from Brooklyn who used common sense and cunning to outsmart the so-called intellectuals with highfalutin ideas.  I never fully bought into that myth but now  after watching three of the lectures I feel as if they can be completely dispelled.  Feynman was extremely intellectual and very interested in the humanities. He just disagreed with how they were being carried out and done at that time.

In the second lecture, Feynman talks about the relationship between mathematics and physics.  He says that mathematics is the language of physics but not the same as physics.  He uses the metaphor of “Greek”  and “Babylonian”  mathematical traditions.  In this metaphor, the Greek approach was axiomatic.  Math is reduced to exploring the logical outcomes of a fixed set of rules or axioms.  Everything connects to everything else within that system.  The Babylonian method is to learn mathematics through examples and heuristics.  The connection between these individual results may or may not be known.  To Feynman, physics uses the Babylonian approach and it is only by doing it that way can new discoveries be made since theorems can pop out where they shouldn’t.    He uses the example of the conservation of angular momentum, which was noticed by Kepler in his law that planets sweep out equal areas in equal times and shown to be true by Newton from his laws of motion and gravitation.  However, it was a leap of faith that the same conservation law was applicable to a figure skater who uses muscle power to spin and even more to subatomic particles.  Feynman argues that one must use the Babylonian method to make these leaps since they could not be deduced axiomatically.  As long as we don’t have a complete theory of physics, the axiomatic approach will not be useful.

Another example Feynman brings up in this context is that there are equivalent formulations of  physical laws that cannot be distinguished experimentally but can lead to different insights so it is important to be aware of all of them and not be biased against any of them.   Classical mechanics can be described by Newton’s laws, (which requires action at a distance), in terms of a field like the gravitational potential (which can be obtained from purely local information), or through a minimization of the difference between kinetic and potential energy (least action principle).  He then says that when you now include more information like there cannot be action at a distance then Newton’s laws fail miserably but the field and least action formalisms can be modified to account for the new information.  Hence, since you’ll never know when modifications will be needed a physicist must be a Babylonian and keep all points of view.  The axiomatic approach of mathematics is not efficient in this regard.

In the final minutes of his lecture, Feynman becomes almost whistful and somewhat agitated.  He says that the laws of nature are described by mathematics and there is no simplification.   You can use all sorts of analogies but the only way to really understand and appreciate nature is to learn her language, which is mathematics.   Just as it is really impossible to truly describe what music is like to a deaf person, you really are missing out on something very beautiful if you don’t learn mathematics so you can understand physical theories.  It is as if he has found something beautiful that he wants to share but not only will no one listen but there are people that are actively thwarting him.  He ends his lecture rather abruptly with a shot at those people in “the other culture” that C.P. Snow wrote about who believe that nature can be understood qualitatively  with the line “It is perhaps that their horizons are [so] limited, which permit such people to imagine that the center of the universe of interest is man”.


12 thoughts on “More on Feynman

  1. I am curious where you would weigh in on the math v. physics debate, particularly since you have a degree in physics and have held an appointment at (an admittedly very applied) math department.

    I tend to think of the situation more as a continuum. There are some pure mathematical results that would be very instructive to physics. One obvious example being the work done on the regularity of solutions to Navier-Stokes.


  2. Do you mean if I agree with Feynman? I think he is correct that physics is not math and vice versa and that an axiomatic approach is not efficient for physics. I also think that a physicist needs to know a lot of math and should not be afraid of math. Feynman certainly knew a lot of math and very well. Personally, I find math much more beautiful than physics.


  3. Carson,

    Thanks for the pointer back to the Feynman lectures on line. I first watched these in at the University of TN when I was there on a summer fellowship working on accelerator detector simulations. I remember sitting in dank little booths at the library with headphones on in awe at the simplicity and power of F’s thinking and style. I watched the first lecture again today and found it a great experience again.

    I am not sure the math v. physics is the most generative way to ask the question. I suppose we could ask what each of us prefers, which is more beautiful, meaningful or elegant. But I don’t think that is what people are getting at when they pose the question as “vs.”

    I think we often want to get at something around fundamental truth. Which approach to knowing allows us to discover the most essential essentials of the Universe? Given adequate resources of time and energy, which way of knowing will get me to the very bottom? I want epistemological superiority.

    But then the question seems to turn from math v. physics into what we are knowing vs. the effectiveness of the way we are knowing? And, I don’t see how to make a clear argument for knowing what is best to know before hand…


  4. Hi Scott,

    Good topic for a future post. I was trying to keep my comments within the confines of Feynman’s lecture, which was more about how math is used by physics and how math and physics are done. On your point, I’ve been arguing in previous posts that if you believe the universe is computable then the epistemological question ultimately boils down to questions of computability. Physics is then an emergent phenomenon of a lambda calculus. I was planning to blog about this at some point but I think that a good test bed for issues in the philosophy of science and epistemology would be to apply it to computer simulated worlds. Then it is possible to separate meaningful from meaningless questions (in the Wittgenstein sense).


  5. I thoroughly enjoyed reading the comments in this blog, and as a working physicist, professor, and long time admirer of Feynman, I am always interested in the many prespectives others have regarding physics, mathematics and the connections.

    As Carson explains, Feynman does make clear that physics is not math. The latter is a formalism that is built upon a few straight forward “rules” or axioms, without any regard for natural phenomena. Mathematics does not look to nature for validation. It exists soley on its own merit. Physics, (or science in general) relies ultimately upon experiment to validate theory. The mathematical description of the theory may be sound, but it is really only a very clever idea (and possibly very wrong). . . until nature through experiment validates it. That’s doing science. Of course, experiment means measuring something, and measurement means you get numbers . . . and mathematics is all about the numbers. Therein lies the connection. The differences are stark, but the connections are quite beautiful.


  6. Hi, I’ve just been watching the superb feynman lecture (rel. betw. Mathematics and Physics) on youtube. It’s great to find others who respond in depth to the things covered by F. I was struck by your thought that F was “philosophical and cultured”. It’s at odds with the startling conclusion of the lecture in which he refers to “limited horizons” of those on the non-mathematical side of CP Snow’s “two cultures” – which you also commented on. I agree that F shows with great clarity the ways that mathematical expressions in physical theory are subtended by particular philosophical prejudices, and, as he says, “it’s not good” (if you want to make progress in physics) to be too attached to any particular view (part of the “Babylonian” approach). I would say that F felt philosophy did not help, and usually hindered, advances in physical theory. And to judge by his closing statement he had little time for philosophers for whom man IS the centre of interest in the universe. I think F was antipathetic towards those philosophising on the “qualitative” side because they are not physicists, and he is interested in physics. However i wonder if he could have been persuaded to be less dismissite if it could have been shown that some things he states in his lecture are bound up with philosophy of the very kind he dislikes. For example, F is clear that there is no correct method for arriving at new physical theories- any method is ok provided the theory makes predictions which can be compared to nature in experiment. We may invent theories any how. Now F was probably unaware (and probably happily so) that this is in agreement with the writing of the philosopher Karl Popper, but KP was aware (where perhap F was not) that this attitude is a very particular response to the philosophy of Immanuel Kant. My view is that F shows himself to be (like KP, but unwittingly so) Kantian in respect of his scientific approach. However, it was Kant’s philosophy that showed that our mental apparatus in part creates the world we perceive (causality being the most often cited example of this), and this is the “Copernican revolution” in philosophy that placed man at the centre of the universe. KP was concerned to use this interpretation of Kant to support his critique of logical positivism and “scientific” Marxism. So in an important way, the philosophy of science may not be useful to scientists such as F, but that does not mean that the philosophical assumptions brought to bear (consciously or otherwise) in science by scientists have no resonance in the “other culture”. This is what i believe led certain philosophers (and physicists of earlier generations to F) to regard F and other scientists of his and later generations as precisely unphilosophical and culturally unsophisticated, despite their brilliance within their disciplines.


  7. Incidentally, i love the part of F’s lecture in which he speculates that our theories (which become inordinately complex in describing what happens in tiny bits of space-time) will be superseded when the workings of things will be revealed and seen to be “just another prejudice” (i.e. the workings will be a particular model such as those postulated by philosopher-physicists). F speculates that the workings will be simple, the complexity arising because of large numbers (like the chequer board, he says). “How can all that [complexity] be going on in that tiny bit of space-time?” At this point i make certain links with the recent writing of cosmologist Paul Davies, who puts forward the idea of information or knowledge as a fundamental constituent of the cosmos, like a fundamental particle or a given dimension of space. (see “The Goldilocks Enigma”). I find it mind bendingly awkward, almost indigestible writing, like viewing Kant down the wrong end of a telescope! I reach for Karl Popper and then a book of poetry!


  8. Hi Alastair,

    Thanks for your comments. I think that Feynman was philosophical in the sense that he was profoundly interested in the meta-questions of physics and science. The fact that he took great public umbrage to the “other culture” shows to me that he took the time to digest what they represented. I’m intrigued by your statement that F was Kantian in his scientific method. I always thought of him more in line with Hume and the skeptical tradition. Feynman didn’t seem to care so much about the “truth” as to “getting the numbers right.”. Perhaps I am misinterpreting your statements.


  9. Hello again,

    I link Feynman to Kant via Karl Popper. This is my understanding: Karl Popper argued that the philosophical question posed by Kant, to which the “Critique of Pure Reason” was a partial answer (there were also the the critiques of “practical reason” and of “judgement”) was prompted by Kant’s belief, shared by leading thinkers of his day and by leading physical theorists right into the 20th century, that Newton’s theory attained true knowledge (episteme).
    Kant had been moved to this point by Hume’s empiricist doctrine (an argument against philosophical rationalism) that we cannot arrive at true knowledge deductively, i.e. through reason alone (which was Descartes’ project), but must rely on our sense impressions. But Hume went further, to demonstrate that while our sense impressions may lead us to infer a natural law, or “conformity” in nature (i.e. through induction), there is no logical necessity underpinning such laws. For example, although we may expect that the brick approaching the pane of glass will ’cause’ the window pane to shatter (on the basis that this is what has always happened in the past), there would be no logical contradiction if this did not happen. Therefore what we regard as natural law can never amount to true knowledge (episteme). In this way Hume curtailed the powers of reason, and arrived at a profound skepticism. But this was anathema to a belief that all things were causally bound up in a God-created universe, that there was a reason for everything to be as it is. This is what woke Kant from his “dogmatic slumber”.
    However, Kant saw that Newton’s theory seemed to defy Hume’s skepticism. Whereas Hume had elevated empiricism against rationalism, yet also shown that laws based on our past sensory observations could not attain to true knowledge (Hume’s skepticism), Newton had deduced a theory from a set of axioms (i.e. from reason, in the manner of the rationalist Descartes) which made predictions about the world which experiments of the day showed to be true. If Hume’s argument against rationalism was sound (and Kant believed it was), then how had Newton achieved true knowledge (which Kant also believed was the case)?
    In answering this, Kant examined reasoning (his first critique), and investigated three types of proposition that can be said to carry truth: ‘analytical a priori’ propositions (which say nothing about the world but merely refer to themselves), ‘synthetic a posteriori’ propositions (which say something about the world and which can be tested against experience) and ‘synthetic a priori’ propositions. The latter amount to what Kant regarded as aspects of our mental make up that are necessary in order to experience anything. For example, the ‘causality’ we believe is out there is actually a part of our own thought (we never observe a ’cause’), but if we did not bring this to organise our sense perceptions then we would apprehend a chaos of unrelated phenomena.
    Kant believed he had demonstrated the truth (i.e. logical necessity) of these ‘synthetic a priori’ propositions, and this had provided the ground, in reason, for Newton’s theory.
    The difficulty then arose for Kant that Newton’s theory (being a complete, deterministic, mechanical description of eveything in the universe) seemed to undermine the notion of free will, and this contention fuelled the Idealist and Romantic philosophical movements coming after Kant.
    Karl Popper was pitting himself, in the 1920s and 1930s against the Logical Positivist movement, which essentially aimed to expunge metaphysics from philosophy and turn philospophy into a branch of science. Popper believed this movement based itself on the inductivist model of science, that scientific theories are ‘justified’ by observation. Popper held that while Kant’s philosophy did open the door to the metaphysics of the Idealist and Romantic movements, his (Kant’s) derivation of synthetic a priori propositions showed that scientific theories (such as Newton’s) stem not from observation, but from conjecture, which for Popper included metaphysical speculation. Popper’s view was that scientific theory evolves from myth and is of the same kind as myth, in other words it results – at least in part – from human invention. This accords with Kant’s doctrine, except that Popper departed from Kant in so far as the “necessary conditions for possible experience”, the synthetic a priori propositions, which Kant had deduced, do not guarantee true theories, and this is demonstrated by the fact that Newton’s theory was shown to be limited and superseded by Einstein’s theory of gravitation.

    It is the emphasis on invention and myth in Feynman’s lectures which, for me, places him on a wavelength with Popper. For example, in Feynman’s introductory ‘Robb’ lecture (1970s) at Auckland University, he calls up the Mayan “theory” to explain the phases of Venus, and identifies their “bean counting” with modern physical theory, in which the bean counting goes on (but with advanced mathematics). Feynman says there is no attempt in modern physics to show “why” the bean-counting gives the “right” answer, and the Mayan priests did not know “why” either. Feynman thinks it’s futile to ask “why”. This brings us back to the F lecture on the relationship between mathematics and physics. Feynman is content not to know “why” theory (from reasoning) can predict stuff in nature like the mass of an electron. He is content that mathematics is just a language and a way of describing. This also agrees with Popper’s outlook, and was what led him (Popper) to regard the early Wittgenstein’s problem (and that of the logical positivists), of trying to bottom-out the relationship between language and facts, as a non-problem.
    The difference between Popper and Feynman seems to be that F did not appreciate Kant’s problem as Popper did, and so I suppose did not care about or bother with the ramifications of Kant’s philosophy (all that stuff about free will) for the other, non-mathematical, non-scientific areas of human life, most notably (in respect of Popper at least) politics. To that extent I think Feynman did not do much to digest philosophy extending into the “other culture”, even though, as you say, he was obviously very interested in “meta-physical” questions.

    I’ve tried to convey something of my understanding. For a while I poured over Popper’s essays in “Conjectures and Refutations”. (Perhaps you’ve read this book?) I found in Popper a defender of the “meaningfulness” of metaphysics. However, while he leaves space for it, he’s not much interested to explore it beyond that. My original concern was with the discipline of painting and I’d found myself in sympathy with a philosophical outlook that is “metaphysical”. For a while this troubled me. But less now. (Apparently Popper hated Martin Heidegger, who famously wrote an essay “What is metaphysics?” Incidentally I think Heidegger’s essay “Modern Science, Mathematics and Metaphysics” is profound and I will go back to it every now and then). While Popper leaves space for myth and metaphysics, he’s pretty intolerant of it. That’s why I reach for the poetry!

    Best wishes


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