## Richard Feynman om mathematics

from **Lars Syll**

In a comment on one of yours truly’s posts last week, Jorge Buzaglo wrote this truly interesting comment:

Nobel prize winner Richard Feynman on the use of mathematics:

“Mathematicians, or people who have very mathematical minds, are often led astray when “studying” economics because they lose sight of the economics. They say: ‘Look, these equations … are all there is to economics; it is admitted by the economists that there is nothing which is not contained in the equations.The equations are complicated, but after all they are only mathematical equations and if I understand them mathematically inside out, I will understand the economics inside out.’ Only it doesn’t work that way. Mathematicians who study economics with that point of view — and there have been many of them — usually make little contribution to economics and, in fact, little to mathematics. They fail because the actual economic situations in the real world are so complicated that it is necessary to have a much broader understanding of the equations.

“I have replaced the word “physics” (and similar) by the word “economics” (and similar) in this quote from Page 2-1 in: R. Feynman, R. Leighton and M. Sands, The Feynman Lectures on Physics, Volume II, Addison-Wesley Publishing, Reading, 1964,

I would suggest that what is lacking in economists is the understanding of science and its requirements. This is similar to what Richard Feynman actually said about mathematicians and physics.

I refer you to my comments in the blog, “Calibration — an economics fraud kit”, at November 8, 2018 at 11:02 am. Here I point out that the failure to address the fundamental errors of thought in economic analysis leaves any hypothesis without the possibility of its being invalidated. Thus economists still fail properly to understand that production functions are simply concrete descriptions of specific data and CAN NEVER be abstract descriptions of theoretical relationships. Discussion then devolves into irrelevancy, arguing about chimera NOT reality.

Yes, I too greatly appreciated Jorge’s comment, and Frank’s point here about mistaking generalisations of specific data for abstract concepts is well taken.

My own interest is in WHY “mathy” economists fail to understand science and its requirements. My argument is three-fold.

(a) Because they have accepted the “Humpty-Dumpty” literary understanding of language, “Words mean what I want them to mean”. For goodness sake, we were given a quote here recently of the editor of the New Scientist insisting we have to use words as others use them now. This has been a consequence of the abandonment of etymological explanation along with the study of Latin and Greek, opening the way for such blatent political obfuscation as using the word “marriage” for same-sex civil partnerships. The point being that science as logically related and communicable knowledge – rather than as a discovery method – requires stable word definitions.

(b) Because literal understanding is more immediate and therefore learned earlier than the abstract relationships between perceptions and words – so valued more highly than wisdom by the literal-minded majority who want to ‘get things done’ at least ‘cost’. [Words undefined]!

(c) Because since Descartes, ‘maths’ has become understood as algebra by teachers and as arithmetic by the majority who don’t understand algebra. But maths began with Roman finger language and Greek geometry; in my own life-time it was still traditionally taught as comprising arithmetic, algebra and geometry, advancing to differential calculus. Digital computing added so much more that, to make room for it, arithmetic was largely automated by calculators and geometry virtually disappeared. What hasn’t been noticed is the international development of iconic as against symbolic language (see heterodox economist Kenneth Boulding’s 1956 book “The Image”) and the re-eintroduction thereby into mathematics of geometry in the topological form of circuit diagrams rather than circles, flow diagrams (as in London Underground maps), relational graphs (as in SSADM ssystems analysis) and Feynman’s diagrams.

Proverbially, “a diagram wis worth a thousand words”. Of Feynman’s diagrams, James Gleick says (in “Genius”, p.275), “physicists would shortly find themselves agonising over pages of diagrams representing catalogues of knots. They found it was worth the effort; each diagram could replace an effective lifetime of Schwingerian algebra”.

Moral? Economists relying on algebraic mathematics are wasting their own and humanity’s time.

As grace is the deeply observed description of the essentially stripped bare dynamic, interactive flowing process of the cosmos itself it is the independent variable in virtually every differential equation and in economics its numerous applicable aspects are the dependent variables.

I think I go along with this, but a simpler, more practicable way of putting it is that we need to give each other time and space to do whatever we are trying to do [i.e. our diverse ‘goods’].

Excellent observations, Dave, as I was once a Berkeley theorist who found himself in a world of computer chip diagrams, logic gates & all sorts of engineering/hard science stuff that was used BOTH to comprehend & to describe existing electronic/physical structures. I have found physicists love physical descriptors, & “rational man” doesn’t make it. Perhaps “environmentally-conditioned & emotional social man” comes closer.

“Under normal circumstances, the liar is defeated by reality; no matter how large the tissue of falsehood that an experienced liar has to offer, it will never be large enough to cover the immensity of factuality.” (Hannah Arendt)

Just adding a woman’s touch, sorry dear Lars and other colleagues.

So during the Hitler war, Hannah was trying to encourage us to believe that “truth will out”? Language “will never be large enough to cover the immensity of factuality”. (I’m thinking of the Heisenberg uncertainty principle). Liars can use it to point us to situations which we will find misleading, but conversely, it can also point us nearly enough to relevant aspects of reality.

(Apologies, Helen, for an old fellow’s pedantry, but at least it shows my seeing the significance of what you have said)!

One of the signatures of imminent need for paradigm change is general confusion/contention regarding the truth in a body of knowledge/area of human endeavor or as we see occurring in American politics…the seeming irrelevance and ineffectuality of truth.

Yes, following on what I’ve just said to Helen, outcomes arise only after information has been acted on, by when we are looking for them in the wrong place and the liars have moved on. What you seem to be implying by “general confusion” is that most people are not liars. Therefore the inadequacies of language suggest the need is not so much for honest people as for language which will better enable us to imagine outcomes in advance of their happening. Hence my arguing for iconic language in advance of symbolic language: i.e. for network circuit diagrams, the structure of which enables one to see and judge the relevance of the types of interaction which symbolic names and equations are referring to.

“The physical is inherently entropic, giving off energy in ever more disorderly ways. The metaphysical is antientropic, methodically marshalling energy. Life is antientropic. It is spontaneously inquisitive. It sorts out and endeavors to understand”

― R. Buckminster Fuller, Synergetics: Explorations in the Geometry of Thinking

On the whole I disagree with this. The physical has evolved, and from the physical life has evolved, and from life thought has evolved. In each epoch the evidence shows that the physical has evolved in four stages. Energetic primaeval motion was free to spread out to form a three-dimensional space (i.e. had three degrees of freedom, and conversely, no degrees of control), most of which (see Craig’s first comment here) became locally constrained in forms with one, two or three degrees of freedom, as in trees growing up, animals free to travel over a surface and humans freed by language to communicate across time. But language also creates a new epoch in which language can be used to start controlling each other and the world we live in, making it less rather than more disorderly (as with empty high streets and a denuded earth). But perhaps I am missing something? Is ‘metaphysical’ just another name for ‘linguistic’?.

As a mathematician, I take Feynman very seriously, but not the quote in the image. Feynman was a mathematics major, and the quote is disputed at https://en.wikiquote.org/wiki/Talk:Richard_Feynman .

I note that even though Newton realised that the precession of Mercury was an anomaly, generations of Physicists took the same attitude to Newton’s cosmology as Feynman notes in many mathematicians. So I think it the attitude that is the problem, not mathematics as such.

Further, when Einstein took the anomaly seriously he was applying mathematics, and his theory involves ‘equations’. Quite rightly, it wasn’t until Eddington conducted his observations of the transit of Mercury that relativity was accepted as ‘proper Physics’. But we generally give the credit for relativity to Einstein, for doing the mathematical theory, not Eddington. As I see it, people (mathematicians or otherwise) with the attitude that Feynman describes rarely make much of a contribution to moving any theory forward. What is often needed is both a good attitude and good mathematics. Would Feynman really have disagreed?

Dave, Feynman was an inveterate joker, and Wikipedia is not disputing the “quote”, only rejecting it because it is “unsourced”, i.e. because it cannot cover its own back by merely republishing previously published sources. When I tried to contribute first hand observations to Wikipedia the net result was that my original posting was replaced by that of a literal-minded wally I had been arguing with, who firmly believed what he had read in hostile books.

“What is often needed is both a good attitude and good mathematics.”

This is most definitely true because it is the integrative perspective.

However, it’s always the intuitors and paradigm perceivers who are first to see the truth and the whole…and sometimes the scientists and mathematicians come to the integrative and basic truth later. This is also why heterodox economists can advocate one off and once removed palliative policies that reflect the new paradigm concept (Gifting) like debt jubilees, government deficits etc. and yet because they have no real consciousness of the concept behind even the concept of the new paradigm (grace) they miss the integrative bigger picture.

[ (Science/Fragmentation x Wisdom/Integration/Wholeness) = The Pinnacle Reality of Grace ]

“What is often needed is both a good attitude and good mathematics.”

The failure of economists to apply real scientific standards and to understand the difference between abstract and concrete relationships. Because of this economic analysis is littered with irrelevant hypotheses which should have been discarded. What is worse is the inability to recognise valid analysis when it is presented to them. Lip service is paid to Poppler and Lakatos, but their message is ignored.

That “Feynman” quote in the image is utterly moronic and there is no evidence he ever said that. Don’t agree with Feynman about everything about his view of mathematics, but never saw him say something that stupid – and blatantly, absurdly false.

A couple of views from even greater physicists than Feynman – there aren’t many – on relations of physics to mathematics:

Maxwell, a first rate mathematician by any measure, relates how he intentionally avoided learning at first the more “mathematical”, continental theories of electricity and magnetism, which would have been child’s play to him, in preference to learning Faraday’s more “physical” and “philosophical” ones first and interpreting the former in terms of the latter, not vice versa.

Maxwell is nowhere near as pejorative as Feynman on that “mathematical” type of work, and imho more accurate, suggesting that they were good and useful work – but just not as great as Faraday. And further, most interestingly and importantly, and showing a rare insight, which is very rarely said, he notes that Faraday was a mathematician, even though he did not think he was! Maxwell felt his own contribution was largely uniting Faraday’s mathematics which the creator could not even see as mathematics with the great body of modern mathematics. The moral is that many people who are not the mathematicians that Maxwell was, who do not have his self-confidence, simply cannot tell what is math and what is not. If you can tell the difference, you see a rule of thumb in econ is that usually the more decoration and ostensible math there is, the less mathematical the work is, and vice versa.

A second note:

Newton’s assistant – forget his name – said that the only time he ever saw Newton laugh was when somebody asked him if his modern stuff could replace Euclid, make it unnecessary to learn geometry.

Calgacus, I don’t agree the Feynman quote is utterly moronic. It is a type of humour called hyperbole, somewhat akin to caricature as an art form. The point is to enjoy the joke – and perhaps the likelihood that it came from someone with the wit and competence to make it.

And sorry: yes. What you say about Maxwell and Faraday is fascinating and very likely true – though you couldn’t have heard him say it … Good for Maxwell (and you).

Incidentally, this difference between the symbolic theorising of Maxwell and Faraday demonstrating and abstractly representing physical gestalts arising after years of patient observation, looks like the difference between the maths of Dave Marsay and myself, He like Maxwell is much better at diplomacy, and I like Feynman at hyperbole. (Perhaps unsurprisingly after sixty years discovering unexpected insight in the paradoxical humour of caricaturist G K Chesterton – he illustrated many Belloc books – while for even longer trying to resolve incoherence in basic physics and economics).

though you couldn’t have heard him say itWhy not? From my name used here, I am 2000 years old. :-)

But it is in the preface to Maxwell’s Treatise.

The Newton anecdote is in some edition of his works (Rupert & Marie Hall?)

Okay. Well thinks anyway: even this is interesting!

… thanks anyway!

Guess he didn’t like Emmy Noether…

Fascinating, but who do you mean by “he”? I’d never heard of her before, though I have been happy enough intuitively with her concepts of symmetry and conservation. Feynman was certainly happy with symmetries, and it seems he and I differ only on the use of the word ‘particle’, as I consider his rapidly vanishing ones as releases of conserved energy.

https://www.sciencenews.org/article/emmy-noether-theorem-legacy-physics-math led me to Ideals, and I found this a very helpful interpretation of complex numbers: an Ideal Element “is any element added to a mathematical theory in order to eliminate special cases. For example, adding the ideal element i = √-1 to the reals allows all algebraic equations to be solved, and the IMPROPER POINTS [at infinity] of the projective plane permit the assertion, without excluding parallel lines, that every pair of lines intersect”. So mathematics is not real unless it recognises absolutely different types of Real?

Symmetries/Dualities are replete throughout nature and the cosmos, for instance the symmetrical sides of a leaf. The real “trick” as Noether and others knew is finding the thirdness greater oneness entity/concept that is there underlying, integrating and uniting the symmetry…like the stem from which both sides of the leaf emerged or applying the various aspects of the underlying natural philosophical concept of grace in economics that integrate and unite the oppositional duality of the monetary and financial paradigms of Debt/Burden and Monetary Gifting.

Noether’s equation has three aspects to it as does my formula of the Cosmic Code. Comprehending and applying the concept of A Thoroughly Integrated Duality Within an Integrative Trinity-Unity-Oneness-Process which is also a description of the concept of grace is extremely important insight.

Feynman misunderstands the role of formal models in a science like physics. This is usual for physicists who are as bad (or worse) than economists in thinking about what they do (in my experience). Firstly:

1. There are other formal models than mathematics better suited to the complexity of what we observe. This is computational modelling. It is true that systems of equations that are analytically solvable are usually far too simplistic, but this is not true of agent-based simulation. Analytic maths is the macho of physics, so they only tend to view simulation as an add-on to accompany the maths. Actually now we are free to choose the most appropriate kind of formal model for each kind of phenomena.

2. Formal models have a much more important role in science than just calculating stuff. They unambiguously encode understanding in a model that can be transmitted without any error or re-interpretation. This allows for scientists to pass around models, tinker with them, critique and improve them, compare them against evidence etc. Thus formal modelling allows for science to be collaborative and cumulative. Discursive economics often fails to be either collaborative or cumulative – changing with each fashion.

Neo-classical economics fails for a number of reasons, one of which is its obsession with analytic mathematics. I would argue that formal modelling is not one of its ‘sins’ but essential to a good science — even a good social science (as economics should be).

As a mathematician I would suggest that “1. There are other formal models than [the mathematics typically used by economists that is] better suited to the complexity of what we observe.”

And perhaps “2. [Mathematics has] a much more important role in science than just calculating stuff. [Mathematical models can] unambiguously encode understanding in a model that can be transmitted [between those who understand such modelling] without any error or re-interpretation”

Sadly, though, many economists seem to almost wilfully misinterpret mathematics.

To me, a formal model that involves mathematical structures is necessarily a mathematical model even if it isn’t what economists normally mean by the term. ;-)

The history of all models is that they are incomplete until someone discovers/stumbles across an entirely new insight that comes from a new breakthrough or from an old tool or analysis. In reality and for all practical purposes the cosmos is a flowing eternity….of everything.

That may be a tautology, but there’s insight to be had from it nonetheless because you can’t very well buck the cosmos and its nature. And if one contemplates that nature until they thoroughly understand it and can put a word to it and then compares it to the state of whatever is under analysis….it may lead the way out of the problem under discussion and the way home…to where one has always been….and didn’t know it.

Craig,

I would rather say that some mathematical models do encapsulate a complete understanding of, for example, some theory of physics, but that however good the mathematics one can only say that the theory is one of many that is internally credible and not falsified by experience. (Think of Euclidean Geometry before Relativity.) It may in some sense be the best of those considered so far, but (at least in physics) there are always always hords of people trying to falsify it and there can be no mathematical reason why they might not succeed.

We agree that economics would be improved if economists were more like scientists in appreciating what you say, but I would add that one sometimes needs to check that the ‘insight’ is credible. This seems to require logic, and in so far as we are interested in numbers seems to require mathematics. My beef with mainstream economics is that from a mathematical perspective it looks like numerology or what Keynes called ‘pseudo-mathematics’, not the real deal. I speculate that economics would need to embrace mathematics more fully if it is ever to get sufficient clarity. Either that, or pray!

Insight plus mathematics, not either alone?

Dave M,

“I would rather say that some mathematical models do encapsulate a complete understanding of, for example, some theory of physics, but that however good the mathematics one can only say that the theory is one of many that is internally credible and not falsified by experience.”

I would agree that this is true, because some things/theories can only be falsified or confirmed by philosophy….before they are implemented…and then everyone says, “oh yeah, this is obviously true and good….because everything makes sense and works better now.” In other words truth or falsification is impossible with human sensorial experience alone and philosophy/conscious self actualization must suffice. Quantum Mechanics is one such example, and so is my contention that the nature of the cosmos is a flowing dynamic, interactive, integrative and puzzling state of grace just sitting there waiting for us to discover and then find ways to apply to our temporal systems.

Much would become more clear in economics if we’d consider what I have said here before:

1) Both micro and Macro-economics have fallaciously accepted that private finance is a legitimate profit making business model

2) Economists recognized that the pricing, money and accounting systems all follow the rule that equal debits and credits sum to zero and the point of retail sale is where policy can be implemented to resolve modern economies’ chronic problems and best benefit all agents.

“Insight plus mathematics, not either alone?”

Yes, this also rings true because it is a duality to integrate to the point of thirdness greater oneness that results in actual change and progress. The integrative ethic/my cosmic code of wisdom stated as an integrated duality within an integrative trinity-unity-oneness-process is the formula that mere science and economics needs to embrace so that it is less prone to becoming confirmation bias like neo-liberalism has become.

There is no permanent truth except graceful continual change and the only way to actually understand that paradox is to embrace it via the integration/resolution of the koan that is our temporal existence.

In those same lectures Feynman describes the scientific method. First, we guess the relationship (Feynman uses the word law since he is a physicist). Second, we figure the consequences of the relationship we guess. What would we likely see if the relationship we guess does exist? Finally, we compare the consequences with experience or experiment. If the relationship’s results don’t agree with experiment or experience, then our guess is wrong. No matter how beautiful or elegant the relationship or its mathematics may be, it’s wrong. As I’ve pointed out here and to dozens of clients, all these steps are problematic, because human experience and capabilities are both limited and can be fooled. And of course humans can lie to themselves, and others.

This is from a speech by Feynman in 1966. His own words. Some misogynistic with some unattractive stereotypes. I believe the speech is still online at https://www.feynman.com.

Under these circumstances of the difficulty of the subject, and my dislike of philosophical

exposition, I will present it in a very unusual way. I am just going to tell you how I learned

what science is. That’s a little bit childish. I learned it as a child. I have had it in my blood from the beginning. And I would like to tell you how it got in. This sounds as though I am trying to tell you how to teach, but that is not my intention. I’m going to tell you what science is like by how I learned what science is like.

My father did it to me. When my mother was carrying me, it is reported–I am not directly

aware of the conversation–my father said that “if it’s a boy, he’ll be a scientist.” How did he

do it? He never told me I should be a scientist. He was not a scientist; he was a businessman, a sales manager of a uniform company, but he read about science and loved it. When I was very young–the earliest story I know–when I still ate in a high chair, my father would play a game with me after dinner. He had brought a whole lot of old rectangular bathroom floor tiles from some place in Long Island City. We sat them up on end, one next to the other, and I was allowed to push the end one and watch the whole thing go down. So far, so good. Next, the game improved. The tiles were different colors. I must put one white, two blues, one white, two blues, and another white and then two blues–I may want to put another blue, but it must be a white. You recognize already the usual insidious cleverness; first delight him in play, and then slowly inject material of educational value. Well, my mother, who is a much more feeling woman, began to realize the insidiousness of his efforts and said, “Mel, please let the poor child put a blue tile if he wants to.” My father said, “No, I want him to pay attention to patterns. It is the only thing I can do that is mathematics at this earliest level.” If I were giving a talk on “what is mathematics,” I would already have answered you. Mathematics is looking for patterns. (The fact is that this education had some effect. We had a direct experimental test, at the time I got to kindergarten. We had weaving in those days. They’ve taken it out; it’s too difficult for children. We used to weave colored paper through vertical strips and make patterns. The kindergarten teacher was so amazed that she sent a special letter home to report that this child was very unusual, because he seemed to be able to figure out ahead of time what pattern he was going to get and made amazingly intricate patterns. So, the tile game did do something to me.)

Now the point of this is that the result of observation, even if I were unable to come to the

ultimate conclusion, was a wonderful piece of gold, with marvelous results. It was something

marvelous. Suppose I were told to observe, to make a list, to write down, to do this, to look, and when I wrote my list down, it was filed with 130 other lists in the back of a notebook. I would learn that the result of observation is relatively dull, that nothing much comes of it.

I think it is very important–at least it was to me–that if you are going to teach people to

make observations, you should show that something wonderful can come from them. I

learned then what science was about: it was patience. If you looked, and you watched, and

you paid attention, you got a great reward from it–although possibly not every time. As a

result, when I became a more mature man, I would painstakingly, hour after hour, for years,

work on problems–sometimes many years, sometimes shorter times; many of them failing,

lots of stuff going into the wastebasket–but every once in a while there was the gold of a

new understanding that I had learned to expect when I was a kid, the result of observation.

For I did not learn that observation was not worthwhile.

What science is, I think, may be something like this: There was on this planet an evolution of

life to a stage that there were evolved animals, which are intelligent. I don’t mean just

human beings, but animals which play and which can learn something from experience–like

cats. But at this stage each animal would have to learn from its own experience. They

gradually develop, until some animal [primates?] could learn from experience more rapidly

and could even learn from another’s experience by watching, or one could show the other, or

he saw what the other one did. So there came a possibility that all might learn it, but the

transmission was inefficient and they would die, and maybe the one who learned it died, too,

before he could pass it on to others. The question is: is it possible to learn more rapidly what somebody learned from some accident than the rate at which the thing is being forgotten, either because of bad memory or because of the death of the learner or inventors?

So there came a time, perhaps, when for some species [humans?] the rate at which learning

was increased, reached such a pitch that suddenly a completely new thing happened: things

could be learned by one individual animal, passed on to another, and another fast enough

that it was not lost to the race. Thus became possible an accumulation of knowledge of the

race. This has been called time-binding. I don’t know who first called it this. At any rate, we have here [in this hall] some samples of those animals, sitting here trying to bind one experience to another, each one trying to learn from the other. This phenomenon of having a memory for the race, of having an accumulated knowledge passable from one generation to another, was new in the world–but it had a disease in it: it was possible to pass on ideas which were not profitable for the race. The race has ideas, but they are not necessarily profitable. So there came a time in which the ideas, although accumulated very slowly, were all accumulations not only of practical and useful things, but great accumulations of all types of prejudices, and strange and odd beliefs. Then a way of avoiding the disease was discovered. This is to doubt that what is being passed from the past is in fact true, and to try to find out ab initio again from experience what the situation is, rather than trusting the experience of the past in the form in which it is passed down. And that is what science is: the result of the discovery that it is worthwhile rechecking by new direct experience, and not necessarily trusting the [human] race[‘s] experience from the past. I see it that way. That is my best definition.

When someone says, “Science teaches such and such,” he is using the word incorrectly.

Science doesn’t teach anything; experience teaches it. If they say to you, “Science has

shown such and such,” you might ask, “How does science show it? How did the scientists find

out? How? What? Where?” It should not be “science has shown” but “this experiment, this effect, has shown.” And you have as much right as anyone else, upon hearing about the experiments–but be patient and listen to all the evidence–to judge whether a sensible conclusion has been arrived at.

Ken, thank you for this – a great find.

“Mathematics is looking for patterns” is perhaps a bit too concise, for his context is about looking to see what patterns one can make, and the reality is usually about getting from one pattern to another: constructing proofs relating premises to conclusions.

Feynman’s justification of science is delightful: “The race has ideas, but they are not necessarily profitable .. And that is what science is: the result of the discovery that it is worthwhile rechecking by new direct experience, and not necessarily trusting the [human] race[‘s] experience from the past”. That’s Descartes, of course, Bacon before him advocating taking this to bit to see how they worked (which was otherwise not visible). I don’t think his “dislike of philosophical exposition” is a dislike of such wisdom so much as of elites thinking themselves wiser than the rest of us.

On Scientific Method, Ken, where you start with ” First, we guess the relationship”, that is not my experience and I don’t think it was Feymen’s either. As a scientist one only makes the guess after a lot of preparatory research and/or observation, and this is usually because of a problem left unresolved by prior scientific work.

Gleick’s book ‘Genius’ on Feynman doesn’t mention the tile-stacking exercises, but it does have Dyson commenting on “this wonderful vision of the world as a woven texture of world lines in space and time” (p.7). “In the 1920s, a generation before the coming of solid state electronics, one could look at the circuits and see how the electron stream flowed. … boys like Richard Feynman, loving diagrams and maps, could see that the radio was its own map, a diagram of itself. Its parts exxpressed theier function, once had learned to break the code of [inductors], resistors, crystals and capacitors” (p.17). “[T]he Depression lessened the market for inexpensive radio repair, and Richard found himself in demand. … Broken radios confronted Richard with a whole range of pathologies in the circuits he knew so well”. (p.46). I likewise entered this scene [just] before the introduction of steady state technology and have had a similar outlook: not as a mathematical mystic but as a practical problem solver.

Dave, thanks for the feedback. Feynman was a practical man. His whole life helped create that practicality. That and his curiosity and imagination made him an effective and combative physicist. On scientific method Feynman did not mention the sources of the guess except to say it could come from anywhere. Regarding your experience, you must keep in mind that the video is of Feynman teaching an introduction to physics class. Going into the sources of the guess would probably be too much detail for such a class. But on another occasion at a professional meeting he did say when asked about scientific method, “use anything that works.” He was not a formalist regarding method.