## 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!