Monday, June 11, 2012

On Truth and Beauty (Golden Oldies)

Here, for you to treasure as you sit with your loved-ones around a fire (well okay, it’s summer -- As you nurse some G&Ts)  are the very first two posts on WDJ -- The essays that began it all.
(These are still in their original locations as well.  Click if you want to read the Comments:

Update:  In the first essay below, I said admiring things about an article by Jonah Lehrer.
Just today, ALDaily links to a review of Lehrer's new book Imagine, that absolutely savages it -- basically calls it (in the metaphor often used on this site) Science Porn:

U B the judge.

~  Posthumous Endorsement ~
"If I were alive today, and in the mood for a mystery,
this is what I'd be reading: "
I Don't Do Divorce Cases
Murphy on the Mount.
(Ich bin Sigmund Freud, and I approved this message.)
~         ~

Truth Decay

I’m currently reading The Shape of Inner Space, by Shing-Tung Yau -- the Yau of Calabi-Yau, which lies at the heart of string theory.    Unlike Smolin’s The Trouble with Physics, let alone Woit's Not Even Wrong, the author is not out to debunk the theory in any way, especially as he was one of its mathematical progenitors:  nor to puff it, like Brian Greene, since  unlike those contentious authors, Yau is not a physicist by trade, but a pure geometer.  But towards the end of the book, he is led to exclaim: 

Given that much of string theory now hinges on compactifications of Calabi-Yau manifolds, which have these moduli with their associated massless scalar fields  and particles that don’t appear to exist, is string theory itself doomed?

And he quotes physicist Burton Richter against those quasi-nihilistic latitudinarians who have (as a recourse of despair) embraced “the landscape” (short version:  Anything Goes):

To them the reductionist voyage that has taken physics so far has come to an end.  Since that is what they believe, I can’t understand why they don’t take up something else -- macramé, for example.

There have, throughout history, been repeated instances of premature prophecying of “the End of Physics”:  but  there   the idea was that we were close to having solved everything;  never, that physics might one day become permanently stuck.

Si cela vous parle,
savourez la série noire
en argot authentique d’Amérique :


It was with these passages ringing in my mind, that I picked up Jonah Lehrer’s essay in the current issue of The New Yorker:  “The Truth Wears Off”.   I won’t summarize it -- it is brilliantly written, go read it -- but merely comment that the widespread scientific predicament there depicted -- in physics and biology and psychology and beyond -- seems even worse that the slightly softened interpretation that the author tries to present as a possible explanation or compromise.   Neither “happenstance” nor unconscious bias  can explain the range of what is supposedly going on.  E.g. the researcher who repeatedly failed to replicate his own results, not for want of trying, should  if anyone  have been prey to such bias.

[Cultural comment, to be developed if anyone’s interested:  the scientific standing of Rhine’s experiments in ESP.
-- Indeed, this just in:  ]
As Pauli wrote to Kronig in 1925:
"At the moment, physics is again terribly confused.  In any case, it is difficult for me, and I wish I had been a movie comedian or something of the sort, and had never heard of physics."
Or Edward Harrison in 1975, saying that endless expansion "would make the whole universe meaningless.  If that were true, I would quit, and spend my life raising roses." 

There is a thread, a thought, that links these observations;  but  once again -- Wovon man nicht sprechen kann, darüber muss man schweigen.

Falls Sie im Doktor-Justiz-Sammelsurium
weiterblättern möchten,
Bitte hier klicken:


The Shape of Inner Space is something of an intellectual autobiography, in addition to an overview of Calabi-Yau.  And quite an engagingly modest one, as these things go.   By the end of it, you have a comfortable familiarity with the author, and are full of friendly feelings.

Immediately after finishing it, I happened to re-skim George Szpiro’s equally well-written volume, Poincaré’s Prize , and was startled to see that the sinister puppet-master depicted in the chapter “The Gang of Four, Plus Two”, is none other than Shing-Tung Yau.  When I originally read the book, the name meant nothing to me; but now… it was like rounding the corner, and encountering your own cousin brandishing a knife.

Now… in the grander scheme of things, so what;  we all have our faults.  But this account of academic rivalries  gibed with my surprise at searching Shape’s index for the name of Woit or Smolin, and not finding them.  Whatever their merits or demerits, these are popular recent book-length treatments of string-theory, and one might expect that Yau would reply to them, if only to rake them over the coals.  But only towards the end of his book  does he mention theirs, in briefest passing:  and then, without uttering their names (as one might be forced to allude to Mein Kampf, but draw the line at penning the name of its author).

Yau does, however, offer a kind of reply, as he demonstrates, pretty convincingly, that String Theory, the beneficiary of much math, has in turn created, and inspired, solid math in its own right, which will survive independently of whether the particular universe of our own sojourn  happens to embody the physics.   Indeed, the fact that Ed Witten received a Fields Medal, rather than a Nobel Prize for Physics, pretty much demonstrates that.

Pauli was not alone in his lament.   Schrödinger to Bohr, 1926:
If we are going to stick to this damn quantum-jumping, then I regret that I ever had anything to do with quantum theory.

And Einstein in 1924, re the idea of renouncing strict causality:
I would rather be a cobbler, or even an employee in a gambling house, than a physicist.

This is rather a rarified kind of job-dissatisfaction.  It is as though a carpenter, towards the end of a long and successful career, were to cry out, “Had I known that wood is mere cellulose, rather than a habitation for dryads,  I would have preferred to have been anything -- a plumber or a physicist -- rather than this!”

But the phenomenon does exist.  The author in which I found those two quotes -- J. C. Polkinghorne, The Quantum World (1984), p. 53 -- after a distinguished career as a particle physicist, resigned his chair, and became a vicar in a country parish in Kent.  It was from this Father-Brown-like living that he published his popular little volume with Princeton University Press.
Similar instances could be cited, notably Alexander Grothendieck.  (Motif: “Goodbye to All That.”)
~    ~    ~

Beauty is Truth, Truth Beauty—NOT

In science and mathematics, theism is a prophylactic (against narrow empiricism), but not a guide (so far as I know).   It is thus to be contrasted with Beauty (the capitalization is here sarcastic), which some scientists, and all popular science writers, have contended  may legitimately guide physical research.  But it is a slippery cicerone of a guide.   Few more beautiful notions have been put forth  than Kepler’s structuring of the solar system upon the quintet of Platonic solids.  For that matter, circular orbits may seem prettier than bulgy ones;  and the vision of the planets being chivvied along on these  by attendant angels, like the blowing winds at the four corners of medieval maps, is charming.  The successors to these pleasing pictures  have their own, more austere, beauty:  but only in hindsight, or to their inventors.  At any given stage, our aesthetics are too underdeveloped to be trusted to guide us aright.

Scientists have indeed sometimes had Beauty in mind, at some point, during their pursuit of an intriguing hypothesis.  The cases in which the hypothesis proved correct, are the ones we hear about.  No-one pens a memoir boasting how the pursuit of pure Beauty led him into a scientific dead end.

But the reason for the prevalence of paeans to Beauty in popular science writing  probably owes less to the former class of experience, than to mere expediency.  The man on the omnibus  figures he knows a bit of Beauty when he spots some, just don’t bother him with a lot of messy maths.   Kekulé  dreams of the Ouroboros, and next thing you know  has figured out the carbon ring.  A cinch!  So the author can flatter such readers’ fancy, while sparing them brain-crunching labor, doling out little toy versions of Black Holes, String Theory, or what have you.

It must be allowed that physicists do sometimes speak in such terms, even when talking quietly among themselves, rather than attempting to stun the public into goggle-eyed Gawsh-Paw stupefaction.   Here is one instance, deliberately cited from a textbook aimed at physics majors, rather than from public lectures or popularizations:

R. Adler, M. Bazin & M. Schiffer, Introduction to General Relativity (1965), p. vii, 1:
Since there are numerous works available which deal with the general theory of relativity, some of them masterful and even classical, it seems necessary to explain the specific intention of the present book.  … Our principal aim has been to show the close interaction of mathematical and physical ideas, and to give the reader a feeling for the necessity and beauty of the laws of general relativity. … General relativity … represents a fusion of mechanics and the theory of gravitation, on the one hand, and of geometry, on the other.  The combination … will result in great formal beauty and mathematical elegance.

(“Elegance” in particular  is a favorite mathematician’s word, less gushy than “beauty”.)

Steven Weinberg, Dreams of a Final Theory (1992), p. 6:

When it turns out that mathematically beautiful ideas are actually relevant to the real world, we get the feeling that there is something behind the blackboard, some deeper truth foreshadowing a final theory that makes our ideas turn out so well.

That Platonic thought is congenial, but let’s look closer at this epithet “beauty”. 
For the actual discoverer, such a frisson is no doubt felt. Platonic Forms get good reviews, from those who have been privileged to glimpse them.  And these essays have tended to a Realist view of these Forms (in tune with a background assumption of theism).  But that much leaves open, where and whether and to what extent these Forms may manifest themselves in the actual rough and tumble of this world.   Our life here below is littered with broken symmetries and broken hearts.

Weinberg is a particularly stellar theoretical physicist, and thus equipped to say such things if anyone is.   But note that scientists who talk like that  tend to be mathematicians or physicists, not chemists or stock-breeders.  (Or syntacticians, for that matter.  Despite the increasingly abstract and structured nature of one well-known line of inquiry, its proponents have never been guilty of marketing it for its “beauty”.)  And the pulchritude alluded to tends to be the clarity of the blackboard, not the messiness of the lab.

In the face of testimony such as that quoted, beware too the selection effect:  What makes it onto the printed page are Winner’s Narratives.  Basking in his Nobel, the lionized scientist allows as how “I gazed on Beauty bare, and she did spread for me  the doors of Truth”, much as the (perhaps accidentally) successful investor will wink and share his Winning Formula ("Always go with your gut" or whatever).  Meanwhile there have been a great many first-rank scientists who thought they had a truly beautiful idea, but you don’t hear about it, because it didn’t pan out (Lord Kelvin with his vortices in the ether, Karl Pearson with his ether squirts).

Aestheticism in general is not notably congenial to the scientific enterprise.  That same Keats who perpetrated the (too-)oft-quoted jingle “Beauty is Truth, Truth Beauty” (adding, in a slogan worthy of Big Brother, “That’s all you know, and all you need to know”) once proposed a toast “to the confusion of Newton” for having explained the rainbow (all this, one imagines, shortly before his cortex melted into a syphilitic soup, the effect of having embraced one beauty too many in Drury Lane).
There is some potentially valid content to this “beauty” motif:  basically, the focus on structure rather than number, clean architecture rather than the kludge.  (Though if Nature herself prove a kludge, as maintained by the Landscape physicists, we’re out of luck.)  Whether the deeper understanding we may thus arrive at is best described as “beautiful” rather than “sexy” rather than “chilling” rather than “scrumptious” rather than “word, dude!”, is unimportant.  The practical reason for all this “beauty” talk  is that it sells books.  And the reason for that is a matter of bad faith:  John Q. Public (commendably) approaches the altar of science, presided over by a handful of high priests; but then his strength fails him; will this be hard, like calculus? and at once comes the coo of reassurance:  “Nooooooo,  wee  ah-rin thee land of byooooooty, all yooo have too doo is feeeeeeel”…  Yeh, right.  That is the attitude which plastered Weinberg’s perfectly clear and level-headed book with the gooey title, “Dreams….”  (presumably that was whelped by some gnome in marketing, not by the author himself).

If string theory should eventually turn out to have been a dead end for physics, then the mathematical Beauty that  for so many years  mesmerized its devotees  may be said to be that of the Sirens.


[Further notes]
Cf.  Daniel Silver, “Knot Theory’s Odd Origins”, in American Scientist, March 2006, ironically imagining the mental state of  Peter Tait and Lord Kelvin as they put forth their theory that “chemical elements were knotted tubes of ether”:

No cumbersome hypotheses would be needed to explain chemical properties;  they were a result of topology.  It was simple and beautiful -- it had to be true.

A healthier attitude, cited by George Szpiro Poincaré’s Prize (2007), re the reception of G. Perelman’s proposed proof of the conjecture:

They both found the papers  beguiling in their beauty.  But somebody needed to check the nuts and bolts.

Arthur Koestler, The Act of Creation (1964), p. 213:
All through his life  Kepler hoped to proved that the motion of the planets round the sun obeyed certain musical laws, the harmonies of the spheres. … Kepler never discovered that he was the victim of a delusion.

Arthur Koestler, The Act of Creation (1964), p.330:
False inspirations and freak theories  are as abundant in the history of science  as bad works of art.

Hadamard is an adherent of the beauty criterion, at least for math, and at least for the practice of math (rather than as a criterion of truth for the results):

These examples are a sufficient answer to Wallas’s doubt on the value of the sense of beauty as a “drive” for discovery.  On the contrary, in our mathematical field, it seems to be almost the only useful one.
-- Jacques Hadamard, The Psychology of Invention in the Mathematical Field (1945), p. 130

The English mathematician Hardy  in effect goes further, since he privileges beauty, not only as a motivation for mathematical praxis, but for the results themselves:

 Beauty is the first test:  there is no permanent place in the world  for ugly mathematics.
-- G.H. Hardy, A Mathematician’s Apology (1940)

[Update]  From Freeman Dyson’s review of a new biography of Paul Dirac (The New York Review of Books, 25 Feb 2010):

The doctrine of mathematical beauty  is itself beautiful,  and there is no doubt that Direc believed it to be true.  But it does not agree well with the historical facts.  During the wonder years when he was making his great discoveries, his thinking was more concerned with practical details  and less with abstract beauty.  And during the long second half of Dirac’s life, when he was preaching the doctrine of mathematical beauty, it did not lead him to important new discoveries.

For more, here (ere I die):

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