Slices of Time

Brian Greene monostich

(Not quite a monostich,

nor a haiku neither.

It is  what it is.)

Every moment is illuminated,

and every moment    remains illuminated.

Every moment  is.

-- Brian Greene, The Fabric of the Cosmos (2004), p. 141

https://en.wikipedia.org/wiki/Everything_Is_Illuminated

~

I have  on occasion  fulminated against “Physics porn” -- the tawdry down-dumbing of physics for a popular audience -- not so much a matter of (necessary) simplification, as of appealing to their baser, sensationalistic instincts.

Brian Greene does not practice that. The books of his that I have read (The Elegant Universe, The Fabric of the Cosmos) -- with titles like the Parthenon, elegant but restrained -- are worthy examples of haute vulgarisation.   The matters he treats of  are difficult to explain, even to fellow-physicists (if they work in a different lab, and thus subscribe to a different groupthink); he does a laudable job of trying.  Moreover, the fellow writes really, really well -- at times even poetically (witness the above).

Nor is the cited haikustich  poetry merely.  The idea behind it, appears in the next paragraph  in plain prose:

Einstein said that the problem of The Now  worried him seriously.  He explained that the experience of the Now  means something special for man, something essentially different from the past and the future, but that this important difference  does not  and cannot occur within physics.

Albert Einstein,  worrying about The Now

That is not to suggest that the Now at all resembles a mathematical instant, as in the calculus and thus in classical physics.  Each perceived ‘moment’ of consciousness presumably corresponds to an integral over some interval.   The ‘density’ being integrated need have no determinate evaluation at a single point of the continuum, any more than does the Dirac delta.  The psychological present is more of a Nowabouts.

The same point, with a different metaphor:

The practically cognized present is no knife-edge, but a saddle-back, with a certain breadth of its own  on which we sit perched.

-- William James, The Principles of Psychology (1890), vol. I, p. 609

The present is simply the past’s ever-moving outer edge.

-- Hendrik Hertzberg in The New Yorker, 18 Dec 2006, p. 33

~

That the “now”, as such, has no special status in physics, is unsurprising, since it is relative to each observer.  That simultaneity (implicitly dependent thereon:  “Both A and B are happening now”) turns out to be untenable, was a shock introduced by Einstein; eventually you sort of learn to live with it.   The real scandal is that physics is likewise agnostic as to any distinction in principle between the future and the past.   And that thesis is cognitively and theologically abhorrent.

Feynman among others calmly accepted solutions to equations, whereby certain particles ran backwards in time.  At its grandest, as a prominent mathmatician-cosmologist writes, “the time-reverse of the universe  is just as much a solution of the dynamical equations” as the one we thought we lived in (Roger Penrose,  The Road to Reality (2004), p. 729).

For humans, the unidirectionality of time’s arrow  is as fundamental as the privileged status of the Now.  America’s premier 19^th-century psychologist, on remembering:

However the associationist may represent the present ideas as throning and arranging themselves, still, the spiritualist insists, he has in the end to admit that something, be it brain, be it ‘ideas’, be it ‘association’, knows past time as past, and fills it out with this or that event.

-- William James, The Principles of Psychology (1890), vol. I, p. 2

eppur’ si muove …

~

James crops up in the first paragraph of a New York Times op-ed concerning durée (subjective time) from 10 May 2015, by Gregory Hickok, a professor of cognitive science:

In 1890, the American psychologist William James  famously likened our conscious experience to the flow of a stream … the stream … of consciousness.

The professor then puts his predecessor in his place:

Recent research has shown that the ‘stream’ of consciousness  is, in fact, an illusion.  We actually perceive the world in rhythmic pulses rather than as continuous flow.

The cognitive scientist then climbs down a bit from the claim that this insight is “recent” -- “Some of the first hints of this new understanding came as early as the 1920s, when physiologists discovered brain waves.”

One suspects, however, that James would not slap his forehead upon being apprized of this newly-minted insight, since he cites “the Humian doctrine that our thought is composed of separate independent parts, and is not a sensibly continuous stream”.  (Hume wrote in the eighteenth century.)

The latest in Math Porn

An attempt at moyenne (ou basse) vulgarisation, by a (slumming) specialist in Category Theory:

To make mathematics palatable for the lay reader, the author must sweeten the pill. There are many ways to do this, but Eugenia Cheng is surely the first to have approached the task literally, writing a math book in which almost every chapter begins with a recipe for dessert.

Cheng never quite overeggs her metaphor of the mathematician as chef, however …

But while she successfully conveys a love of her subject, I felt shortchanged; Cheng never explains exactly how category theory has shaped math, never shares its major results and its great unsolved questions. Perhaps she thought the answers would be too arcane or complicated for a book aimed at general readers.

http://www.nytimes.com/2015/06/14/books/review/how-to-bake-pi-by-eugenia-cheng.html?emc=edit_bk_20150612&nl=books&nlid=5160164&_r=0

Hard to get more random than that.   How mathematics is like a poker game;  how mathematics is like baseball;  how mathematics is like a chimpanzee riding a bicycle …

It is not that one cannot introduce ideas of category theory to an intelligent general audience, without flattering their baser natures with similes from the kitchen. Lawvere & Schanuel do just that in Conceptual Mathematics (1997): elementary in the sense that it begins from the elements, without assuming technical prerequisites from special fields, but sophisticated in that it doesn’t glide or gloss over.  But you won't find that sort of thing reviewed in the New York Times, where (increasingly) puff-pastry drives out the protein.

Taylor Swift nude pixxx!

Among the challenges for anyone attempting haute vulgarisation in the exact sciences, is the following phenomenon, epigrammatically summed-up by Stephen Hawking:

“Every equation  halves the number of readers.”

Now, blogspot.com helpfully supplies realtime stats;  so we shall test that proposition experimentally.

This post has been up for twenty minutes now, and … lessee … by the meter, it is presently enjoying roughly a million pageviews, based upon the subject-line alone.  (Were we to add an actual photograph, it would probably crash the server.)

Let us then add one equation, and re-sample:

2 + 2 = 4

[Update, twenty minutes later]  Well, even that proved too much for most:  viewership has plummeted by half.

(Rather a simple repellent, that;  like the storefronts that play classical music to shoo away the teenagers.)

Let’s try again, with something more substantial:

Einstein field equation

Whoa -- overkill!  That one knocked out all but a hardy hundred-thousand!

Okay, let’s dial it back:

Fresnel formula

Aww, c’mon, gang, that’s just trig!  But ninety-percent of Web-surfers to this page have just dropped out, leaving a bare thousand.

 

Probably just a statistical fluke.   Let’s try again:

Klein-Gordan

D-d-dang!  Hawking if anything put it too mildly.   Now there are only a sturdy hundred viewing this page.

 

Well, those formulae were all from physics (Hawking's field).   Let’s try again, with one from number-theory:

Riemann zeta function

Alright, end of experiment.   At this moment, there are only a bare ten readers viewing this page.

But these are the readers we want!

~

For many mathy goodies, click here:

http://worldofdrjustice.blogspot.com/2015/01/miscellanea-mathematica-quater-renovata.html

http://worldofdrjustice.blogspot.com/2014/11/topics-in-math-remise-jour.html

[Update]  Advice to onanists:
Do not indulge that private vice.  It can lead to insanity, and it grows hair on your palms.

Prison Mathematics (sentence extended)

We earlier spoke of the prison experiences of the stellar mathematicians André Weil and Neil Koblitz (“Adventures on Algebraic Geometry”).  It turns out that the author Arthur Koestler -- though not himself a mathematician --  likewise had fruitful recourse to math while imprisoned;  and, like Weil and Koblitz, was in prison for (roughly speaking) an unjust war (in this case, that of the Nazi-backed Franquistas against la  República in the Spanish Civil War).  As recounted in an excellent biography:

Koestler concluded that his hours spent by the prison window  scratching equations  had brought mystical insights into another realm of being.  He was filled “with a direct certainty that a higher order of reality existed, and that it alone invested existence with meaning.”  Koestler likened it to “a text written in invisible ink;  though one could not read it, the knowledge that it existed  was sufficient to alter the texture of one’s existence.”

-- Michael Scammel, Koestler (2009), p. 150

From this metaphor, Koestler drew the title of his psycho-political memoir, The Invisible Writing.

[Footnote:  One might include Galois -- another anti-tyrant -- in this company.  Though not imprisoned, he carried out his last great work  under effective sentence of death.]

[Post-footnote:  We are each of us, actually, under sentence of death.]

[Update 23 November 2013]  From the memoir of a front-rank mathematician, and refugee from Soviet oppression:

While in prison, Weil wrote a letter to his sister Simone Weil, a famous philosopher and humanist.   This letter is a remarkable document;  in it, he tries to explain  in fairly elementary terms (accessible even to a philosopher -- just kidding!) the “big picture” of mathematics  as he saw it.  Doing so, he set a great example to follow for all mathematicians.  I sometimes joke that perhaps we should jail some of the leading mathematicians  to force them to express their ideas in accessible terms, the way Weil did.

-- Edward Frenkel, Love & Math (2013), p. 96

~            ~            ~

Other historical examples:

     Poncelet in prison, reviving projective geometry.

Not everyone is so tough:

Brouwer would spend many a university holiday in the army.  The most lasting effect of his military training  was that it ruined his health and his nerves.

-- Dennis Hesseling, Gnomes in the Fog:  The Reception of Brower’s Intuitionism in the 1920s (2003), p. 28

.

ON DEPTH AND BREADTH (überarbeitet)

            Someone (and since I forget who, it is as if the words had passed into proverb) once said: “A brilliant person is one of whom I think: I could have done such work, if only I were ten times smarter.  But in the case of a genius [here the reference was, if memory serves, to Feynman, and the epithet might actually have been not “genius” but “magician”], I can’t even imagine how it might be done.” 

            That is the depth dimension, often commented upon.

            Less obtrusively, because  by its nature  never to be noticed save over time,  is a baffling precellence of breadth.

   
  This thought arises as I finish Ian Hacking’s The Taming of Chance.  Hacking is unfailingly intelligent, but not deep beyond one’s reach.  He has a modest, easy style.  He’s not a bibliographic bully, forever quoting Kant or Toqueville or whoever you haven’t read, a propos of everything and not always with necessity (“Will the Red Sox prevail next season?  Only time, as Aquinas would have it, will tell.”).  He does not throw up a Potemkin village of supposed sources, a bibliography stuffed with Lukacs and Plato, longer and denser than the slender article it supports, topped off with epigraphs from Wallace Stevens and Valéry. Yet with everything of him I come across, he reveals a new side of him.  A polymath;  forsooth, a polytope.

            The first thing of his I read – and warmly recommend – was The Emergence of Probability. Here he seemed one of those philosophical mathematicians-manqués of the stripe of Putnam or Quine, who write with wit and erudition about technical subjects, but (one eventually finds) pretty much plow the same furrow in their various works.  Only, in later works he reveals himself as a closet Foucault fan (to this reader, as far from Kolmogorov as, I don’t know, a Red Sox fan).   And he’s written complete books on purely psychological subjects.  In The Taming of Chance, he returns to the subject of Emergence from a (crucially) slightly different angle, so that the book covers much of the same ground  but with a very different feel and specificity.   It doesn’t even have a bibliography, you have to dig it out of the footnotes.  Yet see what the spade unearths! Page after page of primary sources, like one William Turnbull’s Treatise on the Strength, Flexure, and Stiffness of Cast Iron Beams (London, 1831), or of secondary ones from obscure nooks, like the Tübinger Zeitschrift für Staatswissenschaft 4 (1863).  He cites Bernoulli, fair enough – but wait, not (or rather, not only) the celebrated Jakob of the Ars Conjectandi (which --though I haven’t read it and probably never will-- is a recognized landmark in the field),  but Johann – yet wait again, not that Johann, that familiar Johann “Jock” Bernouilli whose works you probably have on your night-table, but the later one; and not his mathematical publications neither, but rather his  no doubt in its day rightly celebrated  Reisen durch Brandenburg, Pommern, Preussen, Curland, Russland und Pohlen, published in four volumes over the course of that busy year of 1779-80 (in memory still green), and of which Hacking’s unobtrusive morsel is quarried from volume two.

            This is not what is meant by being merely, or even hugely, “well-read”.  Well-read means you’ve read all the classics throughout history in every major language in every field, and absolutely every scrap of anything at all in your own particular specialty (published or in preprint – or in papyrus --  ancient or modern), plus the odd condiment from among contemporary novels, Doonesbury,  or the folks at Port-Royal.  That’s hard enough-- I read all the time; always have; and am still just hitting the high points (and forgetting much).  Yet given 400 hours in a week instead of forty, and a couple of lifetimes tacked end to end, plus total recall, one can imagine doing it.  But the “Compte rendu des travaux de la Société phrénologique pendant le cours de l’année 1839”, which Hacking uses to such telling effect, is not on anybody’s reading list.  The ergodic reader ranging over all space  would perish in the heat death of the universe before striking upon this. 

            In fact, the whole situation puts me in mind of what Lszlew Brnzowlski so memorably said in his (partially encrypted) diary entry for 3 April 1648 (U. Tbilisi MS #9784-K) --…  No it doesn’t.  Haven’t read it.  Never heard of it.

Postscript.

            

Hacking himself can strike a stance of amazement at (allegedly) recondite knowledge.  In a chapter on philology (in Historical Ontology, p. 141), citing Foucault’s discussion of Schegel, Bopp, and Grimm, he exclaims: “Who on earth was Bopp?”  (One of the most celebrated names in the history of philology, that’s who.)  This is no doubt a pose, to let the reader catch his breath, and to chummily pretend that we’re all just struggling along here together, lads -- the way someone expounding physics for a lay audience will strive to make it all “more accessible” by sprinkling-in little apology-markers (“what physicists call the ‘spin’ of a particle known as the ‘electron’”;  “the so-called ‘Higgs boson’”;  “something called a ‘photon’”).  But shortly thereafter, Hacking himself calmly goes on to dust off such truly obscure proto-philologists as, um, “Chladenius”...

And if all that is making you feel stupid (as it certainly should),  here’s something to make you feel even stupider:

        De Stultitiâ

*

One naturally does not notice, upon first or second acquaintance, any lack of breadth  in any favorite author of your own.  You go to him for some few things, whatever they might be, and are delighted to find them again.  We do not reproach the humble hamburger, for failing to be a quail;  nor the quarterback, for lacking the qualities of a third-baseman; nor Dickens, for his obstinate indifference to the more recent developments of the higher calculus; nor indeed the Gospels, for lacking tomorrow’s weather forecast. Yet if some author comes to be our guide, our lens upon the variety of life, we do  in time  notice any astigmatism, or narrowness of the field of view.

            For some time, Orwell was my cherished author, seemingly spanning great territories: as novelist, memoirist, and critic – nay, ever as a fighter at the front --: noted in particular for his splended essay attacking insularity, “Inside the Whale”.   It was only a chance remark of his, apologizing for not having read more than several dozen of the (delightful, but) trifling novels of P.G. Wodehouse, that it struck me, how much had escaped his notice while he was so occupied:  scilicet, virtually every world-shaking intellectual development, be it in physics, mathematics, biology, philosophy,  from the mid-19^th century   on.

            Tolkien created a world, Middle Earth,  commended (in Webster’s Encyclopedia of Literature) as “one of the more detailed of all fantasy worlds”, yet which always struck me as narrow to the point of suffocation.  GKC  creates an  in some ways  similar world, but which has airholes into the infinite, which let us breathe. C.S. Lewis, in his childhood, together with his brother, created such a puppet-theatre world, reminiscences of which survive in his adult fiction; but he bursts its walls decisively  in all his essays.  His world is wider; retaining (in his own metaphor) the furniture of the nursery, side by side with the cold hard sunlight of the new world.

            It was in the course of reacquainting myself, with the saga of Greek antiquity, and Roman valor, that I happened to notice  the absence of any echo thereof, in any of the aforementioned authors. (The mindworld of Lewis embraces Northern mythology, but nothing earlier.)

*

Other such instances.

Re Otto Rank, Ernest Jones speaks of

… his truly vast erudition;  it was quite mysterious  how he found the time to read all that he did.  One of the compliments I treasure in my life  was when he asked me wherever I had found all that material in one of my non-medical essays;  that the omniscient Rank should be impressed, signified much.

-- Ernest Jones, Freud: Years of Maturity (1955), p. 160

Richard Fortey, Earth (2004), p. 314:

            One of the chief proponents of the [Snowball Earth] theory is Paul Hoffman at Harvard, one of those American academics who seem to have twice their fair share of energy. If expertise is defined as knowing  more and more  about less and less,  I am at a loss to describe what it is to know more and more  about more and more – but that is the Hoffmann condition.

*

In a work, written in English, and  ostensibly directed at engineers and physicists, subsequent to a discussion of infinitesimal deformation and path systems, we read:

We shall not go further into this approach here.  It is done quite simply and naturally in a classic paper by J. Radon.  Indeed, since this paper is one of the clearest and most elegant in the entire history of the calculus of variations, we prefer to suggest to the reader  that he consult it directly.

-- Robert Hermann, Differential Geometry and the Calculus of Variations (1968), p. 257

An admirable suggestion!  One hopes, however, that our pocket-protector-sporting anglophone engineer has been keeping up his German, and has ready access to an enormous research library, since it was published in that language (“Zum Problem von Lagrange”) back in 1928, in a relatively obscure series (Hamburg. Math. Einzelschriften, Leipzig).

*

[Update Jan 2012]  Freeman Dyson on his depth stage and his breadth stage:
http://moreintelligentlife.com/content/ideas/charles-nevin/60-year-job-freeman-dyson

~            ~            ~

For a different essay covering distinct though similar ground, try this:
http://worldofdrjustice.blogspot.com/2010/12/on-scope-and-difficulty.html

For depth itself, as deep as it gets (which is in mathematics),  this:

http://worldofdrjustice.blogspot.com/2014/01/a-dive-to-depths-expanded.html

Math Porn

As we remarked earlier (Mathsex) the intersection of mathematics and literal pornography is a set of measure zero.   (A perhaps/perhaps-not  related fact, is that mathematicians themselves are entirely sexless.   They certainly do not reproduce biologically;  in fact, they do not even reproduce academically, most great mathematicians having been lousy lecturers -- and I mean really, really bad.  Instead, each individual mathematician-to-be  receives an Annunciation -- from which archangel, I alas do not know, never having received one, despite fervent prayers.)

Even “porn” in the journalistic sense, not of actual pornography, but of tawdry crowd-pleasing shallow presentations of deep subjects, seldom if ever is to be found in the same bar-booth with Mathematics.  (For a list of subjects that do so lend themselves to marketplace exploitation, consult our definitive document:  Funporn.)

Yet it is now our sad duty to report, that we have, for the very first time in our young life (young with respect to the afterlife, that is;  w.r.t. any of you-all whippersnappers, ancient), encountered an actual specimen of “math porn” (although in a very limited sense, as we shall see):  Popular Lectures on Mathematical Logic (sic, sic, sic), published in English in 1981, by the philosopher-logician Hao Wang.

There is a long tradition of lectures to the general educated public on scientific topics, by men preëminent in their field.  These were often later collected and published as volumes, sometimes with “Popular Lectures” in the title, by such true luminaries as Mach, Kelvin, Helmholtz (these in physics, though, note;  not mathematics).  The heyday for this activity was the late nineteenth century.   Their success presupposed a pool of educated laymen keenly interested in learning more about the intellectual forefronts of the day.

In America, the tradition survives sparingly, in university towns.   While our family lived in Princeton, I used to attend evening lectures at the IAS, held in their largest lecture hall.  Occasionally the audience was overflowing -- standing, or sitting on window-ledges.

Wang’s book likewise originated in public lectures -- though not perhaps to the general public, since they were given at the Chinese Academy of Science  (in 1977; translated  and published in English  four years later).   But by no stretch of semantics do they qualify as “Popular Lectures”, nor even as “Introductory Lectures for Logic Majors”.   (Of course, Wang himself may not be responsible for the English title of his book;  it may have been cooked up by some hunchbaked, drooling drone in the marketing department.)   Already on the eighth page of the introductory lecture, we read this (typical) passage:

Around 1960, Hanf numbers appeared, and Scott proved that measurable cardinals yield nonconstructable sets.  Results often mentioned as being impressive  are Morley’s theorem on categoricity in power, and applications to algebraic problems by Ax and Kochen.

Solovay soon proved the consistency without dependent choice  of the proposition that every set of reals is Lebesgue measurable.  (He has to assume that there are inaccessible cardinals;  it remains an open problem whether this stronger assumption can be avoided.

(There is no definition of any of these terms, like “inaccessible cardinals”, in early pages.  You’re supposed to already know this stuff.)   Now, for a non-specialist, it will be hard to judge just where that passage stands in the spectrum of difficulty;  but as a thumbnail comparison:  at Harvard, I took introductory logic in the philosophy department, and then straight logic in the math department, and we never got anywhere near these topics.

Lest  for some reason  Wang might have shoved all the hard stuff into the very first lecture, so as to clear the auditorium of lightweights, and become more pedagogical later on, I opened the book at random, happening upon this:

Exercise 2.  Find a direct proof of Corollary 1.3 without appeal to Lemma 1.1

You do not pose such homework in a “popular lecture”.  The book’s title amounts to false advertising  -- publishing-fraud.

~

The infraction perpetrated by the Wang book is minor -- a scattershot gallimaufry of sketches-for-an-idea-for-an-article on unrelated subjects, mislabeled as a popular introduction to a single subject -- and may well be laid at the door of the publisher rather than the author.    But now we must notice something more serious:  actual pandering to the public’s ignoble propensities, in the matter of math.  The book is titled The Math Instinct:  Why You’re a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs), by Keith Devlin.

It has been well remarked, “As a rule, perjury in subtitles should be forgiven”.  This formulation was by Tony Rothman of Princeton, writing in American Scientist (March 2007), reviewing a biography by Siobhan Roberts, of the solid geometer Coxeter, King of Infinite Space, bone-headedly subtitled The Man Who Saved Geometry.  (It didn’t need saving, and he didn’t do it.)   But in the “Why You’re a Mathematical Genius” case, it is not just something tacked on by the publisher, it goes to the heart of the book:  “Devlin tries to make the subject less intimidating by demonstrating that math is all around us.”   That formulation is already cognitively-impaired;  “math” is all around us only in the sense that relativistic quantum mechanics is all around us.  Stuff is all around us, and a very few people (not you, not me) are able to make sense of some of it, somewhat (though less than is popularly assumed) by deploying a mathematical armamentarium:  neither Nature’s intricate hidden design, nor the occasional successes of experts, make you a mathematical “genius”.   And actually, few would be fooled by such transparent flattery (though it is of a left-handed sort, since the reader’s putative “genius” is, with the next breath, set at the level of lobsters);  one wonders why the publishers thought the public would be suckered-in by such fluff, rather than nauseated.   The answer no doubt is that such an approach is in tune with the general trend in America to “celebrate” one another’s narcissism.   That frame of mind does not make for keen exposition; as the reviewer in American Scientist remarks (Nov 2005, p. 572),

Devlin seems uncertain what his readers will need to have explained.  He reminds us that bats are mammals, but doesn’t define Ohm’s Law.

The case is the sadder since Devlin himself knows better.  He once wrote a very good semi-popular survey (only “semi-“, since equations do appear), Mathematics:  The New Golden Age (1999).   In this case, the rather grand subtitle is actually warranted: for while the great age of math as a handmaiden to physics is behind us, in the past half-century or so  it has effloresced to an astonishing extent as a multiply-connected enterprise in its own right -- with just enough new practical uses in cyptography and (if this one prove more than a dream) string theory, to keep it anchored.

~

It is now our happy privilege, likewise to report, that the other book occupying us this weekend, is precisely the opposite to the sugar-coating of the Wang packaging:  The title austere, uninviting;  the content as propaedeutic and intuitive as it is possible to be.  We refer, with reverence, to a book likewise originating in (semi-) public lectures (at UCLA, in the early 1980s):  Richard Feynman’s QED, published by Princeton in 1985.

The title might inspire a spurious sensation of familiarity:  quod erat demonstrandum, in which case it might fit a set of lectures on high school geometry.  But no, the acronym denotes something much more fearsome, something …. (but send the children to bed, before you scroll down)

…

…  nothing less than …

(horresco referens)

…

 =>  QUANTUM ELECTRO-DYNAMICS.

For years (decades, actually) I avoided this slender volume, though it stood on my shelves, owing to the misapprehension that, based on its titled subject-matter (which presupposed basic quantum mechanics) it must be significantly more difficult than the Big Red books, aimed at physics-major freshmen, on which I was weaned.  Yet not so.  Feynman, a master of exposition, offers the most intuitive account possible, of a highly non-intuitive subject.   Intuitive, yet not dumbed-down:  it takes a genius to tackle that.

But nota bene:   He never endeavors to coax you into thinking something is easier than it is, nor to flatter you that you have understood something when you have not -- both being common expository strategies of popularizers of science in this Age of Self-Esteem.

Rhetorically -- engagingly -- Feynman adopts the opposite strategy, hinting at what you are up against, though not bullying.  In the opening of the introductory lecture, he makes the quite accurate though socially/intellectually scandalous observation that

Everybody who comes to a scientific lecture  knows they are not going to understand it, but maybe the lecturer has a nice, colored tie to look at.

The second lecture, raising this observation to the status of a meme, opens thus:

This is the second in a series of lectures about quantum electrodynamics, and since it’s clear that none of you were here last time (because I told everyone that they weren’t going to understand anything), I’ll briefly summarize the first lecture.

The next begins:

This is the third of four lectures on a rather difficult subject -- the theory of quantum electrodynamics -- and since there are obviously more people here tonight than there were before, some of you haven’t heard the other two lectures  and will find this lecture almost incomprehensible.  Those of you who have heard the other two lectures  will also find this lecture incomprehensible,  but you know that that’s all right:  as I explained in the first lecture, the way we have to describe Nature  is generally incomprehensible to us.

This stance, though fey in a way, is yet preferable to that of the Theory-of-Everything charlatans who babble on about Beauty, implying that they can share their vision by mere dermatological osmosis.   There was one such on NPR’s science show last week  -- a string theorist yet, which is to say:  a specialist in a fashionable but drastically unintuitive math-packed would-be-physical theory, which, additionally, may well be actually wrong as a description of the real world -- or, worse, “not even wrong”.  But the interviewer kowtowed and pandered, and the interviewee luxuriated in his 15 famous minutes, as in a warm bubble-bath, complete with rubber duck.

A far more prominent string-theorist, Frank Wilchek, of the IAS, has a similar piece in a recent issue of Nature / Physics (Nature, by the way, seems to be in some ways following Scientific American down the path of corruption), calling on us all to “celebrate Beauty”.  -- By all means, say I, let us do so, and preferably in the altogether;  but don’t go calling it physics.

~

[Update & after-reflection]  The title (and thesis) of Devlin’s book are misconceived in a rather subtler and more substantial way than the undraped pandering of the subtitle:  The Math Instinct.     Because, in fact, there isn’t any.

I satirized the thesis that there is one -- honed, like the other instincts, by Natural Selection -- here:

The Urysohn Metrization Theorem:

an Adaptationist Account

However, the Ultradarwinians were not our real quarry in that sotie, but rather the mathematical Nominalists.

Devlin’s title echoes that of an earlier and much better work of scientific popularization, Steven Pinker’s The Language Instinct.   Here, the title is no mere gimmick from the marketing department:  the author is well aware that, properly understood (something that itself is no easy task), the positing of a language instinct constitutes a highly contentful, counterintuitive, scientifically testable, and in some quarters bitterly controversial hypothesis.   It is one that Chomsky and those in his intellectual wake  have been investigating with great ingenuity, for over half a century now.   They have made a telling case (though one that has become more difficult to understand as the theory itself advanced, rather the way Galilean mechanics are more intuitively accessible than Quantum Field Theory), one which need not here be passed in review.

With mathematics, matters lie quite otherwise. …

[To be continued, if reader interest warrants.  In the meantime, consult our counterthrenody to the thesis of universal mathematical genius:   Oligophrenia Mathematica.  ]

[Update Oct 2013]  Continued here.

The Rapid Rate of Change (changed)

~ “Plus ça change, plus c’est la même chose.” ~

The other day I happened upon this passage:

News travels fast and far in the Internet age.  The pulse of all humanity is quickening, as if our planet, after traversing, on its journey through space, some somnolent and bemused zone of the Universe, were now emerging into a region bathed in vivifying rays, or filled with cosmic benzedrine in the insterstellar dust.  It seemed to act simultaneously on all levels of the nervous system of mankind … as a stimuland and aphrodisiac, manifesting itself as a thirst of the spirit, an itch of the brain, a hunger of the senses, a toxic release of the passions.  The human glands seemed to produce a new hormone. 

Only…. not quite that passage.   The quotation is from Arthur Koestler’s The Sleepwalkers, chapter “Rumour and Report.”  It begins:

News travelled fast and far in the sixteenth century.

and otherwise continues as above, though in the past tense ("was quickening", etc.).   The technological element then was the invention of the printing press;  but as Koestler represents the scene, that was not the essence.   He describes a scene (we’re in the 1500s, mind) that could almost be our own of YouTube and Twitter, where the rapid spread of information is

a process of dilution and diffusion and distortion, which affected ever-increasing numbers, including the backward and illiterate… [reaching people not from the original texts, but] through hearsay and echo.

~

The plaint is perennial.  Here is another instance.

In 1908, Freud published a work of haute vulgarisation, "Die 'kulturelle' Sexualmoral und die moderne Nervosität”, in the charmingly titled periodical Mutterschutz.  The title is very modern, in the Modernist sense of ‘modern’ (which by now, of course, in Webworld, is old hat).  It suggests that classic of nervousness, Berlin Alexanderplatz, which  however  it anticipates by a couple of decades.  Characterizing the essay, Jones writes:

Freud quoted several writers who were alarmed at the increase of neurotic affections.  They drew a terrifying picture of the severe condidtions of life at the beginning of the century, which read strangely to those of us who look back on that epoch  as a golden age. … The essential trouble  was the incredible speed of communication in those days.

-- Ernest Jones, Freud: Years of Maturity (1955), p. 253

 ~“Nothing new under the sun” ~

~  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.)

~        

.

Physics Strip-Tease

By now I’ve read a fairish number of general overviews of modern physics, written for the layman  by physicists of note (Arthur Eddington, George Gamow, Werner Heisenberg, Richard Feynman, Heinz Pagels,  J. C. Polkinhorne,  P. C. W. Davies, Steven Hawking, Steven Weinberg, Kip Thorne, Martin Rees, Paul Davies, Roger Penrose, Brian Greene,  …..), along with a smattering of actual textbooks;  and thus managed  with time  to acquire  a veneer of acquaintance  with things that, for the most part, I don’t truly understand.  This is not intended to be as shocking a confession as may sound:  Few of us really understand much of anything;  we just get by.  And many a physicst has ‘fessed up to not truly understanding quantum theory, though able to do the calculations well enough.  (For an emo outgushing  about the similar situation in mathematics  -- if anything more severe -- click here.)

There is a metaphor  beloved of analytic philosophers:  “Our spade is turned.”  Meaning, after immense intellectual labors  continuing those going back to Plato, we can finally dig no further into the ontological fundament.   Only,  for the layman, in contemporary physics, our spade gets turned rather early.   We seldom get past the state of gaping (by the reader) and hand-waving (by the author).

It’s not the expositor’s fault.  This stuff really is hard.  It’s not enough anymore even to be a professional physicist:  if you are not a string-theorist, you probably won’t understand string theory.

So there are two things the would-be popularizer (meaning this in a good sense -- haute vulgarisation) can do.

            (1)  Sink to “physics porn”:  enticingly fluttering colored veils, till the readers are panting (Time travel !  Parallel universes !!  Higgs effing boson !!!)  and have the illusion that they have learned something.   But they will never actually enter that dark portal …

            (2) Patiently, patiently  lay it all out. -- The most successful attempt in this vein is Richard Feynman’s concise but trenchant The Character of Physical Law.  More generous with the mathematics (though short on shareable physical insight) is the not-at-all concise (doubles as a doorstop  if you never make it through) and perhaps not maximally-modestly titled  The Road to Reality, by Roger Penrose.  And even here, at its least-good, this brick-of-a-book is essentially just more abundant and more elaborate mathematical window-dressing;  I must reluctantly concur with the stern but just review here.

There is so much to learn … but the head hurts so …  Sometimes I envy the hamsters … …. ………