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:
*
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-19th 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:
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