## Monday, December 31, 2012

### Abstraction and Generality

In the following post (q.v.)

we examined some related ideas -- analogy, generalization, abstraction -- that characterize the practice of doing math.  Herewith some further terminology along similar lines:

Geometry (especially differential geometry)  clarifies, codifies, and then generalizes  ideas arising from our intuitions about certain aspects of the world.
The theory of differentiable manifolds  is a natural result of extending and clarifying   notions already familiar from multivariable calculus.
-- Jeffrey Lee, Manifolds and Differential Geometry (2009), p. xi - 1

I find it unsatisfactory to “classify” partial differential equations:  this is possible in two variables, but  creates the false impression that there is some kind of general and useful classification scheme  available in general.
-- Lawrence Evans, Partial Differential Equations (1998, 2nd. edn. 2010), p. xix

In contrast to ordinary differential equtions, there is no unified theory of partial differential equations.  Some equations have their own theories, while others have no theory at all.  The reason for this complexity  is a more complicated geometry.   In the case of an ordinary differential equation, a locally integrable vector field (that is, one having integral curves) is defined on a manifold.  For a partial differential equation, a subspace of the tangent space  of dimension greater than 1  is defined at each point of the manifold.  As is known, even a field of two-dimensional planes in three-dimensional space  is in general  not integrable.
-- Vladimir I. Arnold, Lectures on Partial Differential Equations (Russian edition 1997; English translation 2004), p.1

His Berkeley colleague concurs:

There is no general theory known  concerning the solvability of all partial differential equations.  Such a theory is extremely unlikely to exist, given the rich variety of physical, geometric, and probabilistic phenomena  which can be modeled by PDE.
-- Lawrence Evans, Partial Differential Equations (1998, 2nd. edn. 2010), p. 3

This shows a becoming modesty, as against the media-physicists “quest” for a “Theory of Everything” -- there may be no ToE even for PDE’s.  Yet the reason he cites for their presumable non-existence seems weak, compared with that given by Arnold:  the unexpectedly rich variety of applications of this or that area of mathematics  is precisely what gave rise to the marveling at “the unreasonable effectiveness of mathematics”.

*     *     *
~ Commercial break ~
Relief for beleaguered Nook lovers!
We now return you to your regularly scheduled essay.

*     *     *

~

In this post

we described the undergraduate ‘crush’ upon abstraction, almost for its own sake.   Herewith a caution, from a very old hand in the game.

Instead of the principle of maximal generality that is usual in mathematical books, the author has attempted to adhere to the principle of minimal generality,  according to which  every idea should first be clearly understood in the simplest situation;  only then can the method developed  be extended to more complicated cases.
-- Vladimir I. Arnold, Lectures on Partial Differential Equations (Russian edition 1997; English translation 2004), Preface to the second Russian edition

Indeed, the point is not one merely of “simple” versus “difficult”:  rather, the “simplest situation” he is referring to is typically the motivating example of the theory.   Thus, the notion of a Boolean semi-ring was inspired by the facts about the Natural Numbers.

He goes on:

Although it is usually simpler to prove a general fact  than to prove numerous special cases of it,  for a student  the content of a mathematical theory is never larger than the set of examples that are thoroughly understood.  That is why it is examples and ideas, rather than general theorems and axioms, that form the basis of this book.

Bringing it all back home:

We could perhaps refer to the fact that both these statements have already been proved in Chaper III … but we prefer to prove them here  without getting involved ... with other more general problems.
-- A. D. Aleksandrov, “Non-Euclidean Geometry”, in: Aleksandrov et al, eds, Mathematics: Its Content, Methods, and Meaning (publication in the original Russian: 1956;  Eng. tr. publ. 1963), III.125.

There is wisdom in this -- not as regards the essence of mathematics in its Platonic sphere, but as regards mathematical truth proportionate to our understanding.
As:   You, the father, could say to your two-year-old, who has just snatched a cookie from the trembling fingers of his little sister:   “No!  Bad!  No steal cookie!”   -- Or you could say:  “Ahh, my young fellow!  A perfect illustration of the application of the Categorical Imperative, presented to the world by Emmanuel Kant.  Thus, let us take as given, that ….”

~

Again, the dialectic, or at least the give-and-take:

Too large a generalisation  leads to mere barrenness.  It is the large generalisation, limited by a happy particularity, which is the fruitful conception.
--  Alfred North Whitehead, quoted in James R. Newman, ed. World of Mathematics (1956), p. 411

A sharper form of generality is duality.   In its full precision, this is a concept by itself, and deserving a separate essay.  But in the following informal treatment, the term is introduced as a sort of way-station:

Before leaving 1-forms,  we digress to point out  that there exists a form of duality between the analysis and the geometrical notions …
Curves: γ is closed iff γ = 0
1-forms: ω is closed iff dω  = 0
-- Creighton Buck, Advanced Calculus (1956, 3rd edn. 1978), p. 506

And likewise for ‘bounding’ vs. ‘exact’.
Now -- this might strike you as striking  for the wrong reason:  ‘closed’ means something different in either case, as do curly-d and d;  these terms and symbols were chosen with insight aforethought, and in themselves indicate nothing.   The real meat comes in the theorems, e.g. every closed 1-form is exact iff every closed curve is bounding.
.
.

## Sunday, December 30, 2012

### Fifteen [redacted] slain in Nigeria

Under the Czars, writers of an insurrectionary tendency became skilled at getting their meaning across to the well-informed, without using certain explicit expressions that might call the censors down on their heads.  This came to be known as the Delphic style.

In our own day, on these shores, the Politically-Correct press is sometimes just as Delphic -- though here, not for the purpose of sneaking ideas across -- quite the contrary:  it is to avoid mentioning the elephant in the room.

Herewith some examples of this craven style.
~

This morning, both the print and the Web editions of the New York Times run an AP story which they headline thus:

Gunmen suspected of belonging to a radical Islamist sect attacked a village in northeast Nigeria, tying up men, women and children before slitting their throats and killing at least 15.

The perpetrators are identified as Boko Haram.  But nowhere in the article do we learn what the victims had in common, nor whether religious sectarianism had anything to do with this;  in particular, the word “Christian” nowhere appears.  Yet in fact, as you can verify from less reticent sources, all the victims were indeed Christian, and were targeted as such.

The Washington Post runs virtually the same story, but supplies a slightly different headline:

Can you imagine the NYTimes or WaPo suppressing the group identity of victims of a hate crime, if the victims had all been women, or gays, or Jews, or newspaper editors?

Note:  There are a couple of small discrepancies between the two versions of the articles.  One has “launched attacks” where the other has “initiated attacks”.  And the WaPo version adds one paragraph at the very end, suppressed in the NYTimes redaction,  still not identifying the victims of the Musari attack, but mentioning a different attack:

And violence continued around the central Nigerian city of Jos, where ethnic, religious and political rivalries have caused mass killings in recent years. Authorities said at least seven had been killed in recent days around Christian villages in the rural plateau.

Here the journalists tiptoe closer to the facts, though still  strictly speaking  leaving unstated the ethnicity of those killed;  in principle, they could have been Hindu traveling-salesmen …

~

French journalists are rather less squeamish.  Thus, Agence France-Presse:

Nigeria's Boko Haram accused of 'slaying 15 Christians'
By Aminu Abubakar (AFP)

The Nouvel-Observateur:

Nigeria: 15 chrétiens égorgés par des islamistes dans le Nord-Est

~     ~

[Update 3 January 2013]

The murder rate has been trending down in many U.S. cities, but Chicago is a sad exception to the trend.   An article in today’s New York Times alludes both to the quantitative and qualitative aspects of the problem, under the headline

What sort of divide they mean, is not immediately clear.   Are opinions divided as to how to address the problem -- more police, more gun control, curfews, perhaps?   No, the divide is, as reported, geographic;  but as every alert reader by now grasps without being told, it is also, let us say, sociological -- i.e. (inside voice) ethnic.   It was not until I read the readers’ comments -- always a useful corrective to the self-censorship of the press -- that I became aware what a remarkable juggling act their P.C. reporter had accomplished, writing an entire article about pachyderms, without once using the word “elephant”.   So to speak.

### A Fun Contest 4 U (mise à jour)

[Latest update!!  30 Dec 2012]
Charlie Hebdo publie mercredi 2 janvier un hors-série intitulé "La Vie de Mahomet", une biographie en bande dessinée "parfaitement halal", concoctée à partir de textes de chroniqueurs musulmans.

This item will sell like hot falafel!  Bulk-order Ur copies now !!!

 There's a price on my head.  That's sexy.

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

*

~  ~  ~  { Original post from June } ~  ~  ~

Think you might have drawing skills?
The famous Famous Artists School ®, where artists go to get famous, and starlets go to get laid, is offering a fab-U-lous contest.  Details here !

(“un concours de caricatures”)

Enter now and Win Big !!!!

[Flash update]  Already the entries are pouring in !!!!

29 Polizisten zum Teil schwer verletzt: Salafisten stechen in NRW auf Polizisten ein

http://www.sueddeutsche.de/politik/eskalation-zwischen-salafisten-und-rechten-pro-nrw-aktivisten-eine-explosion-der-gewalt-die-wir-lange-nicht-erlebt-haben-1.1349490

Street scenes:

[Historical footage from May Day:]
"Wir haben die Juden [noch] nicht vergast."

*
Für psychologisch tiefgreifende Krimis,
in pikanter amerikanischer Mundart,
und christlich gesinnt,
klicken Sie bitte hier:

*
For merry antics in a detective setting:
Murphy on dames

### Acrimony Among the Acolytes

[A further footnote to this:
to be incorporated later, d.v.]

The world is well familiar with the fallings-out of Freud with Fliess, and Jung with Freud.   But even at the next level down, among the tadpoles in the acolyte pool, there were acute horizontal dissensions.

Ernest Jones, an Englishman, lasted long enough in the graces of both Freud and Freudianism, to write what is or long was the standard -- and admiring -- biography of the man.    Perforce  he recounts the various fractures between protector and protégé, largely taking Freud’s side in each case.  But in the third and final volume, he is obliged to treat of a case involving himself.  Not, to be sure, any feelings of his own  of falling-out with Freud; but rather, a disasterous falling-out with Otto Rank -- or again rather, as Jones (the innocent, passive, baffled spectator here)sees it:  of Rank with him, for reasons connected with the “manic phase of his cyclothymia”.   And the rub of it was, Rank had Freud’s ear, and (per Jones’ account) poured anti-Jonesian innuendo into it -- nay, even as that vile hebenon was poured into the ear of Hamlet père -- spoiling their relations, to the point that Jones received from his beloved master  a letter of sharp rebuke, which he wincingly reproduces for his readers, as though displaying the scars of the cane.
Yet that is not the ultimate nub;  for “Rank had suffered much in childhood  from a strongly repressed hostility to his brother; and this usually covered a similar attitude toward a father.”  Already you sense where this is going:

For three years  I lived with the fear  lest Rank’s “brother-hostility” [i.e., towards Jones] regress to the deeper “father-hostility” [towards papa Freud].
-- Ernest Jones, Freud: The Last Phase (1957), p. 47

And in the next grim pages, he recounts how that tragedy  did in fact come about.

## Saturday, December 29, 2012

### Viennese Street-scene, 1926

Der kleine Hans:  Kuck mal, Mutti, den Mann da!
Die Mutter:  Pfui!  Nicht mit dem Finger zeigen.
Der k. H:  Awe Mut-tii…. Der da, der hat ja halt keine Eigenschaften!
Die M:  Sch!  Das ist gar nicht artig von dir.

[So:  A Man Without Qualities.
--  Or is he ??? !!!
Secret details here:
http://worldofdrjustice.blogspot.com/2012/07/memoires-de-la-conspiration-riemann.html ]

Weiteres zum Thema:
http://worldofdrjustice.blogspot.com/2011/01/brandenburg-parable.html

*

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

### Minimalism in Mathematics (updated)

A disclaimer:   What follows is not a substantive proposal, but a suggestive meditation, turning over this minute but multifaceted notion of “minimalism” and seeing how the light glints off.  It is neither better nor worse than a metaphor.

A couple of years ago,  a book-length treatment was published  that similarly plays with the notion of (in this case) “modernism”  -- which, like “minimalism”, is originally a term of the arts -- in relation to math:  Plato’s Ghost:  The Modernist Transformation of Mathematics, by Jeremy Gray.   To the extent that such an enterprise is worthwhile, it is in casting a bit of light from innovative angles, rather than deepening one’s understanding of math itself (though it did manage to get published by Princeton University Press):  it is more like a bull-session than a milestone.    Reviewing the book for American Scientist (Sept 2009), the mathematician Solomon Feferman sums up by quoting a remark by the historian Leo Corry, to the effect that
Extending the appellation modernism to mathematics … is like “shooting an arrow and then tracing a bull’s eye around it.”

Our own effort, in seeking resonances with the prior notion of minimalism, in mathematics, physics, and linguistics, is open to the same remark;  but it is what it is.

In the stylistic spirit of minimalism (and of that pointilliste Wittgenstein), we shall begin with a Delphic  epigram:

Logicism:  a kind of reductionist minimalism.

*

Considering that he took on the whole universe, in his methods  Newton was surprisingly Spartan.  Not only as regards “hypotheses non fingo”, but methodologically:

Newton consistently preferred Euclidean-style proofs.  He used his own calculus only where strictly necessary, and barred algebra from his treatise  entirely.
-- Leo Corry, “The Development of the Idea of Proof”, in Timothy Gowers, ed., The Princeton Companion to Mathematics (2008).

(Cf. a laborious non-analytic “elementary” proof in number theory.)
As fastidious as an Intuitionist!

*

Not a matter of method, let alone of taste, but sheer fact:
The Löwenheim-Skolem theorem: if a first-order theory has a model, then it has a countable model.
*

The attempts, lasting centuries, to do away with the Parallel Postulate by deriving it from the other Euclidean axioms, represent a remarkable early manifestation of the minimalist instinct.  Success would not have added to our fund of theorems about geometry, nor led to more perspicuous proofs.  The impulse was in part aesthetic.

A topic to explore:  the relation between abstraction in mathematics (an intellectual quality) and mathematical minimalism (which is not antecedently defined, but I have in mind the aesthetic, even spiritual side).

Contrast Finitism, Intuitionism, etc.:  Not Minimalism, but self-castration.

 Zijn lange, magere  maar gespierde gestalte,  zijn scherp ascetische gelaatstrekken…

There is also a sterile sort of minimalism:  as, the replacement of the standard set of logical symbols AND, OR, NOT, by a single one --   NOR or  NAND (Sheffer’s stroke).  It led nowhere.

*

A variety of the Minimalist instinct  characteristic of abstract mathematics  is the notion of elegance.   Its role in mathematical practice (it has no purchase on mathematical fact) is reminiscent of, though practically distinct from that of beauty in the practices of physics.

This, from a man with one foot firmly in either camp, math and physics:

The development of mathematics may seem to diverge from what it had been set up to achieve, namely  simply to reflect physical behavior.  Yet, in many instances, this drive for mathematical … elegance takes us to mathematical structures and concepts  which turn out to mirror the physical world in a much deeper and more broad-ranging way…

-- Roger Penrose,  The Road to Reality (2004), p. 60

*

We earlier noticed what we called “the Dialectic of the Topological Enterprise” -- abstracting-away from rich familiar entities, extracting what seem the essentials, and seeing what happens.   The first step might seem Minimalist, but the consequence is an effusion and exfoliation of new spaces which meet the newly relaxed criteria, and which turn out to have an even richer riot of properties than we began with.   Per se, there is little in all this that might justify bringing in the aesthetically-tinged label of “Minimalist” (not a traditional term in mathematics; the closest you get is “abstract”):  but the aesthetic ethos is there, for all that.  Thus Shing-Tung Yau, The Shape of Inner Space (2010), p. 77:
We start with some raw topological space, which is like a bare patch of land that’s been razed for construction.  On top of that, we’d like to build some kind of geometric structure that can later be decorated in various ways.

*

In the arts, Minimalism is a preference:  which, once adopted, is striven for.  In mathematics, you might like to keep things as simple as can possibly be:  but the mathematical facts seem to have a will of their own, at times.   Roger Penrose gives several instances of this, in The Road to Reality (2004).  For instance, with real functions, you can do pretty well as you like; but complex functions have a built-in naturalness.  You can try to define one on a given domain, but they have a mind of their own, and expand to their natural maximal domain by analytic continuation.   Thus, the larger set of numbers, the complex, spanned by the reals and the imaginaries, turn out to be in some sense more ‘real’ -- more round, more natural -- than the “reals” themselves.
Or again:   Suppose, once-bitten by the set-theoretic antinomies, you become twice-shy, and (p. 373)
adopt a rigidly conservative ‘constructivist’ approach, according to which a set is permitted only if there is a direct construction for enabling us to tell when an element belongs to the set.

(I picture this hypothetical constructivist as being played by Graham Chapman doing his officer’s shtick.)   But alas!  Penrose runs through the Turing/Cantor diagonal arguments and concludes (p. 376):
What this ultimately tells us is that, despite the hopes that one might have had for a position of ‘extreme conservatism’, in which the only acceptable sets would be the ones -- the recursive ones -- whose membership is determined by clear-cut computational rules, this viewpoint immediately drives us into having to consider sets that are non-recursive. … We are always driven to consider classes that do not belong to our previously allowed family of sets.

This is either a baffling, even a provoking mystery, or a simple consequence of what the Cantorian Realist indeed believes:  that these things are Out There, independent of ourselves (this might remind you of a certain Deity), and you can’t just methodologically sweep them away.   U B the judge.

*

Pedagogical observation from a wise observer, who has been around the block:

Instead of the principle of maximal generality that is usual in mathematical books, the author has attempted to adhere to the principle of minimal generality,  according to which  every idea should first be clearly understood in the simplest situation;  only then can the method developed  be extended to more complicated cases.
-- Vladimir I. Arnold, Lectures on Partial Differential Equations (Russian edition 1997; English translation 2004), Preface to the second Russian edition

*

The nec plus ultra  of mathematical minimalism  is probably Category Theory -- which, however, I cannot elucidate, since I do not understand it.  It contains such things as the Forgetful Functor (this pops up in several introductory treatments, so it’s not as though I’m grasping at straws), which, given an algebraic group, “forgets” the group structure, leaving you with just a set  (excuse me: an element of the Category of Sets.)   Great -- die Gruppe ohne Eigenschaften.   The only way this even begins to seem to have a point  is if you then consider the adjoint functor, from sets to… free groups (these being a desolate Last Year at Marienbad landscape, again groups with the flavor removed).   Category theory looks at the bare bones common to many a different area of mathematics -- rather as though one were to study portraiture by looking at stick-figures.
(Actually, there is an analogy with the motif-index in folklore.  So, not knocking it here...)

(All so difficult.  Why not relax with a mystery story instead?  Cool ones here: )

### Entartung im Zauberberg

In Thomas Mann’s great novel, we see a microcosm of decaying European culture  on the eve of the Great War, depicted in an elite mountain-top sanatorium.   There a particular self-generating and self-coddling culture  grows as though in a petri dish.

And now the virus has descended zum Flachland:

Après Paris, l'université d'Aix-Marseille va créer une formation diplômante en santé pour les patients qui s'impliquent autour de leur maladie.
Les patients sont devenus des acteurs de santé à part entière. Fort de ce constat, le président de l'Université d'Aix-Marseille, le Pr Yvon Berland, a annoncé le 14 décembre, lors du 4ème colloque Médias & santé, la création à la rentrée 2013 d'une «Université des patients» ouverte exclusivement aux malades chroniques.

Such are the honors of our post-Arrowsmith age,  where we celebrate as heroes (or more usually, heroines) not the physician, but the valetudinarian.  (The article is accompanied by a photograph of invalids in mortarboards.)
An American counterpart of such sensiblerie would be the cult of Henrietta Lacks, crossed with the para-academic “credit for life experience” movement.

The broader phenomenon is nicely analyzed by Pamela Haag, here:
http://theamericanscholar.org/death-by-treacle/

*
Pour d’autres friandises
de la confiserie
du docteur Justice,
consultez:

*

~

Superficially, the antics in Marseille and Paris might seem heart-warming, or, at worst, just the sort of goofy things people do, like dressing up dogs in little outfits, or electing a kitty-cat “King for a Day”.  (“For a day-y …?!%!#!”)  But like blood in the urine (an apt metonomy for this sort of glurge) it is pathognomonic of a deeper malaise.

To cull stray citations almost at random from current reading:

From a noted historian:
These days, my discipline and our culture  like to deny the historic importance of individuals.  … Ours is an age of denigration. … The denial of greatness traduces experience  and diminishes our collective lives.
-- Fritz Stern, Einstein’s German World (1999), p. 250-1

A caveat against a lax misreading:
“Individuals” are indeed central to contemporary PC-thinking;  but these are essentially individuals ohne Eigenschaften, save such as they inherit automatically by virtue of their membership in some identity-group.   And crucially, these individuals are without historical importance since, across a broad socio-political spectrum, the trend of the Zeitgeist is the denial of history.

Likewise  someone might stick at “an age of denigration”.  There is also exaltation -- but of a self-undermining kind.  When the likes of Lady Di or Lindsay Lohan can become celebrities, it makes a mockery of any genuine achievement.

Within my lifetime, there arose in America, the practice of applying the word genius  not to rocket-scientists (or mad scientists -- our colonial relation to the essentially European notion of genius  has ever been rocky), but to, um, baseball-players, footballers, like that.   Those, that is, of a certain cast.  This -- along with the gleeful self-flagellating pouncing upon the entity bordering the Kaap die Goeie Hoop -- was part of the reparational self-abasement of the cowed and right-thinking, a peace offering toward those who, truth to tell, mostly just wanted jobs.  It seemed a quintessentially late-American moment.  Yet, what was my surprise, upon encountering this passage, in chapter 13 of the first book of Der Mann ohne Eigenschaften (1930), referring to Austria in the years immediately following the Great War:

Es hatte damals schon die Zeit begonnen, wo man von Genies des Fußballrasens  oder des Boxrings  zu sprechen  anhub.

*
Für psychologisch tiefgreifende Krimis,
in pikanter amerikanischer Mundart,
und christlich gesinnt,
klicken Sie bitte hier:

*
Related posts:

## Friday, December 28, 2012

### The Agony and the Acolyte

[Note:  This anecdote is a footnote to a larger topic treated in a previous essay

into which it should  in time  be incorporated; but meanwhile, here you go.]

"I was wearing my herringbone jacket, and when the other man came in -- he was ten years older than me -- he was wearing an almost identical herringbone jacket.  The woman turned to him and said ‘What a nice jacket!’ … There I sat in the same jacket, making self-satiric gestures of Hey, look at me!  But they went right on talking about his jacket."
-- Janet Malcolm, Psychoanalysis:  The Impossible Profession (1981), p. 53

Analogs of this anecdote have been experienced by many;  I’ll only mention mine because it ties in with the theme of Chomsky and his acolytes.

~

At Berkeley, after switching from the Ph.D. program in math to that of linguistics, I T.A.’d one semester, during my first year as a graduate student, for George Lakoff, who at that point (ca. 1974) was a highly visible figure in linguistics, but not yet outside it.   George too had started out in mathematics, and we were both interested primarily in semantics, so it was a natural fit.  George had sat in Chomsky’s seminars, and had begun his career contributing to -- or thinking he was contributing to -- the fashionable generative enterprise that Chomsky  more than anyone  had set rolling.  So, I was  at that point  potentially a sort of Chomskyite acolyte paravail.  (Though by then, Chomsky and Lakoff had had a sharp falling-out, that was only to sharpen.  In theoretical content, their differences -- and subsequent careers -- somewhat recall those dividing Freud from Jung.)

Anyhow -- a bunch of us were sitting around a table  at a lively and informal discussion  in an upper room of Sproul Hall.  As a newbie, I was reticent about presuming to contribute, but at one point  something really germane occurred to me, and I said -- whatever, “Blah de blah de blah de blah.”
Crickets.  -- No, not even crickets:  that at least implies a pause.  No, the waters of discourse were in no way ruffled, but rolled on as though I -- or rather the empty spectre occupying my chair -- had said nothing.
OK fine.  But then around one minute later, Geoge Lakoff gets this really thoughtful look on his face, and says, “Hmmm….. “ -- The buzz of conversation is suspended as we await what the great man might say. -- “Y’know…” now smiling, and warming to the idea, “y’know, what I think, is,  Blah de blah de blah de blah.”
Almost everyone gasped at the brilliance of the insight.  Everyone except me, and Miriam P., who was sitting immediately to my right, and with whom I had casual but friendly relations.  She turned to me, uncertain if she had heard aright, and said:  “Didn’t you just say that?” -- I shrugged.  And soon disassociated myself from that particular clique.

That proved to be a fateful step career-wise, since I never essayed to join another one.  Among the faculty, I probably hung around Malkiel more than anyone;  but since I was not in the Romance Philology program (and had not the requisite genital configuration), I was nothing like a Malkielita (as some were known).
After college, I had the option of accepting the offer of either Berkeley or Stanford (for the math program);  in either case  I probably would soon have switched to linguistics:  since in math, as in monasticism, one must have a Vocation.  As chance had it, UC Berkeley was increasingly a hotbed of anti-Chomskyism;  with a different fall of the die, at Stanford, I might well have enrolled among the Chomskettes/Chomsquinos/Chumaysikaat (an Arabic joke, that last one; a physics, the one in the middle).

## Thursday, December 27, 2012

### A moral fable: Murphy on the Mount

Sales of this deep meditation, in the form of a wise-cracking detective novel, have suddenly begun to skyrocket.  You can read a free excerpt here:

and view of video of another excerpt here, read by the detective himself:

Or, you can just take our word for it, and -- unlike Doubting Thomas -- simply buy it, sight unseen:

"Lord, I believe;  help Thou mine unbelief."