Thursday, October 31, 2013

Happy, happy Hallowe'en

[Herewith, to get us into the spirit, some notes on a Halloween past.]

A couple of days ago, Blondie twits Dagwood as they head off to a Halloween party, saying he'll be a laughingstock  for his lazy excuse of a costume:  nothing but a Groucho facepiece (glasses, moustache, and nose).  Punchline:  When they arrive, every single male is dressed exactly like that.

Well, if Dagwood had attended the officially announced "party" in the corridor outside Division yesterday, he would have been one of only three entitled to "compete" in the "costume" "contest".  (I had considered putting on my old Maple Leaf pin, from Edmonton days; and if anyone asked, I'd say I was dressed up as a Canadian.)  The two that did dress up were not so much in costume, as in an amplification of their normal personalities:  Alice as a cowgirl (barely), and Curdy (most convincingly) as Hunter Thompson. 
Hypothesis:  People are not so enamored of Division Management, that they want to play dress-up for them.


Back at the homestead, I encounter the little girls next door, and as they run up, I tell them not to tell me what they'll be wearing, I want to be surprised.  (Somehow, every Halloween, I fail to guess their identities.  "WHO is this little princess person???  Who can she BE????!!!!!")  The younger one says: "I'm going to be Tinkerbell".  -- "Oh, uh, OK, Tinkerbell's cool.  But there might be more than one of them, so I still won't know whether it's you."  -- Her slightly-elder sister chimes in, "I'm going to be a cheerleader."  "Kewl."

Evening arrives -- lights on, penguin in place, candy on a platter -- to welcome the little ones.
In the event, when the neighbor girls show up, the elder has plunked for some quite other costume, not easily identifiable; and the little one, well, sort of princessy, but no wings, nor suit of forest green, yet in her mind:  she is Tink.

As always, my favorite was the very littlest, someone from another cul-de-sac, clearly going out on her very first Halloween: a cross between Swee'Pea and the Velveteen Rabitt, she can barely stand.  But as (kneeling) I proffer the candy with a reverence reminiscent of the wafer, she does manage to squeek out, "Theenk you".

One little boy, clad in a fashion reminiscent of stegosaurus (had these beasts been yellow and green), informed me:  "I'm a dinosaur."
One wonders how precisely to take this.  He *might* have been speaking as an epistemologist, cognizant of the ambiguity of sense-impressions, the ever-presence of the Subject, and the pitfalls of interpretation; aware that his get-up might be misinterpreted as that of a dragon, he promptly set the homeowner straight.  More likely, he has been walking round and round in the dark, thinking, "I'm a dinosaur"; and was forward to share this intelligence.

Try this spooky story:
A private detective  confronts the uncanny;
an ecclesiastical mystery:
Murphy Calls In a Specialist

It's the inner dangers  that lie deepest ...

Monday, October 28, 2013

Thomas Wolfe: an assessment

When he was good,
he was very very good;

and when he was bad --
he was tolerable.

1900 - 1938


Sunday, October 27, 2013

The Editors Regret the Error

The New York Times finally acknowledges (on the front page, no less) the fact that, no-o-o-o-oo, New Delhi and Steubenville are not equivalent:

For our earlier essay on the matter, click here:

Good Grief, *More* Math Porn!

In our original essay on the subject, and its follow-up here, we noted that there exists very little pandering journalistic treatment of mathematics.   Popularizations and simplifications, yes;  this is a public service, if done well.  It only becomes ‘porn’ if some marketing-type tries to sex it up with references to mysteries or hidden realities -- or sex, for that matter.
This morning’s New York Times Book Review offers a worthwhile summary (by a physicist) of a probably quite worthwhile new book (indeed, I have already ordered a copy):

The book itself sounds straightforward enough;  it’s the title and the subtitle that are porn-y:

The Heart of Hidden Reality
By Edward Frenkel

One wishes to think, that the author’s proposed title was something like “Conformal Field Theory and the Langlands Program” or even “Langlands for Dummies”, and that some Dilberty drone over in marketing went to tart it up.  In much the same way, perfectly reasonable newspaper articles can be turned into ostensible kitsch or glurge, by micro-brained headline writers.  
But on second thought, had it had that for a title, rather than this bodice-ripping conspiracy-theory thing, the book would probably never have been reviewed by the New York Times.

[Update]  Bought it and read it; it's excellent.  Discussion here.

Reification: Substantive and Trivial

We have been upholding a Realist (Platonist) account of mathematics;  and while this position is best understood in terms of patterns and implications rather than “the existence of mathematical objects”, let us relax our vigilance for an instant, and consider the Ontology of Things.

Thus, consider that feline prototype of a statement,

~ The cat is on the mat. ~

Life is simplified if we admit that cats and mats exist, as sets of objects.  Likewise mammals;  and since the set of cats (real ones, we mean, not Putnam’s perverse pet) is a subset of the set of mammals, we can conclude from the above that “A mammal is on the mat,”  and from that deduce the non-emptiness of the set of mat-borne mammals.   All quite convenient.

But what of “on”:  Is that too  an object, or an entity?  Or, onness, maybe, or onning (as in: This cat ons this mat).
If you like, you can talk that way (and there are academics who have been paid to do so). The set “Onness” consists of all the ordered pairs of tops and bottoms;  exempli gratiâ:  <that cat; this mat>.  Nothing hinges upon this.

In mathematics, by contrast, where relationships, and the implicational interrelations among such relationships, are key (while objects not so), such nominalization comes naturally.
Thus, a topological space is second-countable (adjective) if its topology has a countable basis.   And:  A topological space is regular (adjective) if … (yadda yadda, look it up).
From this, we quite smoothly segue into a nounier style of speech, which often brings greater concision (rather than less, as with "Onness").  Thus this statement of the Urysohn Metrization Theorem:

In 2-countable spaces, regularity is equivalent to metrizability.
-- James Dugundji, Topology (1965), p. 195.

Or, going the whole hog into the nomina substantiva style of formulation:

For a topological space:  Second-countability plus regularity equates to metrizability.

Or consider:

Compactness and separability are each more fruitful properties than connectedness or paracompactness in terms of further implications.

Such a proposition would be cumbersome to word in a de-nominalized style.


Quine, who likes his whisky neat and his universes spare, takes an opposite tack of “entities explained away” (with the aid of variables and quantifiers), abolishing those unaesthetic singular terms in favor of quasi-verbal predicates.  Here Pegasus disappears in a puff of “pegasizing”.  (Caveat:  Do not yourself attempt to pegasize at home;  only Pegasus himself can do that.)   Ontologically, perhaps, we are back where we began, though psychologically it is quite otherwise:   You can fall in love with Juliet;  you cannot fall in love with that x such that x julietizes  and, for all y, if y julietizes, then y = x.

Pegasus explained away


Since we shy away from the dry well of “the existence of mathematical objects” (being interested in the Platonist account  more in the context of epistemology and theology, than in pure ontology), it isn’t really a theme of these essays;  but we touch upon the matter tangentially here:

For a deconstruction of the dubious conjunction “language and math”, cf. this note:

For terrific detective stories (hey, gotta support my family in retirement), cf. this:

Saturday, October 26, 2013

Fitness Tips for Fifty-somethings

We’re all supposed to get a good half hour of moderate exercise, three or four times a week.  But, what counts as “moderate”?
A recently offered rule of thumb is:  Such that you can still talk, but you can’t sing.
So I guess that disqualifies taking a shower as “moderate exercise.”   :-(

For hot (albeit 50,000 years old) diet tips, click here.

Bunny Break

The news these days has been depressing.
Let’s read about bunnies instead:

Hi, my name is Fluffy, and I'll be your personal bunny-friend.

Here's a bunny-verb  I'll bet you didn't know!

with the swiftness of a conjurer  de-rabbiting a top hat
-- P.G. Wodehouse, The Girl in Blue (1970)

Or, we can learn about hamsters !
(BLUF:  Hamsters are our friends.)

Wednesday, October 23, 2013

Curiouser and Curioser

In an earlier post, I blogged briefly about two  local events, fascinating enough to anyone who experienced them directly, but ultimately no more than Facebook fodder, soon gone from the mind, like the wind.

One of these, however, continues to develop, and to prompt reflections of a larger compass than Gee-whiz lookit this shiny coin.

We begin partway through the earlier post, then elaborate.


[Later update]  The story is getting weirder, so I’d better elaborate.  This, from an e-mail sent to friends:

Early this evening, S. and I walked to the library, via the dockside on Lake *****.   There were half a dozen people standing around, and a couple of policemen.  Someone pointed to what they thought looked like a human corpse floating not far from the dock.  I peered to make it out;  it looked like Hollywood’s idea of a zombie.
Now, today at work, a friend had given me a nice Halloween drawing, so the first thing that occurred to me was that it was a Halloween prank.  A couple standing beside us concurred.

Twenty minutes later, as we returned from the library, we saw: half a dozen patrol cars; two or three fire engines; a large inflatable boat labeled “marine rescue”; an ambulence or two; and various other vehicles with flashing or whirling lights.  Some firemen were trudging back from the scene, one of them holding a long gaff.  “Uhh… looks like it wasn’t a Halloween prank”, I said.  The fireman would neither confirm nor deny, saying only “The police are handling it.”
The dock was now surrounded by yellow tape.  No attempt had been made to fish the body out, though an officer in a yellow rubber wading-suit was maneuvering waist-deep next to the body.  From a new angle, and now taking the whole thing more seriously, I could see that it was indeed human, or had been;  its hands stuck up from the water, rigid as claws.

This is pretty much what it looked like, only on its back.
[Update 10/10/13]   I shared this incident with some friends and coworkers, current or former residents of this town, and however slight it be in the larger scheme of things, it piqued their interest.  One of them today asked whether the “Flyer”, the local giveaway rag, had reported on the story (which is indeed a big one for our sleepy hamlet).   And so I dragged today’s issue from our sopping front lawn, dried it, and perused.
My heart gave a start, confronted with a large color photograph of the dockside area of that very lake!  Only -- no mention of the body.   Instead, a story about the little three-foot-by-three-foot artificial boxed islands, planted with tall grass, which have been dubbed “floating wetlands”.  Cute, but actually a silly designation, since the point of wetlands is to absorb excess water, whereas this particular lakelet, itself brought into being only by the labors of engineers, suffers rather from chronic aqueous insufficiency.

[Update, a couple of days later]  Finally, the briefest of mentions has appeared on the Web.  The deceased was in his thirties, of no known address.  But -- get this -- the police are saying, “No signs of foul play.”
Corpse appears in broad daylight in six inches of water, looking like a mummy that has been dead ten thousand years.  No-one knows how it got there.  Hands turned into zombie claws.  “No signs of foul play.”

[Update, evening of 20 October 2013]  No -- Wait -- this is too weird.
My wife was driving home from the computer lab this evening, on **** **** Parkway, which runs by that very lake, and noticed two squad cars.  Between them, on the roadway … a large, compact pile of (possibly human intestines).  But otherwise no body.   “They looked fresh,” she said.
[Update 22 October 2013]  And again, no reflection of this in any news source that I can discern.
My wife commented:   If we just chanced upon these incidents, within a few days and within walking distance of each other, and they go unreported -- how much else might be going on that we don’t know about?

Both these bizarre incidents look less like accidents, or any sort of crime that makes straightforward sense -- more like warnings, like the horse’s head in the bed.

More generally, the situation suggests the layers of oddity beneath the surface of things.  A historian remarked, anent the “Umbrella Man”,  that as you brought up the focus on the lens of history, new and inexplicable features begin to appear:  much as, beneath the solidity of macroscopic objects, lies the tracery of molecules and atoms;  and beneath these, obeying different laws, the quarks and other elementary particles.


So, possibly a couple of crime-scenes, though not reported as such, and evidently destined to be forgotten with the facts forever undiscovered.  Might there be anything there, if someone were to dig?
There might;  but eventually you also might find that (as philosophers say) “your spade is turned”.    For, consider a vastly more high-profile case, which  has received intensive attention from professionals and from the commentariat, turned every whichway, examined from every angle, for several years: the murder of one Meredith Kercher, in Perugia, Italia, in 2007.
In the international panoply of crime, the incident was of scant inherent moment.  A total unknown with a lot of louche friends winds up dead, no political angle, nothing there, really.   What launched the case to international attention, and kept it there,  was that one of the accused (the only one people cared about) was a Foxy Young Female -- de rigueur for the fickle public to give a darn about anything -- cast ambiguously in the role of villain or victim (and certainly vixen):  Amanda Knox.

We touched briefly on this case in a note focused  not on the crime but on its massage in the media.   And now this week’s issue of the London Review of Books has a retrospective on the case.  The LRB’s coverage is immeasurably better than the fawning glurge from the New York Times Book Review which prompted our original rant.   (People who read, or riffle through, the NYTBRev, probably imagine that they are holding something pretty highbrow in their hands.  They are not.)  A vast range of evidence has been adduced and argued-over, from something as sophisticated as Luminol, or as absurd as a turd. (Memo to murderers:  Don’t forget to flush!)
I’ll spare you the details of the new account.  The takeaway is that, after all these years, and all the forensics and analytics, we still don’t really know who, how, or why.

Felix qui potuit   rerum cognoscere  causas …

It has well been said, that the unexamined life is not worth living.  But even examined life may  not yield to our understanding.


Hamster Break

This hamster is not a suspect in any of these cases.  At least, according to its lawyer


Probably these local anomalies will fade with as little left behind them as a day of unsettled weather.   Yet possibly, years later, after the smoke from the Zombie Apocalypse has cleared, historians will gasp:  My God.  So that hamlet was the new Sunnydale -- the location of the Hellmouth.


[Update 25 October 2013]  On the matter of  Can we ever really know anything about what happens -- From this coming Sunday’s NYTimes Book Review:

Kennedy, the Elusive President

With roughly 40,000 books about John F. Kennedy published to date, and hundreds planned on the 50th anniversary of his assassination next month, why is it we still know so little about the man and the president?

Sunday, October 20, 2013

Vowon man nicht sprechen kann, darüber muss man schweigen

[Herewith the latest update to our survey of French politics as viewed through the particular prism of the New York Times.  The full essay can be read here.]

This morning’s New York Times published an article, datelined Paris, which  from a European perspective  is astonishing in its candor:

Are the Roma Primitive, or Just Poor?

In fact, even for America, the notion that any ethnicity, now matter how primitive, could be publically discribed as, err, “primitive” (of course with chaperoning quotes) is no longer widely accepted.
I monitor the French press daily (though not intensively), and have never encountered a depiction as unvarnished as this:

THE cluster of Roma, handcuffed and caged-in behind glass walls, listened in silence as prosecutors accused them in court of selling child brides for up to about $270,000 in cash, valuing them based on their ability to steal. In a case that has riveted France, the prosecutors accused three family clans from Croatia of grooming girls and boys as young as 11 to steal as part of a gang that committed 100 robberies in France, Belgium and Germany in 2011.
One 20-year-old witness told the court he had stolen about $600,000 in cash and jewels for his parents, or more than $7,000 a month, since age 13. Less skilled thieves could face punishment, including beatings by Roma elders.
All but one of the 27 accused were convicted on Oct. 11 in Nancy, in eastern France, of forcing the children to steal, and received sentences from two to eight years. At the top of the network was a 66-year-old grandmother.
The case highlighted an increasingly rancorous debate here and across Europe about what some politicians call, rather ominously, the “Roma question,” a reference to the nomadic people, also known as Gypsies, who came from India to Europe centuries ago. An estimated 11 million are scattered across Europe.

In Europe, you just don’t say that.   Or rather, you don’t print it;  meanwhile the murmur of vox populi grows louder and louder, and may produce surprises in the next French general elections.   But in the U.S. (so far at any rate), gypsies need no more be treated with evasion and kid gloves than, say, Armenians.

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

For a typical example of how the French press -- even the relatively politically-incorrect right-of-center Le Figaro -- reports such matters, consider a much less sensitive case, involving the theft of agricultural equipment out in the fields:

Telle une nuée de criquets, une bande de pillards a fondu sur la récolte début octobre pour faire main basse sur pas moins d'une tonne de pommes de terre. Les auteurs de cette razzia pastorale ont sévi à la nuit tombée, s'immisçant entre deux parcelles de maïs avant de se volatiliser dans la nature avec leur encombrant butin.
Ni vu ni connu, sans aucune traçabilité de provenance. «Les empreintes de pas, plutôt de petites tailles, ont témoigné de la présence d'environ vingt pillards», note un gendarme qui estime la marchandise à une valeur de 10.000 euros. Et la facture s'envole avec les vols en série de tracteur. Bien que valant bien souvent le prix d'une Ferrari, ces engins ultrasophistiqués ont été volés avec une simplicité déroutante, comme de vulgaires scooters.

Here and in the rest of the article, there is no indication whatsoever of what group might be responsible for these noctural larcenies, nor even whether the thieves share any traits at all in common -- perhaps some slip in from the local nunneries, while others are physicians on a country vacation, who knows.   There is not so much as a code-phrase like “venus de l’Europe de l’est”, which every European has long learned to decipher.
But there is one clue, which those familiar with the hieroglyphics of European discourse about prickly matters  will understand:  that Sherlock-Holmesian detail concerning the “footprints in the flower-bed”, so to speak:  “rather on the small side.”
Instantly French readers know what is at stake.  The allusion is to the well-known practice of Romany Fagins of employing little Artful Dodgers in their schemes, since these, if caught, are usually simply released, to steal another day.   The French by now are hip to this, and in their Comments, the readers pull no punches and name names. (“Gens du voyage” -- ‘travelers’, as in Britain -- began as a euphemism, but simply means gypsies.)

Tout ces vols, c'est archi connu, sont le fait de gens du voyage et de gens venus de pays de l'est qui mettent sur le terrain des mineurs qui se savent en totale sécurité face à la justice française !
A propos comment appelait-on ces gens qui faisaient des razzias sur les côtes de France pendant des siècles?
La France est pillée par les nomades des pays de l'est, merci Schengen et les frontières ouvertes, et que fait Monsieur Hollande et son gouvernement de d'abrutis ? Ils parlent de soit disant fascisme et marine Le Pen qui danse au bal de Vienne. Il ne voit pas notre Président Moi je, que la France est livrée à la criminalité.
Ce sont les mêmes qui volent des kilomètres de cables en cuivre, et rassurez vous il n'ont jamais souhaité travailler.
L'excuse de paupérisation ne passe pas, c'est clairement un choix de mode de vie.
Arrêtons la culture de l'excuse !
L'europe passoire que nous ont fabriqué nos élites, entre-autre pour soit-disant nous éviter une guerre, ne nous protègera de la guerre civile qui nous pend inéluctablement au nez.

"C'est le symptôme d'une paupérisation croissante de la population qui va se servir dans les champs pour survivre."
Heuuu, le vol d'engins de plus de centaines de milliers d'euros n'ont rien à voir avec la paupérisation.
Pas plus que le vol de tonnes de légumes ou de fruits.
Il faut une sacrée organisation et des réseaux, mafieux, pour écouler tout ça.

For Americans still clueless about this exotic wandering community, you may read a brief introduction here:

Spot the Odd Man Out

There is much, much more along these lines;  but that is not the point here, our focus being rather on rhetoric and euphemism in different styles of journalism.

Incidentally, that last story has been garnering international headlines, in a way that other much more dramatic examples of Roma crime (after all, this one might involve little more than illegal adoption plus welfare fraud and other scams) are never heard of on this side of the Atlantic.  And the reason is obvious:  Not the inherent importance of the story, but because it involves a Little Blonde Girl.  The whole thing is, in other words, just the latest example of Victimology Porn.

[Update, 22 October 2013]  Whenever the Blond Child Female Victim motif is introducted, expect the limbic system to take over from the cortex:

Authorities in Ireland have taken custody of a child described as a blond-haired, blue-eyed girl in the care of a Roma family she did not resemble, the second such case in Europe in a week.
Police said Tuesday that they took the girl into custody Monday afternoon in a neighborhood in southwest Dublin.


DUBLIN — Two blond, blue-eyed Roma children were removed from their families in different parts of the country this week — only to be returned when DNA testing confirmed their parentage.

Tales from my Boxing Career

Betcha didn’t know I was a pugilist, huh?  Well, not professionally;  “a lover, not a fighter”, as the saying goes, and as many a Mädchen can attest.  Only twice in my life  have I actually been involved in fisticuffs.

(1) The first occurred when I was about seven or eight, back when Eisenhower was in flower.  It happened at the dead end of Mulberry Place.   What occasioned the fight, I have not the slightest idea -- some stupid kid thing.  But the key point here is that I had squared off with someone both taller and older than I was.  It was in a yard beside this same cul-de-sac that we all played a hyperdemocratic game of pickup baseball, with rules tailored to the age and size and talents of each individual player (unlimited strikes allowed to the peewees) [French has a term for this:  it's called playing "pour du beurre"]: and this leveling sentiment applied now.  For, though I was a fairly dim figure on the periphery of the Mulberry Place gang, I was pleased and startled to hear the crowd (apparently) cheering me as my opponent and I circled each other, neither having yet landed a blow.   Playing no personal favorites, but in accord with the neighborhood children’s proto-Maoist bias towards the underdog, in unison they chanted:

Fight -- Fight -- Nigger and White!
Come on, Justice -- Beat that White!

(All the children in the neighborhood were white;  the chant had a certain impish novelty.)
The match soon petered out without issue.  Who my opponent had been, again I have no idea -- not someone I knew well.   All I recall is the warm glow of having been (seemingly) backed by vox populi.  Yet since then, a couple of nuancing considerations have occurred to me:

(a)  In the context of the racial assumptions of the time (ca. 1957), the chant could easily be interpreted as ironic  -- a “left-handed compliment”, as the saying goes.  I was only seven, and had not yet been exposed to such attitudes by my liberal-Unitarian parents, so I didn’t get that at all.
(b)  That much is obvious to any contemporary adult.  But -- a subtler, linguistic point.  Namely:  We children had only a very limited repertoire of stereotyped chants.  So the production of this one (which I have never heard before or since) doesn’t necessarily exactly mean anything, neither in denigration nor support of the lad nominally addressed.  It was just something to say at the time.

Doctor J, in his younger days

 (2)  The Stamm family was really nice to me.  Their son Bob and I were best friends.  They sometimes took me on family jaunts to Bear Mountain, places like that.  We had lots of fun.
            But one time -- I must have been about ten or eleven -- on one such rural retreat,  despite the mild sunny weather that should have proved soothing, somehow Bob and I got into a scuffle -- again, for a reason utterly forgotten, but undoubtedly trivial and stupid. 
            His parents and little sister were standing right there, as we shoved and wrestled (but did not punch) there on the sylvan greensward -- a venue in which the penning of pastoral poetry might more profitably have occupied our time.  Soon the father intervened -- as any adult would -- saying “Break it up, boys.”  We did.
            But then (essaying a loftier level of guidance) he added:  “Shake and make up.”
            Warily, we each extended our right hand.  And clasped.  -- At which point, Bob let loose with his left, and clipped me on the ear.

            Uproar.  His father of course was mortified, to a degree I intuited to some extent even then, though could fully appreciate only much later, when fatherhood fell in turn to my lot.   Naturally, at the time, I felt a certain smugness at this unexpected turn of events.

            Yet again, with the passage of years, a deeper level of understanding  rises to the level of consciousness.  For, though Bob was of course wrong to throw a sucker-punch, his father had been overambitious in prescribing a formal reconciliation  so soon.  Emotions have their meaning, and their own inertia, and need to subside of their own accord:  to attempt thus externally to command them, is like Canute commanding the waves.   Bob understandably was not yet ready to “shake and make up”.    Such is not an unusual state of affairs after bloody broils.  Woodrow Wilson attempted a similarly irenic gesture (the “Fourteen Points”) at the close of the Great War, to as little effect.

[Footnote:  Though Bob was the only one to actually land a punch in this contest, and thus would formally have won on points, I still believe I could have taken him in a fair fight. --  Ha!]

(3)  Right, I said “twice”, so what’s this third bullet-point doing here?  Well, it concerns the one time I almost got into a fistfight, but ultimately didn’t.

This happened much much later;  I was twenty-two or so.   And living an exceedingly impecunious bohemian life in Berkeley, with no job, and having dropped out of the graduate program in mathematics owing to inability to pay the out-of-state tuition they were charging .   In short, not much of a marital prospect.  And yet, young S. (who was, incidentally, and still is, the most beautiful girl in the world, though this detail is not strictly germane to our story) had for some reason taken a fancy to me, and set her cap for (as it proved) matrimony;  as a result of which we were (to use the expressions of a more decorous era) “seeing a lot of each other”, or “keeping company", or even (as you might say) “courting”.
All very well:  But her former/current/not-yet-repudiated boyfriend, whom she had been dating since high school, thought otherwise.  -- Understandably so:  When I think back to that tiny roominghouse-room in which I then dwelled, unable to afford so much as a telephone, usually clad in a chemical-blasted labcoat from freshman year, and finding any further apparel, either at St. Vincent De Paul, or in the garbage-can in the alley adjoining, it is difficult to fault him in his doubting my sincerity, or my suitability as a “catch”.
Anyhow, he came up to my dwelling in a white heat, demanding that I renounce all interest in the maiden, upon pain of something painful.  At which point I deployed, not my golden gloves, but my silver tongue.  Which soon succeeded in soothing him, and convincing him of my bona fides.  (And lest you think this scoundrelly, I actually did marry her  shortly thereafter;  and we are still together, till death us depart.) 
Ruefully, he admitted the legitimacy of my position, and her own right to choose her beau;  adding, as he departed,

I’d come up with the intention of thrashing you.”

Well, fine;  I let this pass;  but again, the male, red of blood and sinew, the blood of Beowulf flowing in his veins, does not lightly sit down for such a thing.   Just as with the epic (not)  Justice-Stamm bout, I silently coolly assessed that, given his age and build (about the same as mine), but in view of my own unsuspected reserves of ferocity (which later would manifest themselves with a vengeance, in the other S., my  iron-fisted son), -- had the matter come to that,  -- -- I coulda took ‘im.

[Update 21 August 2014]  Today my bride and I are celebrating our thirty-eighth wedding anniversary;  thanks be to God.   And our son has outgrown the fists-up stage, and is now industriously pursuing mathematics.
For a glimpse of all three of us, click here:

Saturday, October 19, 2013

Let us be fair to our Republican friends

There is much malfeasance among Republicans, which it is appropriate to address.  But let’s cut them some slack when they’re right on some given issue, even when their stance is adopted for self-interested reasons.

Thus, consider the various bills to tighten up on voter registration fraud.   The Left protests that this is far less prevalent than the Right proclaims.  Fine, what of it?  How do you defend fraud?  The only thing to bear in mind is:  What’s sauce for the goose, is sauce for the gander.  We must likewise scrutinize:  Tax fraud, financial fraud, agribusiness fraud -- all of these activities being, in dollar terms, Republican specialties.

Or again:  The one legitimate point made by the G.O.P. about Obamacare is that those who solicit subsidies should be evaluated as to whether they qualify.  So be it!  And at the same time, let us vet the much more lucrative petitions for subsidies, from millionaires pretending, purely for tax purposes, to be farmers or ranchers.  And as for ethanol subsidies, try to find a shred of an excuse for those.

"Die Vermessung der Welt"

 Gauss saw things in terms of sheets embedded in three-space, the natural abstraction from his experience as a land-surveyor.  Riemann shifted the view to that interior to the space.
-- John Derbyshire, Prime Obsession (2004)

In an earlier essay,  we exulted (as sober man of science) and lamented (as blogging satirist) that there exists very little indeed by way of “math porn” (in the non-sexual journalistic sense), as against “physics porn”.  However, we did come across a (rather pale and marginal) example of that seldom-met genre, and now share it with you here.

I recently attended a screening of the 2012 German film “Die Vermessung der Welt” (literally geo-metry, in the etymological Greek sense) presented to a select circle of the deutschgesinnt.  What moved me to tear myself away momentarily from my usual daytime occupation of hand-to-hand rooftop combat with our adversaries, was the fact that the film was billed as a sort of dual biography of two scientific figures very much worth biographizing:  Alexander von Humboldt, the naturalist brother of the philologist Wilhelm, and Carl Gauss, probably the greatest mathematician who ever lived.   We watched it off a DVD;  had I known that the original theatrical version was 3-D, I would have lowered my expectations accordingly.  (Actually, 3-D could be put to very good use in the exploration of the Gaussian geometry of manifolds, but that was not its use here.)

The movie begins, as all Gauss sagas must, with the tale of how the young schoolboy, given a pensum  along with his fellows  of reckoning up the sum of the integers from one to a hundred, shot back an answer instanter, by finding a clever shortcut, rather than, as John von Neumann would have done, simply adding the series instantly in his head.  (That’s a joke.)   Our eighth-grade algebra class was regaled with this (and wisely so;  it’s one of the few things I remember), and our son, in the Princeton Friends School at a tender age, was instructed in the same as well.   But in the film, the anecdote was given what I take to be a possibly Germanic twist, for the scene opens with the explicitly filmed rhythmic  

of a supple and vicious-looking cane upon the bared buttocks of a lad of around nine;  graphic enough as it was, but probably even more disquieting in a theatre, with Surroundsound and 3-D.   Somehow, this sequence alone marked the movie out as not of American provenience -- here, you might be sent to prison for even watching it.  (Later, after Gauss has solved the arithmetic problem, the scene is repeated with Gauss as victim, for any viewers who didn’t manage to come to climax during the first sequence.)

So:  a rather pornographic presentation of what was in reality an utterly asexual and indeed incorporeal milestone in the annals of mathematical awakening.   But as long as we’re here, let us dwell -- as the film alas did not -- for just a moment  on the math part.
That sequence 1 + 2 + 3 + … + 100   equals, as it happens, 5050.  That fact is of no mathematical interest whatsoever, but belongs rather to the Museum of Particular Results.  (We presented a jolly fable of this notion here.   Be sure to click on that essay, it’s full of woodchucks.)   Of marginally more interest is the shortcut found by young Gauss:  pair the outermost integers in turn and you get 50 × 101.   That is clever enough;  but at the lowest level, it might be simply one of an unrelated jumble of dodges used by a Calculating Idiot-Savant, and thus belong to the Museum of Particular Tricks, just one step up from brute-force addition.  A significant step up from this recognizes that the trick is (with some tiny extra cleverness) generalizable to any sequence 1 + 2 + … + n.   Now it has risen to the level of a general trick, and thus belongs to the Museum of Particular Algorithms.   But then this finding generalizes to the idea of summation-formulas überhaupt:  for instance the sum of the squares of the first n integers, or the cubes, or any power.   The resulting infinite collection of formulas belongs to the Museum of Particular Strokes of Genius.   Striving to generalize these, you eventually wind up with Analytic Number Theory, and its sought-after crown jewel, the Riemann Hypothesis;  which is where things stand today.
None of this is even hinted at in the movie;  but really, such a development is the only reason to treasure that Gaussian anecdote:  otherwise the whole thing can seem a mere transient bit of precious cleverosity -- as it did (in the film’s telling) to Gauss’s schoolfellows, who give him a beating for his trick, and no doubt to the bulk of the audience.   And this is the “math porn” aspect of the presentation:  Even in the absence of any mathematical understanding whatsoever, we spectators are nonetheless supposed to be tremendously impressed with young Gauss, who is presented as a romantic and tragic figure, his attraction being thus, not Gaussian, but Byronic.

A superb mathematician -- and you can take that to the bank!

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



Thus far, the perspective is that of male narcissism.   That stance applies as well to the portrayal of von Humboldt, as he goes stalking about the Amazon in his seven-league boots, freeing slaves as he goes, and making immortal discoveries.   Both portraits involve a certain taste of algolagnia (in the naturalist’s case, it involves his naked back and an electric eel -- all for science, you understand).   There is nothing explicitly homoerotic, though perhaps a touch of a repressed version of that, by implication, when von Humboldt goes apeshit upon discovering his handsome French traveling companion  dallying with a local squaw.

Subsequently, the movie tosses a bouquet in the direction of unearned autogynophilia as well, in the incident of young-man Gauss, still all sturm-und-drangy, brought wisdom from the Tree of Knowledge by a chance remark of a comely though uneducated Fräulein  posing Evelike with an apple.
Mathematically, the scene will almost certainly have soared over most of the audience’s heads.   Gauss chats about measuring the Earth (Vermessung der Welt) by adding up triangles;  the lass objects that the Earth is not flat …. (not a Euclidean surface, as we say in the trade) … portentous pause … Gauss, reflecting, says, Well, you’d need lots of leeetle weeentsy triangles (infinitessimal, mathematicae linguâ).  She sensuously/attentively pares the apple;  and the penny drops, the scales fall from his eyes, and he rushes off to scribble calculations.
What just happened -- and the viewer may well be excused for having missed it -- is that Gauss has (apple-prompted, like Newton and gravity) just discovered Gaussian curvature, differential geometry, and much of modern mathematics.  This episode will be utterly opaque to anyone coming fresh to the movie;  apparently, we are expected to have read the book, as with the Harry Potter movies (the latter of which were incoherent, and would have baffled anyone who hadn’t already read the series).  Which, indeed, the director had cause to suppose, since the movie is based upon a novel that was a humongous German bestseller.

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~ Commercial break ~
For a mini-movie of our own, try this:
We now return you to your regularly scheduled essay.

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The depiction of the wisdom-from-the-mouth-of-babes Mädchen is likewise Byronic -- namely it recalls Lord Byron’s daughter, Ada the countess of Lovelace, an associate of Babbage.  She has been exalted by those who go hunting in history for neglected heroines;  a summary can be found here:

In fact, though, Ada is a reasonably admirable and realistic role-model for girls, since she did hang around a really smart guy and did work hard and did achieve some understanding if not any actual original results, which is all that most of us can ever hope to do.  Gauss, by contrast, is no role-model at all, for anyone, since none of us have been born with his genius, which is almost unexampled in history.  Indeed, for any actual stellar mathematician, his example is yet worse, since he was notorious for hoarding results.  Hopeful young mathematicians would make the pilgrimmage to Göttingen to present their results (much as young Gauss himself is shown as doing, in a singularly infructuous interview with Immanuel Kant), only to be told that he himself had discovered those results long ago, and had them in his drawer, but had never bothered to publish them. (His dismissal of Bolyai in this regard  is notorious.)

Lagniappe:  Mathematically inclined lasses seeking ipsigeneric role-models would do better to follow Noether, Kovalevskaya, Julia Robinson, or Ingrid Daubechies.  Though, once you reach that level, you have come to realize that pure mathematics is entirely genderless, and even (so we have argued here and there in this series of essays) extraspecific.

Note:  Eventually, after an hour or so, weary of its pieties, and disinclined to take in  yet another sex scene (Memo to directors:  That is not why moviegoers flock to a film about mathematicians and scientists), I walked out.  So maybe I missed some dazzling final mathematical exposition.  But I doubt it.

Lesen Sie die Geschichte  spesenfrei !

[Footnote:   For another psychologically attuned analysis of movies, click here.]