Saturday, December 31, 2011

New Year’s Resolutions


Here’s what’s on-deck for 2012 !!!

(1)  To contemplate the blessed doctrine of the Trinity.

(2)  To, um, ….

(3) To ….    ?????

(x)  ???????????????????????????????????????????????????????????


~ ~ ~

My mind’s as yet too weak to compass this.  But the pen may yet mechanically record, such glimpses as I come across in the writings of others.

~

Father Schall, S.J., in The Order of Things (2007), calls the Trinity “the inner life of the Godhead.”

~

Roger Scruton, in whom the light of logic burns  brightly alive, draws an intriguing conclusion:

God, says the Christian, has three natures, and we come to him by three separate paths:  when we worship him as transcendental law-giver;  when we encounter him incarnate;  and when the Holy Spirit moves through us in its work of concord.  It follows that there are three modes of rebellion against God:  the repudiation of law;  the assault on the sanctity of the human person;  and the desecration of the work of the spirit.
Modern Philosophy (1994), p. 474

Thursday, December 29, 2011

Take it from a Troglodyte


By now, hopefully most of you visitors to this site have at least tried, if not converted to, Dr Massey’s patented Bible-compatible© version of the “Paleo diet”.  (Key improvement:  Red wine.  I am at this very moment  religiously following this aspect of the diet.)  Both my wife and I have read his book, Original Thin, and we both enjoyed it, though neither of us changed our actual opinions by one micron, because, well, that’s the way minds work, and those are the limits of books. 

For many years, the Battle of the Sexes  as it played out in our household  consisted of me, trying hard to get some beef into the house, and she, trying very much not to.   But this morning, when I phoned her, she happened to be at Dave’s Health Foods (where most of our income goes these days), and enumerated the Neanderthal-friendly items in its protein bin:  among them,  to my surprise, elk-burgers.  Aren’t elks like endangered or something?  Is Dave’s just a front for a charcuterie out of “The Freshman”?   And, to my surprise again, she readily consented to try some.

The package lamely pretends that the animals in question were “farm-raised”, dining on nothing but organic delicacies while listening to piped-in Mozart.   But me I know different.   They were hunted in the northern fir-forests, by half-naked men using arrowheads fashioned from whalebone.    And after just a single “Big Mac”-sized portion, it’s impossible not to notice that my virility is now that of ten men.

Oh and -- how it tastes?  You’ll never guess.  It tastes like, well, like hamburger -- though in a sort of cave-dwelling, elkish kind of way.




[Footnote:  Old Murphy, never one to let well-enough alone,
ventures his untutored opinions here: ]

Wednesday, December 28, 2011

Word of the day: “attritely”


A note to the attrition community

The original sense of attrition is that of traditional Church terminology:

sorrow for one’s sins that arises from a motive considered lower than that of the love of God (as a fear of punishment or a sense of shame) : imperfect contrition
-- Webster’s Third New International Dictionary (i.e., “Webster’s Unabridged”)

It is certainly a word for our times, an age from which genuine contrition has largely disappeared;  indeed, even the lower standard of “sense of shame” becomes harder and harder to find, unless the culprit is actually caught before the rolling TV cameras, in which case you might see, if not any actual sense of shame, at least shame-in-a-sense -- sham shame.  (Among the linguistic reflexes of this fact  is the “non-apology apology”.)    Someone who feels contrition is contrite;  if merely attrition, attrite  (“A man in confession, of attrite  is made contrite  by virtue of the keys” -- 1625, cited in the OED).   If you say something in an attrite way, you say it attritely.

Which brings us to our hot newsflash of the day!
As of even date, the only site on the entire Web that actually uses the word attritely (as opposed to simply sticking in into an alphabetical list, or calling it “rare”), and uses it correctly (there’s one weird quote that is probably a solecism or a typo), is this one:

You’ll find it in the “Mailbag” column, second letter down.

And for Murphy’s own approach to attrition, click here:

http://murphybros.blogspot.com/2011/01/murphy-considers-his-sins.html

[Update 31 Dec 2011]
In addition to our era's characteristic non-apology apology ("I apologize for doing X, though there was nothing wrong with it and anyhow it isn't my fault"), there are apologies that had better gone unsaid:

http://www.latimes.com/news/nationworld/nation/la-na-pointless-apologies-pg,0,4642116.photogallery

[Update 22 Mar 2012]  A good op-ed on the subject, with recent examples:
http://www.nytimes.com/2012/03/22/opinion/please-stop-apologizing.html?src=me&ref=general

Cf. also this:
http://worldofdrjustice.blogspot.com/2012/02/false-umbrage.html

The Latest Updates

The following posts have been significantly updated:

Categories and Sameness : introducing cryptomelodia.

The concluding portion of A Minimum Axiomatization:  a new take on the Ontological Argument  for the existence of God.

Spaces  metric and uniform

Is the empty set really all that empty?



André Weil, international man of mystery.

Do Christians have better orgasms?  (I have slightly re-presented this essay, so as to draw in the holiday sidewalk crowds.)

Tuesday, December 27, 2011

What I know for sure about the Trinity


[This space intentionally --  though reluctantly --  left blank …]










(For an alternate perspective, from a Catholic detective, click here.)

Monday, December 26, 2011

Adventures in Algebraic Geometry


The closest I ever came -- and that  unwittingly -- to a brush with algebraic geometry,   was in freshman calculus.  (This was back in the ‘sixties -- before your time.)  The instructor was Robin Hartshorne, a young and winsome elf of a man.  He was an engaging lecturer, teaching from  or at least in parallel to  a beguiling text (Spivak’s Calculus, so utterly different in spirit from the dry Thomas treatise that had repelled me in high school to the point of dropping the class);  moreover he was -- now that I think back on it -- the first deeply intelligent teacher I’d ever had (though there were to be others -- notably Gleason):  up through high school, there had been no hint that such creatures even existed.
Still, he wore his learning lightly, like his tweeds.  The class was fun.  Particularly endearing -- though also startling, at the time -- was one day in the second semester, when he was presenting the topic of definite integrals -- painful but necessary, rather like a rectal exam.   He was chalking away, when all at once he seized up, staring in bemusement at the blackboard;  then turned to us with a sheepish grin.
“It’s been a long time since I’ve done one of these,” he said.

~

Now -- if the anecdote stopped there, it would be just one more ultimately stupid instance of Genius Porn :   the populace cooing contentedly when told that Einstein flunked grade-school math,  or that Gauss was late to learn to speak, or that Erdös tried to cut a grapefruit with a butter-knife  (which indeed he did, though it was a craftily calculated move).   These falsely flatter our vanity.  They are the opposite of a much better genre of joke, which you need a bit of math to actually understand, such as the one about von Neumann and the summation of infinite series.
For the incident, trivial until viewed in the light of later developments, did  there and then  plant the seed of doubt and wonder, as I sat theretofore clueless in the second row.   His being momentarily at a loss  struck me  at the time  as quite surprising, almost inexplicable:  as though a test-pilot, stepping from his aircraft into his roadster, were to stare at the ignition and say, “Remind me how to start one of these.”

Had I continued with a chemistry major as originally planned (well, originally-originally an English major, until I realized, with chill horror, the error of my ways), and thus retreated or perhaps advanced  depending on how you look at it, into ever-more-technical intricacies  and mechanical practicalities, the significance of that incident would never have become apparent.  But as it was, Hartshorne’s class (and Spivak’s sparkle) were instrumental in turning me towards a concentration in pure mathematics -- which was the only kind of mathematics they really taught at Harvard (golden memories of that climate of abstraction here), and eventually towards having a go at Berkeley towards a Ph.D.   Accordingly I was to be introduced to as-yet-unsuspected levels of intellectual depth, such that each, compared with the one before (I speak loosely;  they are basically incomparable), is as the definite integral to 2 + 2:  rising like the serried ranks of angels.  And though I myself never progressed beyond the level of the cherubim, it was sufficient to glimpse that empyrean wherein, indeed, you might forget the particular monkey-tricks used to solve thorny individual definite integrals (basically you just memorize these, storing them for reference like tools in a toolkit, unless you’re Euler or von Neumann, in which case you re-derive them instantly from scratch, or simply perform a brute-force numerical calculation in your head).

As each glowing level is added, the one below  becomes obsolete ...
Moreover, the tired old cart-horse of the calculus was, it turns out, very far from the centers of Hartshorne’s research interests, which are almost unimaginably abstract.   In that pokey little classroom in Massachusetts, he was really only on loan to us from Sagittarius, having once studied with Grothendieck, a confirmed extraterrestrial.  It was bruited about that he had something to do with something called projective geometry;  but only much later was I to learn that he is one of the pioneers of …

sheaf theory

… a topic so ferociously abstract, that even to define what sheaves are  is utterly beyond me.  (Wikipedia doesn’t even try, observing that “their correct definition is rather technical”.)  Nay, wert thou to gaze upon this theory naked -- not even to speak, not even to breathe of its further generalizations in topos theory -- ‘twould make thine eyes, like stars, to start from their spheres, and thine each particular hair -- nay more, thou wouldst  in sooth  explode in flames,  as did dame Semele,  when  all unheeding she beheld,   unveiled,  great Zeus in all his lightning !
 


~
~  Posthumous Endorsement ~
"If I were alive today, and in the mood for a mystery,
this is what I'd be reading: "
(Je m'appelle Evariste Galois, and I approved this message.)
~         ~
~

~

As so often when some movement of math has been seen streaking off westwards  out into the void, presumably never to been seen again by mortal man, it reappears shining in the east, reborn in some applicable form -- thus suggesting, you will notice, that the global topology of the noösphere is toroidal.  In the present case, algebraic topology has come to be crucial in such applications as: string theory (via its prior discovery of Calabi-Yau manifolds), coding theory,  cryptography and steganography -- which means that the juicy bits are probably highly classified.
And this raises the interesting paradox, which Epimenides would have relished, whether someone like Hartshorne is Cleared for the contents of his own head.

Robin Hartshorne as seen in a recent spectral image.  Since the old days, he seems to have sprouted quite a bundle of fibres over his base-space.
~

I recently happened upon an essay by the usually abstruse Samuel Eilenberg (of Eilenberg-and-Steenrod notoriety), written for a collection sponsored by the Office of Naval Research.  In deference, perhaps, to the needs of our seamen, Professor Eilenberg permits himself some observations and analogies   that lie within the reach of the common folk.  Thus:

The analogy between sheaves and covering spaces  is very close.
-- Samuel Eilenberg, “Algebraic Topology”, in: T. L. Saaty, ed.  Lectures on Modern Mathematics, vol. I (1963), p. 110

Bingo !  Covering-spaces I get.  Of course, I don’t actually see the analogy, but at least it’s a comfort, knowing that there is one.

~

We earlier discussed  the memoir Souvenirs d’Apprentissage, by a pioneer of algebraic geometry, André Weil.   Avid for more, we got hold of a copy of the memoir Random Curves (2008), by a contemporary algebraic geometer,  Neal Koblitz, well known to anyone with an interest in Elliptic Curve Cryptography. (It came in via InterLibrary Loan -- interestingly, the lending institution turned out to be the U.S. Naval Academy in Annapolis.    Compare the publishing venue of the Eilenberg article referenced immediately above.  We salute the broad interests of our midshipmen!)

Both authors have a wide range of interests and experience outside of mathematics;  both engaged in extensive foreign travel;  and it is of this that they principally write:  the reader will enjoy these accounts for their own sake, but we set down the volumes with a twinge of disappointment, that we are no closer to insight about algebraic geometry than we were before.  However, one biographical detail did strikingly stand out.  Both authors took a principled stand against unjust wars:  and this, not simply by penning valiant Letters to the Editor from the safety of their studies, but by a brave and almost reckless defiance while actually serving in the armies of their respective countries:  actions that could easily have led to their injury or even death, and which did actually lead to their imprisonment (and, in Koblitz’s case, to a severe beating).  But what is truly remarkable is that, in both cases, they used their time in the slammer far more profitably, mathematically, than most of us  use ours  even in the best of circumstances.   It was there that Weil did his seminal work, and there that Koblitz returned in concentrated form to the practice of algebra which he had largely abandoned during two years of political turmoil.

Intrigued, I wrote to the latter author, inquiring whether, from the standpoint of Kolmogorov-style measure-theoretical probability theory, we may validly generalize from this sample of two (2);  and he was kind enough to reply:

I love generalizations based on small samples.  I'm sure a lot of algebraic geometry was nursed at the Indiantown Gap army stockade!

Thus encouraged, I here make bold to speculate about the martial philosophy of Robin Hartshorne.  I know nothing of his politics, but truly cannot imagine the man wielding an M-16.   Or a flyswatter, for that matter.   Were a mayfly to venture into his office, Hartshorne would no doubt observe the pattern of its flight (musing all the while on the brevity of this earthly life) and calculate whether that trajectory describes an elliptic curve. -- Which, come to think of it, it just well might.   Many mathematical treasures remain to be unearthed in the field of biology!  (For a few of these, see the fine book by Ian Stewart, Life’s Other Secret.)

~

A rather huffy response to modern algebraic geometry, which it is a pleasure to reproduce  mainly because I do not understand the subject, and which suggests (like the characterization of Category Theory back when I was in college, as “the higher macramé”) that (as with these new-fangled things called “computers”) I am perhaps not missing much:

Attempts to extend the geometry of second-order surfaces  and the algebra of quadratic forms  to objects of higher degrees  quickly leads to  the detritus of algebraic geometry, with its discouraging hierarchy of complicated degeneracies, and answers that can be computed only theoretically.
-- Vladimir I. Arnold, Lectures on Partial Differential Equations (Russian edition 1997; English translation 2004), Preface.

Harumph!  Hear hear!

Mitt Romney: the Early Years


With the message “Treat your family like a multinational corporation” ( © M. Romney enterprises.  All Rights Rigorously Reserved) still glowing in our hearts, let us join the Romney family during those difficult early years of struggle at the Harvard Business School, when young Mitt didn’t have one million to rub against another (apart from the trust fund).  Their travails are your travails.  Doesn’t this all remind you of you ??
We join them around the breakfast table on a sunny Saturday morning.

“Maggots again?”  wails Sis.
“Cashflow problems,” grunts Mitt.  “That last gamble on sow-belly futures cost me a bundle.”
“Daddy, Billy’s eating his fingers.”
“Protein.”
“But, the fingernails? Won’t he choke?”
“Roughage.”

[Literary sidenote:  Connoisseurs will recognize the echo of the "mommy mommy" jokes of the 1950s.   In memory still green.]
~

“Daddy, who’s that lady over there in the matching ribbed écru sweater?”
“That’s an asset -- and a major one, I might add."  He nods approvingly.  "Solidly in the black.”
“But who is she?”
He glances over his reading-glasses.  “Susie, I’m surprised at you.  That’s the COO of the Maternity Department, colloquially known as `your mother’.”
“But why is she crying?”
Here an empathetic frown creases his manly mien.
“Kind of got burned on that last deal -- the infant male.  Runt of the litter.”

~

The Mat.Dept.  COO  gets the CEO alone in “the boardroom” (their fun pet name for the bedroom).
“Dear I’d -- I’d like to have another baby.  The ones I’ve got aren’t good enough.”
“Hmm,” he frowns, practical but not unkind.  “What is the estimated outlay over the life of the investment?”
“We-ell, I had Finance run the numbers, and I think we can afford it.  There’s the diapers, and the nannies, and the exclusive pre-pre-preschool, and the orthodontia and the cosmetic surgery to achieve the perfect Romney Look in case the merchandise should prove in any way defective … plus prep school and the horses and all that … We’re estimating, on a twenty-year cost bases, it’ll come to an even ten mill.”
“And what is the expected R.O.I.”
“Er -- normally nothing.  No-one has figured out how to securitize a baby.”
“Expenditure denied.”
“But dear -- consider the factor of corporate “Good Will’.  Kid’ll look great in photo ops when you later quit with your winnings before the bought-out companies collapse, and run for President, posing as a Man of the People.”
A broad grin suffuses his signature handsome face.  “Y’know, kiddo, you might just have a career in marketing.”

~

Oh -- excuse me -- you think that’s cruel ?  Just wait till the Wall Street sharks have taken over the White House, as their minions already infest the Senate and the House.  They’ll show you cruel.   You’ll breakfast on maggots and like it.

Thus, for your dining pleasure, a recipe for “Maggots in mercury, à la mode de Mitt”:

[Update 2 Jan 2012]
The Europeans are wise to this guy:
http://www.faz.net/aktuell/wirtschaft/wirtschaftspolitik/mitt-romney-der-kandidat-der-wall-street-11586962.html
America, heads up.

Sunday, December 25, 2011

A Christmas Message from Mitt Romney


Mitt Romney was twitted for saying “Corporations are people, my friend.”  But it gets better.  According to this morning’s New York Times:

A few years after Mitt Romney graduated from Harvard Business School, he returned to share a simple, timeworn lesson … Invited to give a presentation on balancing work and family, he began by telling students that they were like multinational corporations…


Note -- not even the “small businesses” or “mom ‘n’ pop stores” that politicians like to pander to, but supranational profit-driven mega-entities, whom you cannot really accuse of “off-shoring”, since  spiritually  they are already far off-shore:  conscienceless, owing loyalty neither to person nor nation, treating labor simply as a cost, like trash-collection.


And woe betide any sentimental fool who allows his family to simply romp about in Dickensian anarchy, or who values his children “off the balance sheets”, in and of themselves!  For then, something terrible may happen:

“Your children don’t pay any evidence of achievement for 20 years,” Mr. Romney said.  But if students failed to invest sufficient time and energy in their spouses and children, their families could become “dogs” -- consultant-speak for drags on the rest of the company.

It is then that the CEO comes up against a decision he dreads to take, but which he faces up to manfully.   He calls little Timmy into his den, and softly closes the door.

Well, young fellow, I see where you have failed yet again to qualify for the Little League.  And your grades -- we’ll, we won’t go into that.   And that baseball through the window … Candidly, Timmy, you’ve been taking up more than your fair pie-slice of my quality-time billable hours.
Son, I’ll be square with you:  I have been very fond of you…. on occasion … but it is time for this family to downsize.

[Note:  That last paragraph is not a quote, but satire.  I think…  The others are all too real.  You can look it up.]

~

We picture the scene as Mitt Romney and his merry band of buyout artists  seized control of Dade International.   Anxiously, uncertain of their future, the workers all crowd into the company cafeteria, where the New Boss, trim and impeccable, holds the microphone.   With calm and steely gaze, he surveys his new though purely temporary underlings, and thinks how much less crowded this cafeteria will be before long. 
And like Gordon Gecko’s address in similar circumstances,  the Big Guy manages to win over the suspicious crowd.  “I think of you all as family,”  he says…

When Mitt Romney says he regards you as family -- be very afraid.



~

Further details on how his scams work  here:

The bottom line:

Under Romney’s leadership at Bain, which spanned from 1984 to 1990 and from 1992 to 1999, at least five companies eventually filed for bankruptcy after being acquired by the private equity firm. In some of those cases, investors still made a profit as workers lost their jobs.  Even more troubling to some, Bain arguably drove some companies to the ground by taking on more debt to give investors dividends earlier.

~

[Update]  We never anticipated having to spring to the defense of Romney’s honor, but in all conscience we now must do so.
An absolutely scurrilous rumor is circulating on the Web, to the effect that, in his younger days, Mitt Romney sold one of his extra unneeded spare children into slavery to raise capital for a credit-default-swap buyback scheme.  Nothing could be further from the truth !
The child -- it wasn’t even the first-born -- was simply offered as collateral for a rather large loan essential for a brilliantly worked-out plan to swap prepackaged subprime supermarket-chain subordinated debt for securities calibrated to the precise gyrations of a contingency fund which -- well, no matter the details.  The point is, Mitt won the bet, and got to keep the kid.  All the little Romneyoids are present and accounted for, with at most one or two minor exceptions.

[Update 14 Jan 2012]
Response from a Nobel-prize-winning economist:
No, It's Not a Corporation, Doofus


Friday, December 23, 2011

The Children's Christmas Eve


The stockings hang beside the hearth,
the holly on the door.
The children hope that they’ve been good --
but they’re not sure.

They think of sometimes thieving fingers,
sticky with cookie-guilt.
A tear creeps to their eye at the corners
as they think of the milk they’ve spilt.

And oh!  What of the times they tried,
but failed, to say their prayers?
Lo, woe!  their whole life seems to proceed
in the spotlight of grownups’ stares.

Untidiness, disobedience,
the list of sins grows long.
Like toddlers walking, they sway on the fence
dividing Right from Wrong.

The stockings hang like judgment
as the children search their souls.
Will sweetmeats by their portion --
or a lump of cold black coal?

Toys left lying, beds unmade,
the Sunday suit awry.
There was even a time, they know to their shame,
when they told -- O coal!  -- a lie!

The children crawl between the sheets
on the night before Christmas day.
The pillow against their cheek is wet.
Their lips begin to pray.

*
The stockings hang from the scaffold.
The dark tree stands by the stair.
Yet as they pray  they hear the toll
of sleighbells in the air.

Behold!  A chariot slices the sky,
the stars roll back in a tide.
Saint Nicholas stands upon the helm,
the Virgin by his side.

And all the angels  whirl like fire,
bearing the carriage along.
The heavens thunder  with the choir
of joyful Christmas song.

Sugarplums shower from the tree
where CHRIST was crucified.
Raised souls join in a jubilee
redeemed by Him who died.

The children stare at Santa Claus
as light streams from his face.
Their present’s the best that ever there was --
the gift of Grace.