Triple Epiphany

 

A  priest -- an imam -- and a penguin:
walk into a bar.

 

(Let us pause, while we contemplate that.)

 

Each has vowed to order a drink that will challenge his faith head-on.

 

~

 

The priest orders a plain glass of water -- even though this is a bar.

After a moment of silent prayer, 

he raises the glass.

 

And just before the liquid hits his lips,

the Holy Spirit intervenes,

changing the water to wine.

 

The priest sighs and gives thanks.

 

~

 

 

The imam, biting his lip, goes ahead and orders a glass of wine.

His hand trembles as he lifts it -- but then, remembering his faith,
grows calm:  and in iron resignation,
drinks.

 

But again, that same saining spirit, that erst intervened,

now changes -- ere the drop upon the lip --

the wine into water:  thus sparing him sin.

 

The imam heaves a sigh and gives thanks.

 

~

 

The penguin orders a glass of orange juice.

He lifts it in the “To your health” gesture  to his companions,

then downs it in a draft:

 

and sits back;  sighs, in refreshed contentment.

 

The priest and the imam  exchange puzzled glances.

“But -- what -- did the orange juice change into?” they ask.

 

The penguin shrugs contentedly. 
“Just orange juice,” he says.

“I take the things of this world as they come,

exactly as God hath made them.”

 

 

An Extra Special Christmas

            The Murphy Brothers were seldom in funds, and could not afford to buy gifts.   They just did the best that they could.

            One year  Joey had managed to scrape together some change  and buy a beer-mug for his brother.   But since it was only a single mug and not a pair, the present proved impractical, and Murphy left it in the box:  until the following Christmas, having nothing else to give, he rewrapped it, and gave it to Joey, placing it under the lone coleus that served them as a tree.

            In this manner the relic passed from one brother to the other, and then from the other brother back, down the years, on each Christmas day:  as the brothers grew slowly older, and the coleus grew dim, and went at last to its reward.   And in time, that practice lapsed,  and the object was put away on a high shelf, until such time as the mug might someday somehow find its mate.

            And then one Christmas,  it snowed and it snowed.

            It was cold in their office-apartment, since the heat had been shut off.  And so they went out to the city streets to gather kindling, though fireplace they had none.  For it was the birthday of the baby Jesus, and it was meet, that they should gather wood.  And yet they found no twig nor stick of it. 

            
 And so they went sorrowing home.

            Yet were astonished, as they opened the door, to be rocked back on their heels by a summer breeze, which blew out from a roomful of snow.

            And there amidmost, stood a towering spruce.   Beneath it, three presents, wrapped in red:  and the fruit of this tree was permitted to them.

            They sat awhile together, and discussed these strange developments.   Where could all this have come from?   Neither of them knew.

            They wondered what might be in the packages.  At length they decided they would have to find out.  Joey motioned for Murphy to begin.

            And so, curiosity overcoming him, Murphy untied the ribbon, and carefully unfolded the paper, and lifted the lid of the box.  Then both brothers leaned forward, and wondering, looked in.

            It was the Gift of Poverty.

            Then both brothers rejoiced, amazed, and embraced.  For this was a wondrous gift indeed:  formerly, they had merely been poor.

            With keen anticipation, Murphy unwrapped the second present.

            It was the Gift of Chastity.

            The brothers sighed, and crossed themselves.   “Thanks be to God,”  they said.  For the solace of connubial bliss had always been denied them, owing to their detective vows;  yet now, their very abstention, might be a sacrament.

 Then gazed together at the final package,  neither one daring to move.

            But yet at last   with terrible trembling fingers,   almost sobbing with expectancy:   as when the bridegroom, as yet untried,  on the wedding night, fumbles at the bodice of his spotless bride, -- managed somehow to unloose the wrapping  (even as the maiden, on that sweet night, bids farewell to her maidenhead, and unloosens her chestnut hair):   and there lay--

            The Gift of Obedience.

            This gift had quite eluded them,  back in reform-school days.  Since that time, the Murphy brothers had always been resigned to their lot in life; but now they did embrace it, as the very will of God.

             “We should drink to this!” cried Murphy, indicating (and just noticing) a vat of ale;  and went to the high shelf, to bring the old package down. 

            And took out -- lo! -- twin goblets of crystal,  and filled them  each  to the brim.

            “This is the best Christmas ever,”  Joey said.

[Notice:  A hymn appropriate to this offering, may be witnessed here:

http://www.youtube.com/watch?v=W2YPsfwSPGg&NR=1 ]

~

For further Murphy mystical mystery

-- a story that will haunt your dreams:

Murphy and the Magic Pawnshop

 Also available for your Nook

Further parables from this pen, may be savored here. 
.

Minimalism in Physics (updated)

Truth is ever to be found in simplicity,

and not in the multiplicity and confusion of things.

-- Isaac Newton

[Note: 
In using the term “minimalism” in evaluating styles of physics, I am importing  into the philosophy of science  a term mostly associated with the arts.  The move may or may not be fruitful.  But here is a well-known parallel move, from Gerald “Mr. Themata” Holton, in The scientific imagination (1978), p. 7:

I have proposed … thematic analysis (a term familiar from somewhat related uses in anthropology, art criticism, musicology, and other fields).  ]

The whole enterprise of physics, from ancient times to today, is itself  in one sense  Minimalist, in that it seeks to sweep aside the riot of epiphenomena, and to discover underlying laws, from which that riot derives.  It does not so much banish the fullness of reality, as bracket it:  we hope later to derive much of it back, in an explanatory manner.  (Note:  Not quite the same thing as Reductionism.)

To some extent, all rational inquiry ‘minimizes’ -- idealizes, works with toy models, etc.   Some more than others -- economics notoriously so, tossing out so much bathwater that sometimes the baby goes missing.   Others roll up the sleeves of their labcoats and go in elbow-deep to the mess of reality, little bothering with economy or philosophy.   Chemists, in particular, seem perfectly content to potter about in labs, to discover stuff, invent stuff, patent stuff.  They literally multiply entities, in that they invent chemicals that weren’t there before.   Whether they thereby multiply them beyond necessity (mustard gas, thalidomide,  napalm, LSD) is a matter of individual taste.  But certainly the ethos is anything but austere.

And likewise, for the most part -- biology, geology, astronomy, engineering, what have you. 

But modern physics  raises parsimony to a central tenet, almost the prime purpose of the whole enterprise as currently understood.  This development being by now taken for granted among those of the guild, it may not be apparent how odd this really is.

The goal for some time has been the “Theory of Everything”.  This certainly sounds like a Maximalist program:  but really it is not.   For the knights who pursue this grail do not actually intend to explain any of the things that real people care about   and that motivated the enterprise of physics in the first place:  why the sky is blue, why snowflakes are the way they are, why clouds are shaped that way, what lightning is all about, why airplanes can fly…  (Purported explanations of these things exist, but the ones I’ve heard seem all fallacious.)   Instead, they want to wrap their arms around a passel of abstractions, so complex as to leave the plain man -- nay, any but the professional physicist -- behind many decades ago, and show that, at a still deeper level, they are all but facets of One Big Thing.  (Hedgehog physics, we might dub this.)  This is Minimalist, and ferociously so.

It may be objected:  All that is nothing but plain reductionism, which is simply to say:  Science.  No call to drag in an arts-related term like “Minimalism”.  -- But I believe there is an aesthetic dimension -- seldom mentioned in journal articles, though over-emphasized in popular writing -- which lies outside the bare logical necessities.  As,

“There shouldn’t be laws of physics,” Strominger maintains. “There should be just one law, and it ought to be the nicest law around.”

(Quoted in Shing-Tung Yau, The Shape of Inner Space (2010), p.  14.)

Gerald Holten, characterizing the attitude of Einstein (The scientific imagination, p. 281):

At stake was nothing less than finding the most economical, simple, formal principles, the barest bones of nature’s frame, cleansed of everything that is ad hoc and redundant.

In his own personal life, the legendary simplicity of the man was an integral part of this reaching for the barest minimum on which the world rests.

*

Central to the program is the “unification” of the various fundamental forces -- meaning, showing them to be symmetry-broken castoffs of an original single Force.    An analogy in evolutionary biology is explaining various related species  as having descended under various environmental pressures  from a common progenitor.   Only -- in physics, the enterprise is far more audacious than this analogy would suggest, if all you are thinking of are the breeds of dog, or the various canine species, or even the various land-mammals.   The forces are so fundamentally different in their phenomenology, that the task is more like tracing the common descent of the penguin, the echinoderm, and the paramecium.   Or even the mastodon, the gnat-swarm (considered as a sort of collective entity), and the sand-dune.   A tall order.

The reason so hubristic a program could come into existence despite the odds, is that it had an early success:  Maxwell’s unification of electricity and magnetism, back in the nineteenth century, truly a monument of the human intellect.  Now, later analysis has suggested that this success was something of a lucky fluke:  in the four macroscopic dimensions in which we reside, electricity and magnetism are both expressed by a vector.  You can not only analogize these, the one to the other, but calculate with them in the ordinary way -- say, forming their cross-product to get the Poynting vector.  In higher dimensions, electricity would be a vector and magnetism would be a tensor, and they would not play so nicely together.

The next success along these lines was far spookier:  the unification of electromagnetism with the “weak force”, into an unassuming-sounding entity called electroweak.   Now, this is far more bizarre than it seems. Electricity and magnetism were always rather like Batman and Robin, typically showing up together in the lab.  Whereas the weak “force” seems, to my untutored mind, like a force in some Pickwickian sense, like the  “force” of a metaphor in a poem.  A thing more different than electrostatic attraction or repulsion  can scarcely be imagined:  it deals neither in repulsion nor attraction, but rather in a handful of obscure and scarcely explicable processes such as beta decay.   Even to have conceived the project of their unification  was an act of extraordinary intellectual audacity;  the eventual success is, well, beyond any but specialist comprehension.

This new composite entity, this hippogriff, the electroweak, was subsequently unified with the “strong force”, yielding the hyperweak of today’s Standard Model.   The next -- and long elusive -- step, is the unification of that with gravity.   Now, to your average toddler, the natural analogy would be rather between electrostatic and gravitation attraction -- both, in their simple nonrelativistic forms, central forces obeying an inverse-square law    But your average toddler, like your average Nobel-Prize-winner-in-anything-but-Physics, would be mistaken.   And so the torch has passed to an ever-more-esoteric brotherhood, in particular  the magi of String Theory:  pale, spectral beings, who neither eat nor defecate, and whose results -- well, they do not as yet have anything so vulgar as actual verifiable physical results, mind you, but they do have theories, and conference papers, incomprehensible to all but the magi.  That does not mean they are on the wrong track;  perhaps they, and they alone, are on the right track, in which case, the more fools we.

*

A startling development in some corners of recent physics  is an actual ‘Maximalism’ -- basically, the catastrophic breakdown of any parsimonious project, yet not taken as a reductio ad absurdum of reductionism itself, but rather embraced, by amor fati (a fancy name for making the best of a bad bargain).   No longer can one really -- nor does one aspire to -- explain anything, since everything that might exist, does exist, and the (now uninteresting) facts of the matter in our own neck of the woods  can be chalked up to Selection Effect.  (We satirized this Rabelaisian Fay ce que voudras  here).   

Templeton-Prize winner Paul Davies,  in The Goldilocks Enigma (2006), p. 264, takes rather understated notice of this:

The disadvantage of the multiverse theory is that it invokes an overabundance of entities, most of which could never be observed, even in principle.  This profligacy strikes many people as an extravagant way to explain bio-friendliness.

Likewise, though for different reasons, the earlier Many-Worlds school (or cabal) of quantum theory,  in which entities -- again, entire universes in this case -- are multiplied, not simply beyond necessity, but beyond common decency.

The ethos of all this is atheistic -- a-anything, really.  It is perhaps no accident that Hugh Everett, an early pioneer of many-worlds, was (in Wiki’s words) “a committed atheist".  Or that the thélémisme of the distinguished hexagonal/pentagonal humanist  was taken up with gusto  by the diabolist Aleister Crowley, the stench of whose cinders may occasionally bother your nostrils, whenever a high wind blows up from Hell.

[Update 27 III 12]  Freeman Dyson in the current NYRB, reviewing a book by Margaret Wertheim about eccentric amateurs:

String cosmology is different. String cosmology is a part of theoretical physics that has become detached from experiments. String cosmologists are free to imagine universes and multiverses, guided by intuition and aesthetic judgment alone. Their creations must be logically consistent and mathematically elegant, but they are otherwise unconstrained. That is why Wertheim found the official string cosmology conference disconcertingly similar to the unofficial Natural Philosophy conference. The insiders and the outsiders seem to be following the same rules. Both groups are telling stories of imagined worlds, and neither has an assured way of deciding who is right. If the title Physics on the Fringe fits the natural philosophers, the same title also fits the string cosmologists.

[Note:  Dyson -- a notably fair man -- has long been a fixture of the Institute for Advanced Studies in Princeton; and the IAS, in recent years,  has been premier in string theory.  So Dyson's assessment here  is by no means that of an envious outsider.]

On the extra profusion of different string theories, a mathematician remarks dryly,

It was hardly an idea calculated to appeal to a man with a taste for desert landscapes  … There are more than 10^500 versions of string theory  lounging indolently about.

-- David Berlinski,  The Deniable Darwin (2009), p. 532-3

*

It will sometimes not be obvious, which proposals are Minimalist in spirit.  Thus, imagine some wretched Nominalist, who balks at the infinite, and proposes that the numbers needed for physics  are finite -- specifically, the field of integers mod a prime p (necessarily quite large, to accord with observation).   Finite’s gotta be simpler, more minimal, than infinite, right?  Roger Penrose retorts (The Road to Reality (2004), p. 359):

A physical theory which depends fundamentally upon some absurdly enormous prime number  would be a far more complicated (and improbable) theory than one that is able to depend upon a simple notion of infinity.

More precisely:   The problem is not essentially that the number is so large, but rather, with infinitely many primes to choose from, the choice would seem arbitrary:  in much the same way that the omniscient computer in  The Hitchhiker’s Guide to the Galaxy reveals, quite disappointingly, that the Meaning of Life is … “26”.

*

Differing from a theory-wide programatic theoretical minimalism, is a kind of personal cognitive-epistemological economy, described by Gerald Holton, The scientific imagination (1978), p. 158:

Fermi ordered the overwhelming and vast amount of knowledge  into a set of very few principles and ‘cases’, which allowed him to understand almost any new problem as an example of one of about seven primitive or primary physical situations.  Fermi would return throughout his career  to a listing or digest of the chief ideas in physics, which he had made when he first organized the field for himself as a young student.

Our own thoughts about such Leading Ideas in other areas, may be surveyed here.

*

A curious philosophico-cosmogonic anticipation of the TOE vs. Landscape divide  goes back several hundred years:

Leibniz … assure que la perfection de Dieu ne lui permettait pas de procéder d’autre manière que de la meilleure … mais Thomas d’Aquin sait que, créant du fini, un Dieu infini pouvait librement créer un nombre illimité d’univers différents, tous bons  et chacun commençant de manière différente.

-- Etienne Gilson, Linguistique et philosophie (1969), p.  163

And indeed, though Leibniz coinvented the calculus, we must say that, here, from a mathematical standpoint, it is Saint Thomas who is closer to the target.

Bonus quote:

Willem de Sitter found an exact solution to Einstein’s field equation … having no matter at all. … Why should we be interested in such a universe?  Because the real universe is of rather low density …

-- J. Richard Gott, The Cosmic Web (2016), p. 16

.

A Parable from Olde Berlin

During the days of hyperinflation:

Once in Berlin,

a man was about to pay ten marks for a box of matches, when he stopped to look at the banknote in his hand.

On it was written: “For these ten marks  I sold my virtue.”

He wrote a long, virtuous story about it,

was paid ten million marks,

and bought his mistress a pair of artificial silk stockings.

-- Malcolm Cowley, Exile’s Return (1934; rev. 1951), p. 81

Meum et tuum (bis)

(I)  Mine and Thine

This morning I am, for my better edification, engaged in reading Roscoe Pound’s classic Introduction to the Philosophy of Law (1922; revised and augmented edition 1959).   It is rather dry; only a concurrent reading of Cozzens’ law-soaked novel  By Love Possessed (most gripping, precisely, in its legal passages) led me to once again  pick up this monograph.

In the penultimate chapter, Pound arrives at the question of Thine and Mine.  To get some clarity on this vexed subject, he begins with a clean desktop by doing what we all should do whenever tackling a difficult problem:  arranging the data into six convenient groups:

Theories by which men have sought to give a rational account of private property as a social and legal institution  may be arranged conveniently into six principal groups, each including many forms.  These groups may be called:

(1) Natural-law theories;

(2) Metaphysical theories;

(3) Historical theories;

(4) Positive theories;

(5) Psychological theories;  and

(6) Sociological theories.

-- (p. 114)

There!  And now (in the word’s of Portnoy’s psychoanalyst, at the end of the book) -- Now we can begin!

Our interest here lies chiefly in the metaphysical theories, which began with Kant.  And Kant began with this:

He begins with the inviolability of the individual human personality. A thing is rightfully mine, he says, when I am so connected with it  that anyone who uses it without my consent  does me an injury.

-- (p. 117)

Ordinarily, philosophical argument is supposed to start with what is self-evident, or at least colorable, and to proceed by ever-cleverer reasoning  to some conclusion  the path to which was not initially plain.  Yet here we find ourselves in quicksand, before the journey is quite begun.

For  consider:

Little Timmy is playing happily with his new toy dinosaur, bought for him by his grandmother the day before.  Along comes Tommy and seizes the object by main force.  Timmy is dismayed, his playtime ruined; tears  well in his eyes.

But now consider Tommy, happily at play with his newfound fun dinosaur.  Let Timmy, or Bobby, or anyone else, come along and likewise appropriate the coveted item, and -- now Tommy is dismayed, his playtime in tatters; salt tears  sting his eyes.

The only way we might distinguish between the sense of grievance of the two boys, is in light of some antecedent theory of ownership  and notions of justice attached thereto, held by one or both boys:  quod erat demonstrandum, sed demonstratum non est.

That, alas, is an actual incident, from America’s tragic past.  Here, ladies and gentlemen of the jury, are the facts (David v. The Cruel World, 1955):

~ The Case of the Purloined Dinosaur ~

I was not quite five years old, temporarily living with my maternal grandmother  in Garden City, Long Island, while my parents, having moved from Tennessee, were off house-hunting in New Jersey.  In the course of a visit to the Museum of Natural History (fondly recalled here) she had bought me a lovely little bronze statuette of a brontosaurus;  I had few or no toys dating from the time of our rather exiguous existence in Oak Ridge, and this brontosaurus  was by far my most precious possession.

I was outdoors alone, playing with this wondrous toy, when along came a neighborhood boy and, liking what he saw, calmly possessed himself of the animal and began walking home.  Stunned at this calamity, I trailed along after him, alternately remonstrating, threatening replevin or trover, and expostulating, citing seriatim the old Roman (“natural law”) theories of possession, along with the metaphysical, the historical, the positive, the psychological, and the sociological -- finally adducing canon law and the opinions of the early Church fathers concerning matters of tortious conversion -- or would have, had I heard of any of that.   He merely shrugged -- then trumped me, with a legal axiom of his own -- and one which stood irrefutable, as it rhymed:

~  Finders keepers,  losers weepers ~

That adage took me aback.  I was amazed that the world here below should be so ill-ordered, but such apparently was the case.

Later that day, I appealed to the local areopagus, in the form of my grandmother -- herself the daughter of a clergyman, and pretty clear on matters of right and wrong.   She phoned the boy’s mother, who then tried to recover the object from her child’s well-stocked toybox;  but by then it had been lost and forgotten.

~

Had we each, I and that larcenous lad (who now, if he yet live, is even older than I am, if such a thing may be conceived) -- had we, I say, myself and that Barabbas rapscallion (prior to his eventual death in the monastery  whither he had  no doubt  latterly repaired, in penance of his depredations, dying finally in an odor of sanctity, his palms emblazoned with stigmata  in the shape of brontosaurs):  had we, say I, either of us, possessed a copy of Pound’s treatise (necessarily the original edition, since the second was not yet out) -- had the two of us sat down, like men of reason, and conned its pages  for guidance in our perplexity -- I might not (contrary to intuition) have been the gainer thereby.  

For in that work, does not the author refer to “the maxim possession vaut titre in continental law” (p. 128);  and does he not likewise allege, that

when one appropriates a thing, fundamentally he manifests  the majesty of his will  by demonstrating that external objects that have no wills  are not self-sufficient

(-- p. 120)

?

Our light-fingered adventurer might well take that as praise.

~

Already  I sense, you are reaching for your well-worn,  dog-eared,  espresso- or brandy-stained copy of The Common Law, by Mr. Oliver Wendell Holmes, Jr., Esq. (1881; which surely graces your night-table) for help in ascertaining what might lie aback of all of this.  To that work, therefore, we now repair.

Holmes’ tract is  if anything  even drier, even more nose-to-the-grounds-of-precedents (some quite ancient) than Pound’s.  Yet he claims to have his eyes as well on higher (or deeper) things:

The interest attaching to the theory of possession  does not stop with its practical importance in the body of English law.  The theory has fallen into the hands of the philosophers.

-- chapter “Possession”

And not merely  for their own abstract amusement;  for Pound goes on to declare the influence bidirectional:

Nowhere is the reciprocal action  of legal rules  and philosophical theories  more strikingly manifest  than in our law of contractual liability.

-- Pound, op. cit., p. 

Anyhow, readers hoping for sure philosophical guidance from Holmes’ book  might be disappointed.  As, consider the following hypothetical case:

A pocket-book was dropped on the floor of a shop by a customer, and picked up by another customer before the shopkeeper knew of it. 

-- Holmes, op. cit., p. 222

(And, be it understood, made off with it;  that is not stated in the text, but apparently was the expected behavior of a shopper.)

Now, for fifty points -- answer this simple quiz from WDJ.  The appropriate holding would be:

(1) The purloiner of the pocket-book is a common thief, and should be prosecuted as such, regardless of whether he repents and returns the stolen item.

(2)  In the event that, unprompted, the purloiner  of his own accord  return the lost property to its owner, no charges should be lodged.

(3)  Screw the owner -- the perp gets to keep it, free and clear.

(4)  Actually the shopkeeper gets to appropriate the mislaid item.

(Pause for reflection;  then read on.)

If you answered (1) or (2), you are (according to Bridges v. Hawkesworth), a patsy, a loser.  “Finders keepers, losers weepers” rules -- the correct answer is (3):

Common-law judges and civilians would agree that the finder got possession first, and so could keep it  as against the shopkeeper.

-- id.

 

~

After that little Gedankenexperiment, we gloomily wonder why a table-sweeping fifth option was not added:

(5) Property is theft.  (La propriété, c'est le vol. -- Proudhon.)

And indeed, Roscoe Pound does cite that 18^th-century ideological Brandstifter  J-J Rousseau, to much that effect:

Rousseau held that the man who first laid out of plot of ground and said, “This is mine”, should have been lynched.

-- Pound, op cit., p. 119

To that we might merely observe that … he probably was.  As was any man who, outside the receptive and self-developing Greco-Roman-Christian current of history, presumed to invent or discover anything (or at best, he was ignored, and his find  died with him). “No such constitutional framework of contractual security as the Roman  was evolved by any other people in the ancient world.” --  Adda Bozeman, Politics and Culture in International History (1960), p. 201. (See also Lord Raglan, How Came Civilization.)

(II)  Adverse Possession

Apart from simply seizing someone else’s property and walking off with it, or invading it by main force, there is a subtler way of annexing the same, which can even cadge recognition by the law.   This trick is called:  Adverse Possession.

Thus, Princeton University owns a bit of woodland, containing a birdwatchers tower, to which access is unrestricted.  Yet one day a year, they bar the access-road and say No Trespassing:  this, lest their title lapse.  

So put, the phenomenon may appear a mere curiosity; but the phenomenon is spreading, as here and there  governments lose their backbone.  This, most strikingly in France, where certain immigrants -- illegal to begin with -- have occupied buildings and even private residence, the authorities seeming powerless to defend the rights of the owners.  Meanwhile the public becomes glumly accustomed  to ever-wider infringements with impunity.

Ogden Nash captured an earlier version  in a celebrated poem of 1938:

How courteous is the Japanese;
He always says, “Excuse it, please.”
He climbs into his neighbor’s garden,
And smiles, and says, “I beg your pardon”;
He bows and grins a friendly grin,
And calls his hungry family in;
He grins, and bows a friendly bow;
“So sorry, this my garden now.”

Such is the sociological landscape of bisounours Europe today;  the frog slowly cooking in the crock-pot;  le grand Remplacement.

(III)  Debts & Promises

The early Romans were serious about debt:

Defaulters (addicti) could be sold into slavery  or even put to death by their creditors.

-- H.H. Scullard, A History of the Roman World, 753 to 146 BC (1935; 4^th edn. 1980), p. 83

Durch das frührömische Kreditrecht in der Form des nexum  hatte der Kreditgeber faktisch ein Zugriffsrecht auf die person des Schuldners.

-- Karl Christ, Die Römer (2^nd edn. 1983), p. 20

That practice found an echo as far away as England, as late as the nineteenth century, in the institution of debtor’s prisons, so memorably depicted by Dickens (who, however, was not an impartial observer in this case).   That institution strikes any contemporary who first hears of it, as wacky (quite apart from the humanitarian aspects), since how can the fellow pay back his debt  if removed from the economy?   A historical view, however, reveals an institution that made sense in a certain social context -- near-universal throughout much of antiquity, and still in effect in many later cultures -- in which the familia, gens, phratry, tribe or what have you, was responsible for each of its members:  imprisoning the prisoner was more like sticking him in a pawnshop until redeemed.  It wasn’t punishment per se;  he simply served as the logical collateral.

[Gist of omitted section:  As is by now notorious, such severity towards debtors has not merely been largely relaxed, but the background culture of… honoring one’s debts  has in many areas collapsed disasterously -- and this, not only at the foot of the economic ladder, but at its tippy-top, the culture of Bain Capital:  a culture of reckless gambling, whose losses are made up by the taxpayer.]

If you live in a nation which disdains to enforce contracts, you can either just shrug and take it as a gamble, or do business elsewhere -- or no business at all, go off and cultivate newts or something.

Transposed to our boyhood memory  in the form of a parable, the scenario would be:

“Could I borrow that brontosaur for a second?”

“Uhh… Yeh sure.”

The boy takes it and walks off.

“Hey!  Give that back!  I didn’t give it to you -- you said ‘borrowed’.”

An indifferent shrug.  “So, I’m an insolvent debtor.”

Pensum vitae

A fore-glimpse of “In der Strafkolonie”  (Oktober 1914):

Letzthin,

als ich wieder einmal    zu regelmäßiger Stunde

aus dem Aufzug stieg,

fiel mir ein,

daß mein Leben

mit seinen  immer tiefer ins Detail  sich  uniformierenden Tagen,

den Strafarbeiten gleicht,

bei denen  der Schüler    je nach seiner Schuld

zehnmal,  hundert-

mal oder noch     öfter    den        gleichen

zumindest in der Wiederholung  sinnlosen

(zumindest in der Wiederholung      sinnlosen)

(zumindest in der

      zumindest            der        )

zumindest in der Wiederholung  

sinnlosen Satz

aufzuschreiben hat :

nur daß es sich  aber bei mir  um eine Strafe handelt,

bei der es heißt:

»   so oft,   als du es  aushältst. «

-- Franz Kafka, Tagebücher, Aufzeichnung für 24 Januar 1914

For more on the matter:

        “Tales of Frontier Times”

~

A fore-glimpse of  "Vor dem Gesetz", incorporated into Der Prozess (1914-5; publ. 1925):

Dieser Gesetzeskundige  hatte vor sich immer die Schrift aufgeschlagen  und studierte in ihr.  Er hatte die Gewohnheit, jeden, der um Rat kam, mit den Worten zu empfangen: » Gerade lese ich von deinem Fall «; hierbei zeigte er mit dem Finger  auf eine Stelle der vor ihm liegenden Seite.

-- Franz Kafka, Tagebücher, Aufzeichnung für 27 Dezember 1914

On “The Nature of Mathematical Knowledge” (enlarged)

That question is about as interesting as the nature of our knowledge of elephants.  We are interested in the zoology of elephants, not in the specificities of classroom biology lessons, or the economics of zoos.  We are uninterested in each blind man’s subjective and partial report upon the individual organs of these splendid creatures.

Mathematical knowledge, like pachydermal knowledge, is imperfect knowledge of something real that exists independently of us. By contrast, just which images we manage to form of these objects  are very much dependent upon ourselves – and to that extent, of interest only to unemployed social workers.

As our former math teacher put it:

Mathematics has a real content which transcends the inadequacies of our efforts to formalize it.

-- Andrew Gleason,  Fundamentals of Abstract Analysis (1966), p. v.

Or, from a philosopher:

For most mathematicians most of the time, having a feel for what is evident is important, but it is also enough: There is no further need for a theory of what that feel is.

-- Shaughan Lavine, Understanding the Infinite (1994)

*

Actually, it should not be deduced from the above, that I am somehow dissing our big friends the elephants.  A Theory of Elephants is considerably more promising than that idle grail of the physicists, a Theory of Everything.

The outstanding problem in the Theory of Elephants is the ontological status of BABAR – THE KING !!!!!

His Majesty ... The King !!!

An agnostic or non-Realist version, wilfully po-faced:

Our deductivist proposes clean answers to philosophical questions.  What is mathematics about?  Nothing … What is mathematical knowledge?  It is knowledge of what follows from what.  Mathematical knowledge is logical knowledge.

-- Stewart Shapiro, Thinking about Mathematics (2000), p. 150

*

*

There is a systematic ambiguity (roughly that of actio versus actum) to the term mathematics:

(I) The praxis of mathematizing.  This is a human pastime, comparable to needlework or basketball.

(II) The truths of mathematics.  Or, more or less synonymously: The real (though invisible) world.  These, in themselves, bear no dependency upon human practice or to any species whatever;  they existed before we were born.

The above may count as a polemical reformulation of roughly the dichotomy in the title of Hao Wang’s fine essay, “The Theory and Practice of Mathematics”.

*

In 1950, Raymond Wilder gave an address, “The Cultural Basis of Mathematics”, reprinted in  various places, and later wrote a whole book on the subject, Mathematics as a Cultural System (1981).   Bien-pensant commentors treat these with grave respect;  but the notion is practically nonsense.  For, if we take mathematics in sense (II) – the only sense of interest to us here – that is like saying “The cultural basis of elephants”:  there is none.  There is a cultural basis of circus stunts, of mouse- and peanut-myths, of Dumbo, but not of elephants themselves.  Their basis is their own four feet.

Why should the culture of mathematics  (necessarily, sensu I) – that is, the foibles of mathematicians – retain our attention?  The purely “human side” of mathematicians  is generally less interesting than that of country music stars.  A lot of mathematicians are pretty Asperger’s, frankly.
(For a poignant illustration of this, read The Genius in My Basement.)

There is, we grant, a certain interest in the sociology of mathematics, or in biographies of the great mathematicians. Intellectually, it is on a level with gossip about the off-court antics of basketball stars.  Fun, but of no mathematical (or basketball) interest.   It’s just a way for the mind to chew gum while it’s too exhausted to do anything substantial.  To get real, do math (or play basketball).

Not to come down too hard on the small geeky community that does follow the doings of math and physics whizzes; I number myself among them.   It would even be neat  if, instead of collecting baseball cards, people collected mathematician cards (“Trajea two Steven Smales for a John Milnor!”) .  -- By “people”, I here mean “eight-year olds”.

*

More interesting is the purported “reduction of mathematics to logic”.  It is not initially clear, however,  to what extent this program, if successful on its own terms, would enlighten us as to mathematics-sensu-(II), as opposed to the sense-(I) territory of our own mathematical formulations and formalizations (these being, after all, largely for mere convenience).  It might be more along the lines of the demonstration of the equivalence of the Heisenberg-style matrix-mechanics formulation with that of the Schroedinger-style wave formulation, of quantum mechanics. That feat didn't tell us all that much about the actual phenomena of physics,  apart from the fact that the world is a many-splendored thing, and can be described -- blind-man-fondling-elephant-fashion -- in a variety of ways.  It’s more like deciding whether today’s symposium shall be conducted in English or in French.

*

That said --

We argued here that the axiomatic method is cognitively post-hoc, and that  only in cases where (as with the Euclidean axioms) their positing is transparently motivated by our experience of the sensible world, is a top-down, axiomatic presentation  pedagogically sound.   Thus similarly in physics:

In lecture after lecture, and essay after essay,  Einstein began, not with an introduction to the subject at hand, but with an overview of how he’d arrived at that subject, or of how scientists in general  arrive at subjects in general. … For Einstein himself, the results of science had become incomprehensible without an understanding of the processes that led to them.

Richard Panek, The Invisible Century (2004), p. 153-4

C'est exact;  and the farther physics wanders from our human experience, and the father math develops beyond anything the world has seen before, the more necessary such a psycho-cognitive ladder does become.

*

Something like the dichotomy outlined above  must have been behind André Weil’s tart remark, in “History of Mathematics” (reprinted in Collected Works v. III as (1978b)):

Some universities have established chairs for “the history and philosophy of mathematics”;  it is hard for me to imagine  what those two have in common.

For:  the one is situated and contingent, the other timeless and beyond place.

*

Footnote:   These remarks about mathematics  apply  mutatis mutandis  to the Deity.  Deliberately confusing the distinction between truth and praxis, Karen Armstrong wrote a book -- a minor best-seller -- with the impudent title A History of God.  (At least she put A, not The; probably saved herself an extra millennium in Purgatory right there.)

*

Lakatos’ classic dialectical-dialogue Proofs and Refutations (you see the Hegel-style paradox already in the title), though focussing on the (as he persuasively argues, in the course of a detailed case-study spanning many decades) micro-level mess of actual mathematical progress, is yet Realist at its core:  the subtitle is “The Logic of Mathematical Discovery”, not “The Sociology of  ‘Mathematical’ Invention”.   We quoted him in another context  thus:

As far as naïve classification is concerned, nominalists are close to the truth when claiming that the only thing that polyhedra have in common  is their name.  But after a few centuries of proofs and refutations, as the theory of polyhedra develops, and theoretical classification replaces naïve classification,  the balance changes in favour of the realist.

-- Imre Lakatos, Proofs and Refutations (1976), p. 92

In an appendix to the main work, he offers a Hegelian formulation, one which (by the time the reader has progressed this far) has a certain paradoxical piquancy:

Mathematics, this product of human activity, ‘alienates itself’ [in the sense of Hegel and Marx] from the human activity, which has been producing it.  It becomes a living, growing organism, that acquires a certain autonomy [emphasis in original] from the activity that produced  it.  … The activity of human mathematicians, as it appears in history, is only a fumbling realisation of the wonderful dialectic of mathematical ideas.
-- Imre Lakatos, Proofs and Refutations (1976), p. 146

Plato, in his Paradise, smiles.

Idea for a Screenplay

Appointment in Tirana

(1)   The supreme head of the [named apostolic entity redacted] no doubt receives hundreds, if not thousands, of utterly bogus threats per year.  Some are pranks, others are from disturbed persons with no genuine capacity for effective action.

Then one comes in, and then another, purportedly (though who can verify a case like this -- it’s not as though there’s a press-office; and anyone can sign a name) from an unlikely source.  But:  said source having been enjoying a certain notoriety in the news of late (which indeed it craves, and seems to live for), a brief back-page notice is issued in the press, and is largely forgotten.  For their part, the entourage of [redacted] dismiss concerns, and announce that they will proceed with the voyage as planned.

(2)  Meanwhile, in a semi-darkened tower, in the corner of a cubicle in what looks like a kind of half-abandoned warehouse, a young man in uniform (for purposes of the screenplay, we may call him “Bob”) stares at the river of pixels as it races past his eyes.   He is tired;  he has put in a long day, he yearns for the embrace of his sweetheart at home.   Yet something tells him to push it just one pace farther.  Then something catches his attention.  It seems a little odd.

Certainly, by itself it means nothing;  but then, you never know.  He shrugs, and sends it on.

Mostly, it is ignored.

(3) Shortly thereafter, an aging and rather eccentric individual (whom the screenplay can feature as “Doctor Jay”), having meant to retire before now  but put that day off  for one reason or another, notices both items, and realizes that they make more sense together than apart.  He studies the matter, without reaching any definite conclusion.  But he continues to turn the matter over in his mind, with growing alarm.

A few days later, something happens on a faraway island continent, and suddenly all the pieces seem to fall into place.

Exceeding his brief, and risking rebuke, he frantically tries to bring the matter to the attention of [deleted], [minimized], and [redacted].   No-one responds.

(4)  Meanwhile, on another continent, in a mountain redoubt, a sinister figure, clad all in black apart from a glinting golden timepiece encircling his hairy wrist, stares at the latest handwritten courier communication  with narrowed eyes.  He gives only the most imperceptible of nods;  but his minions pick up the signal.  The op is a go.

Synchronize your watches ...

(5) Simultaneously, on the top floor of the palace, an elderly figure in a white skullcap practices his big speech before an antique gilded mirror.  What an occasion this will be!   He hopes the weather will be fine.

(6)  Halfway around the globe, in a little town in Iowa (sun shining brightly above, with radiant unconcern), a tiny child drops its lollipop on the sidewalk, stares at it with round eyes, first of incomprehension, then of of dismay;  and bursts into tears.  Little does he realize that he will ere long have greater cause for weeping, which shall mark the fate of his entire generation.

(7)  [Need to somehow work in the love-interest or it’ll never get airplay.  Our screenwriters are working on that angle.]

“Goldberg Variations” variations

[Update Sept 2014]  For a beautifully analytic visualization of variation #10, try this:

https://www.youtube.com/watch?v=83tCGa_NIJ4&index=45&list=PLEB5B1DFA5C94D5EE


[Here is the original post from 2011:]

For some years now, I have gradually withdrawn from the regular appreciation of music.  Darwin reported the same symptom in later life, and I imagine that our reasons are similar.  The sole exception has been sunny Sunday mornings, which I have marked by a listening  of the “Goldberg Variations”, either in the 1981 recording of Glenn Gould, or any of various harpsichord renditions.  Lately, as I concentrate ever more thoroughly on philosophy and logic, this piece has received repeated playings – partly for the mere negative reason of shutting out all contingent noise from the fallen world beyond the windowpanes, and partly to channel my own attention.  It is not, in and of itself, anywhere near my favorite piece of music; indeed, its suitability for present purposes lies in part in a certain dryness which is undistracting.  Yet with time, the piece  in all its iridescence  has become an audio equivalent of the air we breathe, of the light we see by.

*

Let us give thanks for the munificence of Amazon-dot-com, which allows us to listen to pretty substantial samples of every CD they sell.  You call up the piece, and can run through every major recording in succession.  Each variation is not quite complete, but you hear easily enough to compare them; and their slight truncation actually renders the experience more mathematically abstract, and less like mere indulgence.  Of interest too are the “Customers who bought this also bought those” annotations:

* For Gould 1955, the co-buys were unsurprising:

The Glenn Gould Edition - Bach: The Well-Tempered Clavier, Book I ~ Johann Sebastian Bach

French Suites - 70th Anniversary Edition ~ Glenn Gould

The Glenn Gould Edition - Bach: The Well-Tempered Clavier, Book II ~ Johann Sebastian Bach

Bach: The Goldberg Variations ~ Johann Sebastian Bach

A State of Wonder: The Complete Goldberg Variations (1955 & 1981) ~ Johann Sebastian Bach

Partitas 1 2 & 3 - 70th Anniversary Edition ~ Glenn Gould

Partitas 4 5 & 6 - 70th Anniversary Edition ~ Glenn Gould

Bach: Goldberg Variations ~ Johann Sebastian Bach

*Similarly for the likewise mainstream Perahia:

Bach: English Suites Nos. 2, 4 & 5 / Perahia ~ Johann Sebastian Bach

Bach: Well-Tempered Clavier ~ Johann Sebastian Bach

Bach: Keyboard Concertos Nos. 1, 2 & 4 ~ Johann Sebastian Bach

Songs Without Words ~ Johann Sebastian Bach

Bach: English Suites Nos. 1, 3 & 6 ~ Johann Sebastian Bach

Chopin Etudes ~ Fryderyk Chopin

Handel/Scarlatti: 3 Suites/Chaconne/7 Sonatas ~ George Frideric Handel

Bach: Keyboard Concertos Nos. 3, 5, 6, 7 ~ Johann Sebastian Bach

*By contrast, for a Deutsche Grammophon recording of the piece transcribed for string trio (not so heretical as it might sound, since even the pianoforte performances are transcriptions), there was no overlap:

‘The Painter's Music - The Musician's Art ~ Warren Lash

Janaki String Trio Debut ~ Jason Barabba

Piano Quintet in F Min / Complete String Quartets (1, 2, 3) ~ Johannes Brahms

Anna Netrebko & Rolando Villazón: Duets ~ Georges Bizet

The Berlin Concert - Live from Waldbuhne DVD ~ Rolando Villazon

Gitano ~ Rolando Villazon & Placido Domingo

Chopin, Liszt: Piano Concerto No. 1 ~ Fryderyk Chopin

Romance of the Violin ~ Joshua Bell

[Note: The transcriptional experiment worked rather well for some variations, much less well for others.]

            Of course, what I’d really like, for guidance,  is not the rather predictable musical co-selections, but something more along the lines of

“Those who bought Recording A, also bought:

Aquinas,  Summa Theologica

Chesterton, The Everlasting Man

Gödel, Gesammelte Schriften

“Those who bought Recording B, also bought:

Hitler, Mein Kampf

Realtor Magazine: the Swimsuit Issue

Anonymous, Jokes for the John.”

which would speed the selection considerably.

*     *     *

~ Commercial break ~

http://www.youtube.com/watch?v=FwzOXzZWUik

We now return you to your regularly scheduled essay.

*     *     *

*

Imagine, indeed, a world in which, for a thousand years, music just was the Goldberg Variations – no other music existed, nor had anyone an idea of composing any new.  The score was thus like the text of the Mass – you didn’t meddle with it.  But apart from that, it lay in the arena of art, not ritual:  Everyone in the society would learn the piece, and play it, with ever greater depth, his whole life.  (Just as everyone must fall in love, not promiscuously with a representative of every species, but with a woman, and marry her.)  It wouldn’t be musically as rich as our own world, but it wouldn’t be a bad thing, either, and in some ways doubtless richer:  More like faith, or philosophy, and less like turning on the TV. 

            This fable would not work so well, if instead of the “Goldberg Variations”, the society had to make do with, say, “Happy Birthday”.  Bach’s exercise is a nice balance of unity and diversity.  Moreover a spiritual task is obvious:  to learn how the reprise of the aria is to be played differently from the first.  For it is not the case, save for degenerates, that “in my end is my beginning”.  Rather, the opening rendition of the aria should be performed straightforwardly, dutifully, naively, with all the trust of a child.  The closing rendition, although note for note identical, should reflect what we have all been through in the course of listening to the work itself, and what we have learned.  (Compare Borges, “The Don Quixote of Pierre Menard”.  -- The variations separating the arias are of course here metonymic for the whole course of human history.)

            The parable is not so counter-factual:  Our present relation to Elizabethan drama is exactly like this.  Only a handful of plays get performed, and those over and over.


[Update:
For an even bleaker, more minimalist  inspissation than this,
click
here ...]

For the whole list of our music-related posts, click here.

~

[Update Dec 2013]

For a quite wonderful cembalo interpretation, or re-invention, or alternative incarnation (rather:  ennoöfication) of the Goldberg Variations, performed by Wanda Landowska back in 1933, listen to this:

http://www.youtube.com/watch?v=HWD-JvJ-6yk

When listening to other pianists performing this work, it is difficult to refrain from comparing them to the classic performances of Glenn Gould.  But Landowska operates in a magical parallel dimension of unexplored topology, and thus is neither better nor worse that Gould’s take on the matter, being rather strictly incomparable:  as would be a mathematical recreation, which should embody the entire structure of that abstract work, in ways not directly intuitable to the musical mind, but which were strictly homeomorphic, or isomorphic within the mutually containing Category, whatever that (as yet unimaginable) Category might turn out to be.