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.

~     ~     ~

For a further story of miracles through grace,  

have a look at this:

Murphy Makes a Mitzvah

Indian Spring

After a frigid week and an all-night drenching, the earth awoke to a remarkable redoux -- a humid, balmy simulacrum of Spring, wedged into a crevice of Winter.   And so, though my son and (since the bereavement) principal hike-mate  was still tarrying up in New Jersey (like Odysseus on Ogygia,  entranced by Calypso), I set out for the lake, alone save for ever-sensed presence of my late beloved bride, ethereally by my side.  (For those of you with a Classical background, this will recall the eidolon of Helen of Troy, in Euripedes.)

The lake, only recently frozen over, was now quite free of ice. A flock of diving-ducks made sport with this, plying their dippy trade; and a few turtles had seemingly emerged from whatever mudhole they hide in to escape the winter’s wrath, and were sunning themselves on a log.  Solitary joggers  in T-shirts and shorts  passed by.

On the far side of the lake, a brisk wind had sprung up, and this fickle, now from in front and now behind.  I sat down on a sunlit bench, half-hoping the Muse might whisper, but in the event  I mostly joined the turtles in a dozy pleasure of motionless, wordless sunbathing.  Such exposure increasingly abundant sun is prophylactic against Seasonal Affective Disorder, a kind of dermal dialysis.

[-- 21 Dec 2018, officially the first day of Winter.]

The Brightening, though Frozen Solstice

This time each year,  the sun doth wend,

signaling days-dying’s end.

Henceforth  throughout  the grateful lands

our daily dose of light  expands.

Thus do we, cheered  by this faint grace,

take heart for Winter’s chill embrace.

And though the brisk winds  scourge the earth,

look forward to  our Spring rebirth.

Christi dedico in nomine;
Gratias agimus, Domine.

Depth Psychology of the Riddling Community

The riddle was originally a sacred game, and as such cut clear across any possible distinction between play and seriousness.

-- J. Huizinga

There seems to be a riddle

behind all riddles

which we have not yet guessed.

-- Northrop Frye

Ding-gedicht

Behold the bold and noble toaster,

ever ready  to brown your bread.

Fie on them who spurn her service

and use a microwave  instead.

Gemmological Footnote

In 1955, the noted gemmologist and contrarian Sir Nelson Goodman, in a brief note published in the proceedings of the Devonshire Horticultural Society, questioned the received wisdom concerning the colour of emeralds.  “Everyone says that they are by nature green,” he noted, “simply because they have always been green.”  (Note that, in Sir Nelson’s quaint dialect, “been” and “green” actually rhyme.)  “But our observations to that effect, however numerous and of however long standing, may equally be marshaled to support the thesis that they are in fact grue:  which is to say, green prior to 18 November 2018, and blue thereafter.”

In the half century or more that has elapsed since that time, all sorts of philosophical fuss about “projectible predicates” and whatnot (green but not grue  enjoying this rather circular distinction), but in all of that, thinkers lost sight of the basic facts of the matter: are emeralds in fact green, or grue, or what?

We need wonder no longer, for the great day -- 18 November 2018 -- has arrived at last.

And it turns out that  last night, all over the planet, and into the deepest recesses of intersteller space, quite at the stroke of midnight, every last emerald  did in fact turn blue.  Or rather, “grue”.

So now we know.

March of the Penguins !

Alluding to the current kerfuffle over the northward-tending “caravan”, the lead editorial in this week’s New Yorker  quotes the following startling statement from POTUS:

“They’ve intercepted wonderful people

from South America 

and from other parts further south.”

I rushed to my globe and immediately confirmed that the only point south of South America is … Antarctica.

And the only beings in Antarctica are… penguins.

Coming soon to a border near you.

The penguins are on the march!

[FLASH UPDATE]  It turns out the Administration (or rather, its IC elements) may have been after bigger game than penguins, when they cast their nets south towards Antarctica.  Those with appropriate clearances can view the following video:

Geheimnisvolle Antarktis

https://www.youtube.com/watch?v=bNROpknHa7o

Blindman’s Ballad

Madame Life's a tart in bloom;

Death's her pimp upon the stair;

she may ask you to her room;

he'll be waiting while you're there.

She may see you as a friend;

you may gyp him once or twice;

but he'll get you in the end;

and you'll have to pay her price.

After it's all said and done;

after laughter, songs, and prayers;

Death takes everything you've won;

and kicks you down the funny stairs.

[ -- a guest contribution from our friend,

the Blind Bard of Indiana]

tableau sur Seine

the Louvre

the river

the green  glass    sky

       [Aldous Huxley, Point Counter Point (1928), p.  311]

Two views of Mr Stokes

(1)   Old Mr Stokes, the gardener,  passed

          carrying a rake.

(2)  Old Mr Stokes,  recognizable

       by the four parallel pencil-strokes 

       issuing from his chin

       [Aldous Huxley, Point Counter Point (1928), p.  186]

Life in the leaf-litter layer

     The waiters darted about  almost invisibly,
        like leaf-insects in a forest

       [Aldous Huxley, Point Counter Point (1928), p.  280]

Motes in Light

     The leaning column  of yellow light   full of motes

       [Aldous Huxley, Point Counter Point (1928), p.  246]

Fixed That For You

* A rising tide lifts all boats.

=>  A rising tide … drowns those with no boat.

* The proof of the pudding is in the eating.

=>  The proof of the pudding is in successfully digesting it. 

(Otherwise, the pudding might have a slow-acting poison.)

* “We demand the right to contradict ourselves!”

(-- student-rebel slogan, Paris 1968)

=>  No, we don’t.

Fixed That 4 U.

Chestertonian footnote

[an addendum to this essay:
http://worldofdrjustice.blogspot.com/2016/03/a-locked-room-mystery-inside-out.html ]

This (let us call it) sub-subgenre of the whodunit, in which it is the (amateur) detective who is “locked in”, and -- denied sight -- must judge by muffled sounds, is brought to the pitch of perfection, and indeed to spiritual depth, in G.K. Chesterton’s short story, “The Queer Feet” (1910; collected in The Innocence of Father Brown).  Here Father Brown is temporarily sequestered in a closed chamber off a back passageway;  and from this vantage, deduces all, both factual and spiritual, based simply upon the footfalls of an unnatural gait.  Indeed, the story is a kind of rhythmic pendant to the visual-geometrical masterpiece, "The Wrong Shape".

Etymology of the Day: goujat

It turns out there is a curious reflex of goy in the French lexicon: goujat.

1. (vieux) valet d’armée
2. (vieux ou régional)  apprenti maçon

3. (vieux) rustre …

[mot languedocien, de l’ancien provençal gojat “gars”, hébreu goya “servante chrétienne”]

-- Dictionnaire de la langue française (Bordas)

 For much more about the background of such  servantes chrétiennes, try this essay:

http://worldofdrjustice.blogspot.com/2013/08/phrase-for-sabbath-shabbos-goy-updated.html

Independence

The Fourth of July celebration -- in origin quite earnest, and a time for historico-political speechmaking and some semi-military display -- has gradually softened and loosened, like an old sweater, into a fairly agenda-free holiday for kids:  Family, fireworks, fun, and french fries -- the four Fs of sweet July.  Well I recall, how we as kids  lined up along Ridgewood Avenue, excitedly half-comprehendingly, to watch the parade flow by.

As you grow older, some of it does get old.  Brief bursts of bright blotches against the night sky  no longer move me -- not, at any rate, so much as the least glimpse of God’s own handiwork, like the more permanent pattern-and-colorburst on the leaves of a coleus, or a lady cardinal in the bush.

But in another way, the meaning of this day grows ever deeper, even sombre.  For the success and permanency of the American Revolution was by no means a foregone conclusion -- we were truly in uncharted territory back then.   The more you learn about history, and the more history itself keeps happening, you are forced to conclude:  Most revolutions  go awry.

To begin with our own.   Contrary to the impression we got in school (back in the fifties, when we all sat dutifully at our desks), at the time of the Declaration of Independence, a bare one third of the American population was in favor of rebelling against Britain; a third against; a third undecided.   The perfect setting for an immediate post-revolution civil war.  Yet it did not happen (the Civil War a century later fell along quite different lines).  The only threat came again externally, in 1812 (“the rocket’s red glare, the bombs bursting in air”), when the wrath of the British Empire was again turned against us, and the nation’s capital was set in flames.   The pinwheels and cherry bombs of latter days  commemorate an actual peril.

Nor were the political logistics of the Revolution so simple as that of one entity rebelling against one other:  at the time, we were not yet quite even America, let alone the United … States;  but an assemblage of upwards of a dozen colonies, founded at different times by various creeds and ethnicities (Catholics in Rhode Island, Puritans in Massachusetts, Quakers and various German sects in Pennsylvania, and so forth) many of which had been at odds with one another back in the mother country, which is why some of them came here in the first place.  Yet they fought side by side;  and when victory was won, did not then fall to quarreling over the spoils, nor into strife as to which should be cock of the walk;  but together founded  a unified nation.
By contrast, India was one country at time of independence from Britain -- yet immediately fractured, savagely, along sectional lines.  What had been contemned as the British “yoke”  turns out to have been a garde-fou (et les fous se sont emparés de l’asile).

Remarkably as well, we managed, over the years and (by now) centuries, to maintain (most of us) extremely cordial, even intimate relations with the Mother Country -- an unusual trans-hemispheric affinity, unmatched by the relations of the Latin American countries to Spain and Portugal (let alone Haiti or Algeria to France).

Consider next the French revolution -- “next”, because in fact it was subsequent to our own, having broken out in 1789;  though the way Europeans run on about it, you’d think it was the first revolution in the history of the world.  Anyhow, it remains a proud occasion;  the French version of Independence Day is Bastille Day, celebrated on July 14, with great fanfare.  (For our friendly nod to our old ally, click here:  Merci la France.)
Yet their revolution was -- franchise oblige -- a gorawful bloody cock-up.  Not content with overturning centuries of monarchy, the revolutionaries proceeded to la Terreur, and to a sort of overreaching ideological Gleichschaltung that foreshadowed the Bolshevik excess, and of successive waves of revolutionaries being eaten by their chilren, in a way that prefigured the Stalin-era trials. And to crown it all, it didn’t even stick:  within a couple of decades, the kings were back.
France did not ultimately found a Republic that stuck, after the imperial and revived-monarchical interludes, until 1871, with the Third Republic (which segued into the Fourth and Fifth, not without strife, but without a relapse into pre-Republican polity).   Nor did this event stem in any direct way from the events of 1789.  As William Shirer tells it, in The Collapse of the Third Republic (1969, chapter “A Freakish Birth): 

It came into being by a fluke.  The National Assembly, elected in 1871 … had not wanted a Republic.  Nearly two thirds of its members were Monarchists.  But they could not agree on a king …

So the lawmakers … sort of backed into the harness of a republic … by a majority of one vote … 353 to 352 -- though there would have been a tie  had one deputy, who was against it, not been late in arriving for the balloting.  Even then it was not clear to many members that they were actually choosing a republic.  The day before, they had rejected it, or thought they had.
By contrast, the Constitution that came out of our revolutionary days  has lasted and guided us down to the present, with comparatively modest and incremental additions.

~

Since the end of the Second World War, world history has been spotted by rebellions and revolts, mostly anti-colonial, in quest of independence.   And for the most part, the results have not been pretty.
Myanmar.  Zimbabwe.   Algeria. Somalia.  Cambodia.  South Africa.  Congo.  The fragment that is Pakistan, and the mini-fragment of Bangladesh.  And now more recently, South Sudan and Azawad.  Names like tombstones along the  the corpse-strewn path of History’s forced-march.
And thus the American declaration of independence, which shone at the time, shines yet more brightly now, against the contrasting dark.  It is as though the metal of which men then were made, deemed sturdy bronze at the time, were revealed, in the fullness of time, with the reckonings in and the dust dispersed, to have been, in actual and astonishing fact, of purest gold.

Sierra Nevada monostich

The shadows of the valley  grew

deeper  and   deeper

till all was dark…

-- Washington Irving, “The Legend of the Moor’s Legacy”

Dedekind on ontology

[A footnote to this essay.]

Footnote re the irrationals:

Dedekind stressed the distinction of category  between cut and number  in 1888; against the view of his friend Heinrich Weber  that “the irrational number is nothing other than the cut itself”, he explained that “as I prefer it, to create something New distinct from the cut, to which the cut corresponds.  We have the right to grant ourselves such power of creation”,  and cuts corresponding to both rational and irrational numbers were examples.

-- Grattan-Guinness, The Search for Mathematical Roots 1870 - 1940 (2000), p. 87

A seemingly slight, even pedantic distinction;  but like many another such, it might have its point.   Cf. my astonished delight in junior high-school, upon meeting the distinction between  x (the thing itself) and ‘x’ (the name of x) -- already adequately foreshadowed in Alice in Wonderland, but encountered now in a new context.  Likewise the difference between  x and {x} (the singleton-set of x).

In the case of an algebraic number like √2, a simple number staring you in the face out of a hypotenuse  versus the infinite train of rational pilgrims (never quite arriving at their destination) of a Dedekind cut,  one is reminded of the variety of definitions of something so familiar as a tangent:  the slope of a curve (at a point); the closest linear approximation to the curve (at that point); versus the distressing definition in Loomis & Sternberg as an infinite equivalence-class of curves (through that point).

http://worldofdrjustice.blogspot.com/2012/02/on-rounding-out.html

More from the Mindscape

A footnote to this essay:

Dedekind … allowed his philosophy of mind  much reign, with a ‘proof’ that “there are infinite systems”;  for he gave  as evidence “the totality S of all things, which may be objects of my thought”, since  as well as any of its elements s,  it contained also “the thought s’ that can be the object of my thought …This ‘proof’ did not gain a good reception.”

-- Grattan-Guinness, The Search for Mathematical Roots 1870 - 1940 (2000), p. 105

Summer Solstice

The sun at apogee, an empire all of light.

The sweet corn basks and ripens in its rays.

All memory of winter  has melted from our minds.

Yet even now the worm lies in the bud, one day to blast it.

The long limbs of daylight   that had stretched and stretched

now imperceptibly  begin to shrink:

even as the cosmos  attains its outmost limit,

and sighs back  to collapse.

Alas, the Elves of Ice  lurk still in northern forests,

plotting their return.

The Beasts: a post-Benthamite assessment (Take Two)

The Beasts:  a post-Benthamite  assessment (Take Two  Three)

[The Sage of Houndsditch, updated]

The question about animals is not, “Can they reason?”,

but  “Can they handle algebraic geometry  Hodge theory  motivic cohomology?”

[Note:  We have further updated this post, in an attempt to outpace the rise in cleverness  among the squirrels, which has been growing at an alarming pace. Already they have laid waste to algrebraic topology]

Ex-Word of the Day: Toplinear

In her diligent book of epistemology, Evidence and Inquiry (1993), Susan Haack steers her bark between the twin cliffs of Foundationalism and Coherentism, before christening her own proposed juste milieu with the,  alas, ungainly name of :

Foundherentism

There was something comical about the coinage which I could not quite put my finger on.

Then this morning, happening to dip into one of Serge Lang’s textbooks on Differential Geometry, discussing topological vector spaces[**], I re-encountered his own stillborn coinage:

“… a Toplinear isomorphism, referring to the topology  and the linearity”

It is gauche in much the same way.

Neither term has much caught on, outside the readership-circle of its coiner.


[**  A TVS is a uniform structure on a linear space.]

Contra Constructivism

“Only an atheist

 need fear infinity.”

Note:   In this place,

 http://worldofdrjustice.blogspot.com/2011/11/ask-dr-massey.html

an unafraid theologian presents an Orthodox account of the doctrine of absolution and the remission of sins,  conscientiously noting  along the way  a possible mathematical objection to the Church’s handling of infinity in this connection, which he is not personally qualified to resolve.

Fortunately, I was able to reply in complete reassurance on this point:  the Church doctrine is fully consonant with set-theory in its post-Cantorian understanding.

For more:

http://worldofdrjustice.blogspot.com/search/label/infinity

A Dactylic Pentamer ad Differential Forms

“Thése are the thíngs which occúr under íntegral sígns.”

-- Bárret O’Néill, Elementary Differential Geometry

[Note:  The author’s name is prosodically a choriamb.]

[Note:  In an alternative terminology, a quantity at home beneath the integral sign  is called a density.  --  Density  is itself a dactyl.]

Apophthegms of Physics

Hertz: “Maxwell’s theory is Maxwell’s system of equations.”
By itself, this is a witty, eminently quotable, and meaningless comment.

-- Abraham Pais, Subtle is the Lord (1982), p. 119

~

There may be such a thing as habitual luck.  It is like hidden parameters in physics.

-- Stanislaw Ulam, Adventures of a Mathematician (1976), p. 119

Or as Yogi Berra once put it:  That is too much of a coincidence to be coincidental.

The Riddle of the Sphinx (mis à jour)

Contemporary Sphinx:  What walks on four legs in the morning, two legs at noon, and six legs at evening?

Modern Oedipus:  A person:   a crawling baby;  an adult with grown-up gait; and an oldster with a walker (which itself is a quadruped, like a rug-rat).

Stately Monostich

Prince Albert,

consort

of the Queen

[Prosodic note:

  Step  from line to line  using the gait traditional at royal ceremonies:

  Right foot forward; bring left foot up next to the right foot and no further.

  Repeat.

  That will automatically assure a measured reading of this noble line.

  It should take about a minute.]

Aufgehoben

My good friend and former workmate Dr Keith A. Massey, though happily still alive and well, is in some sense no longer quite with us, or not in the same way:  you might say that he has been (rather literally) “spirited away”.

For -- Laus Deo -- he has just been ordained a priest, in the Orthodox Church.  And as such, he now enjoys a new name:

~  Father Andrew ~

Properly understood,  such a step up  does not abolish the former self, which rather is preserved (though in no easily stateable sense) within a higher and more general complexus:  as we say in the trade, such a one has been sublated (or, as Hegel has it, aufgehoben).

~

There are many partial analogues to such an assumption-cum-subsumption, falling under the general rubric (in analytic philosophy) of Continuity of Identity.  Thus, to take a biodevelopmental example:  By moment-wise imperceptible  though ultimately (indeed, repeatedly) qualitative stages, the initial conceptus becomes successively an embryo, a fetus, a neonate or nurseling, an alalic but multimodally aware infant (etymological notelet:  a-lalia = in-fancy), a voluable toddler, a child, a teen, a Young Adult (a tweenie stage  for which Dr Massey has extensively catered, both pedagogically and novelistically), an undergraduate, a grown-up (that is, an active agent in societal self-regeneration), and ultimately, if matters so shake out (allow me a smile here) a Ph.D.   All these stages, most of us have traversed, disparate in appearance  yet inwardly united and aligned by an indwelling thread of ontological continuity.  The whole traversal is not less dramatic (though less sudden) than the development of caterpillar into butterfly.

Another example:  the Transubstantiation of the Elements.

Another (taken on faith, not seen)  the continuing presence of some version or analogue of our sublunary self, in nuce, in the soul post-mortem:  ultimately to be clad in the Resurrected Body.   What all that might be, we cannot imagine, any more than the dim embryo foresees the adventures ahead of it.

A practical, so to speak sociolinguistic perplexity, is how his old friends  who have not followed him on that path, are now to address him  I tried out “Father Andrew” subvocally, but that somehow does not work.  I soon realized why:  I would need myself to be converted, and welcomed into his congregation, thus meetly and meaningfully to address him.   So I shall continue to call him “Keith”.  But best blessings to those of his fortunate flock, who, as naturally as sipping water from a spring, may call him:  Father Andrew.

Frontiers of Pachydermy

Quantum theory takes this subjectivity  to a strange extreme:
 There is no elephant,

 only blind men.

-- George Johnson, Fire in the Mind (1995), p. 140

For more about our bulky friends the elephants, click here!

       Here come the Elephants

~

That epigram, pried from its context,  has a pleasingly Minimalist ring, rather like “Garfield minus Garfield”, though in our case  what is missing  is any elephant.

As for the sense in context:  The elephant represents a sought-for deterministic objective value for some quantized parameter (such as position, velocity, polarization).  The blind-men are the scientists or their measuring-instruments.  To their dismay, they discover that no such value exists:  the elephant is absent.

~

String theory, too, has (as in the parable of the blind-men) suffered from an overplus of versions, none canonical.  But now:

For the five string theories,
M-theory serves as  the unifying pachyderm.

The Beasts: a post-Benthamite assessment

[The Sage of Houndsditch, updated]

The question about animals is not, “Can they reason?”,

but  “Can they handle noncommutative geometry?”

A Hilbertian take on the riddle of Agency

“Who put the bomp in the bomp ba-bomp ba-bomp?
Who put the ram in the rama lama ding dong?”

Wir müssen wissen!  Wir werden wissen!!

[Brouwer dagegen:   Immo  ignorabimus.]