The following meditations were inspired by an ad today in the online New York Times obituaries section--

"Been somewhere interesting? Tell us about it for a chance to win a trip for 2 to Paris."

Country song, quoted here Dec. 17, 2003--

"Give faith a fighting chance."

Malcolm Lowry, Under the Volcano--

"I sit now in a little room off the bar at four-thirty in
the morning drinking ochas and then mescal and writing
this on some Bella Vista notepaper I filched the other
night.... But this is worst of all, to feel your soul
dying. I wonder if it is because to-night my soul has
really died that I feel at the moment something like
peace. Or is it because right through
hell there is a path, as Blake well knew,
and though I may not take it, sometimes lately in dreams
I have been able to see it? ...And this is how I
sometimes think of myself, as a great explorer who has
discovered some extraordinary land from which he can
never return to give his knowledge to the world: but the
name of this land is hell. It is not Mexico of course but
in the heart."

From an obituary of mathematician Gian-Carlo Rota linked to here on April 18, the anniversary of Rota's death:

Gian-Carlo Rota

From a novel, Psychoshop, quoted here in an entry on the Pope's birthday, "The Gates of Hell" --

His manner was all charm and grace; pure cafe society....

He purred a chuckle. "My place. If you want to come, I'll show you."

"Love to. The Luogo Nero? The Black Place?"

"That's what the locals call it. It's really Buoco Nero, the Black Hole."

"Like the Black Hole of Calcutta?"

"No. Black Hole as in astronomy. Corpse of a dead star, but also channel between this universe and its next-door neighbor."

"Here? In Rome?"

"Sure. They drift around in space until they run out of gas and come to a stop. This number happened to park here."

On April 16, the Pope's birthday, the evening lottery number in Pennsylvania was 441. The Log24 entries of April 17 and April 18 supplied commentaries based on 441's incarnation as a page number in an edition of Heidegger's writings.  Here is a related commentary on a different incarnation of 441.  (For a context that includes both today's commentary and those of April 17 and 18, see Gian-Carlo Rota-- a Heidegger scholar as well as a mathematician-- on mathematical Lichtung.)

From R. D. Carmichael, Introduction to the Theory of Groups of Finite Order (Boston, Ginn and Co., 1937)-- an exercise from the final page, 441, of the final chapter, "Tactical Configurations"--

"23. Let G be a multiply transitive group of degree n whose degree of transitivity is k; and let G have the property that a set S of m elements exists in G such that when k of the elements S are changed by a permutation of G into k of these elements, then all these m elements are permuted among themselves; moreover, let G have the property P, namely, that the identity is the only element in G which leaves fixed the n - m elements not in S.  Then show that G permutes the m elements S into

From the obituary of physicist John Archibald Wheeler at Princeton:

From Log24 last year on this date ("Happy Birthday, Benedict XVI"):

From Dante, The Inferno, inscription on the gates of Hell:

From Psychoshop, an unfinished novel by Alfred Bester completed by Roger Zelazny:

Best summary of Obama's sneer:

"Xenophobia, San Francisco Style."

Have some wine and cheese, Barack.

"It is said that the students of medieval Paris came to blows in the
streets over the question of universals. The stakes are high, for at
issue is our whole conception of our ability to describe the world
truly or falsely, and the objectivity of any opinions we frame to
ourselves. It is arguable that this is always the deepest, most
profound problem of philosophy."

-- Simon Blackburn, Think (Oxford, 1999)

Michael Harris,
mathematician at the University of Paris:

"... three 'parts' of tragedy identified by Aristotle that transpose to fiction of all types-- plot (mythos), character (ethos), and 'thought' (dianoia)...."

-- paper (pdf) to appear in Mathematics and Narrative, A. Doxiadis and B. Mazur, eds.

Mythos --

A visitor from France this morning viewed the entry of Jan. 23, 2006: "In Defense of Hilbert (On His Birthday)." That entry concerns a remark of
Michael Harris.

A check of Harris's website reveals a new article:

"Do Androids Prove
Theorems in Their Sleep?" (slighly longer version of article to appear in Mathematics and
Narrative, A. Doxiadis and B. Mazur, eds.) (pdf).

From that article:

"The word 'key' functions here to structure the reading of the article, to draw the reader's attention initially to the element of the proof the author considers most important. Compare E.M. Forster in Aspects of the Novel:

[plot is] something which is measured not be minutes or hours, but by intensity, so that when we look at our past it does not stretch back evenly but piles up into a few notable pinnacles."

Ethos --

"Forster took pains to widen and deepen the enigmatic character of his novel, to make it a puzzle insoluble within its own terms, or without. Early drafts of A Passage to India reveal a number of false starts. Forster repeatedly revised drafts of chapters thirteen through sixteen, which comprise the crux of the novel, the visit to the Marabar Caves. When he began writing the novel, his intention was to make the cave scene central and significant, but he did not yet know how:

When I began a A Passage to India, I knew something important happened in the Malabar (sic) Caves, and that it would have a central place in the novel-- but I didn't know what it would be... The Malabar Caves represented an area in which concentration can take place. They were to engender an event like an egg."

-- E. M. Forster: A Passage to India, by Betty Jay

Dianoia --

"Despite the flagrant triviality of the proof... this result is the key point in the paper."

-- Michael Harris, op. cit., quoting a mathematical paper

Online Etymology Dictionary:

flagrant c.1500, "resplendent," from L. flagrantem (nom. flagrans) "burning," prp. of flagrare "to burn," from L. root *flag-, corresponding to PIE *bhleg- (cf. Gk. phlegein "to burn, scorch," O.E. blæc "black"). Sense of "glaringly offensive" first recorded 1706, probably from common legalese phrase in flagrante delicto "red-handed," lit. "with the crime still blazing."

A related use of "resplendent"-- applied to a Trinity, not a triviality-- appears in the Liturgy of Malabar:

-- The Liturgies of SS. Mark, James, Clement, Chrysostom, and Basil, and the Church of Malabar, by the Rev. J.M. Neale and the Rev. R.F. Littledale, reprinted by Gorgias Press, 2002

Judy Davis in the Marabar Caves

In mathematics
(as opposed to narrative),
somewhere between
 a flagrant triviality and
a resplendent Trinity we
have what might be called
"a resplendent triviality."

For further details, see
"A Four-Color Theorem."