Thursday, April 27, 2006

For Every Serious Post, A Frivolous One

That's our motto here at Orthonormal Basis.

We grad students also wasted time by looking up famous failed assassins; my favorite for years has been Richard Lawrence, the man who tried to assassinate President Andrew Jackson. To Lawrence's horror, both of his pistols misfired at the crucial moment, and Old Hickory proceeded to pummel his would-be murderer. (Lawrence was later found not guilty of his crime by reason of insanity, and passed the rest of his days in an institution.)

And yes, the fascination is partially that of fishing for compliments, but it's still intriguing: go here and choose five or six positive adjectives that best apply to me, or here for negative traits. You don't have to leave your name if you don't want to, but you shouldn't be afraid to. Because I didn't list "violent" as one of my negative traits. Thanks to Cory for the link.

Today's Math Department Colloquium with Danish physicist Robbert Dijkgraaf, The Unreasonable Effectiveness of Quantum Physics in Modern Mathematics, was entertaining and enlightening; I'm even more excited to take Quantum Mechanics next year! The MSRI lecture even included an explanatory allusion to Plato's Cave (though I think Dijkgraaf's analogy was backward with regard to the Cave, but what do I know?) and a physicist-meets-mathematician joke...
Mystic, Martyr, Mathematician

Recently, my officemates and I were looking up famous mathematicians' biographies (and no, we don't do this all the time), and we came across Dmitrii Egorov, a Russian mathematician of the early 20th century, now immortalized (to us, at least) for a highly useful theorem of real analysis. (No, I won't go into Egorov's Theorem here.)



Doesn't he look intense? Anyhow, having heard of him, I was greatly amazed to find out how he died:
However Egorov was a deeply religious man and when the Church was repressed after the revolution, Egorov defended them. In 1922-23 there were mass execution of clergy and in 1928 the attack was renewed. Egorov was in a position of power in the Moscow Mathematical Society and he tried to shelter academics who had been dismissed from their posts. He tried to prevent the attempt to impose Marxist methodology on scientists.

In 1929 Egorov was dismissed as director of the Institute for Mechanics and Mathematics and given a public rebuke.

Some time later he was arrested as a "religious sectarian" and put in prison. The Moscow Mathematical Society continued to support Egorov, refusing to expel him, and those who presented papers at the next meeting, including Kurosh, were to be expelled by an "Initiative group" who took over the Society in November 1930. They expelled Egorov denouncing him as "a reactionary and a churchman".

Egorov went on a hunger strike in prison and eventually, by this time close to death, he was taken to the prison hospital in Kazan. Chebotaryov's wife was working as a doctor in the prison hospital and, although it sounds rather unlikely, it is reported that Egorov died at Chebotaryov's home.
Needless to say, I was greatly impressed by this account, and started looking for more on the man. The search led me to an absolutely fascinating essay, A Comparison of Two Cultural Approaches to Mathematics, on the conflicts of the early 20th century over the reality of non-constructible mathematical objects, and how this related to a divide between milieus of French rationalism on the one hand and Russian mysticism on the other.

If that description appealed to you at all, I urge you to forget the rest of what I write, and go read it for yourself. For those of you bored, baffled, or both, by the above, I promise I'll drop the pedantry and try and explain why this is so awesome, and where exactly Egorov fits in.

Essentially, a number of discoveries in the late 19th century threw mathematics into a flurry of controversy. Apart from the logical paradoxes found at that time (which make for another fascinating story), the most earth-shattering claims were staked by the German mathematician Georg Cantor, who once and for all exploded our original naive intuitions of infinity. (For an explanation of what he did and how, this isn't bad.)

One of the pieces of fallout from this was that the most intuitive definitions of mathematical concepts like "real number" or "function" postulated the existence of real numbers or functions that are inaccessible to our finite minds, because they aren't the results of any formula or the limits of any intelligible process. (I want to stop and prove this assertion, but I'll resist the temptation.) Many of the leading French mathematicians balked once they realized this; Henri Lebesgue wrote of it, "Can we convince ourselves of the existence of a mathematical being without defining it? To define always means naming a characteristic property of what is being defined." Ultimately, the authors of the essay argue that the philosophical presuppositions of the leading French mathematicians led them to abandon their early successes in these areas; a widespread Cartesianism and a secularist positivism made it inconceivable to these men that anything could meaningfully exist which was not intelligible. (Um, about dropping the pedantry: mea culpa?)

Emile Picard sneered at those who engaged with such matters:
All problems of this type are caused by a lack of agreement on what existence means. Some believers in set theory are scholastics who would have loved to discuss the proofs of the existence of God with Saint Anselme and his opponent Gaunilon, the monk of Noirmoutiers.
(His derision toward Catholic philosophers and detailed ontology is not incidental to the topic.)

When the French left the field, it was the Russian mathematicians who rescued the field from the tyranny of epistemology over ontology. Egorov and Nikolai Luzin were foremost among them, and their willingness to interact with non-constructible (non-knowable) mathematical objects was not unrelated to their shared religious faith in the God who truly existed but was beyond all human understanding.

UPDATE: Edited to read: (It must be noted that they were Imiaslavtsy or "Name-Worshippers", who believed that God was wholly present in and even identical to the Name of God. Their like were deemed heretics by the Orthodox Church a few years before the Communist Revolution, which adds an additional note of wonder to Egorov's self-sacrificing defense of that Church against the Marxists. I'd say more about this, but I really hadn't heard of them before.)

In the end, the mathematics produced by these Russian scholars was so beautiful, so useful, so eminently true, that it triumphed over the epistemological snobbery of the French school. Today we learn about non-constructible reals, nowhere differentiable continuous functions, and non-measurable sets in undergraduate classes, and we think little of it besides a passing note of weirdness. Thanks to the Russian mystics like Egorov, we have now realized that it is simply sophomoric to deny the existence of something on the sole grounds that we cannot define or comprehend it ourselves.

Well, most of us have realized it. There's still the V=L wackos.

It is said that Egorov died from the effects of his hunger strike and prison treatment, in the house of the mathematician whom the Party chose to replace him at the Moscow Mathematical Society, chanting the name of Jesus. Requiem aeternam dona eis Domine: et lux perpetua luceat eis.

Saturday, April 22, 2006

Still, That Explains Why French People Keep Slapping Me

I've decided to eliminate that entire joke, except for the punchline.

Day 3 (Friday) of my coffee habit was going OK, until I was cruelly tricked into drinking an evening mocha just before embarking on my Plato discussion. It is really frightening to realize that your mind isn't working properly; it's like waking up blind. I couldn't read a sentence without forgetting how it had begun. Fie on you, Mary!

But things could always be worse.

Thursday, April 20, 2006

The Gospel of Judas

I know I'm after the news cycle. So sue me.

As I've said on another blog, the Gospel of Judas is an interesting find for several reasons, but not for any new light it might shed on the actual Jesus, Judas and the disciples. I had the good fortune to take a graduate class on New Testament Literature with Margaret Mitchell at the University of Chicago Divinity School, and I survived the long exposure to the historical-critical method with a few new insights. (Dr. Mitchell has a short article on these "New Revelations".)

You can download the translated Gospel of Judas here at the National Geographic site; it's only 7 pages. I warn you, you're going to be disappointed in the actual gospel after reading all the news articles on how 'revolutionary' it is.

The scholarly context that journalistic integrity ought to have provided is that the Gospel of Judas is a text written in Egypt in the second century (most likely 150 AD or later; its first reference is in St. Irenaeus' letter Against Heresies in AD 180) by Gnostic thinkers, and that it is only one of many such documents (which tend to agree very little with each other).

In essence, such Gnostic gospels were works of historical fiction, based on situations and events recounted in the canonical Gospels, but with characters (usually Jesus) made into mouthpieces for the writer's theology. This explains why such gospels don't cohere well with each other on, say, how Jesus taught the universe was created, or on whether we ought to pursue a Buddhist-like detachment from the physical world or a Rasputin-like plunge into all its illusory pleasures. The Gnostics had many different theological strains, and no Gnostic gospel was bound by any oral tradition of what Jesus actually taught.

The core of agreement between most Gnostics was the idea that the material world was evil and that the physical body was a hateful thing. Thus the Jewish God Yahweh, who created the physical universe, was actually an evil God, and Jesus had come to free us through a special knowledge (gnosis) that would release us from the material world after death. This knowledge concerned, usually, the vast and complicated angelic battle going on, and all the names of the angels ruling the underworld, etc. If you read the Gospel of Judas, the depiction of the complicated angelic generations (and the "Everyone has his own star" bit) reads like nothing so much as what I know of Mormonism.

Incidentally, if you were wondering, the scholarly consensus dates the canonical Gospels as the only known gospels from the first century, composed between 70-100 AD when witnesses were still alive. I was pleasantly surprised to find that mainstream scholarship was pretty well agreed on the existence and ministry of Jesus, His teaching about the coming Kingdom of God, and His Crucifixion. They tend to get squeamish about the miracles and in particular the Resurrection, naturally; in general, their reason for disbelieving in those events isn't that the textual evidence is less present, nor that there are signs of fabrication (as there are in the Gnostic gospels and other documents like The Acts of Paul and Thecla), but that those events would have to be miracles.

Anyway, that's a digression. It's just refreshing to note that the historical-critical analysis of the canonical Gospels generally concedes a historical basis, and that such approaches to the Gnostic gospels have generally shown marks of fictive composition. The Church, essentially, got the canon of Scripture right the first time.

What the Gospel of Judas does tell us, aside from the glimpse into another branch of Gnostic theology, is a confirmation of what we know of Church tradition. It gives external verification that in the second century AD, the Eucharist was widely celebrated by ordained priests who traced their priesthood back to the apostles, and that this was one of the most important aspects of Christian life.

Where does it say all this? One of the things that the author of the Gospel of Judas puts into Jesus' mouth is a denunciation of the apostolic Church. (Naturally, the Gnostics wanted to claim that the Church wasn't what She professed to be.) In particular, there's a "prophetic dream" about the apostles and the priests who succeed them, simultaneously saying the Mass and engaging in foul wickedness, serving the evil Yahweh. 'Jesus' interprets,
For to the human generations it has been said, 'Look, God has received your sacrifice from the hands of a priest'- that is, a minister of error. But it is the Lord, the Lord of the universe, who commands, 'On the last day they will be put to shame.'
Just underneath, he makes it clear that he's ridiculing the Eucharist: "A baker cannot feed all creation under heaven."

This is at the heart of the Gospel of Judas' attack on the Church: that She uses the evil material world to confer God's grace, that She seeks to feed all humanity with bread and wine become (most despicable to the Gnostics) Christ's body and blood. The Gospel of Judas' author writes this 'flash-forward' into the account to attack the Church of his day for having an apostolic ministerial priesthood and the Eucharist; the polemic against it is external testimony to its existence. (Of course, this wouldn't even be an issue but for the historical conspiracy theorists who claim that Constantine invented the hierarchical Church and the sacraments in the fourth century, and that extra-biblical Church documents were all changed/fabricated to reflect the conspiracy.)

Oh, and if you're wondering why the Gospel of Judas can be trusted to have not made up that part too, remember that it was written for the purpose of converting people away from the Church. So it would attack the Church of 150 AD in specific terms, using dialogue it made up from Jesus in 30 AD. It wouldn't make sense to write a polemic against a Church that didn't exist.

The Gospel of Morford

But just try and get that story into the news. The real question with the media is, "Why was this announced just before Palm Sunday, when the translation has been finished for months?" And the short answer is, "Because it'll get more publicity if it makes more Christians angry." The timing couldn't have been more predictable: as Dr. Mitchell wrote in her article,
When I gave my lecture on "The Historical Jesus: What Do We Know and Why Do We Care?" to my Intro to New Testament class in early March, I warned the students that, with the ironic regularity of the liturgical calendar, the major newsweeklies would somehow find a way to put "Who Was Jesus? - New Revelations" on the cover.
It's frustrating to see how successful the yellow journalism of Jesus-related findings can be, year after year. By only quoting the fringe historians (as did the New York Times, sadly) without a mainstream voice to note the things I mentioned above, the newspaper can set up a 'controversy' beloved since H.L. Mencken: scholarly revisionists against angry Christian fundamentalists. The plain fact that the Gospel of Judas was made up becomes 'spin'. Newspapers sell extra copies, National Geographic produces a hit feature on it, everybody in the media world is happy.

This particular news cycle also gave a few people the coveted chance to express open mockery and contempt for Christianity under the heading of "news commentary". I should have known that it was a bad idea to read the San Francisco Chronicle's Good Friday issue, but this article by Mark Morford, Slyboots Judas is winking at you, went a bit over the edge:
Is it not just tremendous heaps of casually blasphemous fun to learn, once again and for the thousandth time, that the Bible -- that happy mishmashed messed-up hodgepodgey cocktail of myths and folklore and revisionist propaganda and who's-your-daddy reproaches intermixed with lovely stories of redemption and hope and oh yes sin and hellfire and death -- is so full of colorful holes it might as well be a bedsheet from the Baghdad Target?
Morford goes on to say that Christianity is reserved for
those who are unable to grasp nuances and unable to think beyond a certain scope, those who are unwilling or unable to follow what is perhaps the single most powerful and significant of all Christ's (and Buddha's, and the Tao's, etc.) teachings: that is, to seek God within. Not in a priest. Not in a building. Not in an organized institution. Within you.
This highest teaching of Christ is best attested, I think, in the third chapter of the Gospel According to Mark Morford, discovered last week in the basement of a trendy San Francisco nightclub. The new discoveries never cease.

I suppose I shouldn't be so hard on Mr. Morford. He may just have wished to honor Good Friday by reenacting the Third Sorrowful Mystery.

Christ Mocked

I'm well aware that faithful Christians aren't being 'persecuted' or anything so dire. I know that there are more pressing problems in the world than an overhyped document that doubles as a hammer to whack the Church with. But you'd feel the same if someone or something you loved was slandered on such a constant basis.

"If the world hates you, remember that it hated me first."

Wednesday, April 19, 2006

Narcissistic Post!

How about using this for my blog title?



(Yeah, I know that the aleph and the phi aren't N or I, but this is for non-mathematicians, and I want them to be able to read it.)

Today I finally broke down and started a mathematician's coffee habit. Watch out, world! (At this point... the test subject... was dead.)

A recent spammer's name was "Usury Utmost". How pithy; if only it had been composed by a real human rather than randomly selected.

Oh, and I think about this scenario ALL THE TIME. That comic is more addictive than the coffee. Curse you Mr. Thompson! Now I better get some sleep.

And yeah, never trust a student phlebotomist.

Surrexit Christus!

Sunday, April 09, 2006

I. Little-Used Papal Honorifics

The Popes are real, the titles ain't. Examples:

Liberius the Pretty Good but for Some Reason did not Make Sainthood (352-66)
Stephen (II) the Brief (752)
Alexander (VI) the... We-Don't-Talk-about-him-in-Public-Anymore (1492-1503)
Pope Innocent (XI) the Vacuum-Cleaner of Nepotism (1676-89)
Pius (VII), You Know, the One Who had to Put up with Napoleon (1800-23)

Courtesy of the Shrine.

II. Even Better: Harsh Truths About Catholicism
CLAIM: Catholicism teaches people to pray for the dead, which is forbidden by scripture.

This is true. Catholicism teaches people all kinds of things that are forbidden by scripture because, as Pope Dwight IX once wrote in a bull excommunicating the nation of Latvia, "we feel like it." Catholics generally say that prayers for the dead are specifically mentioned in something called "2nd Maccabees," which is not part of the real Bible, but only the phony baloney fake Catholic Bible, which also contains recipes, for all we know. The pope, as I mentioned earlier, won't tell us what's in it.
Thanks to The Medicine Box, whose comments section contained the best quote ever about the new "Gospel of Judas":

"Dear everyone:

the gospel of judas is not going to 'rock the foundation of christianity'. we dealt with the gnostics a while ago. and we won."

III. I've Been Wanting To Make One Of These For Years











This uses the Warning Label Generator, naturally enough. Brought to my attention by Happy Catholic.

UPDATE: Come to think of that, the description above doesn't apply to me as much as it did when I first came up with it. I've become more pastoral (or maybe more pusillanimous) over the years. However, there are still some lines drawn in the sand:

Sunday, April 02, 2006

It is impossible to say just what I mean!

In the next world war/ [in a] jackknifed juggernaut/ I am born again...

I often quote frivolously, but not this time. Airbag has it right: after the five near-crashes of that night, I am suddenly alive. The short and strange Prufrock phase of my life has passed, the iron chain of self-consciousness has been broken, I'm gloriously happy these days- and from the most unlikely cause, rejection. (If I confuse you, forgive me. If I embarrass you, forgive me.)

I awake to find myself surrounded by friends, beer in hand, talking of science, music, theology, literature, the Church. And I'm no longer concerned what they think of me, for they enjoy my company, and I theirs. There was that barrier before, that additional filter of "Will this impress them?", but it wasn't necessary, wasn't even good.

Then ten-year-olds pelt me with dodgeballs, and I twist out of the way with surprising celerity (I guess my E. Scis days aren't that far behind me after all) and lead the countercharge in the rain. I'm muddy and soaked, and tomorrow I'll be sore, but I am happy.

And I'm back to reading at my Chicago pace, starting or finishing or continuing or rereading Waugh, and St. Augustine, and David Foster Wallace, and Gene Wolfe, and Tolstoy, and now Thackeray and Trollope. I'm saving Cervantes and Hugo for later, the next correspondence books after War and Peace, perhaps? (Why did I ever waste the time I could have used for reading? Sloth is lunacy when the library goes five floors underground.)

In short, I'm back from the dead. I've been frustrated with this shy shadow-self I've been for the past year, one who like Prufrock is paralyzed by the cognition of his own social awkwardness, or by the fear of giving offense. It wasn't me, not at all. If you don't understand how I could be described as crazy, you don't know me yet.

I finally went and tried, lived, made myself vulnerable; and my failure was nothing to the fear of failure that had held me so unnaturally.

So why send this odd, self-centered boast off into the vasty deeps of the blogosphere? I don't know; as Calvin said, "I must obey the inscrutable exhortations of my soul." I note that he then added, "My mandate also includes weird bugs." Indeed.

Would it have been worth while,
To have bitten off the matter with a smile,
To have squeezed the universe into a ball
To roll it towards some overwhelming question,
To say, 'I am Lazarus, come back from the dead,
Come back to tell you all, I shall tell you all'-
If one, settling a pillow by her head,
Should say, "That is not what I meant at all.
That is not it, at all."

In a word, yes. Yes. Yes.

In an interstellar burst, I'm back to save the universe...