Happy Reformation Day

This is what everyone celebrates, right?

Martyrdom of a Mathematician

I finished reading Naming Infinity a while ago, but I never did get a chance to wrap up my blogging on the book. The end really is quite tragic, and all the more so because it's a true story.

There is so much to say about all that Dmitri Egorov, Nikolai Luzin, and Pavel Florensky did for mathematics and science, and how their faith influenced their work. But since I have to choose what to focus on in a little blog post, I will choose to talk about how they were treated on account of their faith.

Pavel Florensky and Dmitri Egorov both died for their faith. It's a complicated story, and they both went down distinctly different paths, but in the end they both had the same problem--they were openly Christian under a militantly atheist regime.

Pavel Florensky was a Russian Orthodox priest, but he was also a scientist and inventor, and he is part of this story because he was very close friends with both Egorov and Nikolai Luzin, the other member of this "Russian trio."

I suppose it didn't help him that he insisted on wearing his white priest's cassock while delivering his scientific papers. You can kind of guess how the Soviet police eventually got to him--they "proved" that he was the leader of a counter-revolutionary organization, which of course he had never heard of. They shipped him off to a prison camp where he continued scientific research, but I guess they didn't even want him doing science as a prisoner.

In 1937, Florensky was sentenced to be shot. He was executed on December of that year. Recent evidence suggests the details of this death were not pleasant:

According to this information, in December 1937 Florensky was brought from the Solovetsk Islands to Leningrad, where for a while he was in a prison cell in the "Big House," the headquarters of the Leningrad secret police.... Then, according to this new evidence, Florensky was forced to undress, his hands and feet were bound, and he was taken along with several hundred other people in a convoy of trucks to the Rzhevsky Artillery Range, near the town of Toksovo, about 20 miles south of Leningrad. There, we are told, they were all shot.

What causes certain regimes to have such an irrational hatred of religion (or any dissenting view) so as to treat someone in this way?

Egorov didn't fare much better. What's crazy is that he simply insisted that his religious views were a private affair, and that all views should be tolerated in the university. Nevertheless, when he was arrested in 1930 the charge included "mixing mathematics and religion." Can you imagine living in a country where that's a crime?

While in prison Egorov prayed daily, including practicing the "Jesus Prayer," despite persecution from the guards. He eventually died there in prison due to digestive failure (which had already been a problem before being sent to prison, where his health only deteriorated). His last words are reported to have been, "Save me, O God, by Thy name!" from Psalm 54--which according to the authors of this book were "appropriate to his Name Worshipping creed."

Nikolai Luzin was not martyred for his faith, but he came pretty close. In the tragic "Luzin affair," he was basically put on trial for his faith--the crime was being tied to anything considered anti-Soviet, including the old monarcy and Christianity. Kind of ironic, considering Luzin at one time had been a sympathizer with the revolutionaries.

It's really depressing to see a lot of those big names of mathematics listed among the people who attacked Luzin, such as Alexandrov, Khinchin, Sobolev, Kolmogorov, Liusternik, and Pontriagin. Most of these are names I've heard at one time or another in my analysis classes.

But that's part of why I write this. Who knows what will ultimately draw us to such evil? It may be that a compelling ideology will grip our hearts so tightly that we lose all sanity. It appears as if a whole country was led into insanity by such an ideology. I don't think any amount of intelligence or wisdom can prevent it. Evil cuts through all of our hearts.

In the end Luzin was spared, thanks to the intervention of a famous physicist of the time, Peter Kapitsa. It's still not entirely clear why Stalin spared Luzin in this instance. He got rid of plenty of other people who were just as valuable as scientists. Perhaps we'll never really know.

What a change it is to think about mathematicians as people who suffered for their beliefs! All you typically hear is about how these child geniuses grew up to prove amazing theorems; but rarely is it ever mentioned that mathematicians have been people who struggled through real trials.

And it puts things into perspective. My friends in grad school were talking about this, and one of us said, "Next time we start to complain about departmental politics, I guess we should keep this in mind." We are so blessed to live in a country where freedom is a given.

But finally, this story really is an inspiration to me, in that it makes me contemplate how to integrate my faith completely with my occupation. It's interesting to read the author's of this book struggle with this idea:

"In concluding that mysticism helped Russian mathematicians in the development of descriptive set theory, we have had to overcome our own natural predispositions. Both of us are secular in our outlooks--far from being Name Worshippers ourselves. We did not start out writing this book in order to come down on the side of religion in the infamous science-religion debates that have occupied so large a place in recent public discussions."

As Jesus Christ put it, Wisdom is vindicated by her deeds. There really is no need to endlessly debate over religion and science. The faithful simply ought to pursue knowledge with all their heart, and they will bear fruit.

That's my goal in life--a unified pursuit of knowledge. Incidentally, that's why I've been loving Florensky's Pillar and Ground of the Truth. Maybe I'll start blogging about that soon.

A Bloody Sacrament

In the midst of all the recent debate on health care, I've realized that conceptually in our culture we have started to lean toward creating a new state religion. This religion has hospitals instead of churches, and doctors instead of priests.

The goal is not to inherit eternal life, but simply long, hopefully comfortable life; faithful obedience certainly has its rewards. Instead of a church treasury, we have insurance companies, and all are required to tithe regularly.

Doctors are entrusted with the salvation of our people. This is clear from the fact that no one asks for the price of health care before going to get it. If you thought you were going to the doctor just to receive goods and services, you'd want to know the price ahead of time.

No, it's not goods and services you go to your doctor to receive. You are not a customer. You are a sinner in need of baptism--you need to be made whole again. Your life is incomplete without it.

(I'm convinced this is why natural market mechanisms have failed to keep health care costs low. It is why every transaction between you and your doctor has to go through your insurance company, and for that reason costs are uncontrollable.)

(Ironically, actual religion has become more market-based, as evidenced by those obnoxious church billboards I see advertising such perks as "great worship, great fellowship." For some reason I see these mostly when I'm in Texas.)

Every Sunday I go forward to receive the Lord's supper at my church. It is "an awesome and unbloody sacrifice," a sacrament to make me whole again, to feed me with the life of Christ.

Someone once referred to abortion as a "bloody sacrament" of our culture. I can see why. Who is in greater need of being made whole than a woman who finds herself in the position of carrying in her womb a human being she cannot care for?

What I hadn't thought about was how the priests themselves, the administrators of this bloody sacrament, actually see what they're doing. A remarkable article on LifeSiteNews.com gave me a lot to contemplate.

The article reports on an abortionist who wants to take seriously the moral dilemmas that come with actually performing abortions, yet does not want to conclude that there should be any legal limits on abortion. In the end, both her stance on the issue and her tone become quite religious.

This excerpt caught me as particularly striking:

To answer the questions, Harris notes that the "violence" of abortion must be acknowledged, and relates a "bizarre" experience she once had of observing a premature baby struggling to survive immediately after dismembering an unborn child the same age:

The last patient I saw one day was 23 weeks pregnant. I performed an uncomplicated D&E procedure. Dutifully, I went through the task of reassembling the fetal parts in the metal tray. It is an odd ritual that abortion providers perform - required as a clinical safety measure to ensure that nothing is left behind in the uterus to cause a complication - but it also permits us in an odd way to pay respect to the fetus (feelings of awe are not uncommon when looking at miniature fingers and fingernails, heart, intestines, kidneys, adrenal glands), even as we simultaneously have complete disregard for it. Then I rushed upstairs to take overnight call on labour and delivery. The first patient that came in was prematurely delivering at 23-24 weeks. As her exact gestational age was in question, the neonatal intensive care unit (NICU) team resuscitated the premature newborn and brought it to the NICU. Later, along with the distraught parents, I watched the neonate on the ventilator. I thought to myself how bizarre it was that I could have legally dismembered this fetus-now-newborn if it were inside its mother's uterus - but that the same kind of violence against it now would be illegal, and unspeakable.

Harris then goes on to explain that she rationalizes the bizarreness of the situation by the "location" of the baby, whether it is "inside or outside of the woman's body," and "most importantly, her [the mother's] hopes and wishes for that fetus/baby." However, she says, "this knowledge does not change the reality that there is always violence involved in a second trimester abortion, which becomes acutely apparent at certain moments, like this one. I must add, however, that I consider declining a woman's request for abortion also to be an act of unspeakable violence."

See with what reverence the abortionist treats the life she is destroying! It is like a priest handling the very body and blood of Our Lord, carefully consecrating it and feeding it to his congregation, who eat gratefully (sometimes ungratefully).

Does the priest ever wonder how he could possibly perform this act on the body of Christ? Jesus had to die on a cross for this. How can such unspeakable violence be justified for the sake of you who want eternal life? Do you sinners actually think your gratitude is enough to justify this?

But the priest knows that nevertheless his flock needs to be made whole again. He cannot withhold the body of Christ, for it is offered even to sinners.

In the same way, the abortionist reveres the aborted fetus--the awesome and bloody sacrifice--as a little Christ, one who has graciously lost his life to make his mother whole.

And this priest of this holy religion continues to preach the good news to all the nation: that enshrined in our Constitution is a bloody sacrament that can never be taken away. Once we were under the law, but now we are under "choice."

The Son of Man goes as it is written of him, but woe to that one by whom the Son of Man is betrayed! It would have been better for that one not to have been born.

It is no small thing that an abortionist would be honest about what abortion is. But on the other hand, should Judas take the credit for the salvation of the world?

Hat tip: Thanks to Sarah and Krissy for this article.

Another math joke

Man, I love dinosaur comics.

Orthodoxy

Now that I've read Naming Infinity (which I mean to blog a bit more about, but I've been busy) I thought I'd dabble a little bit in Pavel Florensky's The Pillar and the Ground of the Truth, adapted from the very same thesis that Nikolai Luzin read on his journey to converting from atheism to Christianity.

The first letter of PGT, "To the Reader," contains some profound statements of what makes Orthodoxy different from Catholicism and Protestantism. Florensky introduces as a main topic this thing called ecclesiality--which he insists cannot be defined!

Ecclesiality--that is the name of the refuge where the heart's anxiety finds peace, where the pretensions of the rational mind are tamed, where great tranquility descends into our reason. Let it be the case that neither I nor anyone else can define what ecclesiality is!

After meditating on this for a little while, he briefly outlines what for him is the fundamental problem with both Catholicism and Protestantism:

Where there is no spiritual life, something external must exist as an assurance of ecclesiality. A specific function, the pope, or a system of functions, a hierarchy--that is the criterion of ecclesiality for Roman Catholics. On the other hand, a specific confessional formula, the creed, or a system of formulas, the text of the Scripture, is the criterion of ecclesiality for Protestants. In the final analysis, in both cases what is decisive is a concept.... But by becoming the supreme criterion, a concept makes all manifestation of life unnecessary.

And finally, he offers what he feels to be the strength of Orthodoxy:

The indefinability of Orthodox ecclesiality, I repeat, is the best proof of its vitality.... There is no concept of ecclesiality, but ecclesiality itself is, and for every living member of the Church, the life of the Church is the most definite and tangible thing that he knows. But the life of the Church is assimilated and known only through life--not in the abstract, not in a rational way.... What is ecclesiality? It is a new life, life in the Spirit. What is the criterion of the rightness of this life. Beauty. Yes, there is a special beauty of the spirit, and, ungraspable by logical formulas, it is at the same time the only true path to the definition of what is orthodox and what is not orthodox. [emphasis added]

...

That is why there is only one way to understand Orthodoxy: through direct Orthodox experience.... [O]ne can become a Catholic or a Protestant without experience life at all--by reading books in one's study. But to become Orthodox, it is necessary to immerse oneself all at once in the very element of Orthodoxy, to being living in an Orthodox way. There is no other way.

In short, my initial reaction is, "Wow."

It's no wonder so many people in the West are discovering Eastern Christian theology and finding it refreshing. To me, the emphasis on beauty as a genuine measure of orthodoxy is profound, and something in me tells me it's just what I'm looking for.

I wonder where Florensky will take me?

Mystical Mathematicians

The essence of mathematics lies in its freedom.

Georg Cantor

I continue on in my reading of Naming Infinity, that book about religious mysticism and mathematical creativity.

Chapters 4 and 5 introduce some of the most fascinating mathematicians I've ever read about. Two of them are familiar names from my graduate level Real Analysis class during my first year: Dmitri Egorov and Nikolai Luzin.

Egorov seems more of a distant character than Luzin. He's described as "a very reserved and modest man, so much so that it would be easy to believe that he lived only for mathematics." But if one looks at his actions, one finds a man driven by strong principles and devout religious faith. This becomes a bit more of an issue later, after the Communist take-over in Russia.

Luzin is Egorov's student, a bright, idealistic intellectual who sympathizes with political radicals of his day--at least as a younger man. What really fascinates me is Luzin's story of conversion from atheism to Christianity. It's a story of real crisis, both intellectually and emotionally.

"From 1905 to 1908 Luzin underwent a psychological crisis so severe that several times he contemplated suicide. One precipitating event was the unsuccessful revolution of 1905, an event that was sobering for many left-wing members of the intellegentsia.... Luzin was shaken not only by the shedding of blood but also by personally witnessing poverty and suffering.

...

Earlier, he had embraced science, materialism, and secularism as the answer to Russia's problems. Now he doubted that these were any answers at all."

Thankfully, Luzin is deeply acquainted with Pavel Florensky, the third member of this "Russian trio." Florensky studies mathematics with Luzin in Moscow and then later becomes an Orthodox priest. The two of them remain very good friends, and later during the time of Luzin's personal crisis, this friendship becomes extremely important, as the two correspond concerning Luzin's troubled thoughts. Luzin writes to Florensky,

"You found me a mere child at the University, knowing nothing. I don't know how it happened, but I cannot be satisfied any more with the analytic functions and Taylor series.... To see the misery of people, to see the torment of life....--this is an unbearable sight....I cannot live by science alone.... I have nothing, no worldview, and no education.

...

"If I do not find a path to seek the truth...I will not go on living."

Florensky himself is a convert to Christianity, having converted from atheism at the age of 17. Despite having been raised in a secular environment, he believes that one of the sources of Russia's problems is that so many of its brightest minds (like Luzin) are attracted to atheism.

Florensky therefore provides Luzin with a "path to seek the truth" from his own religious insight. Luzin reads Florensky's thesis "On Religious Truth" (a version of which I happen to have at the moment, thanks to a kind uncle who seems to have every book in the world).

This reading combined with a continued friendship with Florensky leads to a full conversion. In 1908 Luzin writes to Florensky, "I felt as if I had leaned on a pillar...I owe my interest in life to you."

Luzin and Florensky press forward from here into a study of mathematics shaped by a shared interest in Christian mysticism. Florensky becomes an avid supporter of the "Name Worshiping" movement which goes back to chapter 1. Luzin surely knows about this development, even if he never becomes an active participant in the movement.

When it comes to mathematics, Luzin and Egorov are the real experts, it seems, but when it comes to fusing religious, philosophical, scientific, and mathematical thought together, Florensky is the real genius. Some quotes from the book illustrate:

"Florensky was convinced that intellectually the nineteenth century, just ending, had been a disaster, and he wanted to identify and discredit what he saw as the 'governing principle' of its calamitous effects. He saw that principle in the concept of 'continuity,' the belief that one could not make the transition from one point to another without passing through all the intermediate points.

...

Florensky faulted his own field, mathematics, for creating this unfortunate monolith. Because of the strength of differential calculus, with its many practical applications, he maintained that mathematicians and philosophers tended to ignore those problems that could not be analyzed in this way--the essentially discontinuous phenomena. Only continuous functions were differentiable, so only those kinds of functions attracted attention... Differentiable functions were 'deterministic,' and emphasis on them led to what Florensky saw as an unhealthy determinism throughout political and philosophical thought in general, most clearly in Marxism.

...

Florensky was convinced that mathematics was a product of the free creativity of human beings and that it had a religious significance. Humans could exercise free will and put mathematics and philosophy in perspective.... Mathematicians could create beings--sets--just by naming them.... The naming of sets was a mathematical act, just as, according to the Name Worshipers, the naming of God was a religious one....

I can't tell you how motivating it is to read about Florensky's religious and mathematical thought, and his influence on Egorov and Luzin. Today's mathematicians often seem inclined to divorce philosophical concerns from mathematics, but that is a sad state of affairs, one from which these early 20th century Russians can liberate us.

I am also deeply moved by the personal struggles of these mathematicians, and how they had to respond to the crisis of their time. I, with them, am persuaded that the best response to the crises of our time is deeper religious thought, not more secular thought.

As much as I am a fan of interacting with secularism in a healthy and open-minded manner, I think that ultimately secular thought lacks the resources we humans need to move forward. Not that religion doesn't often hold us back; but I think the best cure for stale religion is fresh religious thought. Man, does one ever find that in Florensky.

Still more to come... This book has been really good so far!

Two can play that game...

So MoveOn.org did a video with a bunch of celebrities attempting to make fun of conservative critiques of the public health insurance option.

Protect Insurance Companies PSA from Will Ferrell

But conservatives can play that game, too, it seems. Here's a video from Catholic Vote Action:



I don't know where this one is from, but I might as well throw it in the mix:



A lot of times I wince when conservatives try to outwit liberal satire, but in this case, the liberal video was so bad it made the conservative videos hilarious. Thanks, Alexa.

I'm most disappointed in Will Ferrell's performances. At least when he impersonates Bush, it's funny.