Thursday, January 08, 2009

sonata in the key of calculus

I have been reading The Rest Is Noise, Alex Ross’s chronicle of the 20th century through the lens (or perhaps microphone) of music. I just completed the section about Duke Ellington and the origins of jazz. Much was made of Ellington’s proclivity towards collaboration (so much so that he never finished the opera he undertook, because it was such solitary and large-scale work), and I was reminded of how I’ve been doing math recently. Whenever I've had some time with someone I thought would be interested, I’ve pulled out a pet project and gotten their perspective on it. I have thereby garnered, synthesized, and built upon a variety of useful insights and motivations.

Then I began to reflect on certain analogies that are often drawn between mathematics and music, as well as between their histories. One compares Euler with Mozart and the Bernoulli family with the Bachs. There are notions of what is “classical” and what is “for amusement” in both mathematics and music. More modern comparisons are less frequently made, and so I thought it would be nice to have a notion of a “jazz mathematician”. Someone with a distinctive sound, but capable of improvising on a thousand different themes with hundreds of collaborators. Based on that description, I guess the nearest mathematical equivalent to Duke Ellington would be Paul Erdős, although many mathematicians fit the profile.

Given how many mathematicians are music aficionados, I wonder that more such analogies between contemporaries in these two fields haven’t been drawn. Who would be paired with Messiaen? Or with Grothendieck? Is Cauchy or Gauss more like Beethoven? There is an increasing voice in the Western world for Eastern music and mathematics. Do these two influxes share distinctive aesthetic qualities, or is one or the other merely another source of human labor for doing “more of the same”? Twentieth century music is characterized by experimentalism and division among radically different movements. One can discern echoes of the same in the mathematical world—neo-classicism and minimalism and stark modernism—so, again, are there pairings that indicate shared aesthetics? Or are all such comparisons in the end folly, because the roots of such tendencies lie in unique individuals and historical paths?

Wednesday, December 03, 2008

things you never thought you'd see #2112

Your fiancée’s father’s workplace shows up in a popular comic.

Girl Genius has high production values for a webcomic; in fact, it started as a graphic novel and then moved to the web. Right now they’re in between acts of the main storyline and so they’re running a retelling of Cinderella just for fun (the story starts here). There are of course lots of inside jokes based on the main strip, but just think “mad science” and “fictionalized late 19th century Europe” and you’ll get the gist.

The story of Cinderella has princes. Princes need a castle. The castle should look science-y, to fit with the theme. So the castle appears in the fourth panel of today’s strip. And what did they choose as a model? The high-rise office building of Fermilab, where Hannah’s dad works.

Friday, November 28, 2008

the ambiguity of pride

A couple of weeks ago, I was reminded of a story by Kahlil Gibran, entitled “The ambitious violet”. The entire story is of course worth reading, particularly for Gibran’s beautiful use of language, but I will summarize for the sake of this entry.

A small violet is in a garden, among other violets, lovely but low to the ground. She is happy with her lot, until she sees a rose rising majestically among all the other flowers and displaying a glory like the violet had never imagined. Then the violet begins to lament her lot in life, consigned to such a humble place when she wants to lift her head high like the roses do.

She is heard both by the rose and by Nature, who try to convince the violet that her place is fitting. The rose says that the violet has a unique beauty and should be content rather than try to exalt herself. Nature asks why the violet has suddenly become so greedy and warns that ambition will lead to disaster. The violet wants nothing more than to become a rose for one day, and Nature grants her wish.

That night, a storm sweeps through the garden. All of the tall flowers are torn up and thrown about, and only the patch of humble violets is spared. They look about, grateful for their salvation; then they see the rose that had been a violet dying on the ground, and they mock her for the result of her greed.

The dying rose replies:
You are contended and meek dullards; I have never feared the tempest. Yesterday I, too, was satisfied and contented with Life, but Contentment has acted as a barrier between my existence and the tempest of Life, confining me to a sickly and sluggish peace and tranquility of mind. I could have lived the same life you are living now by clinging with fear to the earth.... I could have waited for winter to shroud me with snow and deliver me to Death, who will surely claim all violets.... I am happy now because I have probed outside my little world into the mystery of the Universe.... something which you have not yet done.

I could have overlooked Greed, whose nature is higher than mine, but as I hearkened to the silence of the night, I heard the heavenly world talking to this earthly world, saying, ‘Ambition beyond existence is the essential purpose of our being.’ At that moment my spirit revolted and my heart longed for a position higher than my limited existence. I realized that the abyss cannot hear the song of the stars, and at that moment I commenced fighting against my smallness and craving for that which did not belong to me, until my rebelliousness turned into a great power, and my longing into a creating will.... Nature, who is the great object of our deeper dreams, granted my request and changed me into a rose with her magic fingers.

She concludes:
I have lived one hour as a proud rose; I have existed for a time like a queen; I have looked at the Universe from behind the eyes of the rose; I have heard the whisper of the firmament through the ears of the rose and touched the folds of Light’s garment with rose petals. Is there any here who can claim such honor? I shall die now, for my souls has attained its goal. I have finally extended my knowledge to a world beyond the narrow cavern of my birth. This is the design of Life.... This is the secret of Existence.
The rose passes away, but with a smile of hope and fulfillment, “a God’s smile.”

The proper balance of humility and pride is a difficult one to achieve in the Christian life. The difficulty is compounded by the dual meaning of both words, particularly pride. We try, without much linguistic success, to laud the pride that leads to good and productive work while deploring the pride that leads to arrogance and damaged relationships. Humility, meanwhile, is a quality we seek as we approach God, even as we know that self-deprecation can be detrimental to our well-being (and we have faith that God desires our well-being).

Gibran himself was a Christian (a Maronite), and much of what I have read of his work is sharp in distinguishing what one learns from the teachings of Jesus and what one encounters in the church. A principal theme of his writing is to speak out against oppression, especially when done in the name of religion. He knew what many people suffer when they are kept ignorant and cattle-like, not just physically but spiritually. This is imposed humility; this is the suppression of pride. One feature of oppressive philosophy is that it exploits the ambiguity of language to confuse the mind to believe that what is good is bad, and vice versa. We may think we are being good for not wanting anything better in life (doesn’t Paul say we should be “content in all circumstances”?), forgetting that God also requires that we give our best back to Him, that we “invest our talents” in a “good and trustworthy” manner.

When I read the story of the violet, amid a collection of other stories and poems, several of which address Gibran’s longing for the people he loves to be released from economic and psychological slavery, I interpreted it primarily as a social commentary. At the beginning, when the rose tells the violet that she should be happy where she is, the violet responds, “How painful is the preaching of the fortunate to the heart of the miserable! And how severe is the strong when he stands as advisor among the weak!” The rose may have thought that her words were comfort, but the violet, already reaching beyond her current place, tells the rose that instead the words are wounding. They are falsely pious and, in the end, contemptuous of the notion that the violet could ever be anything greater than what she is. Notice the word “yet” in the violet’s speech to her sisters the night after the storm: even as she chastises them for not realizing what greatness she herself has experienced, she lets them know that it is still possible for them to reach for the same heights and to know, before they die, what it is to live. She is, in a way, very nearly a martyr.

When I told the story to Hannah, who has read less Gibran but has a keen sense of the meaning of text qua text, her first question was, “Do you think Gibran was an existentialist?” She saw the point of the story less as overcoming oppression and more as finding purpose and meaning in life. It is rather existentialist, in that sense. The rose’s life is richer than that of the violets, even though it only lasted a day. Victory is gained not by pushing away the end of life, but by ceasing to fear it.

Let us not seek quietness and contentment simply because it is easier and safer. Let us be daring and humble; let us find all that is good in the meaning of pride and humility and life and existence. Let us not merely consume, but let us find the richness of life and enjoy it and develop it. I will not say that if we have been violets, we should become roses, but instead that we should seek freely and joyfully, without constraint, to live life fully. We should praise those who have reached what they desired, and we should work to lift the hindrances to others’ achievement. The tempest will not cease, but it is no reason for us to remain small.

Thursday, August 28, 2008

how it happened

Hi, all.

Many readers of this blog already know via other means of communication that Hannah and I became engaged last night. Quite reasonably, it was suggested that I tell the story here in full detail so that it could be easily shared. (I love the information age.)

My main goals in the design of the proposal (obviously, my main goal in the proposal itself was to make official and public our pledge to marry each other) were as follows: surprise Hannah, include a certain piece of music she had requested on a previous occasion, and get it done in time for classes to begin. Clearly the last one was a success by dint of the date; I am happy that the other two worked out just as well.

Let me start with the piece of music, because it came first chronologically in the plan (and essentially at the beginning of the proposal). One day, almost two years ago, we were sitting in Hannah’s apartment listening to Rachmaninoff’s 2nd Symphony. The third movement of this piece is a breathtaking Adagio, starting with a clarinet solo and passing through several swells and some of the loveliest melodies in the orchestral repertoire. While we listened to it, she said “You should play this piece when you’re going to propose.” Thus the kernel was planted. I immediately knew that, when the time came, this piece would have to emerge from somewhere unexpected as a first clue of the event to come. Later, I began thinking of having a band or small ensemble appear as we were walking around campus or out on the Arts Quad. I started thinking about what instruments are played by my friends around here. And I began to converge on a woodwind quintet. As it turned out in the end, I only knew one of the musicians that came to play for us, but she assembled a fine quintet that made the experience a great one.

Last night, at the end of a long day of other activities, we were at Anabel Taylor Hall (for those who don’t know, this building houses the Cornell United Religious Works) for a start-of-year Graduate Christian Fellowship event: the annual ice cream social. I had worked out ahead of time that the social would probably be wrapping up around 8:30, so that’s when I asked the musicians to arrive. Except instead of coming into the meeting space, they set up in the chapel down the hall. I tapped Hannah (who was in the middle of a very interesting theological discussion that normally I would have loved to see continue) and asked her to come check on something with me.

We began walking down the hall, and I stopped by the office, where I had stashed some flowers earlier in the day. When I brought them out, she began looking at me suspiciously, and the musicians (whom we couldn’t yet see) began to play.

Now, Hannah knew I was going to ask her at some point—indeed, I already had and had just warned her that I wanted a chance to make it “official” in a special way. In her mind, however, that point was still some weeks off. I had a “deadline” of Fall Break, which takes place in the middle of October. However, she also mentioned recently that, when we first began dating the day before classes started two summers ago, she delighted in the sudden change in our relationship at a time already so full of change; she appreciates liminal times in life, as she put it. And although the calendar date of our anniversary was last Sunday, the “day before classes” seems more intimately related to the start of our relationship than August 24.

The music drifted towards us as I pushed Hannah (with her increasingly pursed lips) towards the chapel. We walked through the doorway, first halting just a few steps in, then proceeding to the middle of the room. We said only a few small things as the music was playing. (Did I mention I wrote the arrangement for the quintet? The original movement is about 20 minutes long, and I don’t think it had been arranged at all for a small ensemble. I took about a four minute selection and spent several mornings pulling parts together.) After it ended, I spoke with Hannah for a few minutes, talking about the last two years and how just in the last few months we really seemed ready to commit. I got down on my knee, as she deserves, and presented her with a ring. People have asked what exactly she said. Mostly I remember there were at least four “Yes”s. (As she reads this, she says her answer was “Yes, yes, forever yes.”)

After I had stood up again, the quintet began playing a waltz I had written for her a long time ago. We danced, and applauded when they were done. The musicians all seemed glad to have been able to help, particularly since it seems to be a rare opportunity for wind players to be part of an engagement proposal.

And that’s how it went, as I remember it. Since then, we’ve been happy and gleeful and tired and making plans and basking in each other.

another friend abroad

Hannah’s friend Jessie (who graduated from Cornell last spring) has started blogging about her studies at Hebrew University in Jerusalem. There’s a link in the “Friends’ Blogs” section of the sidebar now. Should be some interesting stories to read coming up…

Sunday, June 29, 2008

flavors of summer

Yesterday, a week after the “official” start of summer, Hannah and I joined in one of the quintessential summer activities in Ithaca: we went strawberry picking. I feel like we managed to join some kind of club, too, because whenever I have spoken with other friends who go out and pick strawberries, the ones who get the largest amounts almost always come back and say they picked 18 pounds. And so did we, this time. Hooray! We went out with one of Hannah’s friends from church, then went back to the friend’s house and prepared all of the strawberries, cutting off all of the tops and freezing eight quarts’ worth in the large freezer at the house. The rest we brought back and made into a wonderful strawberry-basil soup for a potluck last night. I recommend this dish highly. Take the strawberries, boil them for a bit (don’t add much water, if any, as the strawberries will produce copious amounts of liquid on their own—this is a technique we learned from cooking squash). Then add some heavy cream and chopped basil. Puree the whole thing. We put in sour cream and a small amount of sugar; some recipes we saw also suggested milk. We chilled it for a couple of hours, and served it with fresh (non-sweetened) whipped cream. Yum. It seemed quite successful.

In other exciting news, this year’s Ithaca festival was moved back two weeks to be held last weekend, so I got to attend it for the first time. Melanie was in town, visiting and working, and we went down to the parade on Thursday afternoon. Lots of local organizations participated: schools, housing programs, the Ithachords (barbershop singing), the SPCA (puppies!), and so on. There was an (apparently traditional) Volvo ballet: several Volvos dressed in tutus and dancing around each other in the street. That was bizarre. The commons were in a fair-type atmosphere for the next couple of days, with food stands and performances and boutiques in tents. There was rain at some points, of course; the theme for the year was “I am Ithaca”, and I suspect the rain felt it needed to make an appearance. In fact, the rain arrived on Saturday afternoon just as we were supposed to be folk dancing in Dewitt Park, where there are no shelters of any kind. One dancer/musician pulled out her pipe and played some familiar tunes as we danced very simple steps under our umbrellas. On Sunday, crowds in Stewart Park made an immense human peace sign, in an attempt to set a world record for the largest such sign. We didn’t make it to this event, but you can see videos of it on YouTube. We did go down to the park on Sunday evening to see a circus and walk among the crowds. It was a beautiful day.

Sunday, March 23, 2008

renewal

Holy Saturday ends the fast of Lent, which has been a fast with a purpose. Many people may not understand fasting, since it’s not making a statement like a hunger strike does. It’s devotional. It focuses one’s consciousness and makes one mindful. The purpose of the Lenten fast is to prepare to welcome Christ as king once again, to acknowledge that we continue to fail at our duty but that we are grateful for God’s mercy. Rejoice! The bells and the hallelujahs sound. Death in all its forms is not lasting.

I am, it turns out, too tired to develop this theme further tonight. Let me, then, share part of tonight’s Easter Vigil service. The Book of Common Prayer leads the congregation, with the pastor, through the following vows:

Do you reaffirm your renunciation of evil and renew your commitment to Jesus Christ?
I do.

Do you believe in God the Father?
I believe in God, the Father almighty,
creator of heaven and earth.


Do you believe in Jesus Christ, the Son of God?
I believe in Jesus Christ, his only Son, our Lord.
He was conceived by the power of the Holy Spirit
and born of the Virgin Mary.
He suffered under Pontius Pilate,
was crucified, died, and was buried.
He descended to the dead.
On the third day he rose again.
He ascended into heaven,
and is seated at the right hand of the Father.
He will come again to judge the living and the dead.


Do you believe in God the Holy Spirit?
I believe in the Holy Spirit,
the holy catholic Church,
the communion of saints,
the forgiveness of sins,
the resurrection of the body,
and the life everlasting.


Will you continue in the apostles' teaching and fellowship, in the breaking of bread, and in the prayers?
I will, with God's help.

Will you persevere in resisting evil, and, whenever you fall into sin, repent and return to the Lord?
I will, with God's help.

Will you proclaim by word and example the Good News of God in Christ?
I will, with God's help.

Will you seek and serve Christ in all persons, loving your neighbor as yourself?
I will, with God's help.

Will you strive for justice and peace among all people, and respect the dignity of every human being?
I will, with God's help.


Simple questions. The answer is harder—“with God’s help.” If we learn anything from Lent, it should be this: that is the only way to say “I will,” the only way we can do anything. Yet we must strive to do it all, persevering, loving, and respecting.