Friday, September 29, 2006

Øieblikket part 4

I finally made it to Copenhagen, and I didn’t see a single Kierkegaard-related building, statue, historical marker, or souvenir. I simply wasn’t ready for this trip.

Of course, that begs the question of why I’m in Denmark at all. There’s a dynamics conference going on at an out-of-the-way guest house belonging to one of the universities here. The topics are currents and bifurcation loci—respectively, those terms refer to very nice, but very general topological/geometric objects and to sets that describe how systems with parameters change as the parameters change. I can’t possibly convey the notion of currents in this medium, but I can at least give an example of bifurcation: say you have a system of one-way paths in the plane, with two distinguished points, one of which absorbs paths (called a sink), and one of which emits paths (called a source), and somehow you’re varying the distance between these two points. One can imagine reducing the distance to zero, so that the points coalesce—maybe then all the paths just flow straight through (the source and sink annihilate each other), or maybe they start orbiting a single point (the source and sink together form a center). The change in the number and kinds of distinguished points is called a bifurcation.

This isn’t really my area of mathematics, at all. I know a bit about currents, from geometric studies, but I’ve never put in time studying bifurcation of dynamical systems. Yet I’m actually excited to be here. I’m looking forward to learning a lot. It’s not a large or a long conference; it just runs two and a half days, and there are perhaps thirty participants. There are dynamical aspects of the areas I do usually study, but I’ve always considered myself a geometer rather than a dynamicist. This is a good chance to learn about other interesting fields—areas in which Dr. Hubbard is very active.

We’ve gotten through the first day of the conference, but I’ve said about all I’m going to for now on that topic. Yesterday Sarah and I had the day to spend wandering about Copenhagen. Mostly we split up and indulged our respective interests. I quickly ended up at the Christiansborg Palace, home of the royal, legislative, and judicial branches of government (the foundation stone reads “Rex, Lex, Jus”—I may get a picture of it posted in the next few days). It is the fifth castle or palace to stand on that site. The first was built in 1167 by Bishop Absalon, and you can go underneath to see ruins from the walls of Bishop Absalon’s castle and the second castle. I like ruins; it’s amazing to see the way buildings were laid out, how homes were shaped, how wells and drainage systems were placed in the community, and all that. I once saw in Geneva a baptismal font that had been used since the 8th century or so; you could see how its size had decreased as practice moved from adult baptism to infant baptism. At the Christiansborg Palace, you could see where walls from the first castle had fallen and been used as foundations for later generations of buildings.

After the palace, I wandered down to the waterfront. I ended up in the Royal Library, rather unintentially. On the ground floor is a café called Øieblikket. I was seriously tempted to buy some coffee there, just because it was the only thing remotely resembling a Kierkegaard connection that I found, but it was very expensive. Instead I wandered the stacks (as much as I could; they were mostly closed except to folk with research purposes). At 1 pm, music began playing throughout the main hall: it was a mixture of massive chords, tinkling bells, and light drumming (I think it was supposed to be a drum; it sounded like claves at first). It lasted three or four minutes and was marvelously relaxing.

Next I starting walking back to the train station, thinking I’d find a cheap cup of coffee and an internet connection there. Instead I was sidetracked by a sign indicating the National Museum was having a special exhibit on the life and times of Tycho Brahe. There were period furniture and costumes, including a full suit of armor. They also had reproductions of some beautiful plates from a 1603 book on astronomy, and instruments like those Brahe used (his tools have apparently been lost). I just browsed for a bit and moved on.

Copenhagen is a neat city. It seems like the bicycles almost match the cars in number. The buildings are a mixture of grand old architecture and chic modern flair. Next time I go, however, I’ll be ready for my Kierkegaard pilgrimage.

Wednesday, September 20, 2006

this morning's experiment

Prickly pears come in different colors. For breakfast, I wanted to learn which color tastes the best. I thought it would be the red ones, so I had bought two reds, one yellow, and one green. I was mildly chagrined that the red ones are not, in fact, the tastiest (they still have the prettiest color, however). Based on this single trial, I would say that the green ones are the best. They taste almost like honeydew, which I adore. Further tests are necessary.

I managed to get only two needles stuck in my hands this time, which is a great improvement. Even better, they were easily found and removed. This may actually be the best-case scenario, but I’m going for zero pricklies from peeling the prickly pears. To the lab! I mean market!

Sunday, September 17, 2006

chez nous

What, exactly, is the first order of business upon arriving in a new place to live? Probably to make some contacts. Because while it seems the first thing to do is find a place to live and move in, knowing people will make those tasks much easier. I’ll get to that.

Indisputably, Dr. Hubbard has been the greatest boon for us here. He’s willing to try just about anything; he follows his nose, and his nose leads him well. We learned of the apartment we’re moving into via a remarkably expensive service that gathers and dispenses information about apartments to rent. It’s something like a highly specialized classified ads section. Some other folk from around here advised against signing up for the service, after we had done so, saying that the information is often misleading or out-of-date, so we count ourselves lucky to have settled on such a marvelous spot out of that investment. It’s still not clear we should have paid as much as we did, but we’ll make up for it in the quality and affordability of our new place. Dr. Hubbard liked the place almost immediately; he quickly developed a rapport with the owner. I was hesitant for a while, mainly because we hadn’t seen any other options. After some reflection and speaking with other property owners, it became clear that it was nearly impossible for a better option to appear.

I’ll describe a bit here about the apartment and where it sits in town. In a later entry I’ll talk more about what the neighborhood’s like. We’re just a few minutes’ walk from the Hubbards’ apartment, which means we’re in the centre-ville, close to a fresh foods market (even better than the Ithaca farmers’ market, in some ways, because it’s every day, the prices are lower than in the supermarket, and almost everyone goes there—these people really care about making food well), the Vieux Port, St. Charles (one of the schools with activities we’ll be attending, such as the Friday seminar on Teichmüller theory), and the operahouse. There’s a newly constructed library nearby, which we haven’t yet had the opportunity to explore. Just up the street from us is the Place des Capucines, from which one can see the façade of the Eglise des Réformés (which, despite its name, is a Catholic church, and a beautiful one at that; we marvelled at the rose window lit from inside this evening as we walked between the apartments).

[Tangential note: I just noticed I can see Notre Dame de la Garde from the Hubbards’ window. It’s atop a hill, from which one can see all of Marseille. We visited there last summer. It’s quite impressive, with a golden statue of Mary placed in watchful benediction on a high tower.]

We have two bedrooms, a large living room with a very high ceiling (for now, while it’s empty, it’s certainly one of those places a chamber choir would love to practice for the acoustics), a bathroom, and a kitchen. All of these were completely empty we we signed the contract for the apartment. And I mean more empty than one might expect, coming from the U.S. The standard in France (or perhaps not quite the standard, but it’s certainly common) is for the kitchen to be unequipped with refrigerator, stove, or oven. Much less were there beds, tables, or any other furniture of the sort. This is where the contacts come in: one of the other professors at the university had some furniture she could donate, and knew that several of her neighbors also had items they were ready to rid themselves of. Just this evening, we picked up a fridge, a sofa, three chairs, a table top, a rug, and some sort of clothes containers from Ikea (they're meant for shoes, but neither Sarah nor I have that many shoes). We would have more still, but getting the sofa and refrigerator up three flights of stairs required so much time and effort that we couldn’t make another trip today. Tomorrow we should have a kitchen table, four more chairs, and an excellent storage unit for kitchen materials. We’re still working on a stove, an oven, and beds. But there’s work to be done first…

Part of the conditions of our contract is that we complete some repairs and a painting job around the apartment. Again, Dr. Hubbard’s expertise has been quite valuable. He bargained with the owner (himself a very kind and capable man; he and his wife loaned us the three chairs currently in our place, and may provide us with a couple more items if we can’t find them elsewhere) for a very nice arrangement, doing so in large part by demonstrating a thorough knowledge of house repairs. A substantial amount of work remains, but we hope to have it completed by the weekend so that we can move in early next week.

I feel a bit strange investing so much in a place I’ll only inhabit for nine months. It’s almost easier for me to think of doing this work for the owner’s sake rather than for Sarah and me. I realize many people feel a need to beautify wherever they live for however long they’ll be there. My life has been sufficiently vagabond (or perhaps just sufficiently bachelor) that I truly can cope with any conditions for a temporary residence (which is what this is). But perhaps that’s part of why I often enjoy spending time outside of my home—it’s not just that I prefer being around people; it’s that I’ve neglected to some extent to make my habitation comfortable and inviting. I don’t lead a slovenly life by any means. I enjoy having my home clean, and I even enjoy arranging furniture, decorations and the like in a pleasing manner. But I don’t typically launch into anything that requires more than a few hours’ purchasing and arranging. I know if I owned a home that would be different—first of all, because there’s hardly a choice but to invest a great deal of time, and second of all, because I would know it as a place of permanance and would want to feel secure in staying there.

So that’s the state of our apartment. I know I’ll have more to say on the subject, particularly as work gets completed and we get familiar with the environs. I wish you could all come see it. It’s going to be a fun place to live.

Tuesday, September 12, 2006

instability and control

This post is directly inspired by a lecture Dr. Hubbard gave yesterday, at an opening conference for the first-year undergraduate math students at the university. He spoke on dynamics, of course, specifically the motion of a pendulum with friction and a time-variable force (say, a magnetic field affecting a metal pendulum). For those interested, the time-dependent differential equation modelling the situation was: x'' = - x' - a sin x + b cos t, where x is the angular position of the pendulum, and the last two terms represent friction and the time-dependent force, respectively.

The topic was clearly a stretch for the students attending (there were a couple hundred), but we think they truly enjoyed it. There was much discussion, and a couple dozen who came down afterwards to look more closely at some of the pictures. These pictures were colorings of the (x, x') = (position, velocity) plane, with each point colored by the periodic solution to which it is eventually attracted. Such a picture might look like this:


(This particular picture was made by Sarah, using a program written by Matt, with a = .825 and b = 1.) Each (attracting) periodic solution, represented by a solid color, is a translation of the others by 2π, since x measures angular position; that is, the periodic solutions differ only in the number of times the pendulum has wound around its pivot before settling into (or nearly into) a regular periodic movement.

Here’s one salient feature of the picture, stated in theorem form: given any point on the boundary of any colored region, and any positive value ε, every other color lies within ε of the chosen point. Put another way, it requires very little change in the initial conditions to effect a great change in the outcome.

Dr. Hubbard gave a couple of practical uses for this phenomenon. When a situation is highly stable (which, one might think, means one has a great deal of control), then the outcome is nigh inevitable. One may try changing a number of things, and still the same result will occur. Hence one has less control than one might have expected. He pantomimed a skier, who when placed in a very sturdy frame has little choice about where he goes, but who when flexible and apparently unstable provides himself with all sorts of options for movement (again, a small movement can effect a great change).

I was struck during the talk by the great metaphorability of this physical observation. How many people try to clamp down on their lives with as complete control as they can muster, only to find that doing so leaves them no options as to their destination? How often do we experience our greatest joys in the unforeseen, which we must be quick to accomodate lest we lose them?

Now it is true that we must also discipline ourselves to manage the instability properly, as the skier must handle his tenuous position correctly to avoid obstacles, so I’m not arguing against planning and practice. And as always the metaphor should not be pushed too far. But this is a nice illustration of the principle that the safe route does not always lead to the best end. (Any investor could have told you that. As I said to Hannah the other day, if I wanted to be safe, I would have stayed in Tennessee. Yet here I am, again a substantial fraction of the globe away from my zone of familiarity. I pray for the wisdom and the discipline to use this instability for growth and excellence.)

Friday, September 08, 2006

if you prick a raw paw, next time beware

First post from France!

This may also inaugurate a series of more blow-by-blow event recap entries that pop up from time to time. I’ll try to avoid them for the most part, but sometimes there are just fun stories. Traveling and arrival stories are fun. And I haven’t slept much in the last three days, so this could be especially fun …

The travel times for this trip were not so terrible. That was compensated by the fact that I had to take three planes. Really, the whole process wasn’t bad; it just took a long time, and broke up sleeping times in a peculiar manner. The trip was Memphis–Charlotte–Frankfurt–Marseille. The leg one might be concerned about for length is naturally Charlotte–Frankfurt, but it took less than eight nours. Problem was, it was an overnight flight, so after watching two movies I only had two hours to sleep. Before that flight I had four and a half hours in the Charlotte airport, which is quite friendly. After it I had five hours in the Frankfurt airport, which is less friendly in atmosphere but had lots of nice people in it. I ate breakfast at McDonald’s—the first time I remember eating anything at that restaurant since I can’t remember when, and it was because they were the only ones serving breakfast. It was a pretty good egg sandwich, though. It beat my expectations, much as The Da Vinci Code had on the flight.

The Hubbards’ apartment was quite easy to find from the bus station, after I caught a shuttle from the airport to the Marseille centre-ville. After I arrived and took a shower, Dr. Hubbard, Sarah, and I went out for a walk around town. We passed by the fresh foods market, which in all honesty beats out the Ithaca Farmers’ Market in some aspects. Mostly just because here everyone is interested in fresh, good food, rather than just the hippie-types back in the States.

I was very excited to see prickly pear fruits (a.k.a. barbary figs, les figues de Barbarie). Before this afternoon, I hadn’t seen them, much less tasted them, outside of Morocco. So I bought a few and we brought them back to the apartment for everyone to try. One website I found (while trying to confirm their name) described the taste as “like watered-down watermelon”, which is close enough. The seeds are tightly packed, as in a guava, however, and you just eat the meat with the seeds. (I so hope guavas make an appearance at some point. I enjoyed having them in India again. The fact that I ate them skin and all freaked out those in the group who hadn’t traveled in developing countries, and were convinced I would make myself deathly ill.)

If you ever get a chance to try prickly pears, heed the following: Warning! These fruits got their name for a reason! Yes, they look innocent enough, but this is the fruit of a cactus! They learned from their maker. See, you peel the outside skin and fibrous layer off, then eat the insides, as described above. And you won’t see them, but DOZENS OF TINY NEEDLES WILL EMBED THEMSELVES INTO YOUR HANDS while you’re peeling the fruit. You still won’t see them. You’ll just feel them, and you won’t be able to get them out. Before, when I had prickly pears in Morocco, the vendor kindly peeled each one and handed the edible portion to me to eat in blissful ignorance of the danger involved in handling these succulent treats.

(Now, you see, I’m definitely exaggerating, to an extent I don’t normally. There were a small number of needles stuck in my hand, and they were mildly annoying for a while, but it’s really no big deal. But like I said, I haven’t slept much, and isn’t the story more fun this way? I haven’t got to do any shouting on previous entries, either. Hooray for sleep-deprivation! I’ll be crashing soon.)

For dinner, we joined friends Pascal and Florence. We sat about and with the meal sampled various bottles of wine, pastis, and liquor. (I was introduced to both pear liquor and another drink made from génépy, a kind of mountain flower.) We talked about math, politics, health, wine, graduate studies, biking, apartments, and who can recall what else. In short, it was a very nice opening dinner to greet Sarah and me to Marseille.

I’m excited about the next year. This is going to be a great place to live.

balance and turmoil

[Author’s note: this took a long time to write. It’s not my longest entry so far, but some of the events it refers to prevented its composition from coming to completion in a timely manner. The result, I fear, is that it may seem disjoint at points. I hope the general argument and mood remain clear.]

Summer is movement. Summer is change. All of life is, really, but since I belong to an academic community, I sense that the activity of most of the year occurs in a relatively restricted area, while summer brings unfettered agitation.

Here’s a small part of what I did this summer: I watched and helped many of my best friends move away from Ithaca more or less permanently. I attended two weddings (I know that’s very much on the low numeric end for many people, but weddings generally come few and far between for me, especially since many of my high school and college friends married while I was in Africa). Among my friends who stayed, several of them needed help moving from one home to another. I myself had to prepare to leave for a shorter time. I fell in love. I traveled several thousand miles to three very different parts of the continent. It seems like everything was either going into boxes (in a physical sense, for packing) or coming out of boxes (in a metaphorical sense—explosive life bursting forth, expanding beyond what had been conceived possible, enveloping new worlds and enchanting one in new directions).

I figure the last thing the blog world needs is a maudlin mediation on goodbyes, so I’m writing about movement—both its continuation and its cessation. The last few weeks have been marked by a great deal of movement; although that statement is true physically, I’ve experienced it primarily internally. An odd occurence for me. I once saw part of a personality profile for my dad, which stated something like “Jerry does not mind change so much as being changed.” In many ways, that description has applied to me, also, for many years. I’ve lived in three states and on two continents (about to add a third continent to the list). I’ve been student and teacher, worked at jobs from a box office to a lecture hall, and I’m still not sure what I want to devote my life to doing. Yet through all the varied milieux in which I’ve lived and worked, I’ve essentially handled things the same way. To a large extent, I described how I handle situations in my first essay on time. And what I wrote there is that my philosophy of handling life asserts an essential immutability about the state of things. My life has been safe despite all the apparently significant changes I’ve made and projects I’ve tackled. I have made good choices, been prudent even in situations some might find risky. I know how to find balance in life.

In complete contrast to that evenly measured way of living, I feel like my life has been overturned in the past months. Events have happened so quickly that I’ve barely had time to breathe in between, much less weigh a response. I’m being a bit vague, but those who know me can divine some of what I’m talking about. It’s exhilarating, to say the least. I’m enjoying it.

Here’s the thing, though: life can’t be spent careening from one event to another. I’ve had friends telling me for years that I need to slow down. And I have learned that important point, to an extent. I reach out to both the intensely emotional and the soothingly calm. You have to look at the stars. You have to sit at a coffee shop and read. You have to sprawl out with friends and chat for a few hours. You have to find a quiet way to meditate; for me, it’s often sealing myself off for an hour to listen to Gorecki’s Symphony No. 3.

(Fortunately, at least for this discussion, stargazing has been a relaxing activity for me of late. Times have been when the depths of space overwhelmed me with their gaze. The first time I made Hannah lie back and look at the stars, I think she found the immensity a bit terrifying, as well. But now she tells me that they help her find peace and calm.)

Moderation and mediation—that is, balance—are essential to productivity. That’s sort of what I thought this entry would be about when I started it. One functions best when one is even-keeled. It’s okay to dive into spontaneity and craziness once in a while; in fact, it’s even advisable to do so, so that one doesn’t become wooden and anesthetized in one’s approach to life. But even the times of cool-headedness and the times of brashness must be held in balance with each other (not necessarily in terms of duration, but in terms of the effect they have to encourage growth in one’s psyche).

I’m struggling with whether that last statement is wisdom or timidity. No one could ever describe me as an extremist, but I’m beginning to think a position originating from calm is less vibrant than one originating from fervor. It’s time to pull in some words of the experts—a selection of observations from the smattering of philosophers I’ve read.

Aristotle spoke on moderation from an ethical perspective. For a long time I would have agreed with him. As recorded in the Nicomachean Ethics, he comes off as somewhat long-winded on the subject, so I’ll sum up rather than quote him at length. The key phrase is “virtue must have the quality of aiming at the intermediate.” The idea here is that excess and defect are the potential flaws in one’s action (he categorizes moral behavior as an art, and first notes that art in general can suffer from excess and defect), and so one must determine what these extremes are and aim in between them. For example, courage is the intermediate virtue between cowardice and bravado. To further support his argument, he observes that “men are good in but one way, but bad in many.” The image is of a target with virtue at the center and a surfeit of vices on the edges. To stray from a balanced, moderated path is to fall into error.

22 centuries later, Henrik Ibsen disagreed with this perspective on ethics. Not by mentioning Aristotle directly; I’m not sure the passage I just described is what he had in mind. In the play An Enemy of the People (En folkefiende), the character Aslaksen is a paragon of prudence and restraint, and in Ibsen’s presentation this makes him a mediocrity and a turncoat. Dr. Thomas Stockmann is seeking to warn his town of the impending health dangers from the public baths. Aslaksen is initially supportive, but he makes clear under what constraints he believes they should operate:
Aslaksen. We shall proceed with the greatest moderation, Doctor. Moderation is always my aim; it is the greatest virtue in a citizen—at least, I think so.
As soon as it becomes clear that repairing the baths will demand a large amount of financial support from the citizens of the town, Aslaksen complains to Dr. Stockmann that he has misrepresented the situation. (Aslaksen expected the situation to resolve itself sans sacrifice.) When Dr. Stockmann insists the problem cannot be ignored, he is increasingly ostracized by the community, led by Aslaksen, at the prodding of Dr. Stockmann’s brother Peter, the mayor and chairman of the Baths Committee.
Aslaksen. By the votes of everyone here except a tipsy man, this meeting of citizens declares Dr. Thomas Stockmann to be an enemy of the people. (Shouts and applause.) Three cheers for our ancient and honourable citizen community! (Renewed applause.) Three cheers for our able and energetic Mayor, who has so loyally suppressed the promptings of family feeling!
Aslaksen is at least partially a straw man. He speaks of “moderation” when he means preservation of the status quo and avoidance of anything which costs him (or the people he represents) anything. He is, in fact, extreme in his caution, not moderate at all. I think Ibsen’s point in creating him is to say that when one is guided by anything other than devotion to truth, one will become devoted to that ideal and slavishly follow it to the detriment of truth.

Although Ibsen was a playwright rather than a philosopher, it seems likely he was influenced by Kierkegaard. For Kierkegaard, the truth always lies in the individual, never in the masses. Very nearly the last line in An Enemy of the People is spoken by the doctor in defiance of the town’s abuses on him:
Dr. Stockmann.I have made a great discovery. … It is this, let me tell you—that the strongest man in the world is he who stands most alone.
For Kierkegaard, the self is developed by sharpening and intensifying. The opening of The Sickness Unto Death defines the self as a being bare before God, reaching towards and uniting the eternal and the temporal. It is a great and terrible way to conceive of one’s self. It also heightens the sensation that we are responsible for what we do and experience in this life; we cannot shuffle off to another, or to a collective (as Aslaksen does), the task of finding our fulfillment.

I've already described in a previous essay the “knight of faith” from Fear and Trembling; I will return to the knight throughout my life. This is not a man of moderation. He has cast himself, at least, fully upon God’s grace. As Kierkegaard describes him, one would think he has taken the impossible step of casting all of existence upon that grace. He is larger than himself, even though he may have a bourgeois appearance. He has emptied himself, and the glorious thing is that he is filled because he trusts in God. No self-restraint can bring about that kind of fulfillment.

I use these three authors to show something of the development I’m seeing in myself. From a careful observer to a moderate risk-taker, I am reaching towards the courage to plunge fully into life. I am grateful for my past of mediation; I have been trying to relate to others’ perspectives my whole life, and I think that has equipped me well to counsel and dialogue. But there is fiery passion in me that is only beginning to wake, and I feel the time has come to seek that out and find what I am to do in this world.

Last spring, I read Secrets of the Heart, a collection of short poems and narrative works by Kahlil Gibran. The opening story, “The Tempest”, tells of a man who seeks out a hermit to understand why he has left human society. The hermit tells him he has not found human society, as it stands, to be capable of providing real sustenance to the spirit. He left to find what is truly important in the universe. I used a passage from this story as my signature quote for a while:
Among all vanities of life, there is only one thing that the spirit loves and craves... It is an awakening within the spirit; he who knows it, is unable to reveal it by words; and he who knows it not, will never think upon the compelling and beautiful mystery of existence.

Amen.