my lord is near me all the time

Inspired by my previous post on the moon, I’m going to use it as the focus of my Lenten meditation this evening, too. It appears pretty early in the Bible, by any reckoning:

And God said, “Let there be lights in the expanse of the heavens to separate the day from the night. And let them be for signs and for seasons, and for days and years, and let them be lights in the expanse of the heavens to give light upon the earth.” And it was so. And God made the two great lights—the greater light to rule the day and the lesser light to rule the night—and the stars. And God set them in the expanse of the heavens to give light on the earth, to rule over the day and over the night, and to separate the light from the darkness. And God saw that it was good. And there was evening and there was morning, the fourth day.

(That passage still reminds me of one of my favorite sections from Copland’s “In the Beginning”, which we sang in the Chorale last spring.) The Israelites were not, I think, very good astronomers. That phrase—“the lesser light to rule the night”—echoes through dozens of conversations I’ve had with people who don’t understand how the solar system works and think the moon is only/always out at night. Even in Guinea, which is the closest situation I’ve been in to ancient Israel, and where people’s schedules depend immensely on the phase of the moon, most people had no idea that when the moon isn’t out at night, it can be visible in the day. I don’t blame Moses, or whoever authored Genesis, for not saying something more precise about the nature of the moon; they had much more important things to discuss, like the fact that God is an amazing creator.

Once you do know something about the moon, though, it becomes a wonderful metaphor. It’s like the mirror Robert Fulghum wrote about in It Was On Fire When I Lay Down On It: not producing any light of its own, it takes the light of the greater light and shares it when the sun is inaccessible. It’s a physical manifestation of grace in the darkness.

This light is also genuinely the most peaceful place I’ve ever found to be. The expanse of stars is terrifying. But the moon is a neighbor, and it feels that way. While the Guineans would dance during the full moon, because it allowed them to stay up all night without fear of darkness, I would stand in awe. Moonlight feels like forgiveness. Debussy’s “Clair de lune” is gorgeous and almost captures it, but walking in moonlight gives an immense feeling of calm and starkness and security.

Tonight I just thank God for the moon, for all the dreams it has inspired and joys it has supported, for its beauty, and for the challenges it poses. May we treat it well, and may it always be a firm stepping stone to the rest of the cosmos.

will we find Alice there?

This evening, a friend asked if I saw the lunar eclipse last night. No, I said, because I didn’t know about it. This was actually an unheard of state of affairs for me; for a few years, I caught every lunar eclipse I could, some unexpectedly. Here’s an email I sent to a friend after the last one I saw (October 2004):

Well, although it seems somewhat unfair to me, I only got to watch about the last 20 minutes of eclipsing. To make up for it, I think I have to stay up past midnight to watch the emergence of the moon from Earth's shadow. I missed the first part because I was teaching. Ah, well.

This is, I think, the sixth total lunar eclipse I've seen since 2000, but right now I can't remember where I was for one of them:

January 2000: Minnesota. A group of friends (who were still attending college in a town a little over an hour from Minneapolis) organized a eclipse-watching bonfire. Which is a good thing to have around when one plans on spending two to three hours outside on a January night in Minnesota.

January 2001: Guinea. This one was completely unexpected. I was sitting around with my host family having dinner, when we noticed it was time for the moon to be out yet remained quite dark. A few minutes later, we realized the moon was rising and eclipsing as it rose. It was incredible. I was super exciting [sic—but not inaccurate as you’ll see], hopping around and shouting in English, French, and Malinke how excited I was. The Guineans were afraid: their story for an eclipse is that a cat is eating the moon, and you have to play drums and beg for the moon to come back. I got to explain the process to a few people, however. It was not only a great astronomical experience, but a great cultural exchange.

May 2003: Memphis. My dad and I went out to a field to watch. On the way there, just a few minutes into the partial eclipse, our tire blew out, and we were changing it as the moon grew darker. We arrived at the field about halfway through the process, and stayed basically until it was done. The other time I went out to that field with my dad was when the Leonids were especially bright, in November 2002.

November 2003: Ithaca. I talked my friend Matt into driving out to Varna, where Cornell has an off-campus observatory. We figured there would be someone there manning the observatory, but no one was. About twenty or thirty other people showed up with the same idea, so we just enjoyed being out there together. I played resident astronomy expert for some folks, which was easy since I was basically explaining rotation and revolution. Also, of course, I took the opportunity to point out my favorite constellations. :-)

May 2004: ? This is the one I don't remember, even though it's the most recent. I figure I must have made an attempt to see at least part of it, but I can't for the life of me remember now where I was.

Tonight: I guess this is the last one until sometime in 2007 or 2008. I'll still be here then.

“2007 or 2008” seemed so far away back then. And now I’ve missed the last three I had a chance to see (since I was in Europe last March I could have watched that one—although as I think back, I may have known about it but it was cloudy—and I didn’t get up last August; see the link above for the list of eclipses this decade). The next one for me will I guess be in 2010, unless I’m in Africa this August.

A bit perturbed at myself for being so ill-informed, and remembering that I used to know when these things were coming because I used to visit Space.com much more often, I hopped over to that site and signed up for their RSS feed. Here’s the first headline I came across: Private Race to the Moon Takes Off. It turns out, Google and X Prize (the latter of which awarded a $10 million prize in 2004 to the creators of a privately-funded spacecraft that successfully reached >100 kilometers altitude twice) are jointly offering $20 million to anyone who can send a privately-funded robot to the moon and complete a set of tasks. It’s called the Google Lunar X Prize, and—to express the obvious—it’s awesome. It’s another example of how Google really is working to make the world of technology better in all the ways we’ve dreamed about. The competition is in the Space.com headlines right now because nine teams have just joined the competition, to join the first team that entered back in December. I imagine there are a few Cornell students aching to make their way onto one of these teams.

There has been a spate of moon-related media lately. Last fall, Hannah and I went to see In the Shadow of the Moon, a documentary that interviews the astronauts who were on the moon, which at this point in history was certainly essential to accomplish. (This movie, inexplicably, is not nominated for an Academy Award. Seriously, this is a fantastic movie. In the metaphorical, not the literal, sense, because it’s not fantasy.) It made Hannah want to watch Apollo 13. Almost everything makes Hannah want to watch Apollo 13. In 2005, Tom Hanks released Magnificent Desolation, an IMAX quasi-documentary that, while it had some good moments, was not the best IMAX film I’ve seen, mainly because so much of it was CGI and sound stage stuff rather than actual footage. (We just saw it this past winter in Memphis.)

And just in the last couple of days, with the landing of Atlantis just in time for the U.S. government to shoot down a potentially dangerous satellite, space activity in general has gotten a lot of news. I personally am still thrilled that we have a permanent human presence in space with the International Space Station. (I along with many others was nervous back in 2003 that the Columbia disaster would abruptly end that promise of a permanent presence.) And who wouldn’t be inspired by the immense success of the Mars Rovers, Spirit and Opportunity, which are still chugging along (and providing images processed by—guess who—the Cornell Pancam Team).

I believe this work in space has to remain a priority. And I’m pleased Google has taken it on, as well. As usual, I don’t have any dreams myself to make it into space, but I will cheer and in fact support in any way I can.

lift me up and let me stand

I have heard that non-Christians may complain the Christian faith is overly simplistic. It gives too many glib answers without taking into account the way the world really is, they say. Yet as I read the Bible and talk with pastors and other believers, it keeps coming up that the record we have of Christianity considers all aspects of human life. Take the Psalms: not only do you find devotion, trust, and piety, you also find fear, hatred, and accusations. The heroes of the Bible are sometimes the most fantastic sinners—proving that God really can work his will through dire circumstances, and that we have hope he can work in us, unworthy though we are. Questions are raised, such as in Job or Ecclesiastes or Romans, and left unanswered. What is constant, and miraculous, is the assurance that God loves us and wants to bless us. If we don’t wrestle with the questions of how God’s love is revealed, how we should share it with those around us, and why God doesn’t operate the way we expect him to, then that is our own shortcoming, not the religion’s. Faith is “the assurance of things hoped for, the conviction of things not seen,” says the writer of Hebrews. It is not a blindfold. We can trust and still inquire. We can pray and still not understand. The benefit in this life of being a Christian is that we gain, sometimes slowly but always in increasing measure, the “fruit of the Spirit”: love, joy, peace, patience, kindness, goodness, faithfulness, gentleness, and self-control; as Paul points out, “against such things there is no law.” And we have the story and the promise of a God who is carefully involved in our history and our lives. There’s nothing simple about that.

because he lives

Somehow, things seem to keep coming back to Romans…

In our Bible study tonight, we began reading parts of Job. We’ve been discussing creation this semester, and the claim from Romans 1 that “what can be known about God is plain … his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made” led into a proposal that we discuss the final chapters of Job, in which God speaks to Job in response to Job’s desire to face God with an accusation of injustice. If you haven’t read those chapters recently, I recommend them as an exceptionally rich depiction of God’s hand in creation and his continued work in the natural world. It is good fodder for discussion, too, as God’s rhetoric is tinged with sarcasm and indignation, while still revealing his great care for the world and the majesty of which he wants Job to be aware. Job has been asking for a chance to accuse God; God reveals that there are so many things in the world that Job can’t understand, he can’t begin to grasp the place and the justice of God.

After the study, I asked about another passage from Job, related more to the theme of justice than to creation. In one of his earlier discourses, Job complains that he has been abandoned (he has friends there with him, but at this point in the book he is finding less and less comfort in their words, which weren’t terribly comforting to begin with) by everyone in his family and household. Then he makes the declaration, using the words Handel chose to open the third part of the Messiah: “I know that my Redeemer lives, and at the last he will stand upon the earth.” Who is he talking about? I asked. Who is it, when he has been abandoned by everyone who should defend him, that will come and save him, will stand with him before God? The standard Christological interpretation (the one used by Handel) is, of course, that the Redeemer is Jesus. But even if you don’t assume that from the outset, it’s hard to interpret the text as indicating anything other than that Job knows he needs God to intercede with God. He must be asserting someone supernatural, or at least not an ordinary human, will come and rescue Job from his suffering, and take him so that he can “see God.”

Which brings me back to Romans. Because, if the good man Job (and he was emphatically good, no question about it, not at a single point is it even hinted that he did anything wrong, except perhaps to question God’s wisdom and justice) was left by all he loved and cared about, what shall become of us, who are so much less good? Paul answers: “one will scarcely die for a righteous person—though perhaps for a good person one would dare even to die—but God shows his love for us in that while we were still sinners, Christ died for us.” This must be the Redeemer that Job looked forward to. The one who gave Job hope can give us hope, too, even when we feel worthless or abandoned.

Coda: if you’ve made it this far, then as a reward let me lead you to the MySpace page of a musical based on Job. You can hear selections from the musical on the site.

wait

I could use some running and not being wearing about now…

Even youths shall faint and be weary,
and young men shall fall exhausted;
but they who wait for the Lord shall renew their strength;
they shall mount up with wings like eagles;
they shall run and not be weary;
they shall walk and not faint.
(Isaiah 40:30–31)

I know what it is to be exhausted. I have faced that in my life, primarily in my college and Peace Corps years. I am not now exhausted. I am tired. I am productively busy. I am keeping up with most things, and falling behind on others. I am, in these aspects, leading a normal life, as far as I can tell. I go to church, and I yawn a bit from not sleeping in, but I focus on the sermon and I pray. Except that these meditations have been making me more thoughtful during the day, I may not seriously pray much by myself during the week. I want that strength Isaiah spoke about. How do I get it? By waiting? What does that mean?

In fact, this whole chapter of Isaiah, despite being beloved and well-known, is perplexing in its logic. It begins with comfort and the proclamation that God will even out the ground, making rough places plain, and his glory will be known throughout the earth. Then it talks about how fleeting human life is, no more enduring than the grass of the field. Next, a return to good news: the shepherd of Israel is returning! He is coming with strength and compassion! There follows an extended discussion of how no other god or creature is worth comparing to the Lord, the God who is. And because of that, we are nothing before him. Nothing we do can be hidden from him. He is all-powerful and inscrutable. Yet that means he knows us intimately, and he can and will uplift those who are struggling. This already is good news and a promise: that God saves his people from their struggles; later he will save them from their guilt.

So can we wait for the fulfillment of our hope? That we will know God and his immense power? I guess that big picture can lift us from any dreariness we might find in daily living. I want that promise. I have it. I will wait, and hope, and maybe with that I’ll find my feet moving more lightly in the present. I can tell that I barely even understand the promise, because my faith is so small. I’m glad God is more patient than I am, and that he will continue to pursue me to give me blessings.

Have you not known? Have you not heard?
The Lord is the everlasting God,
the Creator of the ends of the earth.
He does not faint or grow weary;
his understanding is unsearchable.

a wonderful savior

To pick up where I left off last time (and yes, I know I’ll have to catch up a few days sometime; I started this entry on Wednesday, and have been hung up finishing it)… Here’s an excerpt from the second chapter of Philippians, which I linked to last time:

…being found in human form, he humbled himself by becoming obedient to the point of death, even death on a cross. Therefore God has highly exalted him and bestowed on him the name that is above every name…

Jesus’ martyrdom (and resurrection, which I’ll address in a different entry) is qualitatively different from the others I mentioned before. Everything in Jesus’ life was supernatural, in the sense of stretching beyond what what is possible for each of us. I can imagine he had charisma (that’s part of what I think was meant when people said he “spoke with authority”) and compassion (favorite verse for elementary school kids to memorize when required to choose one: “Jesus wept.”), but that he displayed them in ways just enough subtly different that every act was miraculous.

At this point, to further contemplate who Jesus was requires a bit of mysticism. I generally make no secret of the fact that I spent several years, at the end of high school and the beginning of college, holding onto anti-Trinitarian theology. I couldn’t make sense of Jesus being God incarnate—not just from an essential perspective, but from a redemptive perspective. I mean that I wasn’t just confused about how Jesus could be both God and man (that’s a mystery never to be explained), but why Jesus could be a savior if he was something so different from us. In one of Paul’s most meaningful but most perplexing metaphors, he describes Jesus as the “last Adam”, exactly paralleling Adam in that sin entered the world through Adam while the world is saved from sin through Christ. For that to be so, I reasoned, Jesus had to be just like Adam in the beginning—wholly created, without any mark of wrongdoing—so that he could choose the right way on behalf of humanity and lead us back to God. (Which reasoning, at the time, obliged me to believe in an historical Adam.) Jesus was still to be exalted as our eternal ruler (good, just, and able to perfectly instruct and uplift us) and our intermediary with God (only the righteous can be in God’s presence and live). But it made no sense for him to be God, as well. (The time when I began to turn from a strong anti-Trinitarian position was when my dad explained to me that Trinitarianism isn’t an answer to the question of God’s nature—it’s simply a statement of that question.)

That position doesn’t really stand up to other parts of the Bible, however. The opening of John’s gospel and the opening of the letter to the Hebrews, among other places, acknowledge that God (the Father) made the world through Christ. I have no idea what that means, but it at least means Jesus is eternal. And Isaiah prophesied that his suffering and death would in fact take the place of our punishment; he humbled himself, then was humiliated.

So much more to say, but it’s gotten late once again and I’ve taken too many days off. So I’ll pick up some of these threads later.

skaters and flying saucers

This one isn’t about Lent; it’s about math. I’m going to describe some excellent examples that came up in Thurston’s seminar this morning. To do so, I’m going to have to assume some pretty sophisticated manifold theory, so this isn’t really a “general interest” post. For those who have some knowledge of manifolds, however, these examples may prove enlightening.

We were talking about different kinds of admissible structures on a manifold $M$—specifically, what kinds of local homeomorphisms can be used to define structures. The last two we discussed were symplectic and contact structures. The former is fairly well-known: you have a non-degenerate, closed 2-form on $M$ that lets you do things like Hamiltonian mechanics. Thurston’s examples of symplectic transformations were flinging a chair around (position + momentum of an object gives a manifold, called the phase space of the object, with a canonical symplectic form) and light passing through lenses (presumably also a phase space-type manifold, but my grasp of Hamiltonian mechanics is relatively weak, having been acquired almost entirely in symplectic geometry classes).

Contact manifolds are less well-known. They’re often brought up to illustrate a “sister” geometry to symplectic geometry: symplectic manifolds are always even-dimensional, while contact manifolds are always odd-dimensional. Here’s the definition: a contact manifold $M$ has a non-degenerate 1-form $a$ whose exterior derivative $da$ is non-degenerate on the kernel of $a$ in each tangent space to $M$. Okay, flung that all out there at once. Here’s the geometry: since a 1-form restricts to a linear functional on each tangent space, its kernel (if it is non-degenerate) is a codimension 1 subspace of the tangent space—i.e., a hyperplane. So a contact manifold has a special collection of “tangent hyperplanes”, and the condition on $da$ tells in what way this field of hyperplanes is special. Here I’m not really interested in the technical reasons this definition is chosen. I just want to give the examples Thurston described.

The first was of an ice skater. On a skating rink, one has both position and direction: that gives a three-dimension manifold $M$, which can be thought of as (rink)x(circle of directions), or can be unfolded into $R^3$ if, as Thurston put it, you keep track of the winding number of the skater. However, at a given position and direction, you can’t move arbitrarily in $M$; the skate can move forward and backward in the direction it’s facing, or it can change direction. So you have a hyperplane $H_x$—i.e., a plane—in the tangent space to $M$ at $x$, which describes these possibilities of movement: one direction in $H$ points in the direction you’re currently facing, and one points in the “direction of changing direction”. This is a contact manifold. Skating a path around the ice rink means tracing a curve in the contact manifold that always remains tangent to the hyperplanes.

The second example shows how the first might be generalized. Suppose you have a jet, or a flying saucer, which can be at any point in $R^3$ and can take any orientation at any point, but can only move to a different point in a direction of the plane of its current orientation. The position-orientation manifold is a product of $R^3$ and $RP^2$ (the real projective plane)—or $S^2$ if you keep track of which way is “up” for the flying saucer—and hence 5-dimensional. The contact structure at a particular pair (position,orientation) is the product of the plane in $R^3$ corresponding to the current orientation and the tangent space to $RP^2$/$S^2$, which corresponds to the fact that you can roll either up-and-down or side-to-side.

Thurston went on to remark that many physical systems with some sort of dynamical possibilities can be described by contact structures, and the dynamics of the system are represented by diffeomorphisms that preserve the contact structure. I know more can be found in his book Three-Dimensional Geometry and Topology. I’m going to have to go look that book up soon.