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Chapter One: Happy Thoughts on a Sunny Day in New York City
Gallileo described the universe in his most famous line: "This grand book is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures." Why should the laws of nature be subject to statement in such elegantly basic algebra? Why does gravity work by the principle of inverse squares? Why do simple geometrics pervade nature--from the hexagons of the honeycomb, to the complex architecture of crystals? D'Arcy Thompson, author of Growth and Form and my earliest intellectual hero (along with my father and Charles Darwin), wrote that "the harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of math ematical beauty." Many scientists, if only to coin a striking metaphor, depict a creating God as a mathematician from the realm of Plato or Pythagoras. The physicist James Jeans wrote: "From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician."
But much of nature is messy and multifarious, markedly resistant to simple mathematical expression (at least before fractals gave us a way to formulate the complexities of a mountaintop, a coastline, or a leaf). And other scientists have developed equally striking metaphors about a creator who revels in the unquantifiable details--as in J. B. S. Haldane's famous quip (see essay 29) that God must have an inordinate fondness for beetles.
We have, in many respects, been oversold on the mathematical precision of nature. Even the preeminent field for abstract, quantified beauty--a domain whose very name, celestial mechanics, seems to evoke ethereal harmony--includes ever so many awfully messy and downright inconvenient irregularities. Why, for example, couldn't God have arranged some simple and decent proportionality between the earth's axial rotation and solar revolution? Why didn't he give the year a nice even number of days, without elaborate fractions that demand complex seat-of-the-pants corrections in our calendars? Why 365 days and almost (but not quite) an extra quarter?--so that we have to add a leap day every fourth time round, but remove it again every hundred years (because God ordained a little less than an extra quarter after 365), except for every four hundred years when we put it back again. (And thus, if you penetrated that sentence, you will grasp why 2000 will be a leap year, even if, among some purists, it will not mark a millennium--see next essay.
Nature also mocks our attempt to encase her in a Platonic straitjacket by establishing an almost laughably fortuitous reason for some apparent, highly visible regularities that have played a major role in human history. In my favorite example, much discussed by many commentators, solar and lunar eclipses produce a gorgeously precise and tight fit (as the moon's shadow snugly covers the sun and vice versa). Must not such exactitude be explicitly arranged, or at least arise as a predictable consequence from one of those mathematically elegant laws of nature? But the effect is only a happenstance of history. The sun's diameter is about four hundred times larger than the moon's. But the sun is also about four hundred times more distant--so their discs appear the same size to an observer on earth. (Now consider how much of human mythology rests upon an image of two guardians, intimately related by their common size: "And God made two great lights: the greater light to rule the day, and the lesser light to rule the night.")
When nature so mocks us, she often comes clean every once in a while, as if to offer confession for such a sublime joke. On May 10, 1994, a rare form of solar eclipse, far less spectacular than the conventional lid of darkness, but immensely fascinating for its own more subtle strangeness, enveloped much of North America. The moon's distance from the earth varies quite a bit during its revolution (planetary orbits are also not so regular as the charts in our high-school textbooks implied). If a solar eclipse occurs when the moon lies at maximal distance from the earth, then the lunar shadow does not fully cover the sun's disc. At totality, therefore, a ring of bright light remains at the sun's periphery. Such eclipses are called annular, from a Latin word for "ring." (Annular eclipses are much less spectacular than total eclipses at normal lunar distances, for a ring of bright sunshine still yields substantial light--as much or more than on an ordinary cloudy day--while the sky turns off as if God threw a light switch when the moon's larger disc fully covers the sun.
I was angry with myself on May 10. The eclipse was eighty-eight percent complete at my Boston home, while totality beckoned only an hour or two north from Concord, New Hampshire, and many other pleasant sites throughout New England. The next annular eclipse in New England will occur on July 23, 2093, long past my watch--so May 10 or never (at least without substantial travel) for me. I ordered all my students to drive into the region of totality on pain of instant expulsion. (Professors--enjoying these odd moments of surcease from Shaw's observation that those who can, do; while those who can't, teach--really do revel in such application of limited power. I so ordered, and not a one of them went-to their eternal shame, but otherwise without consequence.) Meanwhile, duty-bound to honor a commitment made before I heard about the eclipse, I went south to New York City, toward less solar coverage by an already compromised lunar shadow.
Many things keep us going in this vale of tears--a baby's smile, Bach's B-minor Mass, a decent bagel. Every once in a while, as if to grant us the courage to go on, the powers that be turn one of life's little disasters into a bit of joy or an episode of instruction. The Lord of the (Partial) Ring must have been smiling on me this May 10, for he brought me in a sour mood to my natal city of New York and then rewarded me with a better experience than totality in Concord could ever have provided.
I love pristine nature, but I am a humanist at heart, and I revel more in complex interactions between fellow members of Homo sapiens and the great external world. Now think of every stereotype you hold about New Yorkers. (They are untrue, of course, but culturally powerful as a recognized type or icon nonetheless.) New Yorkers are harried, selfcentered, cynical, rushed, acquisitive, uncurious, uncommunicative, and downright nasty to all humans who cannot be wheedled or manipulated for material gain. Right? Of course, as all Americans know, even those who have never been east of the Mississippi! A solar eclipse must therefore rank as the last thing that could ever intrigue a real New Yorker. I mean, gimme a break mister. You want me to stop what I'm doing and look into the sky--at a partial and annular eclipse? Get lost--and screw in your own light bulb.
Yet, as Joshua once stopped the sun over Gibeon, New York City returned the compliment on May 10. In midtown Manhattan, in the middle of a busy working day, New York stopped to watch the sun. Let me not exaggerate. Many folks just went on about their business, as the human tide of midday swept down Seventh Avenue. But large knots of eclipse watchers also stood their ground on every street. What features in this less spectacular version of the general phenomenon--partial and annular, rather than total and completely covered--could have inspired the interest of New Yorkers? Consider two aspects of this remarkable event.
First, in this age of artificially induced full-body shake-me-ups, from rollercoasters to all the electronic powers of film, video games, and amplified sound, we hardly think that anything so subtle, albeit pervasive, as the character of surrounding sunlight could move our passions, or even invite our notice (but then the Impressionist painters did have some insights about the power of light's quality). It does not get very dark when the sun is occluded by eighty percent on a bright day; an ordinary cloud cover reduces visibility by more than this. Thus, the sky did not darken precipitously over New York on May 10. But we are exquisitely sensitive to the usual character of light, even though we may not explicitly credit our awareness, and may not be able even to state what feels so odd.
It did not, I repeat, get very dark over New York, but the cloudless sky implied brightness, and the day turned eerily somber, while sunlight continued to reign--and people noticed, and trembled ever so slightly. "Moses and the children of Israel" sang a song to God to praise the stunning power of altered celestial events (Exodus, chapter 15): "The people shall hear and be afraid . . . the dukes of Edom shall be amazed; the mighty men of Moab, trembling shall take hold upon them . . . they shall be as still as a stone." And so New York, mightier by far and incomparably more sophisticated than these old kingdoms of the Middle East, noticed and stood still as a sky full of daylight darkened to the level of a clearly nonexistent thunderstorm. A woman said to her friend, "Holy shit, either the world is about to end, or it's going to rain--and it sure as hell ain't gonna rain."
Second, the sight of a crescent sun is so unusual, so outside our daily experience, that people do pause to notice, and wonder. If the first phenomenon, eerie (if slight) darkness, impelled a kind of visceral attention, the crescent sun, by contrast, provoked a more intellectual response.
At every eclipse, official purveyors of the news deluge us with warnings about grave dangers to our sight should we stare at the eclipsing sun. Don't look up, even for a moment. The sun will burn a painless hole in your retina faster than masturbating boys went blind in the bad old days of dire warnings. I do understand why such exaggerations must be presented. Staring at the sun for minutes on end is a very bad idea and can have all the consequences stated in eclipse warnings--so news sources must say, "Don't look at all," in order to impart sufficient fear for preventing these longer starings. So strident are these warnings that many people actually come to believe in a special power of eclipse light to do such harm. But one can, of course, stare directly at the sun for a moment without danger on all days, both regular and eclipsed. After all, we do glance inadvertently into the sun's disc every once in a while, and we do not go blind.
But most people, and quite rightly, did not look directly at the sun, and took official advice for observation by a clever set of devices for filtering or projecting images. And I became grateful for this panoply of strategies during my humanistic "field trip" for science through the streets of New York, for the viewing devices provoke discussion and encourage sharing, thus helping to forge the eclipse community.
Some people look up through filters. A young man had prepared several strips of overdeveloped film, and he passed them around, a double layer for each observer (as the newspapers had advised), to all interested parties. A welder on 53rd Street spent his work break sharing his goggles with the gathering crowd.
Others took advantage of a wonderful phenomenon in optics, using the principle that almost any small hole or space will act as a pinhole camera to project the image of the crescent sun. Here New York City even holds an advantage over the country--for an image projects badly upon rumpled ground, but ever so well against a smooth white sidewalk. New York is such a wondrous mixture of colors, classes, dress, and activity (I have seen many cities more beautiful and more exotic, but none more diverse). But we so rarely come together, for what can transcend our differences and forge common concern? And what answer to this query could be more elegant or literal than the pervasive sun itself?
On 58th Street, a West Indian janitor in his work clothes stood in front of an apartment building, where a ripped awning contained several small holes, each projecting a beautiful image of the crescent sun upon the sidewalk. The janitor, acting the part of a carnival barker, gathered in the passersby under his awning to see the grand sight, gratis of course. At the next building, like the proprietor of the adjacent stall at the same carnival, an Asian man pierced holes in envelopes, sheets of paper, and manila folders, showing people how to project the sun's image upon the ground--again for free and for the sheer pleasure of sharing.
People gathered on every street to show off their newly discovered devices for projecting images. Trees attracted the greatest crowds, for the spaces between leaves act as little cameras, and hundreds of dancing crescent suns appeared on the sidewalk amid the shadows of branches and leaves. One woman, elegantly dressed and dangling a cigarette from her lips, held up her hand into the path of sunlight at the eclipse's acme, and a crescent image appeared at the bottom of the space between each pair of adjacent fingers. She squealed with delight, and the people around her cheered. A boy then took off his adjustable baseball cap, unsnapped the connecting band, and projected a sun through each tiny hole of the band. And again, the people cheered.
I have watched eclipses with relish for all my conscious life. Like all devotees, I have my favorite stories and main events. I remember my best lunar eclipse, seen when I was a teenager from the twenty-fifth floor of a friend's apartment, high over Manhattan. The fully covered moon often turns dark, but may also glow with a variety of colors. On this night the entire disc of the eclipsed moon turned red, a deep, dark red that I had never seen in the heavens, or perhaps even on earth. And I understood that two verses from "The Saints" are descriptions of solar and lunar eclipses, not abstract scare stories of eschatology (I played washtub bass in a folk group at the time, and we often performed this song): "When the sun refuse to shine . . . when the moon turns red with blood; oh Lord, I want to be in that number, when the saints go marching in"--a description, after all, of the Last Judgment, when eclipses will accompany the panoply of awful events. Did not the prophet Joel (2:31) also speak as an astronomer in citing the same image for the same purpose "The sun shall be turned into darkness, and the moon into blood, before the great and the terrible day of the Lord come."
And I remember, for how can one blessed with an opportunity to witness this most spectacular of all celestial events ever forget, the total solar eclipse of early 1970. Our department rented a fishing boat to sail off Nantucket, the only bit of New England real estate privileged with a view of totality. I longed to see the moon's shadow fully cover the sun; I thrilled at a chance to observe the sun's corona. But I had not understood the most awesome phenomenon of all. We live in a natural world of shadings. Even catastrophes have foreshadowings; clouds precede thunderstorms, and tornadoes can be seen in the distance. But when the sun enters total eclipse, the sky turns off as if a celestial janitor threw a switch. For the sun is powerful, and a fraction of one percent of sunlight is daytime, while totality is nighttime--and the transition is a moment, a twinkling of an eye. The sky turned off, and my infant son cried in my arms.
We hear so many dire warnings about the poor quality of science teaching in our schools, so many lamentations over the profound ignorance of most Americans about nearly any phenomenon of the natural world. Perhaps these jeremiads have validity; half of my own students could not explain to me why our planet has seasons. Surely we should be struggling to increase literacy in science, for no issue of education could be more important.
But I am convinced that the problem does not arise from lack of interest. Such a false charge is often made amid the litany of correct accusations mentioned in the last paragraph. Interest is immense, but not always expressed as activity traditionally called science or ranked among its pursuits (and our misattribution therefore arises from our inadequate taxonomies of intellectual enterprise). My colleague Phil Morrison is fond of cataloguing the large number of common activities requiring a good deal of scientific understanding, but not usually so classified: the astronomical knowledge of people who build and maintain telescopes; the deep botanical experience of members in gardening clubs (a fine example of power concentrated in older women); or even the people who frequent racetracks and bet intelligently on horses, for misunderstanding of probabililty, may be the greatest of all general impediments to scientific literacy.
May I now add to this list the aggregate intellectual power (how I wish we could quantify it) of all the dinosaur names accurately memorized (and spelled) by millions of five-year-old kids in America today. And also the accumulated joy and pleasure of millions upon millions of Americans who paused to watch the sun and to wonder on May 10, 1994. New York City was the best place to be on that date; my faith in raw interest is fully affirmed--and raw interest is the substrate and sine qua non of any real reform in education and larger understanding.
We often argue that only misfortune can bring us together. We do help each other during snowstorms; we do open our hearts and our houses to victims of an immediate disaster in our vicinity; we will search all night in the woods for a lost child we do not know. All these observations properly give us hope about common humanity in a world more often characterized by thoughtlessness, self-serving action, and even downright cruelty. But we also suppose that only disaster can provoke this effect, never pleasure, and certainly not intellectual as opposed to purely visceral delight. But interest and curiosity can also bring us together--and my observations of New Yorkers reveling in nature and spontaneously talking about the sun somehow give me more hope than our joint courage in times of crisis can provide, even though unity in disaster may make me cry in sublime appreciation, while the bonding of eclipses only makes me smile.
And so I end this essay by quoting the greatest of all tributes to the sun. I have often stated my personal theory about popular writing in science. I divide this genre into two modes, which I call Galilean, for intellectual essays about nature's puzzles, and Franciscan, for lyrical pieces about nature's beauty. I honor Galileo for writing his two major works as dialogues in Italian, and therefore addressed to all thinking people in his orbit, and not in the formal Latin of churches and universities. And I honor Saint Francis of Assisi for his tributes to nature's loveliness.
I am an unrepentant Galilean. I work in a tradition extending from the master himself, to Thomas Henry Huxley in the last century, down to J. B. S. Haldane and Peter Medawar in our own. I greatly admire Franciscan lyricism, but I don't know how to write in that mode. I began this essay with a quotation from the eponymous hero of my literary bloodline, Galileo himself. But my essay talks about the power of the sun to unify our diverse cultures and concerns, so I must end with a man I have never quoted before in these columns, the eponym of the other style--Saint Francis of Assisi. Saint Francis composed his beautiful "Canticle of Brother Sun" in 1225. He wrote in the Umbrian dialect of his local people, and his poem is often regarded as the first preserved in any modern language:
Brother Sun, who brings the day . . . How beautiful is he, how radiant in all his splendor!
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