Archive for March, 2007
The Beginnings of Western Science
The European Scientific Tradition in Philosophical, Religious, and Institutional Context: 600 BC to 1450 AD
David C. Lindberg (Chicago University Press, 1992)
473 pp. First reading.
As the title indicates, this book is a survey of the western scientific tradition from its origins until the early Renaissance, focusing on the disciplines of astronomy, mechanics, optics, and medicine. At each stage in the narrative, Lindberg’s intention is to put the scientific questions and practices into context, helping the reader to see why they asked the questions they did, and why they came to the conclusions they did.
The entire western scientific tradition is rooted in the Greek achievement. The Greeks themselves borrowed from the ancient Egyptians and Babylonians, but they greatly improved and expanded on those early foundations. They did fine work in astronomy, optics, and medicine, and founded a number of schools of natural philosophy.
When the Romans conquered the Greeks, they had the good sense to recognize the quality of their vanquished foes and absorbed into their own culture many of the Greek ideas. With the passing of time, however, there were few original Roman contributions to speculative science or natural philosophy, and gradually Roman discourse on science was reduced to a popular level, most of it read in Latin translations and popularizations. Knowledge of Greek was slowly eroded, and by the time of the Empire’s collapse there were few who could read Greek, and fewer still who understood the ancient Greek scientific texts. In a word, the Romans dropped the ball, and bequeathed to the early Middle Ages only a rudimentary scientific literature.
The Greek texts were not entirely lost, of course. Nestorian Christians, driven to the east, took many Greek books with them. They were conquered by the Islamic armies in the seventh century, and in the course of time the books were translated into Arabic. Greek natural philosophy seems to have made relatively little impact on Muslim thought, but Muslim scholars made a number of notable contributions to scientific knowledge. For instance, they invented the astrolabe for making precise astronomical measurements, developed the mathematics of trigonometry, and produced an impressive – and substantially correct – theory of vision.
In the twelfth century the slow Christian reconquest of Spain brought Western scholars into contact with their Islamic counterparts. The newly founded universities of Europe were hungry for new material, and a vigorous translation effort began. Year by year, European schools were flooded with new Latin translations of the ancient Greek texts, and they were taken up eagerly.
This story is, of course, well known (and I have written about it in more detail elsewhere). To some extent, that familiarity made this book a disappointment for me. I had been hoping for a detailed, technical discussion of the history of scientific ideas, and for the most part this book did not provide it.
On the other hand, a major merit of the book is the unwillingness of the author to sneer at the efforts of early natural philosophers. He sees, quite rightly, that if one views the problems they faced using the conceptual framework they possessed, they came consistently to reasonable conclusions. He is appreciative, for instance, of the work of the medieval alchemists, for he sees that their technical and procedural innovations stood ready to serve early modern chemistry when the theory of matter ripened. He is also alert to the fact that scientific breakthroughs often came from directions which surprise modern sensibilities. Most of pre-modern astronomy, for instance, was driven by astrological interests or religious (in the sense of calendrical) concerns.
One of my favourite instances of this unexpected cross-pollination concerns the origins of kinematic theory. In the twelfth century Peter Lombard wrote his famous Sentences, an enormous commentary on Scripture compiled from the writings of St. Augustine and other Church Fathers. The Sentences was structured as a series of ‘questions’, each of which addressed a particular point of doctrine or matter of dispute. The Sentences became a popular theology textbook at the medieval universities, and advanced students were required to write their own enormous commentary on it. Importantly, these commentaries tended to retain the division of the subject matter into ‘questions’, such that a scholar with an interest in a particular question could easily locate the pertinent section in each commentary. One of Lombard’s questions concerned the manner in which divine grace was increased in the soul; some held that the soul participates in grace without actually possessing or receiving the grace into itself, and that the degree of participation may wax or wane, which process we understand as increasing or decreasing grace ‘in’ the soul; others held that the soul could possess or receive into itself grace in greater or lesser quantity. As the commentaries on this question piled up, a quantitative theory of change was produced: rates of increase and decrease, for instance. All of this was in the context of what in Aristotelian natural philosophy was called motion of quality, grace being a quality of the soul that possesses it. But motion of quality was but one kind of motion enumerated in Aristotle’s Physics; another was motion of place. It was therefore a natural transition – natural to an Aristotelian physicist, that is – to apply a theory of change developed in a theological context to the motion of physical bodies. This is exactly what was done, at Oxford University, and from those efforts emerged the first definitions of velocity, instantaneous velocity, uniform and non-uniform motion, and even the mean speed theorem – all of which are basic to modern kinematic theory.
Lindberg’s discussion of early kinematics is one of the best sections of the book, since he does go into considerable detail. Two natural philosophers were especially important in developing the conceptual framework upon which the subject was built. John Buridan (c.1295-c.1358) was a priest, a student of William of Ockham, who worked at the University of Paris. In his efforts to understand the motion of bodies he developed the concept of impetus, obtained by combining the velocity of an object with its ‘quantity of matter’ (they had not yet arrived at the concept of mass). This concept of impetus bears a striking quantitative resemblance to our modern concept of momentum, yet it was conceptually quite different; impetus was conceived as being a property that causes motion, not just a quantity that describes it. Nevertheless Buridan’s ideas about impetus were a step toward the concept of inertia. He also voiced important clarifications about relative and absolute motion, and pointed out that astronomical models would be more economical if the earth, rather than the sphere of the fixed stars, rotated once per day. He argued, correctly, that the two scenarios would be observationally indistinguishable, but also concluded, incorrectly, that a rotating earth was impossible on the grounds that objects thrown directly upward would not fall at the same location. (This because he lacked the concept of inertia.)
Buridan’s general line of thought was taken up by a second fascinating figure, Nicole Oresme (c.1323-1382), also at the University of Paris. Oresme corrected Buridan’s error about falling bodies on a rotating earth, and did so using the analogy of a moving ship, very much as Galileo would do several hundred years later (and as physics classes do today). He also argued that Scriptural passages which seem to imply that the earth does not rotate could be understood as an instance of accommodation to our conventional manner of speaking of things. In fact, he refuted all of the objections to the idea that the earth rotates. Curiously, he nevertheless rejected the conclusion, interpreting the question as an illustration of the unreliability of natural reason (in the sense that it can seem to make plausible things which are false). He also took up the kinematic work of the Oxford philosophers, and developed a geometric method of representing kinematic quantities that bears a close resemblance to graph techniques. He showed, for instance, that the area under a velocity-time diagram is the distance travelled. Using his techniques, he was able to produce several geometric proofs, including one of the mean-speed theorem. Many of Oresme’s ideas seem very similar to those with which Galileo began his Discourse on Two New Sciences, and I am very curious to know whether Galileo was familiar with Oresme’s work.
Since I had never heard of either Buridan or Oresme before, it would certainly be too much to claim that I didn’t learn anything new from this book. There was also new material about early theories of vision, and of medical theory and practice, for instance, that I found fascinating, but most of this came in the final few chapters of the book. The earlier sections, which cover much the same ground as other histories of Western thought, were less rewarding for me. The book is very well written, with many explanatory diagrams, and, for someone new to the subject, would make an excellent introduction.
This coming weekend I will be flying to Amsterdam. The primary occasion is to attend a conference, but I planned my flights such that I would have several days of holiday in advance of those duties. As I have been reading about the city, however, my enthusiasm has been waning. I am told that it is a great city, and to some extent I can see it, but I haven’t been able to quite shake the thought of the city as one large drugged-up prostitute, and the prospect of spending eight nights there has been losing its lustre.
And so I have decided not to take my holiday there at all. I will fly to Amsterdam, and shortly thereafter take another flight to la bella paesa, to the Eternal City itself, Rome. A few days there will do my heart good, and I’ll return to Amsterdam in time for the conference. Even with this itinerary I will have two evenings and one full day free to take in the sordid spectacle, which methinks will be sufficient.
Ah, Roma, a city of marvels. This will be my third visit, and I am already beginning to compile a long mental list of things to see and do. I’ll want to revisit some favourite spots, of course: San Clemente, Santa Sabina, Santa Maria sopra minerva, Santa Maria in Trastevere. Needless to say I will be making my way to the Vatican a few times, and I hope to both visit the tomb of the late pontiff and catch a glimpse of our new one. There are a number of sites, too, that I have missed on my previous visits: San Paolo fuori le mura, Sant’Agnese fuori le mura, Santo Stefano Rotondo, the catacombs of St. Sebastian, the Villa Borghese. The riches of Rome are inexhaustible. This entire visit has about it the character of a gift, for just two days ago it was not even in my thoughts, and today it is a reality. I want to receive it as such and, mindful of the approach of Holy Week, let it be an occasion for thanksgiving.
If you would like to leave a comment with a tip or suggestion as to how best to pass my time, please do so. Now if I could only find those guidebooks…
Over the past few weeks I’ve encountered an unusually high number of good online lectures and radio shows.
News from Lake Wobegon. Garrison Keillor’s weekly tale about the goings-on in his hometown, out there on the edge of the prairie, is now available as a podcast from A Prairie Home Companion. I used to listen regularly to Keillor’s show, but for some reason in the past few years I’ve stopped doing so. These stories have renewed my appreciation for him and his remarkable town, where “all the women are strong, all the men are good-looking, and all of the children are above average”.
Anglo-Saxon Aloud. Michael D.C. Drout, a professor of English at Wheaton College, has launched an ambitious project to read the entire Anglo-Saxon Poetic Records, and make the readings available online. He is starting with the so-called Codex Junius, and is currently reading the Book of Genesis. The project should eventually take him into the world of Anglo-Saxon poetry, including Beowulf. It’s not very easy, of course, to understand what he is saying, but I expect that some of my friends will take an interest anyway.
A set of lectures on Dante’s Divine Comedy by Anthony Esolen are now available online. I read Esolen’s own translation of Dante last year, and he is an excellent guide. (I wrote some thoughts about the books at the time: I, II, III.) UPDATE: the source for the files seems to have disappeared. I will try to find another.
Robert P. George, professor of jurisprudence at Princeton University, delivered a set of lectures at Southern Baptist Theological Seminary on a variety of contentious social issues. George is an articulate man, and his thoughts on these matters are well worth hearing.
Finally, a couple of archived broadcasts from the CBC. Michael Enright recently interviewed Fr. Richard John Neuhaus for The Sunday Edition. From one side the interview is fairly tiresome: Enright seems unable to do much more than recite the standard canon of criticism that exercises the liberal left – Magisterial authority, women’s ordination, priestly celibacy – but Neuhaus’ handling of it is a model for the rest of us: patient, articulate, and winsome. An older broadcast from the same program has Enright interviewing British philosopher Roger Scruton. Not only does Scruton have interesting, and thoughtful, things to say, but he has that English way of saying it. My favourite exchange? Enright: “Don’t you think that the fox hunt is cruel?” Scruton: “If the fox is caught by the hounds it is killed quickly, certainly much more quickly than your doctor will kill you.”
The Riemann Hypothesis
The Greatest Unsolved Problem in Mathematics
Karl Sabbagh (Farrar Strauss Giroux, 2003)
342 pp. First reading.
Posted 11 March 2007.
It has now been more than 150 years since Bernhard Riemann, the great German geometer and analyst, set forth his famous hypothesis, and efforts to prove (or disprove) it have occupied many of the finest mathematical minds of each succeeding generation. The hypothesis is tantalizing for many reasons, but perhaps chief among them is that, if true, it would yield deep insight into the nature of prime numbers. More precisely, the zeros of the complex-valued Riemann zeta function could, if known, be used to calculate the distribution of the prime numbers along the number line. The Riemann hypothesis states that the zeros of this function can all be written in the form . That is, they all lie on the so-called critical line defined by .
A proof of this seemingly simple statement has turned out to be perniciously difficult to produce, and Sabbagh’s book is partly an account of the history of attempts to do so, and partly an introduction to contemporary mathematicians whose work circles around the problem. In this sense it is an interesting view into what motivates mathematicians, and Sabbagh has some intriguing things to say about the art of mathematical thinking. He also makes clear that though the Hypothesis itself has resisted all efforts at proof, the attempted proofs (and there have been many) have greatly enriched mathematics in the meantime. Connections to the Riemann hypothesis have been found in number theory, of course, but also in operator analysis, geometry, and even quantum theory.
Sabbagh is himself a non-mathematician, and while this might make him just the man to explain the topic to non-mathematical readers, it does make the book a little odd for someone with a decent mathematics education. He wanders among the mathematicians like a stunned explorer among the natives, marvelling at their strange thoughts, their impenetrable language, and their peculiar sense of humour. This tone of astonishment adds considerable charm to the narrative, but it also means that when the subject matter becomes technical the writing begins to grasp at analogies and metaphors, and one struggles to ascertain what he’s really trying to say.
I was able, however, to glean a few hard technical facts. I learned, for instance, that the first ten trillion zeros of the Riemann zeta function have been checked by computer and they all lie on the critical line. This might be enough to convince one that the Riemann hypothesis is true, but cases have been known in the past where even such apparently uniform behaviour has been shown to change when pushed further. And besides, that kind of empirical verification doesn’t satisfy a truly mathematical mind. More formal methods have been able to establish a number of interesting results. For instance, all of the zeros of the Riemann zeta function are known to lie in the critical strip , and it has been proven that at least forty percent of the zeros fall on the critical line. Furthermore, if there is a zero away from the critical line it will be paired with a second, the two arranged symmetrically around the critical line. All of which is very interesting.
[A mathematician speaks]
Someone who had begun to read geometry with Euclid, when he had learned the first proposition, asked Euclid, “But what shall I get by learning these things?” whereupon Euclid called his slave and said, “Give him three-pence, since he must make gain out of what he learns.”
The season of Lent has a distinctive character: solemn, austere, and quiet. It is a season not merely of waiting, but of inward preparation. This preparation has devotional and intellectual aspects, of course, but I find that I enter most fully into the Lenten spirit when I also cultivate the aesthetic qualities of the season. Since I am a music lover, this means locking up the operas and the flashy or opulent recordings and taking instead a steady diet of quieter, simpler fare. In this post, I thought I would share some of the special pieces which I have taken as my companions for these forty desert days.
Arvo Part: Sarah was Ninety Years Old. Someone, I forget who, once observed that many barrels of ink had been spilled to write about musical compositions, but wondered why so little music had been written to comment on texts. In part this is no doubt because music cannot usually convey meaning with any great precision. The most that music can hope to do is penetrate the spirit of a text and give it musical expression. Even this is difficult to do well; Arvo Part’s Sarah was Ninety Years Old is perhaps the most successful such effort that I know. It is a commentary, of course, on the story of Abraham and Sarah as found in Genesis. With a minimum of means – a drum and un-texted voices – Part nevertheless manages to create a moving meditation on fortitude, faith, and glory. To my knowledge, this piece has been recorded just once, but the performance is so good that we hardly need another. Arvo Part: Miserere: The Hilliard Ensemble (ECM New Series).
J.S. Bach: Suites for Solo Cello. These are not explicitly religious works, of course, but that hardly matters. The music, pervaded throughout by the warm austerity of the solo instrument, is a rare marriage of beauty and solemnity. My favourite recording of the works is a marvel: the cellist is somehow able to find and hold the fine point at which the music dances easily without ever losing its inward concentration. Bach: Suites for Solo Cello: Pieter Wispelwey (Channel Classics).
Alfred Schnittke: Psalms of Repentance. Schnittke believed that in the process of creation, a composer “should be a medium or a sensor” who interprets and translates into music something that is of divine origin. This mystical turn of mind led him, a Russian Jew by birth, to convert to Catholicism in his early 50s. Late in life, Schnittke suffered a number of debilitating strokes, and was even declared clinically dead on more than one occasion. Nevertheless, some of his best music dates from these last years, including the Psalms of Repentance, which was finished in 1988. This is a large-scale work for unaccompanied choir, in 12 sections. The texts are not actually psalms; rather, Schnittke chose to set a selection of penitential writings of Russian desert monks. ‘O my soul, why art thou unafraid of the dead in their graves…’. This music is dissonant and turbulent, but serves the intentions of the texts admirably. Alfred Schnittke: Psalms of Repentance: Swedish Radio Choir; Kaljuste (ECM New Series).
George Frederic Handel: Messiah. Many people are unaware that Messiah was written for Lent, not Christmas. In England at the time the opera houses were required to close their doors during Lent, and, in a fine example of observing the letter but not the spirit of the law, concert halls scheduled oratorios instead; Messiah was written for just such an occasion. If I find, therefore, that the austerities of Lent are becoming too much for me, I feel I can justly turn to this joyful work for refreshment. Handel: Messiah: Monteverdi Choir; John Eliot Gardiner (Philips).
If you have music that you particularly associate with Lent, let me know in the comments.
You know the classics already: Sad Eyed Lady of the Lowlands, Visions of Johanna, Desolation Row, and It’s Alright, Ma (I’m Only Bleeding). Now, it seems, we can add the immortal epic The Cat in the Hat to that illustrious company.
It’s unclear whether this is meant as a parody or an homage. It is certainly one of the oddest projects I’ve yet encountered, and, in a strange sort of way, it is somehow fitting. Judge for yourself.
Thomas Wharton (NeWest Press, 1995)
275 pp. First reading.
Posted 5 March 2007.
Icefields was Thomas Wharton’s first novel, and when it appeared a decade ago it caught the attention of the Canadian literary establishment. The young Alberta writer was honoured with an armful of awards, though I confess that at the time the book passed beneath (or above?) my radar. I’m glad to have now caught up with it.
It begins matter-of-factly enough. “At a quarter past three in the afternoon, on August 17, 1898, Doctor Edward Byrne slipped on the ice of Arcturus glacier in the Canadian Rockies and slid into a crevasse.” Byrne was quickly rescued, but not before he saw, or dreamed that he saw, the mighty form of an angel encased deep in the ice, wings outstretched. Byrne tells no one of his vision, but it becomes the seed out of which the rest of the story grows, the tether that keeps Byrne tied to the glacier for the rest of his life.
It is a splendid premise for a novel. Curiously, Wharton chooses not to pursue the angelic theme very assiduously. One might think that such an experience could flower into a religious ardour, or at least a spiritual quest; one might expect to find Byrne huddled by candlelight over the calm expositions of the Angelic Doctor; one might hope to find him taking a stone for his pillow in imitation of those favoured with angelic visions in the past; one might fear to find him perched feverishly over Milton’s account of the terrible fall of Lucifer, or of Dante’s ice-encased Accuser. But no — Byrne never develops any specifically angelic interests. The angel serves only as an anchor, a hazy initial vision of power and glorious mystery that casts a shadowy wing over a human life. I suppose that considered simply as such, it serves the role admirably well.
Byrne is a lonely soul, cold and distant. Near the glacier’s terminus the village of Jasper – a name derived from J’espere, says one of the characters – is taking shape, but he remains inwardly detached from that activity. His focus becomes the glacier itself. By the novel’s end he is living alone in a small hut on the ice, tracing the slow progress of the glacier as it flows down the mountain, calculating the position of the buried form he had seen so many years before, hoping perhaps to see it spill out onto the rocks one day.
Like the setting itself, Wharton’s prose is crisp and cool. The story is told quietly, with a minimum of fuss. There is a consistent simplicity in his sentence structures that lends a welcome clarity to the writing. Sometimes the simplicity threatens to overwhelm the sense, and the writing lapses into sentence fragments. Needing no subject. He also chooses to write significant portions of the book in the present tense, which I find affected and distracting. Occasionally he relies on that Timothy-Findlian convention of expressing the character’s inner thoughts in italics. These are all irritating practices that I seem to encounter only in Canadian literature, and I am wishing they would go away. Far.
The emotional coolness of the protagonist and the prose produces a certain muted tone in the drama. There is a dreamy quality that permeates the entire story. If it were a film, I have the feeling that it would be shot in soft focus, and that the camera would be constantly panning across scenes, never resting on any one feature long enough for it to become clearly delineated. This isn’t necessarily a problem, but it does risk sacrificing the reader’s emotional engagement with the characters. In my case I confess that I had trouble staying aboard. Happily, Wharton finds a delightful way to wrap the story up on the last page, bringing things to a close in a very satisfying way.
“Do not be conformed to this world but be transformed by the renewal of your mind, that you may prove what is the will of God, what is good and acceptable and perfect.”
- Romans 12:2
“…if he nevertheless is unwilling to be like an instrument of war in the service of inexplicable drives, indeed, in the service of the world, because the world itself, the object of his craving, stimulates the drives; if he nevertheless does not want to be like a stringed instrument in the hands of inexplicable moods or, rather, in the hands of the world, because the movement of his soul is in accord with the way the world plucks its strings; if he does not want to be like a mirror in which he intercepts the world or, rather, the world reflects itself; if he does not want this, if he himself, even before the eye aims at something to make a conquest, wants to capture the eye so that it may belong to him and not he to the eye; if he grasps the hand before it grasps for the external, so that it may belong to him and not he to the hand; if he wants this so earnestly that he is not afraid of tearing out the eye, cutting off the hand, shutting the window of the senses if necessary – well, then everything is changed; the power is taken away… He struggles not with the world but with himself.”
- Søren Kierkegaard, “Four Upbuilding Discourses”