Review: Epitome of Copernican Astronomy & Harmonies of the World

Review: Epitome of Copernican Astronomy & Harmonies of the World

Epitome of Copernican Astronomy and Harmonies of the WorldEpitome of Copernican Astronomy and Harmonies of the World by Johannes Kepler

My rating: 3 of 5 stars

The Earth sings MI, FA, MI so that you may infer even from the syllables that in this our domicile MIsery and FAmine obtain.

Thomas Kuhn switched from studying physics to the history of science when, after teaching a course on outdated scientific models, he discovered that his notion of scientific progress was completely mistaken. As I plow through these old classics in my lackadaisical fashion, I am coming to the same conclusion. For I have discovered that the much-maligned Ptolemy produced a monument of observation and mathematical analysis, and that Copernicus’s revolutionary work relied heavily on this older model and was arguably less convincing. Now I discover that Johannes Kepler, one of the heroes of modern science, was also something of a crackpot.

The mythical image of the ideal scientist, patiently observing, cataloguing, calculating—a person solely concerned with the empirical facts—could not be further removed from Kepler. Few people in history had such a fecund and overactive imagination. Every new observation suggested a dozen theories to his feverish mind, not all of them testable. When Galileo published his Siderius Nuncius, for example, announcing the presence of moons orbiting Jupiter, Kepler immediately concluded that there must be life on Jupiter—and, why not, on all the other planets. Kepler even has a claim of being the first science-fiction writer, with his book Somnium, describing how the earth would appear to inhabitants of the moon (though Lucian of Samothrace, writing in the 2nd Century AD, seems to have priority with his fantastical novella, A True Story). This imaginative book, by the way, may have contributed to the accusations that Kepler’s mother was a witch.

In reading Kepler, I was constantly reminded of a remark by Bertrand Russell: “The first effect of emancipation from the Church was not to make men think rationally, but to open their minds to every sort of antique nonsense.” Similarly, the decline in Aristotle’s metaphysics did not prompt Kepler to reject metaphysical thinking altogether, but rather to speculate with wild abandon. But Kepler’s speculations differed from the ancients’ in two important respects: First, even when his theories are not testable, they are mathematical in nature. Gone are the verbal categories of Aristotle; and in comes the modern notion that nature is the manifestation of numerical harmonies. Second, whenever Kepler’s theories are testable, he tested them, and thoroughly. And he had ample data with which to test his speculations, since he was bequeathed the voluminous observations of his former mentor, Tycho Brahe.

At its worst, Kepler’s method resulted in meaningless numerical coincidences that explained nothing. As many a statistician has learned, if you crunch enough numbers and enough variables, you will eventually stumble upon a serendipitous correlation. This aptly describes Kepler’s use of the five Platonic solids to explain planetary orbits; by trying many combinations, Kepler found that he could create an arrangement of these regular solids, nested within one another, that mostly corresponded with the size of the planets’ orbits. But what does this explain? And how does this help calculation? The answer to both of these questions is negative; the solution merely appeals to Kepler’s sense of mathematical elegance, and reinforced his religious conviction that God must have arranged the world harmoniously.

Another famous example of this is Kepler’s notion of the “harmonies of the world.” By playing with the numbers of the perihelion, aphelion, orbital lengths, and so forth, Kepler assigns a melodic range to each of the planets. Mercury, having the most elongated orbit, has the biggest range; while Venus’s orbit, which most approximates a perfect circle, only produces a single note. Jupiter and Saturn are the basses, of course, while Mars is the tenor, Earth and Venus the altos, and Mercury the soprano. He then suggests (though vaguely) that there are beings on the sun, capable of sensing this heavenly music. (The composer Laurie Spiegel created a piece in which she recreates this music; it is not exactly Bach.) Once more, we naturally ask: What would all this speculation on music and harmonies explain? And once more, the answer is nothing.

Kepler’s writing is full of this sort of thing—torturous explorations of ratios, data, figures, which strike the modern mind as ravings rather than reasoning. But the fact remains that Kepler was one of the great scientific geniuses of history. He was writing in a sort of interim period between the fall of Aristotelian science and the rise of Newtonian physics, a time when the mind of Europe was completely untethered to any recognizable paradigm, free to luxuriate in speculation. Most people in such circumstances would produce nothing but nonsense; but Kepler managed to invent astrophysics.

What gives Kepler a claim to this title was his conception of a scientific law (though he did not put it as such). Astronomers from Ptolemy to Copernicus used schemes to predict planetary movements; but there was no one underlying principle which could explain everything. Kepler’s relentless search for numerical coincidences led him to statements that unified observations of all the planets. These are now known as Kepler’s Laws.

The first of these was the seemingly simple but revolutionary insight that planets orbit in ellipses, with the sun at one of the foci. It is commonly said that previous astronomers preferred circles for petty metaphysical reasons, seeing them as perfect. But there were other reasons, too. Most obviously, the mathematics of shapes inscribed in circles was well-understood; this was the basis of trigonometry.

Yet the use of circles to track orbits that, in reality, are not circular, created some problems. Thus in the Ptolemaic system the astronomer used one circle (the eccentric) for the distance, and another, overlapping circle (the equant) for the speed. When these were combined with the epicycles (used to explain retrogression) the resultant orbits, though composed of perfect circles, were anything but circular. Kepler’s use of ellipses obviated the need for all these circles, reducing a complicated machinery into a single shape. It was this innovation that made the Copernican system so much more efficient than the Ptolemaic one. As Owen Gingerich, a Copernican scholar, has said: “What passes today as the ‘Copernican System’ is in detail the Keplerian system.”

Yet the use of ellipses, by itself, would not have been so useful were it not for Kepler’s Second Law: that planets sweep out equal areas in equal times of their orbits. For when a planet is closest to the sun (at perihelion) it is moving its fastest; and when it is furthest (at aphelion) it is slowest; and this creates a constant ratio (which is the result of the conserved angular momentum of each planet). Ironically, of the two, Ptolemy was closer than Copernicus to this insight, since Ptolemy’s much-maligned equant (the imaginary point around which a planet travels at a constant speed) is a close approximation of the Second Law. Even so, I think that Kepler moved far beyond all previous astronomy with these insights, jumping from observed and analyzed regularities to general principles.

Kepler’s Third Law seemed to have excited the astronomer the most, since he even includes the exact date at which he made the realization: “… on the 8th of March in this year One Thousand Six Hundred and Eighteen but unfelicitously submitted to calculation and rejected as false, finally, summoned back on the 15th of May, with a fresh assault undertaken, outfought the darkness of my mind.” This law states that, for every planet, the ratio of the orbital period squared to the orbital size cubed, is constant. (For the orbital size Kepler used half the major axis of the ellipse.)

While it is no doubt striking that this ratio is almost the same for every planet (this is because the planet’s mass is negligible compared with the sun’s), it is difficult to completely sympathize with Kepler’s excitement, since the resultant law is not useful for predicting orbits, and its significance was only explained much later by Newton as a derivable conclusion from his equations. Kepler, being the man he was, used this mathematical constant to fuel his metaphysical speculations.

However much, then, that Kepler’s theories may strike us nowadays as baseless, crackpot theorizing, he must be given a commanding place in the history of science. The reason I cannot rate this collection any higher is that Kepler is extremely tiresome to read. In his more lucid moments, his imaginative energy is charming. But much of the book consists of whole paragraphs of ratio after ratio, shape after shape, number after number, and so it is easy to get lost or bored. Since I have a decent grasp of music theory, I thought I might be able to get something out of his Harmonies of the World, but I found even that section mostly opaque, swirling in obscure and impenetrable reasoning.

The great irony, then, is that Kepler’s writings can strike the modern-day reader as far less “scientific” than Ptolemy’s; but perhaps we should expect such ironies from a man who helped to inaugurate modern science, but who made his living casting horoscopes.

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Review: Howl and Other Poems

Review: Howl and Other Poems

Howl and Other PoemsHowl and Other Poems by Allen Ginsberg

My rating: 3 of 5 stars

When can I go into the supermarket and buy what I need with my good looks?

On my recent trip to San Francisco I was obliged to buy a copy of this book from the City Lights bookstore. Well, that isn’t the whole story. I visited the book store without knowing anything of its history, left with a copy of Galileo’s Sidereus Nuncius, and then shamefacedly returned to pick up this book when my mother informed me, five minutes later, that it is famous for the “Howl” trial. I had heard recordings of Ginsberg reciting “Howl” many times, but I had never actually owned a copy of this poem. Now, thanks to the timely intervention of my mom, I am bona fide hip.

Like so many obscene books of bygone ages, “Howl” seems remarkably tame nowadays, and it is hard to believe any institution would go through the bother of banning and confiscating it. As in so many other cases of censorship, the attempt to suppress the work backfired, helping to turn poem and poet into icons. In our present, enlightened age, we have realized that, when anything can be published, nothing can be shocking or subversive; so oversaturation accomplishes in a stroke what censorship failed to accomplish in generations. But I am getting rather off the track of this book review.

It is difficult to evaluate “Howl,” since everything innovative about it has been thoroughly absorbed into the culture: obscenity, drugs, jazz, eastern mantras, free-form poems that follow the breath, and so on. Ginsberg’s voice is still with us; and you can hear it for yourself if you go to the right college campus—to pick just one example, New Paltz, in upstate New York, has many psychedelic, socially conscious, very enlightened free-form poets. This is not to say that this poem is no longer enjoyable, only that its appeal is more as a fossil than as a revelation now.

But it is a delightful fossil. For with Ginsberg’s “Howl” I hear the first grumblings of a new phenomenon in society: a group of disaffected youths becoming self-aware as a loose movement—as a counter-culture. Now, there have always been disaffected people who have turned to alcohol, drugs, sex, foreign faiths, and in general that peculiar mix of mysticism and hedonism that gives solace to those who feel they do not have a place in their own society. Yet it was not until the Beats, I believe, that this now quintessential experience was turned into art that defined a whole generation. The irony, of course, is that as soon as a counter-culture becomes faddish, its harmless aspects are absorbed into society, and its radical aspects swept to the side, until the revolt loses its teeth.

In both Ginsberg’s “Howl” and Kerouac’s On the Road I see young men, profoundly disenchanted and disconnected with their world, deeply disgusted with the values of their society, but without much to offer in the way of replacement. Instead they wander “starving hysterical naked” across the country, in search of some sort of epiphany that will clarify their predicament—an elusive truth, to be pursued on highways, in bedrooms, and in the altered states of the mind. Yet until they reach this truth, all they have to offer in opposition to “Moloch” is hedonism—which is exactly the same dilemma unsuccessfully faced by Babbitt.

Needless to say I do not find either alternative convincing, but that does not mean I cannot enjoy Ginsberg’s poems. Now, I do think the book format does not do Ginsberg justice, since the lines are organized by his breath and demand to be read, preferably by him. I will always remember laying awake in my bed in high school, listening to Ginsberg reciting “Howl” and “America,” and feeling strange stirrings of literary rebellion that I could not hope to articulate. A literary triumph, perhaps not, but an essential landmark on the country’s and my own maturity.

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Review: The Great Bridge

Review: The Great Bridge

The Great Bridge: The Epic Story of the Building of the Brooklyn BridgeThe Great Bridge: The Epic Story of the Building of the Brooklyn Bridge by David McCullough

My rating: 4 of 5 stars

… on a day when two young men were walking on the moon, a very old woman on Long Island would tell reporters that the public excitement over the feat was not so much compared to what she had seen “on the day they opened the Brooklyn Bridge.”

On the inside cover of my copy of this book its previous owner has inserted a little love note. The brief message is written in a very neat script, in red ink, apparently on the eve of a long separation. Now, you may think that a book about the Brooklyn Bridge is a rather odd gift for a lover—and, considering that the book ended up in a used book shop, this may be what the recipient thought, too—but, now that I have read McCullough’s chronicle of the Brooklyn Bridge, I can see why it might inspire such sentimental attachment. For it is a thoroughly lovable book.

This is my first McCullough work, and I am pleased. He is a fine writer. His prose is stylish yet unobtrusive, striking that delicate balance between being intelligible but not simplified. He has a keen eye for the exciting details of a seemingly dry story; and effectively brings together many different threads—the personalities, the politics, the technology—in such a way that the past looms up effortlessly in the imagination. The only parts which I think could have been improved were his explanations of the engineering, since he used too many unfamiliar terms without explaining them, perhaps thinking that such explanations might swell the book to unseemly proportions. In any case, he is a writer, not an engineer, and he shines most when discussing the human experience of the Bridge.

The bridge’s designer was John A. Roebling, who deserves a book unto himself. An eccentric polymath, who among other things studied philosophy under Hegel, he came to America to found a Utopian village and ended up the foremost expert on suspension bridges. The Brooklyn Bridge was his project; but tragically he died during the first year of the project, after his foot was crushed, his toes amputated, and he contracted tetanus. His son, Washington, immediately took over—in many ways just as remarkable a man. A Civil War hero with a tenacious memory, the bridge ruined his health, too, through a combination of stress and the bends.

In those days the bends were known as “caisson sickness,” named for the compartment sunk underwater in order to excavate for the bridge’s foundations. These were filled with pressurized air in order to prevent water from seeping in. Unfortunately, in those days the dangers of rapidly depressurizing were not understood, so many people fell ill during the construction—including Roebling himself, who spent the final years of the bridge’s construction as an invalid, observing the work through a telescope from his apartment. Luckily for him, his wife, Emily, was a remarkable woman—diplomatic and brilliant—and helped to carry the project to completion.

These personalities come alive in McCullough’s narration, turning what could have been a dry chronicle into an enthralling book. And this is not to mention the political corruption, the manufacturing fraud, the deadly accidents, and the glorious celebrations that took place during the fourteen years of the bridge’s construction.

Yesterday I revisited the Brooklyn Bridge, which is beautiful even if you know nothing about it. As a friend and I strolled across in the intense summer heat, elbowing our way through crowds of tourists, I blathered on about all the fun facts I had learned from this book—which I am sure my friend very much appreciated. Sensing his discomfort, I made sure to emphasize that a fraudulent wire manufacturer had tricked the engineers into using sub-par cables, and that a panic broke out a week after the bridge’s opening, which resulted in twelve people being trampled. You see this book has already helped my social life. Maybe next I can write my own love note inside.

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Review: Don Quixote

Review: Don Quixote

Don Quijote de la Mancha: puesto en castellano actual íntegra y fielmente por Andrés TrapielloDon Quijote de la Mancha: puesto en castellano actual íntegra y fielmente por Andrés Trapiello by Miguel de Cervantes Saavedra

My rating: 5 of 5 stars

“I know who I am,” replied don Quijote, “and I know who I can be…”

I bought this book under the sway of a caprice which, if it were not too hackneyed to say so, I would call quixotic. This was two years ago. I was in the royal palace in La Granja de San Ildefonso, near Segovia. I had just toured the palace—one of the finest in Spain—and was about to explore the French gardens, modeled after those in Versailles, when I encountered the gift shop. Normally I do not buy anything in gift shops, since half of it is rubbish and all of it is overpriced. But this book, this particular volume, called out to me and I obeyed.

It was a foolish purchase—not only because I paid gift-shop prices, but because my Spanish was not anywhere near the level I needed to read it. And at the time, I had no idea I would be staying in Spain for so long. There was a very good chance, in other words, that I would never be able to tackle this overpriced brick with Bible-thin pages. At least I left myself some hope. For this is not the original El ingenioso caballero don Quijote de la Mancha—written in Spanish contemporaneous with Shakespeare’s English—but a bastardization: its style diligently modernized by the writer Andrés Trapiello. Even with this crutch, and even with an additional two years of living in Spain, this book was a serious challenge.

Before charging headlong into the thickets of criticism, I want to say a word in praise of Trapiello’s edition. Cervantes’s Spanish is not as difficult as Shakespeare’s English, but it still foreign enough to prove an obstacle even to native speakers. I know many Spaniards, even well-read ones, who have never successfully made it through El Quijote for this very reason (or so they allege). Trapiello has done the Spanish-speaking world a great service, then, since he has successfully made El Quijote as accessible as it would have been to its first readers, while preserving the instantly recognizable Cervantine style. And while I can see why purists would object to this defacement of hallowed beauty, I would counter that, if ever there were a book to painlessly enjoy, it is El Quijote.

To get a taste of the change, here is Trapiello’s opening lines:

En un lugar de la Mancha, de cuyo nombre no quiero acordarme, vivía no hace mucho un hidalgo de los de lanza ya olvidada, escudo antiguo, rocín flaco y galgo corredor. Consumían tres partes de su hacienda una olla con algo más de vaca que carnero, ropa vieja casi todas las noches, huevos con torreznos los sábados, lentejas los viernes y algún palomino de añadidura los domingos.

And here is the original:

En un lugar de la Mancha, du cuyo nombre no quiero acordarme, no ha mucho tiempo que vivía un hidalgo de los de lanza en astillero, adarga antigua, rocín flaco y galgo corredor. Una olla de algo más vaca que carnero, salpicón las más noches, duelos y quebrantos los sábados, lentejas los viernes, algún palomino de añadidura los domingos, consumían tres partes de su hacienda.

Now, undeniably something is lost in the transition. Cervantes’s “duelos y quebrantos” (lit. “aches and pains”), for example, is undeniably more evocative than Trapiello’s “huevos con torreznos” (eggs with bacon); but without Trapiello I would have no idea what Cervantes meant. It is also worth noting how similar the two are; Trapiello has taken care to change only what he must.

Onward to the book itself. But I hesitate. The more I contemplate this book, the more I think that a critic must be as daft as the don and as simple as his squire to think he can get to the bottom of it. Cervantes was either extremely muddle-headed or fantastically subtle, since this book resists any definite conclusions you may try to wring from its pages. Perhaps, like many great books, it simply got out of the author’s control. Just as Tolstoy set out to write the parable of a fallen woman and gave us Anna Karenina, and as Mark Twain set out to write a boys’ book and invented American literature, it seems Cervantes set out to write a satire of chivalric romances and produced one of the great works of universal art. It is as if a New Yorker cartoonist accidentally doodled Guernica.

The key to the book’s enduring beauty, I think, is Cervantes’s special brand of irony. He is the only author I know who can produce scorn and admiration in the same sentence. He is able to ruthlessly make fun of everything under the sun, while in the same moment praising them to the heavens. The book itself embodies this paradox: for it is at once the greatest rejection of chivalric romance and its greatest embodiment—an adventure tale that laughs at adventure tales. There is no question that Cervantes finds the old don ridiculous, and he makes us agree with him; yet by the end, Quijote is more heroic than Sir Galahad himself.

The central question the books asks is whether idealism is noble or silly. There is no question that the Knight of the Sorrowful Countenance is a hilarious figure. But do we laugh at his expense, or at our own? Is his idealism pathetic, or is it our realism? The book resists both horns of this dilemma, until finally we must conclude that we are all—dreamers and realists alike—equally ridiculous. For we all reside in a social world whose rules only exist in our beliefs and in our actions, a world which we create but do not design. It is only Quijote who seems to realize (however unconsciously) that, by changing the script, we can recreate the world. And he does. By the time we get to Part Two, everyone is playing along with Quijote.

Even so, I am not able to go so far as Miguel de Unamuno, and consider Quijote a sort of messiah. I do not think Cervantes’s irony permits this. For Quijote truly is out of touch, and frequently gets pummeled for it. And even when his fantasy inspires others to play along, and to help him create his new world, they never do so for disinterested reasons. Some, including Sancho, play along for gain; others do so to control or to help Quijote; and most do it just to have some fun at his expense. This is the dilemma faced by all revolutionaries: they have the vision to see a better world, the courage to usher it in with their actions, and the charisma to inspire others to follow them; but most worldlings chose to play along for ulterior motives, not for ideals; and so the new world becomes as corrupt as the old one. To put this another way, Quijote’s problem is not that he is out of touch with the social order, but that he is out of touch with the human heart.

Much of the greatness of this book lays in the relationship between the don and his squire. Few friendships in literature are so heartwarming. Sancho, in his simplicity, is the only one who can even partially meet Quijote in his new world—as a genuine participant in Quijote’s make-believe. Of course, Sancho is not free from ulterior motives, either. There is the island he is to rule over. But the longer the story goes on, the more Sancho believes in his master, and the less he pursues material gain. We are relieved to see that, when finally offered his island, the squire comes running back to the don in a matter of days. As the only two inhabitants of their new world, as the only two actors in their play, they are homeless without one another.

It is useful to compare Shakespeare’s and Cervantes’s method of characterization. As Harold Bloom points out, Shakespeare’s characters are most truly themselves when they are alone, soliloquizing. When together, on the other hand, even close friends and lovers never seem to communicate perfectly, but talk past each other, or talk for their own benefit, or simply show off. But don Quijote and Sancho Panza are most truly themselves when they are with each other; they draw one another out and spur one another on; they ceaselessly bicker while remaining absolutely loyal; they quibble and squabble while understanding one another perfectly. When they are separated during Sancho’s sojourn on the island, the reader feels that each has lost more than half of himself. For my part, though I am not sure it is more “realistic,” I find Cervantes’s friendship more heartening than the bard’s. Though they begin as polar opposites, the squire and the knight influence one another as the story progresses, eventually coming to resemble one another. This beats Romeo and Juliet by a league.

What strikes most contemporary readers of this ur-novel is its modernity. Formally, Cervantes is far more daring than his Victorian successors. This is admittedly more apparent in Part Two, when Cervantes has his characters travel around a world where Part One has already been published and read widely, and where the spurious Part Two by Alonso Fernández de Avellaneda (a pseudonym) has just been released. This leads to self-referential tricks worthy of the coolest postmodernist: the duo encountering readers of the prequels and commenting on their own portrayal. Another daring touch was Cervantes’s use of the Arabic historian Cide Hamete Berengeli—whose Arabic book, found on the streets of Toledo, he is merely transcribing into Castilian—which allows him to comment on the text he is writing: praising the historian’s scrupulous attention to detail and skipping over boring sections in the “original.”

All this is done, not merely to be clever, but to reinforce the sense of infinite irony that pervades the text. The gap opened up by these tricks is what gives Cervantes room to be so delightfully ambiguous. As the authorship is called into question, and as the characters—who are imaginative actors to begin with—become aware of themselves as characters, the sense of a guiding intelligence crafting the story becomes ever more tenuous. The final irony, then, is that this self-referential irony does not undermine the reality of the story, but only reinforces it. In Part Two, especially, the characters leap from the book into reality, becoming both readers and writers of themselves—so real, indeed, that we risk repeating the don’s error of mistaking the book with reality.

Having said all this in praise of El Quijote, I should mention some of the book’s flaws. These are mostly confined to Part One, wherein Cervantes inserts several short novelas that have, for the most part, aged poorly. At the time there was, apparently, a craze for pastoral love stories involving shepherds and shepherdesses, which nowadays is soppy sentimental trash. One must also admit that Cervantes’s was a very mediocre poet, so the verse scattered throughout these pages can safely be skipped. On the whole, though the book’s most iconic moments are in Part One, Part Two is much superior and more innovative.

Part Two is also far sadder. And this is the last ambiguity: the reader can never fully decide whether to laugh or cry. Tragedy and comedy are blended so deeply together that no emotional response seems adequate. I still have not decided with any certainty how I feel or what I think about this book. All I know is that I wish it could go on forever—that I could read another chapter of don Quijote’s and Sancho Panza’s adventures for the rest of my life. To reach the end is unbearable. Don Quijote should live eternal life. And he will.

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Review: On the Revolutions of Heavenly Spheres

Review: On the Revolutions of Heavenly Spheres

On the Revolutions of Heavenly SpheresOn the Revolutions of Heavenly Spheres by Nicholas Copernicus

My rating: 4 of 5 stars

And though all these things are difficult, almost inconceivable, and quite contrary to the opinion of the multitude, nevertheless in what follows we will with God’s help make them clearer than day—at least for those who are not ignorant of the art of mathematics.

The Copernican Revolution has become the prime exemplar of all the great transformations in our knowledge of the world—a symbol of scientific advance, the paradigmatic clash of reason and religion, a shining illustration of how cold logic can beat out old prejudices. Yet reading this groundbreaking book immediately after attempting Ptolemy’s Almagest—the Bible of geocentric astronomy—reveals far more similarities than differences. Otto Neugebauer was correct in calling Copernicus’s system an ingenious modification of Hellenistic astronomy, for it must be read against the background of Ptolemy in order to grasp its significance.

The most famous section of De revolutionibus was, ironically, not even written by Copernicus, but by the presumptuous Andreas Osiander, a Lutheran theologian who was overseeing the publication of the book, and who included a short preface without consulting or informing Copernicus. Knowing that Copernicus’s hypothesis could prove controversial (Luther considered it heretical), Osiander attempted to minimize its danger by asserting that it was merely a way of calculating celestial positions and did not represent physical reality: “for it is not necessary that the hypotheses should be true, or even probable; but it is enough if they provide a calculate which fits the observations.”

Though this assertion obviously contradicts the body of the work (in which Copernicus argues at length for the reality of the earth’s movement), and though Copernicus and his friends were outraged by the insertion, it did help to shield the book from censure. And arguably Osiander was being a good and true Popperian—believing that science is concerned with making accurate predictions, not in giving us “the truth.” In any case, Osiander was no doubt correct in this assertion: “For it is sufficiently clear that this art is absolutely and profoundly ignorant of the causes of the apparent irregular movements.” Neither Ptolemy nor Copernicus had any coherent explanation of what caused the orbits of the planets, which would not come until Newton.

After this little interpolation, Copernicus himself wastes no time in proclaiming the mobility of the earth. In retrospect, it is remarkable that it took such a long stretch of history for the heliocentric idea to emerge. For it instantly explains many phenomena which, in the Ptolemaic system, are completely baffling. Why do the inner planets (Venus and Mercury) move within a fixed distance of the sun? Why does the perigee (the closest point in the orbit) of the outer planets (Mars, Jupiter, Saturn) occur when they are at opposition (i.e., when they are opposite in the sky from the sun), and why does their apogee (the farthest point) occur when they are in conjunction (when they are hidden behind the sun)? And why do the planets sometimes appear to move backwards relative to the fixed stars?

But putting the earth in orbit between Venus and Mars neatly and instantly explains all of these mysteries. Mercury and Venus always appear a fixed distance from the sun because they are orbiting within the earth’s orbital circle, and thus from our position appear to go back and forth around the sun. Mars, Jupiter, and Saturn, by contrast, can appear at any longitudinal distance from the sun because their orbits are outsider ours; but if Mar’s orbit were tracked from Jupiter, for example, it would, like Venus and Mercury, appear to go back and forth around the sun. Also note that Mars will appear to go “backwards” from earth when earth overtakes the red planet, due to our planet’s shorter orbital period. And since Mars will be closest when it is on the same side of the sun as earth (opposition from the sun), and furthest when it is on far side of the sun (conjunction with the sun), this also explains the apogee and perigee positions of the outer planets.

This allows Copernicus to collapse five circles—one for each of the planets, which were needed in the Ptolemaic system to account for these anomalies—into one circle: namely, the earth’s orbit. The advantages are palpable.

Nevertheless, while I think the benefits of putting the planets in orbit around the sun are obvious, perhaps even to a traditionalist, it is not obvious why Copernicus should put the earth in motion around the sun rather than the reverse. Indeed, this is exactly what the eminent astronomer Tycho Brahe did, several generations later. For it makes no observational difference whether the sun or the earth is in motion. And in the Aristotelian physics of the time, the former solution makes a great deal more sense, since the heavens were supposed to be constituted of lightest elements and the earth of the heaviest elements. So how could the heavy earth move so quickly? What is more, there is no concept of inertia in Aristotelian physics, and so no explanation for why people would not fly off the earth if it were in rapid motion.

Copernicus takes a brief stab at answering these obvious counterarguments, even offering a primitive notion of inertia: “As a matter of fact, when a ship floats on over a tranquil sea, all the things outside seem to the voyagers to be moving in a movement which is the image of their own, and they think on the contrary that they themselves and all the things with them are at rest.” Even so, it is obvious that such a brief example does not suffice to refute the entire Aristotelian system. Clearly, a whole new concept of physics was needed if the earth was to be in motion, one which did not arrive until Isaac Newton, born nearly two hundred years after Copernicus. It took a certain amount of boldness, or obtuseness, for Copernicus to proclaim the earth’s motion without at all being able to explain how the heaviest object in the universe—or so they believed—could hurtle through space.

In structure and content, De revolutionibus follows the Algamest pretty closely: beginning with mathematical preliminaries, onward to the orbits of the sun (or, in this case the earth), the moon, and the planets—with plenty of tables to aid calculation—as well as a description of his astronomical instruments and a chart of star locations, and finally ending with deviations in celestial latitude (how far the planets deviate north and south from the ecliptic in their orbits). Copernicus was even more wedded than Ptolemy to the belief that celestial objects travel in perfect circles, which leads him to repudiate Ptolemy’s use of the equant (the point around which a planet moves at a constant speed). The use of the equant upset Copernicus’s sense of elegance, you see, since its center is different from the actual orbit’s center, thus requiring two overlapping circles.

Copernicus’s own solution was an epicyclet, which revolves twice westward (clockwise, from the celestial north pole) for each rotation eastward on the deferent. And so, ironically, though Ptolemy is sometimes mocked for using epicycles, Copernicus followed the same path. I also find it amusing that the combined effect of these circular motions, in both Ptolemy and Copernicus, added up to a non-circular orbit; clearly nature had different notions of elegance than these astronomers. In any case, it would have to wait until Kepler until it was realized that the planets actually follow an ellipse.

Perhaps the greatest irony is that Copernicus’s book is not any easier to use than Ptolemy’s as a recipe book for planetary positions. Now, it is far beyond my powers to even attempt such a calculation. But in his Very Short Introduction to Copernicus (which I recommend), Owen Gingerich takes the reader through the steps to calculation the position of Mars on Copernicus’s birthday: February 19, 1473. To do this you needed the radix, which is a root position of the planet recorded at a specified time; and you also need the planet’s orbital speed (the time needed for one complete orbit, in this case 687 days). The year must be converted into sexigesimal (base 60) system, and then converted in elapsed Egyptian years (which lack a leap year), in order to calculate the time elapsed since the date of the radix’s position (in this case is January 1st, 1 AD). Then this sexigesimal number can be looked up in Copernicus’s tables; but this only gives us the location of Mars with respect to the sun. To find out where it will appear in the sky, we also need the location of earth, which is another tedious process. You get the idea.

I read the bulk of this book while I was on vacation in rural Canada. Faced with the choice between relaxation or self-torture, I naturally chose the latter. While most of my time was spent scratching my head and helplessly scratching the page with a pencil, the experience was enough to show me—as if I needed more demonstration after Ptolemy—that astronomy is not for the faint of heart, but requires intelligence, patience, and care.

There was one advantage to reading the book on vacation. For it is the only time of year when I am in a place without light pollution. The stars, normally hiding behind street lights and apartment buildings, shone in the hundreds. I would have seen even more were it not for the waxing moon. But this did give me the opportunity to get out an old telescope—bought as a birthday present for a cousin, over a decade ago—and examine the moon’s pitted surface. It is humbling to think that even such basic technology was years ahead of Copernicus’s time.

Looking at the brilliant grey circle, surrounded by a halo of white light, I felt connected to the generations of curious souls who looked at the same moon and the same stars, searching for answers. So Copernicus did not, in other words, entirely spoil my vacation.

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Review: Travels with Charley

Review: Travels with Charley

Travels with Charley: In Search of AmericaTravels with Charley: In Search of America by John Steinbeck

My rating: 4 of 5 stars

In literary criticism the critic has no choice but to make over the victim of his attention into something the size and shape of himself.

This little volume must rank as one of the great American travel books—though I am not quite sure what that means. Travel literature, by its nature, finds itself in a paradoxical position: to search for truth by becoming briefly acquainted with a wide and disconnected series of experiences. Steinbeck addresses this in his opening salvo: “So it was I decided to look again, to try to rediscover this monster land. Otherwise, in writing, I could not tell the small diagnostic truths which are the foundations of the large truth.” But the riddle is to figure out which truths are diagnostic and which distractions. Steinbeck seems later to have thrown up his hands in despair at the prospect, as he retreats into subjectivism: “I feel that there are too many realities. What I set down here is true until someone else passes that way and rearranges the world in his own style.”

Yet if the cliché is true, and the journey is more important than the destination, then Steinbeck’s search for America is more important than what he finds. That sounds reassuring, at least. In any case, the search is a pleasure to read. Steinbeck presents himself as an aging everyman, puttering about with his poodle and his camper, making small-talk with locals, sampling diner breakfasts, and getting lost on country roads. Very little of consequence happens; nothing much is discovered that the fifty-eight year old author did not already know; and it is lovely to read about. True, Steinbeck could, and did, narrate a fly buzzing around a dirty kitchen and turn it into poetry; but his writerly skill is not the only virtue this book possesses.

The book’s most consistent note is that of resigned obsolescence. Steinbeck looks upon the country—one which he once knew so deeply that he created its most representative novels—and finds it unfamiliar. He is past his prime, and knows it; and, more impressively, accepts it. He was writing in the wake of On the Road, another iconic travel book; and though Steinbeck’s work is far more mature and, I think, much better written, it nevertheless fails to capture the ethos of the time in the way Kerouac or, indeed, the younger Steinbeck was able to do. I am not saying this in criticism, but in admiration, since Steinbeck still managed to create a classic book. Like any great artist, he found the great universal in his tiny particular; and he transformed his sense of being out of touch into a great sighing comment on his changing country.

Now, of course much of this book isn’t true. All novelists are born and bred liars. But it sounds true enough, and that is all I want from a travel book.

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Review: The Mountains of California

Review: The Mountains of California

The Mountains of CaliforniaThe Mountains of California by John Muir

My rating: 3 of 5 stars

Few places in this world are more dangerous than home.

It is difficult to spend any time in northern California without coming across the name of John Muir. He is the patron saint of the state’s wild beauty. The John Muir Trail, passing through Yosemite Valley and the Sequoia & Kings Canyon National Parks, and Muir Woods, home of the majestic redwoods, are just two of the most prominent monuments to his life’s work.

I picked up a copy of this book on a recent trip to North Cali, while visiting the Donner Museum—near Donner Lake, up in the Sierra Nevada—which commemorates not only the unfortunate party of lost pilgrims, but some of the other epochal events of the region, such as the goldrush, the building of the North Pacific Railroad, and construction of the major highways. Not many years after the Donner Party lost themselves in the Snowy Range, this infrastructure tied the previously isolated region to the rest of the country.

Perhaps it would have seemed grimly ironic to the Donner survivors that, a generation later, people would be fighting to keep this dangerous place pristine, resisting the encroachment of civilization. Yet in hindsight we can only regard this effort as prescient. That there is any nature left at all is largely thanks to Muir and his ilk, who not only directly intervened to preserve wilderness, but through his writings helped to evoke a groundswell of appreciation for natural beauty.

This book is a piece of propaganda on behalf of wilderness. Though Muir was highly knowledgeable in botany, geology, and in the study of glaciers, the information he presents is strictly secondary to his fundamental purpose: to evoke the beauty of the place. Few people in history, if any, had such a sensitivity to nature. Squirrels sent him into ecstasies, bird calls lifted him into mystic regions of delight, and mountain scenery brought him close to death with pleasure. Indeed, one quickly gets the impression that he could be equally happy in the rainforests of South America, the deserts of Arabia, or the bogs of Scotland. This, ironically, makes the book rather monotonous. Since the bees and birds, the flowers and ferns, the pine trees, fir trees, cedars, sequoias, and all the rest are equally majestic, noble, exquisite, etc.—in every season and all times of day—the descriptions become difficult to attend to. The emotional tone is endlessly euphoric.

Muir’s writing comes most alive when he switches from descriptions of nature to first-person accounts of his explorations. For he was not a note-taking Darwin or a rhapsodizing Wordsworth with a walking stick, but a serious adrenaline junkie. He describes, for example, climbing to the top of a 100-foot tall tree during a heavy storm, and clinging to the end while it got whipped about in the wind, and assures us that “never before did I enjoy so noble an exhileration of motion.” He goes on to describe the experience:

The slender tops fairly flapped and swished in the passionate torrent, bending and swirling backward and forward, round and round, tracing indescribable combinations of vertical and horizontal curves, while I clung with muscles firm braced, like a bobolink on a reed… I kept my lofty perch for hours, frequently closing my eyes to enjoy the music by itself, or to feast quietly on the delicious fragrance that was streaming past. … from the chafing of resiny branches against each other, and the incessant attrition myriads of needles, the gale was spiced to a very tonic degree.

Passages like this are entirely typical. Never is there even a hint of discomfort or fear. Everything he does is unselfconsciously joyful. Muir gives us a (perhaps unwitting) self-portrait in his description of the Water Ouzel: “he never calls forth a single touch of pity; not because he is strong to endure, but rather because he seems to live a charmed life beyond the reach of every influence that makes endurance necessary.” The rest of the descriptions applies equally well: “For both in winter and in summer he sings, sweetly, cheerily, independent alike of sunshine and of love, requiring no other inspiration than the stream on which he dwells. While water sings, so must he, in heat or cold, calm or storm, ever attuning his voice in sure accord; low in the drought of summer and the drought of winter, but never silent.”

So must Muir sing his cheerful tune, whether hanging from cliffs, being buffeted in snowstorms, or crawling through thick brush on all fours. It is hard not to envy a man so seemingly impervious to all negative feeling, sensation, or thought. One suspects that Muir is not giving us the whole picture; but he could not have lived such a life if it did not fulfill him. And, as Bill McKibben states in the introduction, in many ways Muir falls comfortably within an American cultural tradition, running from the exhuberance to Whitman, the nature-worship of Thoreau, and the transcendental enthusiasm of Emerson, on through Muir to the drug-fueled ravings of the Beats and beyond. Muir is a shining exemplar of the outdoorsy woodsman, actuated by individual grit and positive thinking, that is so dear to the national myth. And, in truth, he did a lot of good.

All this being said in his praise, I still must give this book a middling rating. Muir is a prime example of a writer who excels on the level of sentences—writing lyrical, poetic descriptions of all he sees—but who falls short on the level of the whole book. The enthusiastic tone and passionate descriptions drift off into homogenous yelps of beauty. And, while evocative and impressionistic, Muir fails to give a fleshed-out, coherent picture of the mountain wilderness. Still, in his best moments Muir is unforgettable; and I confess that he did inspire in me some faint longings to go out hiking myself—though I would prefer a well-marked trail.

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Review: TITAN: the Life of John D. Rockefeller

Review: TITAN: the Life of John D. Rockefeller

Titan: The Life of John D. Rockefeller, Sr.Titan: The Life of John D. Rockefeller, Sr. by Ron Chernow

My rating: 4 of 5 stars

He played golf assiduously, always alone, matching his record on one day against his record on another; just what the saints do when they daily examine their conscience… Such was probably also the interest dominating Rockefeller’s chase after millions. He was beyond comparing himself with his competitors; he compared himself with himself.

—George Santayana

As a child of Sleepy Hollow, I have almost literally grown up in Rockefeller’s shadow. The best walking paths in the area are in the Rockefeller State Park Preserve, an expansive and beautiful slice of forest made from a part of Rockefeller’s former estate. I can also walk to Rockwood, a park with a gorgeous view of the Hudson River, where John’s brother William had his mansion (since demolished). John D. Rockefeller’s own mansion, Kykuit, sits atop the nearby Pocantico Hills, and is a popular tourist destination. And yet, aside from his reputation as an ultra-rich monopolist, I knew almost nothing about the man.

Thus I turned to Ron Chernow, and I am glad I did. For Rockefeller presents a challenging subject for would-be biographers. A private, reserved, and even a secretive man, John D. Rockefeller was a beguiling mixture of avarice and piety; and throughout his life he has provoked both passionate praise and vicious criticism. Since Rockefeller himself was so guarded during his lifetime, never spontaneous or candid, while achieving such historical importance, it is hard to resist the urge to simplify his character—merely to fill up the lacunae he left. Luckily, Chernow’s patience and sensitivity allow him to paint a convincing and unforgettable portrait of this evasive figure.

As Chernow himself says, Rockefeller was the walking embodiment of Max Weber’s Protestant Ethic. He was actuated by a faith which told him that it was his holy duty to work zealously, and which taught him to see his own success as divine favor and his rivals’ failure as divine retribution. This faith in his mission and his rectitude gave him a purpose and a justification, pushing him to work more devotedly than his colleagues, and to feel no pangs of remorse for those he bruised along the way. His outstanding strengths were his iron will and his extreme deliberation. He kept to a rigid schedule, never acted impulsively, tabulated all of his personal expenses in a little booklet, and even showed up to work on his wedding day. This was a man who made money with the morbid devotion of a saint.

During the sections charting Rockefeller’s rise to success, I was filled with a horrified disgust with the man. Such a joyless, self-righteous hypocrite—filling his pockets with gold and wagging his fingers at the poor. I did not see anything to praise in his religion of money. Simple greed is noxious enough, but sanctimonious greed is revolting.

Yet by the end of the book I found that I both liked and admired the man, or at least the man he later became. For Rockefeller, while full of his own vices, was free of many of the vices we associate with the rich. He was neither ostentatious nor profligate; and if his puritan strictness seems joyless—his hatred of drink, cards, smoking, or anything remotely racy—it at least saved him from hedonistic debauchery. And as he grew older, he became more playful, giving away dimes to strangers, riding around in sporty automobiles, and obsessively playing golf. I was surprised to learn that Rockefeller retired early from his post at the helm of Standard Oil, ceasing all regular duties in his fifties, only retaining a symbolic title. Clearly, he saw more to life than work and money.

But Rockefeller’s greatest virtue was his charity. He gave profusely and generously throughout his life, even more than Andrew Carnegie. Much of this was new to me (for example, I had no idea he founded the University of Chicago); and this is no accident, since Rockefeller did not like putting his name on things. (His name was so vilified anyway it would likely have hampered his charities.) And contrary to what you might expect, Rockefeller’s philanthropic impulse was deep and genuine, something he had from the beginning of his life. According to Chernow, Rockefeller’s contributions to medical research revolutionized the field. So on a purely utilitarian tabulation of pain and pleasure inflicted, Rockefeller probably comes out positive in the end. (Rockefeller himself, of course, thought that his life had been virtuous from beginning to end, and never conceived charity as recompense.)

As I hope I have made clear, Rockefeller was a complex man—or, perhaps it is more accurate to say that he continually resists attempts to stereotype him, which is always uncomfortable. And it is a testament to Chernow’s ability that he captures Rockefeller in all these aspects. Now, this was my first Chernow biography and, I admit, I was somewhat disappointed at first. Naturally, I measured this book against Robert Caro’s The Power Broker, and found Chernow’s book very thin on historical background by comparison. But Chernow partially compensates for this with his fine psychological sensitivity, as sharp as a first-rate novelist. The result is a thoroughly engrossing biography, so good that I am left wishing Chernow had made it longer—specifically during Rockefeller’s early years. And you know a book is good when 700 pages does not satisfy.


(As an afterthought, I would like to note how gratifying it is when different books serendipitously overlap. I knew of Charles Strong as one of George Santayana’s best friends, familiar to me from Santayana’s autobiography and his letters. But I did not remember that Strong married Bessie Rockefeller, John’s eldest child, who went insane and died at the age of forty. Santayana helped to look after Bessie’s daughter, Margaret, and even handed her off during her wedding.)

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Review: Sidereal Messanger

Review: Sidereal Messanger

Sidereus Nuncius, or The Sidereal MessengerSidereus Nuncius, or The Sidereal Messenger by Galileo Galilei

My rating: 4 of 5 stars

A most excellent a kind service has been performed by those who defend from envy the great deeds of excellent men and have taken it upon themselves to preserve from oblivion and ruin names deserving of immortality.

This book (more of a pamphlet, really) is proof that you do not need to write many pages to make a lasting contribution to science. For it was in this little book that Galileo set forth his observations made through his newly improved telescope. In 50-odd pages, with some accompanying diagrams and etchings, Galileo quickly asserts the roughness of the Moon’s surface, avers the existence of many more stars than can be seen with the naked eye, and—the grand climax—announces the existence of the moons of Jupiter. Suddenly the universe seemed far bigger, and stranger, than it had before.

The actual text of Siderius Nuncius does not make for exciting reading. To establish his credibility, Galileo includes a blow-by-blow account of his observations of the moons of Jupiter, charting their nightly appearance. The section on our Moon is admittedly more compelling, as Galileo describes the irregularities he observed as the sun passed over its surface. Even so, this edition is immeasurably improved by the substantial commentary provided by Albert van Helden, who gives us the necessary historical background to understand why it was so controversial, and charts the aftermath of the publication.

Though Galileo is sometimes mistakenly credited with inventing the telescope, spyglasses were widely available at the time; what Galileo did was improve his telescope far beyond the magnification commonly available. The result was that, for a significant span of time, Galileo was the only person on the planet with the technology to closely and accurately observe the heavens. The advantage was not lost on him, and he made sure that he published before he got scooped. In another shrewd move, he named the newly-discovered moons of Jupiter after the Grand Duke Cosimo II and his brothers, for which they were known as the Medician Stars (back then, the term “star” meant any celestial object). This earned him patronage and protection.

Galileo’s findings were controversial because none of them aligned with the predictions of Aristotelian physics and Ptolemaic astronomy. According to the accepted view, the heavens were pure and incorruptible, devoid of change or imperfection. Thus it was jarring to find the moon’s surface bumpy, scarred, and mountainous, just like Earth’s. Even more troublesome were the Galilean moons. In the orthodox view the Earth was the only center of orbit; and one of the strongest objections against Copernicus’s system was that it included two centers, the Sun and the Earth (for the Moon). Galileo’s finding of an additional center of orbit meant that this objection ceased to carry any weight, since in any case we must posit multiple centers. Understandably there was a lot of skepticism at first, with some scholars doubting the efficacy of Galileo’s new instrument. But as other telescopes caught up with Galileo’s, and new anomalies were added to the mix—the phases of Venus and the odd shape of Saturn—his observations achieved widespread acceptance.

Though philosophers and historians of science often emphasize the advance of theory, I find this text a compelling example of the power of pure observation. For Galileo’s breakthrough relied, not on any new theory, but on new technology, extending the reach of his senses. He had no optical theory to guide him as he tinkered with his telescope, relying instead on simple trial-and-error. And though theory plays a role in any observation, some of Galileo’s findings—such as that the Milky Way is made of many small stars clustered together—are as close to simple acts of vision as possible. Even if Copernicus’s theory was not available as an alternative paradigm, it seems likely to me that advances in the power of telescopes would have thrown the old worldview into a crisis. This goes to show that observational technology is integral to scientific progress.

It is also curious to note the moral dimension of Galileo’s discovery. Now, the Ptolemaic system is commonly lambasted as narcissistically anthropocentric, placing humans at the center of it all. Yet it is worth pointing out that, in the Ptolemaic system, the heavens are regarded as pure and perfect, and everything below the moon as corruptible and imperfect (from which we get the term “sublunary”). Indeed, Dante placed the circles of paradise on the moon and the planets. So arguably, by making Earth the equal of the other planets, the new astronomy actually raised the dignity of our humble abode. In any case, I think that it is simplistic to characterize the switch from geocentricity to heliocentricity as a tale of declining hubris. The medieval Christians were hardly swollen with pride by their cosmic importance.

As you can see, this is a fascinating little volume that amply rewards the little time spent reading it. Van Helden has done a terrific job in making this scientific classic accessible.

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Review: Almagest

Review: Almagest

The Almagest: Introduction to the Mathematics of the HeavensThe Almagest: Introduction to the Mathematics of the Heavens by Ptolemy

… it is not fitting even to judge what is simple in itself in heavenly things on the basis of things that seem to be simple among us.

In my abysmal ignorance, I had for years assumed that tracking the orbits of the sun and planets would be straightforward. All you needed was a starting location, a direction, and the daily speed—and, with some simple arithmetic and a bit of graph paper, it would be clear as day. Attempting to read Ptolemy has revealed the magnitude of my error. Charting the heavenly bodies is a deviously complicated affair; and Ptolemy’s solution must rank as one of the greatest intellectual accomplishments of antiquity—fully comparable with the great scientific achievements of European Enlightenment. Indeed, Otto Neugebauer, the preeminent scholar of ancient astronomy, went so far as to say:

One can perfectly well understand the ‘Principia’ without much knowledge of earlier astronomy but one cannot read a single chapter in Copernicus or Kepler without a thorough knowledge of Ptolemy’s “Almagest”. Up to Newton all astronomy consists in modifications, however ingenious, of Hellenistic astronomy.

With more hope than sense, I cracked open my copy of The Great Books of the Western World, which has a full translation of the Almagest in the 16th volume. Immediately repulsed by the text, I then acquired a students’ edition of the book published by the Green Lion Press. This proved to be an excellent choice. Through introductions, preliminaries, footnotes, and appendices—not to mention generous omissions—this edition attempts to make Ptolemy accessible to a diligent college student. Even so, for someone with my background to attain a thorough knowledge of this text, he would still require months of dedicated study with a teacher as a guide. For the text is difficult in numerous ways.

Most obviously, this book is full of mathematical proofs and calculations, which are not exactly my strong suit. Ptolemy’s mathematical language—relying on the Greek geometrical method—will be unfamiliar to students who have not read some Euclid; and even if it is familiar, it proves cumbrous for the sorts of calculations demanded by the subject. To make matters worse, Ptolemy employs the sexagesimal system (based on multiples of 60) for fractions; so his numbers all must be converted into our decimals for calculation. What is more, even the names of the months Ptolemy uses are different, bearing their Egyptian names (Thoth, Phaöphi, Athur, etc.), since Ptolemy was an Alexandrian Greek. Yet even if we put these technical obstacles to the side, we are left with Ptolemy’s oddly infelicitous prose, which the translator describes thus:

In general, there is a sort of opacity, even awkwardness, to Ptolemy’s writing, especially when he is providing a larger frame for a topic or presenting a philosophical discussion.

Thus, even in the non-technical parts of the book, Ptolemy’s writing tends to be headache-inducing. All this combines for form an unremitting slog. So since my interest in this book was amateurish, I skimmed and skipped liberally. Yet this text is so rich that, even proceeding in such a dilettantish fashion, I managed to learn a great deal.

Ptolemy’s Almagest, like Euclid’s Elements, proved so comprehensive and conclusive when it was published that it rendered nearly all subsequent astronomical work obsolete or superfluous. For this reason, we know little about Ptolemy’s predecessors, since there was little point in preserving their work after Ptolemy summed it up in such magnificent fashion. As a result it is unclear how much of this book is original and how much is simply adapted. As Ptolemy himself admits, he owes a substantial debt to the astronomer Hipparchus, who lived around 200 years earlier. Yet it seems that Ptolemy originated the novel way of accounting for the planets’ position and speed, which he puts forth in later books.

Ptolemy begins by explaining the method by which he will measure chords; this leads him to construct one of the most precise trigonometric tables from antiquity. Later, Ptolemy goes on to produce several proofs of spherical trigonometry, which allows him to measure distances on the inside of a sphere, making this book an important source for Greek trigonometry as well as astronomy. Ptolemy also employs Menelaus’ Theorem, which also uses the fixed proportions of a triangle to establish ratios. From this I see that triangles are marvelously useful shapes, since they are the only shape which is rigid—that is, the angles cannot be altered without also changing the ratio of the sides, and vice versa. This is also, by the way, what makes triangles such strong structural components.

Ptolemy gets down to business in analyzing the sun’s motion. This is tricky for several reasons. For one, the sun does not travel parallel to the “fixed stars” (so called because the stars do not position change relative to one another), but rather at an angle, which Ptolemy calculates to be around 23 degrees. We now know this is due to earth’s axial tilt, but for Ptolemy is was the obliquity of the ecliptic. Also, the angle that the sun travels through the sky is determined by one’s latitude; this also determines the seasonal shifts in day-length; and during these shifts, the sun rises on different points on the horizon. To add to these already daunting variables, the sun also shifts in speed during the course of the year. And finally, Ptolemy had to factor in that the procession of the equinoxes—the ecliptic’s gradual westward motion from year to year.

The planets turn out to be even more complex. For they all exhibit anomalies in their orbits which entail further complications. Venus, for example, not only speeds up and slows down, but also seems to go forwards and backwards along its orbit. This leads Ptolemy to the adoption of epicylces—little circles which travel along the greater circle, called the “deferent,” of the planet’s orbit. But to preserve the circular motion of the deferent, Ptolemy must place the center (called the “eccentric”) away from earth. Then, Ptolemy introduces another imaginary circle, around which the planet travels with constant velocity: and the center of this is called the “equant.” Thus the planet’s motion was circular around one point (the eccentric) and constant around another (the equant), neither of which coincide with earth. In addition to all this, the orbit of Venus is not exactly parallel with the sun’s orbit, but tilted, and its tilt wobbles throughout the year. For Ptolemy to account for all this using only the most primitive instruments and without the use of calculus or analytic geometry is an extraordinary feat of patience, vision, and drudgery.

Even after writing all this, I am not giving a fair picture of the scope of Ptolemy’s achievement. This book also includes an extensive star catalogue, with the location and brightness of over one thousand stars. He argues strongly for earth’s sphericity and even offers a calculation of earth’s diameter (which was 28% too small). Ptolemy also calculates the distance from the earth to the moon, using the lunar parallax (the difference in the moon’s appearance when seen from different positions on earth), which comes out the quite accurate figure of 59 earth radii. And all of this is set forth in dry, sometimes baffling prose, accompanied by pages of proofs and tables. One can see why later generations of astronomers thought there was little to add to Ptolemy’s achievement, and why Arabic translators dubbed it “the greatest” (from which we get the English name).

A direct acquaintance with Ptolemy belies his popular image as a metaphysical pseudo-scientist, foolishly clinging to a geocentric model, using ad-hoc epicycles to account for deviations in his theories. To the contrary, Ptolemy scarcely ever touches on metaphysical or philosophical arguments, preferring to stay in the precise world of figures and proofs. And if science consists in predicting phenomena, then Ptolemy’s system was clearly the best scientific theory around for its range and accuracy. Indeed, a waggish philosopher might dismiss the whole question of whether the sun or the earth was at the “center” as entirely metaphysical (is it falsifiable?). Certainly it was not mere prejudice that kept Ptolemy’s system alive.

Admittedly, Ptolemy does occasionally include airy metaphysical statements:

We propose to demonstrate that, just as for the sun and moon, all the apparent anomalistic motions of the five planets are produced through uniform, circular motions; these are proper to the nature of what is divine, but foreign to disorder and variability.

Yet notions of perfection seem hard to justify, even within Ptolemy’s own theory. For the combined motion of the deferent and the epicycle do not make a circle, but a wavy shape called an epitrochoid. And the complex world of interlocking, overlapping, slanted circles—centered on imaginary points, riddled with deviations and anomalies—hardly fits the stereotypical image of an orderly Ptolemaic world.

It must be said that Ptolemy’s system, however comprehensive, does leave some questions tantalizingly unanswered. For example, why do Mercury and Venus stay within a definite distance from the sun, and travel along at the same average speed as the sun? And why are the anomalies of the “outer planets” (Mars, Jupiter, Saturn) sometimes related to the sun’s motion, and sometimes not? All this is very easy to explain in a heliocentric model, but rather baffling in a geocentric one; and Ptolemy does not even attempt an explanation. Even so, I think any reader of this volume must come to the conclusion that this is a massive achievement—and a lasting testament to the heights of brilliance and obscurity that a single mind can reach.

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