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Thomas Kuhn switched from studying physics to the history of science when, after teaching a course on outdated scientific models, he discovered that his notion of scientific progress was completely mistaken.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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Rome Posts Update

Rome Posts Update

Writing my series of posts on Rome, back in 2016, was an educational experience for me. It was the first time that I tried to break up a single city into multiple installments, and the first time that I tried to be as brief and as useful as possible (a practice I have since abandoned). Nevertheless the posts’ photographs and formatting were a little rough compared to my later posts. To rectify this, I have given these original posts a makeover. You can see the results below: