Review: Treatise on Light

Review: Treatise on Light
Treatise on Light (Illustrated Edition)

Treatise on Light by Christiaan Huygens

My rating: 4 of 5 stars

But sound, as I have said above, only travels 180 toises in the same time of one second: hence the velocity of light is more than six hundred thousand times greater than that of sound.


This little treatise is included in volume 34 of the Great Books of the Western World, which I used to read Newton’s Principia and his Opticks. In this edition the Treatise comes out to about 50 pages, so I decided it was worth combing through. Christiaan Huygens is one of the relatively lesser known figures of the scientific revolution. But even a brief acquaintance with his life and work is enough to convince one that he was a thinker of gigantic proportion, in a league with Descartes and Leibniz. His work in mechanics prefigured Newton’s laws, and his detailed understanding of the physics of pendulums (building from Galileo’s work) allowed him to invent the pendulum clock. His knowledge of optics also improved the technology of telescope lenses, which in turn allowed him to describe the rings of Saturn and discover the first of Saturn’s moons, Titan.

Apart from all this, Huygens was the progenitor of the wave theory of light. This is in contrast with the corpuscular theory of light (in which light is conceived of as little particles), put forward 14 years later in Isaac Newton’s Opticks. Newton’s theory quickly became more popular, partially because of its inherent strength, and partially because it was Isaac Newton who proposed it. But Huygens’s wave theory was revived and seemingly confirmed in the 19th century by Thomas Young and Augustin-Jean Fresnel.

Essentially, Huygens’s idea was to use sound as an analogy for light. Just as sound consists of longitudinal waves (vibrating in the direction they travel) propagated by air, so light must consist of much faster waves propagated by some other, finer medium, which Huygens calls the ether. He conceives of a luminous object, such as a burning coal, as emitting circular waves at every point in its surface, spreading in every direction throughout a space.

Like Newton, Huygens was aware of Ole Rømer’s calculation of the speed of light. It had long been debated whether light is instantaneous or merely moves very quickly. Aristotle rejected the second option, thinking it inconceivable that something could move so fast. Little progress had been made since then, because making a determination of light’s speed presents serious challenges: not only is light several orders of magnitude faster than anything in our experience, but since light is the fastest thing there is, and the bearer of our information, we have nothing to measure it against.

This changed once astronomers began measuring the movement of the Jovian moons. Specifically, the moon Io is eclipsed by Jupiter every 42.5 hours; but as Rømer measured this cycle at different points in the year, he noticed that it varied somewhat. Realizing that this likely wasn’t due to the moon’s orbit itself, he hypothesized that it was caused by the varying distance of Earth to Jupiter, and he used this as the basis for the first roughly accurate calculation of the speed of light. Newton and Huygens both accepted the principle and refined the results.

Huygens gets through his wave theory, reflection, and refraction fairly quickly; and in fact the bulk of this book is dedicated to an analysis of Icelandic spar—or, as Huygens calls it, “The Strange Refraction of Icelandic Crystal.” This is a type of crystal that is distinctive for its birefringence, which means that it refracts light of different polarizations at different angles, causing a kind of double image to appear through the crystal. Huygens delves into a detailed geometrical analysis of the crystal, which I admit I could not follow in the least; nevertheless, the defining property of polarization eludes him, since to understand it one must conceive of light as a transverse, not a longitudinal, wave (that is, unlike a sound wave, which cannot be polarized). In the end, he leaves this puzzling property of the crystal for future scientists, but not without laying the groundwork of observation and theory that we still rely upon.

All together, this little treatise is a deeply impressive work of science: combining sophisticated mathematical modeling with careful experimentation to reach surprising new conclusions. Huygens illustrates perfectly the rare mix of gifts that a scientist must have in order to be successful: a sharp logical mind, careful attention to detail, and a creative imagination. The world is full of those with only one or two of these qualities—brilliant mathematicians with no interest in the real world, obsessive recorders and cataloguers with no imagination, brilliant artists with no gift for logic—but it takes the combination to make a scientist of the caliber of Huygens.



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Review: Le Morte d’Arthur

Review: Le Morte d’Arthur
Le Morte d'Arthur: King Arthur and the Legends of the Round Table

Le Morte d’Arthur: King Arthur and the Legends of the Round Table by Thomas Malory

My rating: 4 of 5 stars

It happened one Pentecost when King Arthur and his knights of the Round Table had all assembled at the castle of Kynke Kenadonne and were waiting, as was customary, for some unusual event to occur before settling down to the feast, that Sir Gawain saw through the window three gentlemen riding toward the castle, accompanied by a dwarf.

I fully expected to dislike this book. The prospect of five hundred pages of jousting knights struck me as endlessly tedious, and I only opened the book out of a sense of respect for its status as a classic. But immediately I found myself entranced. This is a thoroughly engrossing read. And I should not have been surprised, since it delves so heartily into the two staples of popular entertainment: sex and violence. Indeed, one of the most amusing aspects of this book is how completely out of harmony is the chivalric code with the Christian religion; the characters do nothing but mate and slaughter, while the name of “Jesu” is on everybody’s lips.

Sir Thomas Malory assembled Le Morte d’Arthur out of several pre-existing legends, some of which he translated from French manuscripts, with a few stories of his invention thrown in. His major innovation was to arrange these traditional tales into a semi-coherent order, beginning with Arthur’s ascension to the throne and ending with his death at the hands of his son. The result is a patchwork of stories nested within stories, all told at a pace which, to a modern reader, can seem ludicrous. Major developments occur on every page, one after the other, in a staccato rhythm which can make the stories appear bluntly humorous, even if it was not Malory’s intention.

The world depicted in these pages is so frankly unreal, the level of violence so constant and gratuitous, that its final impression is that of a cartoon: “They fought once more and Sir Tristram killed his opponent. Then, running over to his son, he swiftly beheaded him too.” Daily life is entirely hidden from view. There are no peasants, no merchants, no artisans; there are no friends or happy families. There are only questing knights, heavily armed men who are obsessed with challenging one another. And though they profess a knightly code of conduct, even the most chivalrous of knights are seen to be unscrupulous murderers and, with few exceptions, unrepentant adulterers. The hero of this book, Sir Launcelot, feels very few pangs of guilt for continuously sleeping with his liege’s wife, Gwynevere; and he is the best of knights.

But the characters are so flat, their actions so stereotyped, their lives so monotonously dramatic, that I found it impossible to view them as moral actors, praiseworthy or damnable. They are, rather, centers of this bizarre world that Malory constructs. And it certainly is an exciting place. Monsters, magicians, enchantresses, prophesies, curses, visions, and of course endless combat and manic love—the small isle of Britain can hardly contain it all. Sure, there are parts of the book that drag, particularly during the tournaments. Malory’s descriptions of combat are heavily stylized, consisting of the same basic elements over and over again; and, as in the Iliad, large engagements are pictured as a series of individual contests between heroic foes. But for the most part Malory combines his traditional motifs together dexterously, enlivening larger stories with innumerable episodes, creating a raucous forward momentum.

As a result of all this, I greatly enjoyed Le Morte d’Arthur, even if it was not for the reasons that Malory intended. I found the book delightfully absurd, almost parody of itself, a sort of whimsical fantasy novel. What Malory hoped to convey with these stories—whether they are supposed to represent a model of heroism, an ironic comment on violence, or a response to the Wars of the Roses—I cannot say; but his book is better than any television show I know.



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Review: The Age of Napoleon

Review: The Age of Napoleon
The Age of Napoleon (The Story of Civilization, #11)

The Age of Napoleon by Will Durant

My rating: 4 of 5 stars

Finally I have come to the last book in this series. It was four long years ago when I first read The Life of Greece; and these have been the four most educational years of my life, in part thanks to The Story of Civilization. Though I have had some occasions to criticize Durant over the years, the fact that I have dragged myself through ten lengthy volumes of his writing is compliment enough. Now all I need to do is to read the first volume of the series, Our Oriental Heritage, in order to bring my voyage to its end. (I originally skipped it because it struck me as absurd to squeeze all of Asia into one volume and then cover Europe in ten; but for the sake of completion I suppose I will have to read it.)

Durant did not plan to write this volume. His previous book, Rousseau and Revolution, ends with a final bow. But Durant lived longer than he anticipated (he died at 96), so he decided to devote his final years to a bonus book on Napoleon. It is extraordinarily impressive that he and his wife, Ariel, could have maintained the same high standard of writing for so many decades; there is no notable decline in quality in this volume, which makes me think that Durant should have written a book on healthy living, too.

The Age of Napoleon displays all of Durant’s typical merits and faults. The book begins with a bust: Durant rushes through the French Revolution, seeming bored by the whole affair, seeing the grand drama only as a disruptive prelude to Napoleon. This showcases Durant’s inability to write engagingly about processes and events; when there is no central actor on which to focus his attention, the writing becomes colorless and vague. Further, it also shows that Durant, while a strong writer, was a weak historian: he provides very little analysis or commentary on what is one of the most important and influential events in European history.

When Napoleon enters the scene, the book becomes appreciably more lively. For reasons that largely escape me, Durant was an unabashed admirer of the diminutive general, and sees in Napoleon an example of the farthest limits of human ability. Though normally uninterested in the details of battles and campaigns, Durant reveals a heretofore hidden talent for military narration as he covers Napoleon’s military triumphs and defeats. Some parts of the book, particularly near the end, are genuinely thrilling—an adjective that rarely comes to mind with Durant’s staid and steady style. Granted, he had an extraordinary story to tell; Napoleon’s rise, fall, rise again, and fall again are as epic as anything in Plutarch.

But as usual Durant shines most brightly in his sections on artists, poets, and philosophers. The greatest section of this book is that on the Romantic poets: Wordsworth, Coleridge, Shelley, and Byron. (For some reason, Durant sees fit to exclude Keats, even though the scope of Keats’ life falls entirely within that of Napoleon.) Less engaging, though still worthwhile, was Durant’s section on the German idealist philosophers; and his miniature biography of Beethoven was a stirring tribute. Many writers who properly belong in this volume were, however, paid their respects in the previous, most notably Goya and Goethe, since Durant thought that this volume would never appear.

Though I am happy to reach the end, I am saddened that I cannot continue the story of Europe’s history any further forward with Durant. He is an inspiring guide to the continent’s cultural treasures.



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Review: Newton’s Principia

Review: Newton’s Principia
The Principia

The Principia by Isaac Newton

My rating: 5 of 5 stars

It is shown in the Scholium of Prop. 22, Book II, that at the height of 200 miles above the earth the air is more rare than it is at the surface of the earth in the ratio of 30 to 0.0000000000003998, or as 75,000,000,000,000 to 1, nearly.


Marking this book as “read” is as much an act of surrender as an accomplishment. Newton’s reputation for difficulty is well-deserved; this is not a reader-friendly book. Even those with a strong background in science and mathematics will, I suspect, need some aid. The historian of mathematics Colin Pask relied on several secondary sources to work his way through the Principia in order to write his excellent popular guide. (Texts by S. Chandrasekhar, J. Bruce Brackenridge, and Dana Densmore are among the more notable vade mecums for Newton’s proofs.) Gary Rubenstein, a math teacher, takes over an hour to explain a single one of Newton’s proofs in a series of videos (and he had to rely on Brackenridge to do so).

It is not that Newton’s ideas are inherently obscure—though mastering them is not easy—but that Newton’s presentation of his work is terse, dense, incomplete (from omitting steps), and at times cryptic. Part of this was a consequence of his personality: he was a reclusive man and was anxious to avoid public controversies. He says so much himself: In the introduction to Book III, Newton mentions that he had composed a popular version, but discarded it in order to “prevent the disputes” that would arise from a wide readership. Unsurprisingly, when you take material that is intrinsically complex and then render it opaque to the public, the result is not a book that anyone can casually pick up and understand.

The good news is that you do not have to. Newton himself did not advise readers, even mathematically skilled readers, to work their way through every problem. This would be enormously time-consuming. Indeed, Newton recommended his readers to peruse only the first few sections of Book I before moving on directly to Book III, leaving most of the book completely untouched. And this is not bad advice. As Ted said in his review, the average reader could gain much from this book by simply skipping the proofs and calculations, and stopping to read anything that looked interesting. And guides to the Principia are certainly not wanting. Besides the three mentioned above, there is the guide written by Newton scholar I. Bernard Cohen, published as a part of his translation. I initially tried to rely on this guide; but I found that, despite its interest, it is mainly geared towards historians of science; so I switched to Colin Pask’s Magnificent Principia, which does an excellent job in revealing the importance of Newton’s work to modern science.

So much for the book’s difficulty; on to the book itself.

Isaac Newton’s Philosophiæ Naturalis Principia Matematica is one of the most influential scientific works in history, rivaled only by Darwin’s On the Origin of Species. Quite simply, it set the groundwork for physics as we know it. The publication of the Principia, in 1687, completed the revolution in science that began with Copernicus’s publication of De revolutionibus orbium coelestium over one hundred years earlier. Copernicus deliberately modeled his work on Ptolemy’s Almagest, mirroring the structure and style of the Alexandrian Greek’s text. Yet it is Newton’s book that can most properly be compared to Ptolemy’s. For both the Englishman and the Greek used mathematical ingenuity to draw together the work of generations of illustrious predecessors into a single, grand, unified theory of the heavens.

The progression from Copernicus to Newton is a case study in the history of science. Copernicus realized that setting the earth in motion around the sun, rather than the reverse, would solve several puzzling features of the heavens—most conspicuously, why the orbits of the planets seem related to the sun’s movement. Yet Copernicus lacked the physics to explain how a movable earth was possible; in the Aristotelian physics that held sway, there was nothing to explain why people would not fly off of a rotating earth. Furthermore, Copernicus was held back by the mathematical prejudices of the day—namely, the belief in perfect circles.

Johannes Kepler made a great stride forward by replacing circles with ellipses; this led to the discovery of his three laws, whose strength finally made the Copernican system more efficient than its predecessor (which Copernicus’s own version was not). Yet Kepler was able to provide no account of the force that would lead to his elliptical orbits. He hypothesized a sort of magnetic force that would sweep the planets along from a rotating sun, but he could not show why such a force would cause such orbits. Galileo, meanwhile, set to work on the new physics. He showed that objects accelerate downward with a velocity proportional to the square of the distance; and he argued that different objects fall at different speeds due to air resistance, and that acceleration due to gravity would be the same for all objects in a vacuum. But Galileo had no thought of extending his new physics to the heavenly bodies.

By Newton’s day, the evidence against the old Ptolemaic system was overwhelming. Much of this was observational. Galileo observed craters and mountains on the moon; dark spots on the sun; the moons of Jupiter; and the phases of Venus. All of these data, in one way or another, contradicted the old Aristotelian cosmology and Ptolemaic astronomy. Tycho Brahe observed a new star in the sky (caused by a supernova) in 1572, which confuted the idea that the heavens were unchanging; and observations of Haley’s comet in 1682 confirmed that the comet was not somewhere in earth’s atmosphere, but in the supposedly unchanging heavens.

In short, the old system was becoming unsustainable; and yet, nobody could explain the mechanism of the new Copernican picture. The notion that the planets’ orbits were caused by an inverse-square law was suspected by many, including Edmond Haley, Christopher Wren, and Robert Hooke. But it took a mathematician of Newton’s caliber to prove it.

But before Newton published his Principia, another towering intellect put forward a new system of the world: René Descartes. Some thirty years before Newton’s masterpiece saw the light of day, Descartes published his Principia Philosophiæ. Here, Descartes summarized and systemized his skeptical philosophy. He also put forward a new mechanistic system of physics, in which the planets are borne along by cosmic vortexes that swirl around each other. Importantly, however, Descartes’s system was entirely qualitative; he provided no equations of motion.

Though Descartes’s hypothesis has no validity, it had a profound effect on Newton, as it provided him with a rival. The very title of Newton’s book seems to allude to Descartes’s: while the French philosopher provides principles, Newton provides mathematical principles—a crucial difference. Almost all of Newton’s Book II (on air resistance) can be seen as a detailed refutation of Descartes’s work; and Newton begins his famous General Scholium with the sentence: “The hypothesis of vortices is pressed with many difficulties.”

In order to secure his everlasting reputation, Newton had to do several things: First, to show that elliptical orbits, obeying Kepler’s law of equal areas in equal times, result from an inverse-square force. Next, to show that this force is proportional to the mass. Finally, to show that it is this very same force that causes terrestrial objects to fall to earth, obeying Galileo’s theorems. The result is Universal Gravity, a force that pervades the universe, causing the planets to rotate and apples to drop with the same mathematical certainty. This universal causation effectively completes the puzzle left by Copernicus: how the earth could rotate around the sun without everything flying off into space.

The Principia is in a league of its own because Newton does not simply do that, but so much more. The book is stuffed with brilliance; and it is exhausting even to list Newton’s accomplishments. Most obviously, there are Newton’s laws of motion, which are still taught to students all over the world. Newton provides the conceptual basis for the calculus; and though he does not explicitly use calculus in the book, a mathematically sophisticated reader could have surmised that Newton was using a new technique. Crucially, Newton derives Kepler’s three laws from his inverse-square law; and he proves that Kepler’s equation has no algebraic solution, and provides computational tools.

Considering the mass of the sun in comparison with the planets, Newton could have left his system as a series of two-body problems, with the sun determining the orbital motions of all the planets, and the planets determining the motions of their moons. This would have been reasonably accurate. But Newton realized that, if gravity is truly universal, all the planets must exert a force on one another; and this leads him to the invention of perturbation theory, which allows him, for example, to calculate the disturbance in Saturn’s orbit caused by proximity to Jupiter. While he is at it, Newton calculates the relative sizes and densities of the planets, as well as calculates where the center of gravity between the gas giants and the sun must lie. Newton also realized that gravitational effects of the sun and moon are what cause terrestrial tides, and calculated their relative effects (though, as Pask notes, Newton fudges some numbers).

Leaving little to posterity, Newton realized that the spinning of a planet would cause a distortion in its sphericity, making it marginally wider than it is tall. Newton then realized that this slight distortion would cause tidal locking in the case of the moon, which is why the same side of the moon always faces the earth. The slight deformity of the earth is also what causes the procession of the equinoxes (the very slow shift in the location of the equinoctial sunrises in relation to the zodiac). This shift was known at least since Ptolemy, who gave an estimate (too slow) of the rate of change, but was unable to provide any explanation for this phenomenon.

The evidence mustered against Descartes’s theory is formidable. Newton describes experiments in which he dropped pendulums in troughs of water, to test the effects of drag. He also performed experiments by dropping objects from the top of St. Paul’s Cathedral. What is more, Newton used mathematical arguments to show that objects rotating in a vortex obey a periodicity law that is proportional to the square of the distance, and not, as in Kepler’s Third Law, to the 3/2 power. Most convincing of all, Newton analyzes the motion of comets, showing that they would have to travel straight through several different vortices, in the direction contrary to the spinning fluid, in order to describe the orbits that we observe—a manifest absurdity. While he is on the subject of comets, Newton hypothesizes (correctly) that the tail of comets is caused by gas released in proximity to the sun; and he also hypothesizes (intriguingly) that this gas is what brings water to earth.

This is only the roughest of lists. Omitted, for example, are some of the mathematical advances Newton makes in the course of his argument. Even so, I think that the reader can appreciate the scope and depth of Newton’s accomplishment. As Pask notes, between the covers of a single book Newton presents work that, nowadays, would be spread out over hundreds of papers by thousands of authors. The result is a triumph of science. Newton not only solves the longstanding puzzle of the orbits of the planets, but shows how his theory unexpectedly accounts for a range of hitherto separate and inexplicable phenomena: the tides, the procession of the equinoxes, the orbit of the moon, the behavior of pendulums, the appearance of comets. In this Newton demonstrated what was to become the hallmark of modern science: to unify as many different phenomena as possible under a single explanatory scheme.

Besides setting the groundwork for dynamics, which would be developed and refined by Euler, d’Alembert, Lagrange, Laplace, and Hamilton in the coming generations, Newton also provides a model of science that remains inspiring to practitioners in any field. Newton himself attempts to enunciate his principles, in his famous Rules of Reasoning. Yet his emphasis on inductivism—generalizing from the data—does not do justice to the extraordinary amount of imagination required to frame suitable hypotheses. In any case, it is clear that Newton’s success was owed to the application of sophisticated mathematical models, carefully tested against collections of physical measurements, in order to unify the greatest possible number of phenomena. And this was to become a model for other intellectual disciples to aspire to, for good and for ill.

A striking consequence of this model is that its ultimate causal mechanism is a mathematical rule rather than a philosophical principle. The planets orbit the sun because of gravity, whose equations accurately predict their motions; but what gravity is, why it exists, and how it can affect distant objects, is left completely mysterious. This is the origin of Newton’s famous “I frame no hypothesis” comment, in which he explicitly restricts himself to the prediction of observable events rather than speculation on hidden causes (though he was not averse to speculation when the mood struck him). Depending on your point of view, this shift in emphasis either made science more rational or more superficial; but there is little doubt that it made science more effective.

Though this book is too often impenetrable, I still recommend that you give it a try. Few books are so exalting and so humbling. Here is on display the furthest reaches of the power of the human intellect to probe the universe we live in, and to find hidden regularities in the apparent chaos of experience.



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Review: 1491

Review: 1491

1491: New Revelations of the Americas Before Columbus1491: New Revelations of the Americas Before Columbus by Charles C. Mann

My rating: 3 of 5 stars

I should begin by saying that this book is not what I expected, which necessarily entails some disappointment. I was hoping for a more in-depth look at the major pre-Columbian societies and cultures. What this book instead offers is a sort of overview of trends in research in this area, highlighting how these trends contradict the popular image of the Americas before European colonization. This is, of course, also a valuable and worthwhile topic—and, considering the book’s popularity, many have found it to be so—but I nevertheless must admit that, after putting down the book, I still have only a hazy notion of the actual cultures in question.

Mann sets himself to undermine the popular notion of scattered groups of savages in a pristine, ahistorical paradise, living lightly off the land in a perfect harmony with nature. He sets out to show that, first, there were orders of magnitude more people in the Americas than was originally suspected; second, that humans arrived in the Americas far earlier than previously thought; and third, that pre-Colombian societies radically altered their environment. The picture that emerges is of a continent teeming with complex civilizations, each one manipulating the world around them in unique ways.

Due to the limited and often indirect evidence available to researchers, and the comparatively nascent state of the field, Mann is unable to give a textbook-like overview of pre-Colombian societies. Our knowledge is simply too fragmentary; there are too many scholarly disagreements. He instead chooses to focus on individual scholars and their lines of research, showing how these converge to suggest the aforementioned new conclusions. The advantage to this method is that his narrative is enlivened with the stories of real research; and it also allows Mann to give a more realistic impression of the state of our knowledge. But the disadvantage is that this book often reads like an extended Nat Geo article—the report of a journalist tagging along on research expeditions—rather than the bird’s-eye view I was hoping for.

Another major drawback is that, by focusing on pioneering research, Mann is unable to give answers that are wholly satisfying, since the field itself has not yet reached a stable consensus. The research he relies on for his section on pre-Colombian population, for example, uses a combination of indirect evidence and simple speculation. Granted, I was convinced even before opening this book that European diseases caused significant depopulation after first contact. But whether the fatality rate was as high as 90%, as he suggests, is difficult to accept without more decisive evidence. Personally I find it hard to believe that one-fifth of the global population (to use his figure) could die off without leaving a far less ambiguous archeological trace.

That the research is in this state is not, of course, Mann’s fault; yet he is not merely reporting the results of different experts in the field, but choosing those whose research most strongly supports this book’s thesis. This put me naturally on guard, since I know from my brief time studying archaeology how varied scholarly opinion can be in a field where evidence is necessarily scanty, incomplete, and suggestive. This being said, I do want to emphasize that I was convinced of Mann’s major points; it was only the details that put me in a dubious state of mind.

Mann’s habit of focusing on the research that most forcefully bolsters his conclusions is part of a more general tendency to overstate his case. For example, I find it difficult to accept Mann’s assertion that the first generation of European colonists did not have a decisive military advantage over their American counterparts (which supports the thesis that disease was the decisive factor in the conquest). Steel blades, guns, and mounted cavalry were all landmarks in military technology in Eurasia, so I do not see why they would not lend an advantage in this context. I also could not swallow Mann’s argument that American Indian cultures played such a decisive role in the emergence of Western liberalism and individualism. Now, I have little doubt that the example of egalitarian, non-coercive societies did play a role in this development; but Mann makes it seem as if Locke, Montesquieu, and Voltaire were reliant on this example.

But I should stop nitpicking a book which is thoughtful, well-written, well-researched, and which dispels many obsolete myths. And, really, it is my fault for choosing a book on new revelations, when I really wanted to learn more about the religion, art, architecture, and science of these vanished civilizations.

(I should note one error I caught. Mann says that the Spanish missionary Gaspar de Carvajal was born “in the Spanish town of Extremadura.” But Extremadura is region, or an autonomous community, not a town; Carvajal was born in Trujillo, which is indeed in Extremadura.)

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Review: A Midsummer Night’s Dream

Review: A Midsummer Night’s Dream

A Midsummer Night's DreamA Midsummer Night’s Dream by William Shakespeare

My rating: 3 of 5 stars

The forms of things unknown, the poet’s pen,
Turns them to shapes and gives to airy nothing
A local habitation and a name.

Both times that I have encountered this play, it has failed to make much of an impression on me. I fear that I am insensitive to the atmosphere of enamorment and enchantment that so pervades this work. A Midsummer Night’s Dream is one of the few of the bard’s plays whose plot he himself wrote. The result shows that, while brilliant in nearly every other dramatical ability, plot was not one of Shakespeare’s gifts. The play is a whimsical tapestry, a historically absurd mélange, a jury-rigged skeleton on which to hang his romantic poetry.

As is typical of Shakespeare, his lovers are mostly devoid of intrinsic interest. There is not much that allows the reader to distinguish Helena from Hermia, Lysander from Demetrius; their love-sick pinning all blends together into an impassioned monotony. This, of course, is wholly intentional; the farcical scheme of the love potion reveals that the lovers’ choice is wholly arbitrary—even random—and that the passions are due entirely to the lover and not the beloved. This is standard Shakespeare fare, even if it is spiced up with the device of the fairies.

The standout character is, as so often happens, not a lover at all, but a jester: Bottom. He is the liveliest and most loveable character in the play, a thoroughly upright and decent man. His most striking feature is his imperturbability. Being transformed into a monster hardly phases him; and meeting the fairies of the enchanted world strikes him as no special cause for alarm. Also notable is his apparent indifference to the amorous advances of the fairy queen. Being so lauded and desired does not augment his ego one bit, nor does it prompt him to

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Review: ¿Qué es filosofía?

Review: ¿Qué es filosofía?

¿Qué es filosofía?¿Qué es filosofía? by José Ortega y Gasset

My rating: 3 of 5 stars

I have always believed that clarity is the courtesy of philosophy…

When I picture Ortega to myself, I imagine a man seated in the middle of a room full of books—the atmosphere smoky from frequent cigarettes—banging furiously away at a typewriter, going at it from morning till evening, rapidly accumulating piles of written pages by his side. Ortega was so prolific, and wrote about so many different things, that he could have filled an entire journal by himself—and nearly did. I have read only a fraction of his collected works, but this has included: an analysis of love, a political reckoning of Spain, a diagnosis of the social ills of Europe, and essays on literature and modern art. Now added to this list is an introduction to philosophy.

What I most admire in Ortega is this flexibility and his fluency: his omnivorous interest in the world and his ability to write smooth prose about complex issues. What I most deprecate is his tendency to rush headlong into a problem, sweep away controversy with grand gestures, and then to drop it at once. In other words, he is profligate with ideas but stingy with systems. His theories are always germinal; he leaves to others the difficult work of rigorous arguments and concrete applications. This is not damaging in cases such as aesthetic criticism, where rigor is hardly possible anyway; but it is ruinous in the case of philosophy, where logical consistency is so crucial.

The result of his approach is this series of lectures, which does not give a coherent view of philosophy’s history or its method. Instead, Ortega offers an essayistic series of opinions about the shortcomings of previous incarnations of philosophy and where he thinks philosophy should go next. I say “opinions” because, crucially, Ortega does not offer anything resembling a formal argument. This makes it difficult to accept his conclusions and, worse, makes it difficult to understand his opinions in the first place, since without the supporting skeleton of an argument his views remain formless.

Nevertheless, a short summary is still possible. Ortega derides science for being concerned with merely “secondary” problems, and mysticism for being irrational. Materialists metastasize existence into something inhuman and discrete, while idealists (such as Descartes) divorce the subject from his surroundings. Ortega’s solution is his phrase, “I am myself and my surroundings,” considering human experience—composed of the interpenetration of subject and surrounding circumstances—the basic fact of philosophy. In this, as in his emphasize on human freedom, he fits in well with existentialists like Heidegger and Sartre. But he differs from then, first, in writing legibly; and second in his strong emphasis on reason.

I think there are the germs of some worthy ideas contained here; but in order to really understand the ontological and epistemological ramifications of his positions, he would have to argue for them in a way entirely absent from this book.

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Review: Marianela

Review: Marianela

Marianela (Los mejores clásicos)Marianela by Benito Pérez Galdós

My rating: 5 of 5 stars

Benito Peréz Galdós is yet another of those Spanish authors whose wide fame in their own language is equalled by their wide obscurity elsewhere. In Spain his reputation as a novelist is second only to Cervantes; and yet the English translation of this book, one of his most famous, is out of print. This is a shame, since Galdós was a writer of rare gifts, a fountain of stories written in beautiful prose. In many ways he is reminiscent of Lope de Vega: both a critical and popular success, whose celebrity did not get in the way of his output. For like the golden age playwright, Galdós was extremely prolific. Apart from his few dozen—and often lengthy—social-realist novels, he wrote five series of historical novels, forty-six novels in all, covering the 19th century in Spain. Dickens was a slug by comparison.

This book is about Marianela, called La Nela, an orphaned, “deformed” adolescent who lives in the mining country in Cantabria. She is described as having spotty skin, thin hair, a malproportioned face, and most notably an underdeveloped body for her age. She is the “lazarillo,” or guide, to Pablo, a blind young man from a rich family. The two fall in love, and share many passionate sentiments on their walks together. But then the brilliant doctor, Teodoro Celepín, comes to visit Pablo, examines him, cures his blindness, and, well, Marianela’s life gets considerably worse. It is a simple story with a tragic arc.

For me the outstanding quality of Galdós’s writing is his prose. It is elegant but readable, balanced but energetic. Though there were many words scattered about that I did not understand, I never felt lost; to the contrary, I read quickly, avidly, completely sucked into the story in a way that is rare for me with Spanish books. As with many novelists, there are two main registers of Galdós’s writing on display: scene-setting description and dialogue. Galdós excels at both. The conversations between La Nela and Pablo, though sentimental in a way that only enamored teenagers can be, was totally convincing. And his description of the desolate, charred, and barren landscape of the mines is an excellent example of how a scene can contribute to the narrative of a book:

El vapor principió a zumbar en las calderas del gran automóvil, que hacía funcionar a un tiempo los aparatos de los talleres y el aparato de lavado. El agua, que tan principal papel desempeñaba en esta operación, comenzó a correr por las altas cañerías, de donde debía saltar sobre los cilindros. Risotadas de mujeres y ladridos de hombres que venían de tomar la mañana [beber aguardiente] precedieron a la faena; y al fin empezaron a girar las cribas cilíndricas con infernal chillido; el agua corría de una en otra, pulverizándose, y la tierra sucia se atormentaba con vertiginoso voltear, todando y cayendo de rueda en rueda hasta convertirse en fino polvo achocolatado.

And in English:

The steam began to hiss in the boilers of the big car, which operated the workshop equipment and the cleaning machines at the same time. The water, which played such a principal role in this operation, began to run through the high pipes, where it had to jump over the cylinders. The guffaws of women and the barks of men who came to take the morning [drink aguardiente] preceded the task; and at last they begun to turn the cylindrical sieves with a hellish shriek; the water ran from one to the other, spraying and splashing, and the dirty earth was tormented with dizzy turning, rolling and falling from wheel to wheel until it became a fine chocolate powder.

Few authors could provide such a gripping description of an industrial process and also present us with a character as memorable as La Nela. She is self-contained but selfless, self-willed but self-abnegating, intelligent but ignorant, a person who was given nothing and so expects nothing, but whose isolation caused her to form a novel perspective. Her notion of the world is pagan; she sees things in mythical, poetic categories that lead everyone around her to chastise her for being unchristian. Her tragedy, like so many, is the plight of undeveloped potential; in other circumstances, she may have done remarkable things; but being born poor, orphaned, and “ugly” has confined her to being a guide.

I have said all this in praise of Galdós prose, his scene-setting, his characterization, but of course there is more to this story. Thematically, this book is also quite rich—the relation between inner and outer sense, between inner and outer worth, the relation between knowledge and love—but I will not get into that. This book was too enjoyable to belabor it with heady analysis. To conclude, this novel has convinced me that Galdós is a master of the craft. I am eager to devour more of his books.

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Review: Bury My Heart at Wounded Knee

Review: Bury My Heart at Wounded Knee

Bury My Heart at Wounded Knee: An Indian History of the American WestBury My Heart at Wounded Knee: An Indian History of the American West by Dee Brown

My rating: 3 of 5 stars

This is one of those books whose great merit was in undermining itself. When it was first published, in 1970, it must have been a shock to the Americans who grew up reading and watching movies about the heroic coy boys, settlers, and soldiers who settled the West. It was—and to an extent, remains—a key part of our national myth. But like so many national myths, it left unnoticed the people who were repressed, marginalized, or exterminated on the road to the country’s greatness. Books like this one, a people’s history, told from the perspective of the vanquished, are a necessary corrective to this, and perform an important moral function in our society: shining a light on the misdeed perpetrated by our national heroes.

The greatest testament to the success of a book of this type is to render itself obsolete, and I think this is what has happened in this case—at least, to an extent. For by the time I went to school it was the Dee Brown version of the West, not the Buffalo Bill version, that was taught to us. (Admittedly this must vary a lot depending on where you go to school; I come from quite a liberal area.) Thus the story told in these pages was, however depressing, entirely familiar: broken promises, cultural misunderstandings, blatant dishonesty, and wholesale slaughter. As a result I admit I did not enjoy this book as much as I expected, for everything that Brown narrated was fully expected. Of course, there were moments that pierced through even my dullness, such as the description of the Sand Creek Massacre, which was as horrible as anything I have read about the Holocaust.

Brown is a strong writer, and evokes people and scenes with the power of a good novelist. But I was disappointed at how much of this book is given over to descriptions of battles and skirmishes. The pattern was always the same: the Indians are promised land, the whites decide they want the land after all, tension escalates, and then conflict ensues—with the American military usually coming out the victor. I think it was important that Brown narrate this fighting from the other perspective, since it formed such a cherished part of our myth, but apart from sheer drama I did get much out of it. I would much have preferred that Brown dedicate space to the customs of the groups he is describing—the Navajo, the Sioux, the Cheyenne, the Arapaho, and many more. Without this, we get a sense of brave cultures being swept away, but not a sense of what was actually lost.

A few more criticisms come to mind. Though this book is well-researched and well-sourced, it is clear even at a superficial reading that Brown has imaginatively embellished quite a bit in order to get the novelistic style he was after. More importantly, now that we are (hopefully) moving past this Spaghetti-Western version of American history, I believe a different kind of book is needed. Any book that tells the story exclusively from one side, either victor or vanquished, will leave important parts of the story out. Apart from more ethnographic description of the American Indians in question, I would also have liked a much deeper analysis of the government and settlers. This would have given more insight into why these interactions played out the way they did.

But these criticisms are somewhat unfair, since they are predicated on the book’s success. Without a doubt this was a necessary book, and Brown did us a service in writing it—and in writing it so well.

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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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