2018 in Books

2018 in Books

Few authors, especially the unpublished, can resist the opportunity to read aloud.

2018 has shaped up to be an excellent year in reading. I somehow finished fifteen more books than I had the previous two years. Admittedly, many of my books this year were quite short; some of Plato’s dialogues are arguably more like pamphlets than books, and I read twelve of them this year. These slim volumes were, I hope, compensated by a few ponderous tomes. I stumbled through the two final books of Will Durant’s The Story of Civilization, at 1092 and 870 pages; George Santayana’s 862 page treatise on ontology; 1300 pages of Plutarch’s Parallel Lives; and finally William Shirer’s Rise and Fall of the Third Reich, weighing in at a tedious 1614 pages. I also attempted to read a 1400 page history of New York City; but I was forced to take a break halfway through to recover from an acute overdose of urbane facts.

The two most prominent themes of this year’s reading have been art and science.

I learned about the works and lives of Picasso, Miró, and Goya, and I savored Santiago Ramón y Cajal’s sketches of brain cells, which are as much artistic as scientific achievements. I also read two books of John Ruskin’s eloquent ravings on the value, morality, and beauty of art. Henry Adams concurred with Ruskin about the superiority of medieval art, as he demonstrated in his book about Chartres. Giorgio Vasari, however, took the reverse position, arguing that the Renaissance saved Europe from centuries of barbarous art; and he proved this thesis in his reverential biographies of Renaissance painters and sculptors. But by far the most compelling book on art I read this year was a collection of Vincent van Gogh’s letters, which reveal a man of extraordinary sensitivity and intelligence.

My reading in science began with two classics in the philosophy of science: Popper’s The Logic of Scientific Discovery and Kuhn’s The Structure of Scientific Revolutions—both excellent. But after learning the theory I wanted to know the practice; so I started blundering my way through the classics of the Copernican revolution. I began with Ptolemy’s Almagest, and followed this with Copernicus’s De Revolutionibus, Kepler’s Harmonies of the World, and Galileo’s Two New Sciences and Sidereus Nuncius; and I finally reached the capstone of the scientific revolution with Newton’s Principia. Looking at this list, I feel rather proud of myself; but in truth most of this “reading” consisted of flipping through pages of incomprehensible mathematics. I needed secondary sources to even achieve a basic understanding, relying on an abridged and annotated version of Ptolemy, Very Short Introductions to Copernicus and Galileo, and a popularization of Newton written by Colin Pask. And am I any the wiser for all this toil?

I had hoped to do half of my reading this year in Spanish; but with a total twenty books I did not even achieve a quarter. Luckily, many of these were excellent. Federico García Lorca’s trilogy of plays is a remarkable look at the force of tradition in rural Spain. The poetry of Antonio Machado was perhaps even more profound, with its blend of metaphysical calm and romantic sensitivity to nature. I also read two superlative novels from Spanish masters: Marianela by Benito Pérez Galdós, and El árbol de la ciencia by Pío Baroja. To do my homework, I sampled Spain’s golden age, reading Tirso de Molina’s El burlador de Sevilla, and Lope de Vega’s Fuente Ovejuna and El caballero de Olmedo. But the highlight of this year’s Spanish books was undoubtedly Don Quijote de la Mancha, which I read in the modernized version by Andrés Trapiello. Not that Cervantes needs any help, but Ortega’s and Unamuno’s commentaries on the Spanish masterpiece did widen my appreciation of that most infinitely entertaining of novels.

The two authors who most dominated my year were Shakespeare and Plato, as I labored under the optimistic delusion that I could read both of their complete works. I still have a long way to go, of course; but any time spent with these two masters is rewarding; and I hope to continue my naive ambition next year. I read very few works of English language fiction this year, of which E.M. Forster’s Howards End was the standout work. As usual, I tried to read about New York and the United States while I was home during the summer. This lead me to pick up Mark Twain’s Life on the Mississippi, John Steinbeck’s Travels with Charley, John Muir’s The Mountains of California, Dee Brown’s Bury My Heart at Wounded Knee, David McCullough’s The Great Bridge, Ron Chernow’s Titan, and Alistair Cooke’s America. None of these was as revelatory as The Power Broker, which I read last summer; but each one shed some light on my vast and aggravating homeland.

The most exciting event on Goodreads this year has been my recent ascension to the most followed reviewer in Spain, with 1,700 new followers just this month. Believe me, I’ve been as baffled as you must be. The mystery was partly solved when I investigated the list of my followers, and found that a large part bear the obvious traces of fake accounts. I would like to take this opportunity to publicly assert that I have not paid for any bot service, and I have no idea why they would choose to follow my reviews. Perhaps the computers have a taste for pretentious prose.

In any case, I would like to thank my fellow reviewers and followers, man or machine, for contributing to this excellent year of reading. You support me in my own endeavors, you inspire me with your intelligence and curiosity, and you provide me a community of thoughtful readers and writers. So may 2019 be as good a year for book enthusiasts as the this one has been.



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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: A Very Short Introduction to Galileo

Review: A Very Short Introduction to Galileo
Galileo: A Very Short Introduction

Galileo: A Very Short Introduction by Stillman Drake

My rating: 4 of 5 stars

There is not a single effect in Nature, not even the least that exists, such that the most ingenious theorists can ever arrive at a complete understanding of it.

One of the most impressive aspects of the Very Short Introduction series is the range of creative freedom allowed to its writers. (Either that, or its flexibility in repurposing older writings; presumably a version of this book was published before the VSI series even got off the ground, since its author died in 1993.) This is a good example: For in lieu of an introduction, Stillman Drake, one of the leading scholars of the Italian scientist, has given us a novel analysis of Galileo’s trial by the Inquisition.

Admittedly, in order to contextualize the trial, Drake must cover all of Galileo’s life and thought. But Drake’s focus on the trial means that many things one would expect from an introduction—for example, an explanation of Galileo’s lasting contributions to science—are only touched upon, in order to make space for what Drake believed was the crux of the conflict: Galileo’s philosophy of science.

Galileo Galilei was tried in 1633 for failing to obey the church’s edict that forbade the adoption, defense, or teaching of the Copernican view. And it seems that he has been on trial ever since. The Catholic scientist’s battle with the Catholic Church has been transformed into the archetypical battle between religion and science, with Galileo bravely championing the independence of human reason from ancient dogma. This naturally elevated Galileo to the status of intellectual heroe; but more recently Galileo has been criticized for falling short of this ideal. Historian of science, Alexandre Kojève, famously claimed that Galileo hadn’t actually performed the experiments he cited as arguments, but that his new science was mainly based on thought experiments. And Arthur Koestler, in his popular history of astronomy, criticized Galileo for failing to incorporate Kepler’s new insights. Perhaps Galileo was not, after all, any better than the scholastics he criticized?

Drake has played a significant role in pushing back against these arguments. First, he used the newly discovered working papers of Galileo to demonstrate that, indeed, he had performed careful experiments in developing his new scheme of mechanics. Drake also points out that Galileo’s Dialogue Concerning the Two Chief World Systems was intended for popular audiences, and so it would be unreasonable to expect Galileo to incorporate Kepler’s elliptical orbits. Finally, Drake draws a hard line between Galileo’s science and the medieval theories of motion that have been said to presage Galileo’s theories. Those theories, he observes, were concerned with the metaphysical cause of motion; whereas Galileo abandoned the search for causes, and inaugurated the use of careful measurements and numerical predictions in science.

Thus, Drake argues that Galileo never saw himself as an enemy of the Church; to the contrary, he saw himself as fighting for its preservation. What Galileo opposed was the alignment of Church dogma with one very particular interpretation of scripture, which Galileo believed would put the church in danger of being discredited in the future. Galileo attributed this mistaken policy to a group of malicious professors of philosophy, who, in the attempt to buttress their outdated methods, used Biblical passages to make their views seem orthodox. This was historically new. Saint Augustine, for example, considered the opinions of natural philosophers entirely irrelevant to the truth of the Catholic faith, and left the matter to experts. It was only in Galileo’s day (during the Counter-Reformation) that scientific theories became a matter of official church policy.

Drake’s conclusion is that Galileo’s trial was not so much a conflict between science and religion (for the two had co-existed for many centuries), but between science and philosophy: the former concerned with measurement and prediction, the latter concerned with causes. And Drake notes that many contemporary criticisms of Galileo—leaving many loose-ends in his system, for example—mirror the contemporary criticisms of his work. The trial goes on.

Personally I found this book fascinating and extremely lucid. However, I am not sure it exactly fulfills its promise as an introduction to Galileo. I think that someone entirely new to Galileo’s work, or to the history and philosophy of science, may not get as much out of this work. Luckily, most of Galileo’s own writings (translated by Drake) are already very accessible and enjoyable.



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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: Howards End

Review: Howards End
Howards End

Howards End by E.M. Forster

My rating: 5 of 5 stars

It is the little things one bungles at. The big, real ones are nothing when they come.


The last time I reviewed a novel by E.M. Forster, I wound up blubbering with praise; and now I find myself in similar circumstances. As with A Passage to India, I find Howards End exemplary in every respect: the themes, characterization, the prose, the pacing, the plot. I ought also to mention Forster’s versatility. Though rarely funny, Forster is capable of romantic lyricism, gritty realism, and flighty philosophy. Most convincing of all is his control. Nothing is overdone or heavy-handed—which requires a mixture of technique and taste. While exploring social problems, one never feels that the novel is being unduly interrupted; while constructing a character into an archetype, one never feels that the individual is lost; and the story, though carefully plotted, rarely feels predictable or contrived.

Yet Forster is not a great novelist for his skill alone. He is great because of his insight. More than any novelist I know, Forster is able to connect the inner with the outer life (which is the theme of this novel, and the source of its most famous quote: “Only connect”). Forster is able to show, in other words, how social and economic circumstances breed characters; and how even intelligent and well-meaning characters fail to escape the bounds of their class and nation. He shows, for example, how the money inherited by Margaret and Helen allows for their mental freedom; how Mr. Wilcox’s life of business molds him into a well-meaning shell; and how, despite his best efforts, Leonard Bast cannot help but be shaped by his poverty.

However, if the novel has a message, it is this: even if the inner life is powerless to change material circumstances, it is ultimately the more important aspect of life. This is because, when a tragedy strikes, and mere business acumen or worldly knowledge will not suffice, it is emotional fortitude that is required. Mr. Wilcox has a sort of false strength—a fragile ego he hides behind, a sort of masculine bluff which is easily shattered. Margaret, by contrast, is able to endure tragedies because of her self-knowledge. She is not afraid of the darker aspects of her mind; thus she can look with equanimity upon herself and others, accepting their flaws while seeing their potential. This is what Forster means by “connect”: connecting “the beast” with “the monk”—that is, admitting one’s desires instead of hiding behind a false screen of decency. Only so can we achieve self-knowledge.



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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: Two New Sciences

Review: Two New Sciences

Two New Sciences/A History of Free FallTwo New Sciences/A History of Free Fall by Galileo Galilei

My rating: 4 of 5 stars

But in what seas are we inadvertently engulfing ourselves, bit by bit? Among voids, infinities, indivisibles, and instantaneous movements, shall we ever be able to reach harbor even after a thousand discussions?

When most people think about the Copernican revolution, the name that comes most readily to mind—more even than that of Copernicus himself—is that of Galileo Galilei. It was he, after all, who fought most valiantly for the acceptance of the theory, and it was he who suffered the most for it—narrowly escaping the tortures of the Inquisition. It was also Galileo who wrote the most famous book to come out of the revolution: Dialogue Concerning the Two Chief World Systems, whose publication most directly resulted in Galileo’s punishment.

Some years ago I read and admired that eloquent work. But lately, after slogging my way through Ptolemy, Copernicus, and Kepler, I have come to look upon Galileo’s famous dialogue with more suspicion. For it was only through the work of Kepler that the Copernican system became unquestionably more efficient than the Ptolemaic as a method of calculating celestial movements; and though Kepler was a contemporary and a correspondent of Galileo, the Italian scientist was not aware of the German’s groundbreaking innovations. Thus the version of heliocentrism that Galileo defends is Copernicus’s original system, preserving much of the cumbrous aspects of Ptolemy—epicycles, perfect circles, and separate tables for longitude and latitude, etc.

Added to this, the most decisive advantages in favor of Copernicus’s system over Ptolemy’s—explaining why the planets’ orbits seem related to the sun’s—are given little prominence, if they are even mentioned. Clearly, a rigorous defense of Copernicanism would require a demonstration that it made calculating heavenly positions easier and more accurate; but there is nothing of the kind in Galileo’s dialogue. As a result, Galileo comes across as a propagandist rather than a scientist. But of course, even if his famous dialogue was pure publicity, Galileo would have a secure place in the annals of astronomy from his observations through his improved telescope: of the lunar surface, of the moons of Jupiter, of the rings of Saturn, of sunspots, and of the phases of Venus. But I doubt this would be enough to earn him his reputation as a cornerstone of the scientific revolution.

This book provides the answer. Here is Galileo’s real scientific masterpiece—one of the most important treatises on mechanics in history. Rather inconveniently, its title is easy to confuse with Galileo’s more famous dialogue; but in content Two New Sciences is an infinitely more serious work than Two Chief World Systems. It is also a far less impassioned work, since Galileo wrote it when he was an old man under house arrest, not a younger man in battle with the Catholic authorities. This inevitably makes the book rather more boring to read; yet even here, Galileo’s lucid style is orders of magnitude more pleasant than, say, Kepler’s or Ptolemy’s.

As in Two Chief World Systems, the format is a dialogue between Simplicio, Sagredo, and Salviati (though Galileo cheats by having Salviati read from his manuscript). Unlike the earlier dialogue, however, Simplicio is not engaged in providing counter-arguments or in defending Aristotle; he mostly just asks clarifying questions. Thus the dialogue format only serves to enliven a straightforward exposition of Galileo’s views, not to simulate a debate.

The book begins by asking why structures cannot be scaled up or down without changing their properties. Why, for example, will a small boat hold together if slid down a ramp, but a larger boat fall to pieces? Why does a horse break its leg it falls down, but a cat can fall from the same distance entirely uninjured? Why are the bones of an elephant proportionately so much squatter and fatter than the bones of a mouse? In biology this is known as the science of allometry, and personally I find it fascinating. The key is that, when increasing size, the ratio of volume to area also increases; thus an elephant’s bones must support far more weight, proportionally, than a mouse’s. As a result, inventors and engineers cannot just scale up contraptions without providing additional support—quite a counter-intuitive idea at the time.

Galileo next delves into infinities. This leads him into what is called “Galileo’s paradox,” but is actually one of the defining properties of infinite sets. This states that the parts of an infinite set can be equal to the whole set; or in other words, they can both be infinite. For example, though the number of integers with a perfect square root (4, 9, 16…) will be fewer than the total number of integers in any finite set (say, from 1-100), in the set of all integers there is an infinite number of integers with a perfect square roots; thus the part is equal to the whole. Galileo also takes a crack at Aristotle’s wheel paradox. This is rather dull to explain; but suffice to say it involves the simultaneous rotation of rigid, concentric circles. Galileo attempts to solve it by postulating an infinite number if infinitesimal voids in the smaller circle, and in fact uses this as evidence for his theory of infinitesimals.

As a solution to the paradox, this metaphysical assertion fails to do justice to its mathematical nature. However, the concept of infinitely small instants does help to escape from of the Zeno-like paradoxes of motion, to which Greek mathematics was prone. For example, if you imagine an decelerating object spending any finite amount of time at any definite speed, you will see that it never comes to a full stop: the first second it will travel one meter, the next second only half a meter, the next second a quarter of a meter, and so on ad infinitum. The notion of deceleration taking places continuously over an infinite number of infinitely small instants helped to escape this dilemma (though it is still unexplained how a thing can be said to “move” during an instant).

Galileo had need of such concepts, since he was writing long before Newton’s calculus and too early to be influenced by Descartes’s analytical geometry. Thus the mathematical apparatus of this book is Greek in form. Galileo’s calculations consist exclusively of ratios between lines rather than equations; and he establishes these ratios using Euclid’s familiar proofs. Consequently, his mechanics is relational or relativistic—able to give proportions but not exact quantities.

This did not stop Galileo from anticipating much of Newton’s system. He establishes the pendulum as an exemplar of continually accelerated motion, and shows that pendulums of the same length of rope swing at the same rate, regardless of the height from which they fall. He asserts that an object, once started in motion, would continue in motion indefinitely were it not for friction and air resistance. He recounts experiments of dropping objects of different masses from the same distance, and seeing them land at the same moment, thus disproving the Aristotelian assertion that objects fall with a speed proportional to their mass. (Unfortunately, there is scant evidence for the story that Galileo performed this experiment from the Leaning Tower of Pisa.) Galileo also makes the daring asserting that, in a vacuum, all objects would fall at the same rate.

There are still more riches to be excavated. Galileo asserts that pitches are caused by vibrating air, that faster vibrations causes higher pitch, and that consonant harmonies are caused by vibrations in regular ratios. He exhaustively calculates how the time and speed of a descending object would differ based on its angle of descent—straight down or on an inclined plane. He also shows that objects shot into the air, as in a catapult, descend back to earth in a parabolic arc; and he shows that objects travel the furthest when shot at 45 degrees. In an appendix, Galileo uses an iterative approach to find the center of gravity of curved solids; and in an added dialogue he discusses the force of percussion.

As you can see, this book is too rich and, in parts, too technical for me to appraise it in detail. I will say, however, that of all the scientific classics I have read this year, the modern spirit of science shines through most clearly in these pages. For like any contemporary scientist, Galileo assumes that the behavior of nature is law-like, and is fundamentally mathematical; and with Galileo we also see a thinker completely willing to submit his speculations to experiment, but completely unwilling to submit them to authority. Far more than in the metaphysical Kepler—who speculated with wild abandon, though he was a scientist of comparable importance—in Galileo we find a true skeptic: who believed only what he could observe, calculate, and prove. The reader instantly feels, in Galileo, the force of an exceptionally clear mind and of an uncompromising dedication to the search for truth.

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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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