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: 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: 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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Review: Kenneth Clarke’s Civilisation

Review: Kenneth Clarke’s Civilisation

Civilisation:  A Personal ViewCivilisation: A Personal View by Kenneth Clark

My rating: 5 of 5 stars

I wonder if a single thought that has helped forward the human spirit has ever been conceived or written down in an enormous room

I must admit immediately that I have never read nor even laid eyes on this book. I’m sure it’s lovely. This review is, rather, about the television series, which I’d wager is twice as lovely.

Civilisation is the best documentary I’ve ever seen. Kenneth Clark takes his viewer from the Dark Ages, through romanesque, gothic, the Renaissance, the Reformation, baroque, rococo, neoclassicism, impressionism, through the industrial revolution and the two World Wars, all the way up to when the program was made in the late 1960s. This is a remarkable amount of ground to cover for a show with 13 episodes, each 50 minutes long.

Not only chronologically, but in subject matter, this documentary casts a wide net. Although the show’s primary emphasis is on architecture and art, Clark also dips into literature, poetry, music, engineering, politics, and wider social problems like inequality, poverty, oppression, and war. Of course, for lack of time Clark cannot delve too deeply into any one of these subjects; but because the presentation is so skillful and economical, and the selection of material so tasteful, the viewer is nevertheless satisfied at the end of every episode.

The documentary generally shifts between shots of Clark facing the camera, talking to the viewer, and extended, panoramic shots of churches, monuments, paintings, drawings, sculptures, and mountains, while beautiful music plays in the background. Clark himself chose the musical accompaniments to these visuals, and they are uniformly splendid (and this is one reason why I recommend the documentary over the book). More than perhaps anything I’ve seen on a screen, this series is rich, lavish, sumptuous. As the camera pans over the altarpiece of a church, while Bach’s St. Matthew’s Passion plays in the background, it’s so lush and gorgeous that it almost gives you a stomach ache.

Aside from these visuals and music, the main attraction of the series is Clark himself. He comes across as refined, cosmopolitan—almost a freak of erudition. But for all that, he is charming and witty, if ultimately a bit cold. One of the strongest impressions I got was that Clark was a man from another time. He looks out of place as he walks through the modern streets, crowded with cars and buzzing with urban life. He has many misgivings about the modern world: he is anti-Marxist, anti-modern art, and certainly didn’t understand the student protests and hippie culture flourishing at the time. In his own words, he was a “stick in the mud,” and I think felt alienated from his time because of his intense appreciation, even worship, of Western art.

This brings me to some of this program’s shortcomings. Most of these are due to the time in which it was made. This is most apparent in the first episode, “The Skin of Our Teeth,” wherein he argues that civilization almost disappeared during the Dark Ages, and comes close to crediting Charlemagne as the savior of all subsequent culture. This requires that he completely discredit both Byzantine and Muslim culture (not to mention Chinese), both of which were doing just fine. He repeats the tired stereotype about Byzantium being a fossilized culture and treats the Muslims as simple destroyers. Later on in the series, he has some uncharitable things to say about the Germans, which I think was a product of growing up during the World War.

A more serious flaw might be that the series bites off more than it can chew. The questions Clark poses to answer are vast. What is civilization? What makes it thrive? What makes it fall apart? Deep questions, but his answers are by comparison shallow. Civilization requires confidence in the future; they cannot be built on fear. Civilization requires rebirth, the constant search for new styles and ideas; but it also requires continuity and tradition, a respect for the past. Civilization is pushed forward by men of genius (and in this series, they’re all men), who enlarge our faculties with their godlike creative powers; men like Michelangelo, Dante, Beethoven, men who are timeless and yet who forever alter the face of culture.

These are interesting answers, but they seem rather superficial to me. They describe, rather than explain, civilization. But of course, this is a documentary, not a monograph. And although Clark asks and tries to answer many questions, I think his primary goal was simply to inspire a sense of the worth, the preciousness, the grandeur of the accomplishments of European civilization. He wants to remind his viewers that our culture is fragile, and that we owe to it not only beautiful paintings and poetry, but also our very ability to see and appreciate the beauty in certain ways, to think about ideas in a certain light, to live not only a happy but a full and rich life.

Maybe this seems pinched and old-fashioned nowadays. Still, I can’t help thinking of all the times that a friend, a fellow student, or even a teacher has made a blanket statement about “Western culture,” “Enlightenment ideas,” “scientific materialism,” or some such thing, while seeming to understand none of it. (I’ve probably done this myself, too.) I’ve been in classes—serious, graduate-level classes—where, amid condemnations of “Western” ideas and gratuitous namedropping of Western philosophers, I realized that I was the only person there, professor included, who actually read some of these authors. I’m not making this up.

I suppose this is just a callow intellectual fashion, and it will eventually pass away. And I also suppose that this might be slightly preferable to the idiotic self-glorification of “European man” that prevailed in earlier times. At present, however, this program is a wonderful corrective to our bad habits of thought. It’s an education, a social critique, and a joy. I hope you get a chance to watch it.

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