Of course, a critic resembles a poet to a hair, except that he has no anguish in his heart, no music on his lips.
This is one of those rare unclassifiable books, whose genre was born the day it was published and which has since left no heirs. Kierkegaard gives us what appears, at first, to be a sort of literary experiment: the papers of two imaginary characters, found inside the escritoire by a third imaginary character. These two characters—referred to as ‘A’ and ‘B’—serve as the titular either/or; and their writings are a study in contrast. Specifically, Kierkegaard uses these two personages to juxtapose the aesthetic with the ethical modes of life, presumably asking the reader to choose between them. You might say it is a ‘choose your own adventure’ book of philosophy, except the adventure chosen turns out to be your life.
Part 1, by A, gives us the aesthetic man. We are presented with extracts from a journal, essays on Mozart’s Don Giovanni and ancient tragedy, a study of boredom, and the famous Seducer’s Diary: A’s record of his carefully planned seduction of a young girl. Part 2 is more focused, consisting of two long letters sent by B (who is supposed to be a middle-aged judge) to A, both exhorting the latter to turn towards a more ethical view of life. The styles of the two writers are suitably different: A is excitable, hyperbolic, and aphoristic, while B is more staid and focused. Nevertheless, it is never difficult to tell that Kierkegaard is the true author.
Neatly summarizing the difference in perspectives would be difficult, since Kierkegaard tends to be flexible with his own definitions. Perhaps the best way to capture the contrast is with the book’s central metaphor: seduction vs. marriage. In the first, A is concerned with attaining a maximum of pleasure. He is not a hedonist, and is not very interested in sex. Rather, he is interested in avoiding boredom by carefully shaping his developing relationship like a well-plotted novel, ensuring that each emotion is felt to the utmost. His primary concern, in other words, is to avoid the stale, the cliché, the repetitive. The judge, by contrast, sees marriage as far preferable to seduction, since it is through commitments like marriage that the inner self develops and becomes fully actualized. While the aesthete prefers to live in the moment, the ethical man notes that, even if every moment is novel, the self remains the same. Change requires commitment.
Interpreting the book is difficult. Are we being asked to make a choice in values? Such a choice could have no basis but chance or personal whim, since no pre-existing value could guide us between two incompatible value-systems. This, you might say, is the existentialist interpretation of the book: the primacy of choice over values. Yet other options are available. For example, despite Kierkegaard’s famous opposition to Hegel’s philosophy, this text is open to a Hegelian reading. Specifically, B’s perspective seems in many respects superior to A’s, since B demonstrates that he is able to understand A, while A presumably cannot understand B. Thus, you can perhaps regard B as the Hegelian antithesis to A’s thesis; and perhaps both of these can be united in a wider perspective, such as in Kierkegaard’s Knight of Faith—a religious unity of inner feeling and outer obligation. There is also the unmistakable autobiographical element in this writing, since Kierkegaard had not long before broken off his own engagement.
This is just to scrape the surface of possibility. And this shows both the strength and weakness of Kierkegaard’s writing. On the one hand, this book is highly rich and suggestive, with brilliant passages buried amid piles of less compelling material. On the other hand, to call a book “rich” and “suggestive” is also to call it confused. Since no clear message emerges, and since there are no arguments to guide the way, the book can easily yield interpretations consonant with pre-conceived opinions. In other words, it is hard to me to imagine somebody being convinced to change their mind by reading this. But Kierkegaard can perhaps better be likened to a good art critic than to a systematic philosopher, for the value in his writing consists more in illuminating comments than in a final conclusion.
On the whole, however, I must say that I emerged with a distaste for Kierkegaard’s writing. At times he rises to commanding eloquence; but so often he seems to wallow in confusing and repetitive intricacies. More to the point, I find the general tenor of his writing to be anti-rationalist; and this is exemplified in the complete lack of argument in his writings. But nobody could deny that, all told, this is an extraordinary book and a worthy addition to the philosophical tradition.
This little book is one of the most read and translated works of the Spanish Golden Age. It has been surprisingly influential. Schopenhauer was a famous devotee, and even learned Spanish so that he could produce a translation (which went on to commercial success). Two English translations have been best-sellers, the first in 1892 and the second in 1992. Advice typically does not age well, but Gracián’s has stood the temporal test.
Yet for the reader of the original Spanish—especially the non-native reader—the book can be perplexing. Gracián was a major writer in the conceptismo movement: a literary style in which a maximum of meaning was compressed into a minimum of words, using every rhetorical trick of the trivium to achieve a style that seems to curl itself into a ball and then to explode in all directions. This can make the experience of reading Gracián quite akin to that of reading poetry—except here, unlike in poetry, you can be sure that there is a sensible meaning laying concealed underneath. When the antiquity of Gracián’s Castilian is added to the mix, the result is literary dish that is difficult to digest.
After a meaning is beaten out of Gracián’s twisted words, however, the result is some surprisingly straightforward advice. “Prudent” is the operative word, for Gracián manages to be idealistic and realistic at once, walking the fine like between cynicism and naïveté. Admittedly, however, the bulk of this advice is directed towards the successful courtier, and so is difficult to apply to less exalted positions. There is, for example, much advice concerned with how to treat inferiors and superiors, but in a world where explicit hierarchies are increasingly frowned upon (or at least tactfully concealed), the poor reader wonders what to make of it.
But much of the advice is timeless and universal. Make friends with those you can learn from (but not those who can outshine you!). Don’t let wishful thinking lead you into unrealistic hopes. Never lose your self-respect. The wise man gains more from his enemies than the fool from his friends. Know how to forget. Know how to ask. Look within… As any reader of Don Quixote knows, Spanish is a language exceedingly rich in proverbs; so it perhaps should come as no surprise that this language—so rhythmic and so easy to make rhymes with—is also an excellent vehicle for maxims. Gracián exploits the proverbial potential of Castilian to the maximum, expressing a sly but respectable philosophy in 300 pithy paragraphs.
Despite all the wit and wisdom to be found in these pages, however, I found myself wishing for amplification. Montaigne, though short on practical advice, is long on examples; so by the end of his essays the reader has a good idea how to put his ideas into practice. Gracián, by contrast, has no time for examples, and so the reader is left with a rather abstract imperative to work with. Needless to say I will not become a successful courtier anytime soon.
Ideas are interesting, but people are vastly more so.
Sarah Bakewell has followed her lovely book about Montaigne with an equally lovely book about the existentialist movement. Comparing the books, one can see an obvious theme emerge in Bakewell’s writing: the interest in practical philosophy. Montaigne and the existentialists share the tendency to write about their own lives and, in various ways, to attempt to live out the tenets of their philosophies. This makes Bakewell’s biographical method especially revealing and rewarding, while at the same time adding a subtle, highbrow self-help aspect to her books—life lessons with the imprimatur of big names and fine prose.
Bakewell attempts to tell the story of the existentialist movement from its twentieth-century beginnings (skipping over precursors such as Dostoyevsky and Kierkegaard) to its apparent end, with the deaths of its principle architects. The four main protagonists are Martin Heidegger, Maurice Merleau-Ponty, Simone de Beauvoir, and Jean-Paul Sartre (who, unsurprisingly, is the dominant personality), along with shorter appearances by other thinkers: Husserl, Camus, Raymond Aron, Karl Jaspers, and Simone Weil, to name the most prominent. When you consider the sheer amount of biographical and philosophical material this list represents, you realize the magnitude of the task set before Bakewell, and the consequent skill she demonstrated in producing a readable, elegant, and stimulating book.
I am sorry to say that I have read very little of the writings of the principle actors, with the exception of Heidegger. Bakewell’s account of him mostly confirmed my own experiences with the infuriating metaphysician, especially in his disturbing lack of character and, indeed, of basic humanity. Sartre comes across as far more human, if not exactly more likable. Few people could hear of Sartre’s enormous philosophical, biographical, journalistic, and literary output, over so many years, without feeling a sense of awe. Nevertheless, Sartre’s opinions rarely struck me as measured or reasonable. Though I often mourn the decline of the public intellectual, Sartre’s example gives me pause, for his influence on contemporary politics was not necessarily salubrious. Perhaps it is true that intellectuals, seeking consistency and clarity, are naturally inclined towards extreme positions. Sartre was, in any case, and it led him into some foolish and even reprehensible positions.
By contrast to these two giants, Beauvoir and Merleau-Ponty come off rather well in this story. The former tempered her political opinions with a greater subtlety, thoroughness, and empathy; while the latter lived a quietly productive and happy life, while creating a philosophy that Bakewell argues constitutes the greatest intellectual legacy of the bunch.
Just as Bakewell argued that Montaigne’s writings are newly relevant for his sense of moderation, so she argues that the existentialists are newly relevant for exploring the questions of authenticity and freedom. Not having read most of their work, I cannot comment on this. But what I found most inspiring was their burning desire to think and to write—and to write like mad, for hours each day, in every genre, for decades on end. Though most of this writing was born today to die tomorrow, each one of them produced a magisterial tomb for future readers to beat their heads against. I suppose I will have to pick them up sometime soon.
There are few phrases more annoying or more effective than “I told you so.”
This is my second encounter with Thomas Kuhn, and again I emerge deeply impressed. To do justice to an event so multifaceted as the Copernican Revolution a scholar must have a flexible mind; and Kuhn is fully equal to the task. He moves seamlessly from scientific data, to philosophical analysis, to historical context, and then back again. The result is a book that serves as an admirable introduction to the basics of astronomy and a thorough overview of the Copernican Revolution, while raising intriguing questions about the nature of scientific progress.
Kuhn first makes an essential point: that the conceptual schemes of science serve both a logical and a psychological function. Their logical function is to economically organize the data (in this case, the position and movement of heavenly objects); their psychological function is to make people feel at home in the universe. Belief is only necessary for this second function. A scientist can use a conceptual scheme perfectly well without believing that it represents how the universe ‘truly is’; but people have an obvious and, apparently, near-universal need to understand their place in, and relation to, the cosmos. Thus, scientists throughout history have insisted on the truth of their systems, despite the history science being littered with the refuse of abandoned theories (to use Kuhn’s expression). Even if this belief cannot be justified philosophically, however, it does provide a powerful emotional impetus to scientific activity.
Another question Kuhn raises is when and why scientists decide that an old paradigm is unsustainable and a new one is required. For centuries astronomers in the Muslim and Western worlds worked within the basic approach laid down by Ptolemy, hoping that small adjustments could finally remove the slight errors inherent in the system. During this time, the flexibility of the Ptolemaic approach—allowing for fine-tuning in deferents, equants, and epicycles—was seen as one of its strengths. Besides, the Ptolemaic astronomy was fully integrated within the wider Aristotelian science of the age; and this science blended perfectly with common everyday notions. The fact that the Ptolemaic science broke down is attributable as much, or more, to factors external to the science as to those internal to it. Specifically, with the Renaissance came the rediscovery of Neoplatonism, with its emphasis on mathematical harmonies—something absent from Aristotelianism—as well as its strain of sun-worship.
Copernicus was one of those affected by the new current of Neoplatonism; and it is this, Kuhn argues, that ultimately made him dissatisfied with the Ptolemaic system and apt to place the sun at the center of his system. We often hear of science progressing as a result of new experiments and empirical discoveries; but no such novel observation played a role in Copernicus’s innovation. Rather, the source of Copernicus’s rejection of an earth-centered universe was its inability to explain why the planets’ orbits are related to the sun’s. His system answered that question. But this was only an aesthetic improvement. It did not lead to more accurate predictions—the essential task of astronomy—and, indeed, it did not even lead to more efficient calculations. The oft-reproduced image of the Copernican universe, consisting of seven concentric circles, is a simplification; his actual system used dozens of circles and was cumbersome and difficult to use.
But the most puzzling feature of Copernicus’s innovation is that it achieves qualitative simplification at the expense of rendering it completely incompatible with the wider worldview. Aristotelian physics cannot explain why a person would not fly off of a moving earth. And, indeed, the entire cosmological picture, such as that painted so convincingly by Dante, ceases to make sense in a Copernican universe. For centuries people had understood the earth as a midpoint between the fires of hell and the perfect heavens above. Now, hell was only metaphorically “below” and heaven only metaphorically “above.” Besides that, the universe had to be expanded to mystifying proportions; the earth became only a small and unimportant speck in an unimaginably vast space. Strangely, however, Copernicus seemed blind to most of these consequences of his innovation. A specialist concerned only with creating a harmonious system, his attempt to render it physically plausible or theologically palatable is, at best, half-hearted.
This leads to the irony that one of the greatest intellectual revolutions in history started with a man concerned with technical minutiae inaccessible to the vast majority of the public, who had access to no fundamentally new data, whose system was neither more accurate nor more efficient than its predecessor, and whose main concern was qualitative harmoniousness. Copernicus was no radical and had no notion of upsetting the established authority; he himself would likely have been appalled at the Newtonian universe that was the end result of this process.
Yet this simple innovation, once proposed, had ripple effects. Though the earth’s motion was near universally rejected as a fact, its use in a serious astronomical work kept it alive as an option. And this new option could not be laughed away when, in the next generation under Tycho Brahe, better observations and novel phenomena upset the Ptolemaic world order. The heavens could no longer be seen as perfect and unchanging when Brahe proved that supernovae and comets do not exhibit a parallax (as in, they do not to change location when the observer moves), and thus could not be atmospheric phenomena. Further, Brahe’s unprecedentedly accurate observations of the planets were incompatible with any Ptolemaic system. This seems to be one of many cases in the history of science when novel observations followed, rather than preceded, a theoretical innovation.
Granted, this incongruence led Brahe to propose his own earth-centered system, the Tychonic, rather than adopt a sun-centered universe. But this new system used Copernican mathematics, and embodied the Copernican harmonies. In any case it is hard to see how the Tychonic system could ever have been anything but a stopgap, since the jump from Ptolemy to Brahe was scarcely easier than the jump from Ptolemy to Copernicus. Besides, it struck many as dynamically implausible that everything in the universe would orbit the sun except the earth and the moon.
Kepler and Galileo were among those unconvinced by the Tychonic system. The two very different men were both of an independent turn of mind, and their work finally made the Copernican universe unequivocally superior. Kepler particularly made the decisive step with his three laws: that planets orbit in ellipses with the sun at a foci, that they sweep out equal areas in equal times, and that they orbit the sun in a ratio of the 3/2 power (the orbital axis to the orbital time). But in Kepler we find further ironies. Far from the dispassionate lover of truth, Kepler was a Neoplatonic mystic, bursting with occult hypotheses. Many parts of his work strike the modern reader as scarcely more rational than the ravings of a conspiracy theorist. Yet the hard core of Kepler’s astronomical work lifted Copernicanism into a league of its own for accuracy of prediction and efficiency of calculation. If the orbits of the planets were related to the sun in such simple, elegant ways, it was difficult to see how earth could be at the center of it all.
This is my best attempt at summarizing the most salient points of the book. But of course there is far more in here, most of it worthwhile. I particularly enjoyed Kuhn’s chapter on the oft-ignored medieval research into physics, such as the impetus theory in the work of Nicole Oresme. The only weak point of the book was the rather brief epilogue to Copernicus. In particular, I would have appreciated an entire chapter devoted to Newton, since it was his Principia that was, in Kuhn’s phrase, the “capstone” of the revolution. But on the whole I think this is a superlative book, serious yet accessible, informative while brief. Kuhn captures the reality of scientific progress, which is far less neat that we may like to believe. Most striking is how a revolution which was guided by many extra-logical considerations—the Neoplatonic belief in celestial harmonies, the desire for mathematical elegance, the weakening of the religious worldview, the need to feel at home in the universe—fueled a process which, taken as a whole, resulted in a science definitively better than the Ptolemaic system it replaced.
Kuhn makes no mistake about this. Here is what the reputed relativist has to say:
The last two and one-half centuries have proved that the conception of the universe which emerged from the Revolution was a far more powerful intellectual tool than the universe of Aristotle and Ptolemy. The scientific cosmology evolved by seventeenth-century scientists and the concepts of space, force, and matter that underlay it, accounted for both celestial and terrestrial motions with a precision undreamed of in antiquity. In addition, they guided many novel and immensely fruitful research programs, disclosing a host of previously unsuspected natural phenomena and revealing order in fields of experience that had been intractable to men governed by the ancient world view.
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.
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.
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.
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.
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.)
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