Review: Sidereal Messanger

Review: Sidereal Messanger

Sidereus Nuncius, or The Sidereal MessengerSidereus Nuncius, or The Sidereal Messenger by Galileo Galilei

My rating: 4 of 5 stars

A most excellent a kind service has been performed by those who defend from envy the great deeds of excellent men and have taken it upon themselves to preserve from oblivion and ruin names deserving of immortality.

This book (more of a pamphlet, really) is proof that you do not need to write many pages to make a lasting contribution to science. For it was in this little book that Galileo set forth his observations made through his newly improved telescope. In 50-odd pages, with some accompanying diagrams and etchings, Galileo quickly asserts the roughness of the Moon’s surface, avers the existence of many more stars than can be seen with the naked eye, and—the grand climax—announces the existence of the moons of Jupiter. Suddenly the universe seemed far bigger, and stranger, than it had before.

The actual text of Siderius Nuncius does not make for exciting reading. To establish his credibility, Galileo includes a blow-by-blow account of his observations of the moons of Jupiter, charting their nightly appearance. The section on our Moon is admittedly more compelling, as Galileo describes the irregularities he observed as the sun passed over its surface. Even so, this edition is immeasurably improved by the substantial commentary provided by Albert van Helden, who gives us the necessary historical background to understand why it was so controversial, and charts the aftermath of the publication.

Though Galileo is sometimes mistakenly credited with inventing the telescope, spyglasses were widely available at the time; what Galileo did was improve his telescope far beyond the magnification commonly available. The result was that, for a significant span of time, Galileo was the only person on the planet with the technology to closely and accurately observe the heavens. The advantage was not lost on him, and he made sure that he published before he got scooped. In another shrewd move, he named the newly-discovered moons of Jupiter after the Grand Duke Cosimo II and his brothers, for which they were known as the Medician Stars (back then, the term “star” meant any celestial object). This earned him patronage and protection.

Galileo’s findings were controversial because none of them aligned with the predictions of Aristotelian physics and Ptolemaic astronomy. According to the accepted view, the heavens were pure and incorruptible, devoid of change or imperfection. Thus it was jarring to find the moon’s surface bumpy, scarred, and mountainous, just like Earth’s. Even more troublesome were the Galilean moons. In the orthodox view the Earth was the only center of orbit; and one of the strongest objections against Copernicus’s system was that it included two centers, the Sun and the Earth (for the Moon). Galileo’s finding of an additional center of orbit meant that this objection ceased to carry any weight, since in any case we must posit multiple centers. Understandably there was a lot of skepticism at first, with some scholars doubting the efficacy of Galileo’s new instrument. But as other telescopes caught up with Galileo’s, and new anomalies were added to the mix—the phases of Venus and the odd shape of Saturn—his observations achieved widespread acceptance.

Though philosophers and historians of science often emphasize the advance of theory, I find this text a compelling example of the power of pure observation. For Galileo’s breakthrough relied, not on any new theory, but on new technology, extending the reach of his senses. He had no optical theory to guide him as he tinkered with his telescope, relying instead on simple trial-and-error. And though theory plays a role in any observation, some of Galileo’s findings—such as that the Milky Way is made of many small stars clustered together—are as close to simple acts of vision as possible. Even if Copernicus’s theory was not available as an alternative paradigm, it seems likely to me that advances in the power of telescopes would have thrown the old worldview into a crisis. This goes to show that observational technology is integral to scientific progress.

It is also curious to note the moral dimension of Galileo’s discovery. Now, the Ptolemaic system is commonly lambasted as narcissistically anthropocentric, placing humans at the center of it all. Yet it is worth pointing out that, in the Ptolemaic system, the heavens are regarded as pure and perfect, and everything below the moon as corruptible and imperfect (from which we get the term “sublunary”). Indeed, Dante placed the circles of paradise on the moon and the planets. So arguably, by making Earth the equal of the other planets, the new astronomy actually raised the dignity of our humble abode. In any case, I think that it is simplistic to characterize the switch from geocentricity to heliocentricity as a tale of declining hubris. The medieval Christians were hardly swollen with pride by their cosmic importance.

As you can see, this is a fascinating little volume that amply rewards the little time spent reading it. Van Helden has done a terrific job in making this scientific classic accessible.

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Gimme Shelter: Santander & Altamira

Gimme Shelter: Santander & Altamira


On Spain’s northern coast, sandwiched between Asturias and the Basque Country, is a little slice of land that makes up the province of Cantabria. Like the rest of Spain’s northern coast, influenced by the Oceanic climate blowing down from the Bay of Biscay, it is a lush and verdant region that gets plenty of rain. Though somewhat less popular as a tourist destination than its neighboring provinces, the region’s capital, Santander, is widely recognized for the eponymous international bank, Banco Santander—Spain’s biggest bank and second-largest company.

And it seems that the capital is bound to receive new visitors, thanks in part to the recently opened Botín Center. This building takes its name from the family that owns the bank (and who financed the project), and is designed to rival the Guggenheim in Bilbao, just a couple hours east by car. Like that Basque museum, designed by Frank Gehry, the Botín Center is a museum of modern art housed in a striking modern edifice, in this case designed by the Italian architect Renzo Piano. I happened to visit Santander in April of 2017, when the building was complete but had yet to open its doors to the public. From the outside the museum looks like an alien spacecraft which has been neatly bifurcated. It is in a beautiful area, right on the water, a fact which has irritated some local critics, but which undoubtedly adds to its charm. Though I haven’t been inside, I read online that there is a room dedicated to drawings by Goya (on loan from the Prado) and another room dedicated to installations by contemporary artists. I hope to visit someday.


This center—looking incongruously futuristic against the serene waters of the bay, surrounded by fishermen—was, by chance, one of my first glimpses of the city. My Blablacar driver had dropped me off nearby. I was, as usual, disoriented and ragged, from having gotten up so early; and I still had several hours to kill before I could drop off my bag at my Airbnb. So I had little choice but to trek heavily around the city for several hours.


Santander is a maritime city, perched on a peninsula wrapped around a beautiful bay. The walk along the water is wonderfully picturesque, with stately building on one side and green mountains across the blue water—and it was especially nice since, when I visited, the sidewalk was the site of a street fair. Proceeding upwards this way, I walked by the memorable Palacio de Festivales, a municipal event space, and then the Maritime Museum, which has an aquarium and some impressive fishy fossils on display. I also saw the monument to the raqueros, or beachcombers, a whimsical group of faceless statues about to dive into the water. Continuing onwards, I got to the end of the peninsula, which consists of a lovely park area. There were several families having a picnic, and I am sure I looked fairly ridiculous as I strode by with my disheveled grey hoodie and my bulging green suitcase.

Walking on in this tiresome manner, I got to the Palacio de la Magdalena, Santander’s royal residence. This was actually built by popular subscription (the royal family was more popular in those days) and gifted to the king, in 1911. The royals did not have very many years to enjoy it, however, since the Second Spanish Republic (1931) and then the Civil War (1936) put an end to their annual peregrinations. The palace is built in a gaudy eclectic style, heavily indebted to the English; but it has an undeniably nice view of the sea. Nowadays it is used for conferences and suchlike things. Looking out from the tip of the peninsula, I saw the azure bay filled with little sailboats. My Santanderino friend, who himself has a sailing permit, informs me that this maritime pastime is very popular in the city. Certainly it is a good place for it.


As I walked on westward, more and more of the Cantabrian coast opened up into view, a rugged rocky coast bathed by serene waves (though I am sure it gets rather stormy sometimes). I walked by an open-air museum, grandly named the Museum of Man and the Sea, but which consists of three reconstructions of old galleons. I believe they were meant to represent the three ships which sailed with Columbus to the New World, the Niña, Pinta, and Santa María, though to my eyes they looked too small. A little further I encountered an open-air zoo, with walkways overlooking a pool in which seals were restlessly swimming.

Finally I reached Santander’s major beach: the Sardinero. This is about as nice a beach as anyone can ask for: with golden sand and ample space. Hotels and restaurants hemm in the coast, of course, while sailboats float out in the distance. In the summer I imagine the place is crawling with people; but when I arrived, a few months before proper swimming weather, the beach was charmingly empty, even peaceful. Looking back from the beach toward the palace, I was struck by how jagged and natural the coast appeared, despite being in the center of a city.


Now it was time to drop off my things. As usual, I had booked the cheapest Airbnb I could find, which was far outside the city center, deep in the industrial part of the city. Also as usual, I did not want to pay for a cab. So I walked an hour and a half, through the city, under the sun, sweating and stumbling, across highways and past strip malls, until finally reaching my destination. By saving money, I also stay thin.

Returning to the city was far less painful, not only because I wasn’t dragging around my bag, but also because my Airbnb host told me which bus to take. Thus in less than half an hour I was back in the center, ready to see more.

Though Santander’s history stretches back to medieval times—its position on the bay is a natural spot for settlements—the visitor will not notice any of the chaotic, jumbled, narrow streets characteristic of old cities. This is largely due to the great fire of 1941, which destroyed most of the old center and left thousands homeless. The conflagration occurred during the lean years following the Spanish Civil War, when the resultant poverty occasioned many accidents around the country. As a result of this catastrophe, the center is crisscrossed with wide, perpendicular streets and full of modern buildings. There is a monument to the blaze—several human figures, looking hopeless and lost—in the park near the Botín Center.

One of the buildings damaged in the blaze was Santander’s medieval Cathedral. What stands today is largely a reconstruction. The cathedral struck me as rather odd, with its stark, white exterior almost wholly devoid of ornament. To go inside one must climb a flight of stairs, for the cathedral is not level with the street. I remember going through one door, only to find it full of a congregation midway through mass. This was the crypt, which is used as an independent church, La Iglesia del Cristo. The cathedral stands on top of this crypt-church; this is why the space is so claustrophobic and full of thick supports. Though finely vaulted, the cathedral’s interior was not any more richly adorned than its exterior. I admit that I left the building feeling rather baffled, since at the time I did not know that the original church had mostly burned down, or that there were two separate churches in the same building.


Quite nearby is the original building of Banco Santander, a stately edifice that projects conservative dignity, very appropriate for a bank. You can pass through the central arch of this building to the other side, and then make your way to the Pedro Velarde Square. The plaza was named after a Spanish soldier who was involved in the much-mythologized uprising of May 2nd against Napoleon’s invading troops (a scene immortalized by Goya). A statue of this fierce patriot stands guard over the entrance to the square. The plaza is surrounded by a uniform row of attractive apartment buildings, much like the Plaza Mayor in Salamanca, making it an excellent spot for photos. I should also note that there are many fine restaurants nearby.

One of the city’s most intriguing sites is right next to this plaza, the air raid shelter, or refugio antiaéreo. As one might expect, this is not very conspicuous from the street, merely consisting of a stairwell. I was fortunate in being able to visit, since you normally need to reserve a spot in advance, and I had not done so. What is more, all visits to the tunnels are guided, which meant I would have to hitch a spot with another group. But by chance, as I approached the entrance to the shelter, another visiting couple (from Madrid) was inquiring about tours, too, so I was able to join theirs. Being a third wheel has seldom proven so educational.


The shelter was built during the Spanish Civil War. Though Santander was not of paramount strategic importance and was not the scene of major fighting, the city was nevertheless the target of bombing raids by the fascist forces. In Madrid, metro stations were refitted to be used as bomb shelters; but lacking a metro system, the people of Santander had to build shelters from scratch—and quickly. This shelter is not very big (maybe 100 people could have squeezed into it, briefly) and consisted of several interconnected concrete passageways. Our tour guide gave us some of the context of the war and the history of the tunnel’s construction. There were a few video clips, examples of uniforms worn by the fascist (many of them Germans) and Republican pilots, and sound clips designed to reproduce the feeling of being underground during a bombing. Although the shelter did not get much use, since Santander was taken by Franco’s forces fairly early on during the war, it remains a moving artifact of the new horrors of aerial warfare, dropping death indiscriminately on enemy cities—something the world had never seen before.

After this, I decided to visit the Prehistory and Archaeology Museum of Cantabria, which is just down the road from the shelter. This was good to save for last, since it is open quite late—until 8 pm during the summer. Here I found myself descending underground once again, for the museum’s collection is below street level. Intentionally or not, the sun-less, cave-like interior of the museum adds to the evocative power of its exhibitions about early humans. I was in the right mindset to learn about stone tools and extinct bears. Even so, I did not expect to encounter such a fine museum. Somehow, I imagined that it would be mainly geared towards children; yet within minutes I was spellbound by the quality of the displays. It is superbly made.

Admittedly I was predisposed to be interested, since I studied archaeology in college and even tried my hand at making stone tools once. Even so, I think anyone can appreciate the scope of information and the skill in presentation to be found there. On display are hundreds of stone tools—choppers, knives, arrowheads—arranged chronologically, showing the increasing sophistication of human ancestors over time. There are also recreations of tools made from wood and antler (which normally do not survive the ages), accompanied by videos of people making and even using these tools. This was not all. There was a recreation of a shellfish midden, a refuse pile left by generations of ancient shellfish-eaters; there were fossils of extinct animals, many of them massive; there were stone megaliths covered with decorative carvings; and there were even some Roman artifacts. When I visited I was the only person there, and stayed until it closed. It was an enchanting experience.

The evolution of tools, from oldest (top) to youngest (bottom)

Though this did not happen on the same day, for the sake of continuity I will mention my visit to the Hermitage of La Virgen del Mar. This is quite far from the city; I was only able to visit thanks to my aforementioned Santanderino, who kindly drove me there. The building of the hermitage itself is quite bare and basic. But its location, like that of San Juan de Gaztelugatxe, is exquisite, standing atop an island (very close to shore) next to a rocky, windswept beach. It is a gorgeous, romantic place that preserves its peaceful, natural beauty, despite the constant trickle of tourists.

This fairly does it for my time in Santander. I was dividing my limited time—a single weekend—between this city and Altamira (which I will describe next), so I did not get to know Santander as well as I should have liked. Even so, I was left with fond memories. Both the city itself and its location on the shore make it one of the great cities of northern Spain, reminding me most nearly of La Coruña in Galicia—one of my favorite places in the country. The rugged coast, oceanic weather, attractive center, and cultural monuments make the city one more delightful stopping-place in the Spanish panorama. And as you will shortly see, Cantabria has much more to offer.



The cave paintings of Altamira are perhaps only behind those of Lascaux in renown. Luckily, the site of their discovery is quite close to Santander, making it an easy daytrip. In a car the trip is around half an hour. And there are fairly frequent buses (every two hours) that run from the city center to town nearest the caves, Santillana del Mar.

I arrived in this town on a Saturday morning, shivering with excitement. Ever since I saw Werner Herzog’s transfixing documentary on the caves of Lascaux—Cave of Forgotten Dreams—I have been fascinated by the artistic power of our early ancestors. As a child I wondered at the enormous antiquity of the artifacts from Egypt in the Metropolitan Museum of Art. Yet the span of time between us and the people who painted these caves is far vaster. That an image created from a human hand could survive so many years—that it could speak to us from an age when strange extinct animals roamed the earth, when the stars in the sky were shifted, when the climate was altered and cold winds blew down from nearby glaciers—and not only speak to us, but entrance us with its beauty—it seemed too miraculous to believe. And thus it seemed even more stupendous that I could, with my own eyes, witness this temporal miracle.

I should stop my melodrama to note at this point that I was not going to see the actual paintings. These are much too precious and delicate to be casually seen by the general public. The organization has a lottery that they hold on Fridays in the museum, to select five lucky people to visit the caves. Since I was visiting on a Saturday, this left me with scant hope. But after closing the caves to public visits in 2002, the authorities have constructed a replica (called the “neocueva,” or “neo-cave”) that can be visited freely. This is what I was going to see.

The bus dropped me off in the center of town. I had bought my ticket ahead, which had a timed entrance to see the neo-cave. (Because of restricted space, smallish groups are allowed in at staggered times.) My entrance was in less than an hour, so I had little time to spare. Without pausing to catch a glimpse of the town, I strode out into the countryside towards the hill of Altamira. Even through my anxiety and morbid determination, however, I could not help noticing that the countryside was absolutely lovely. Gentle rolling hills, green with grass, dotted with trees, crisscrossed with plots of farmland, spread out ahead of me. White mist clung to the distance, as black-and-white cows grazed before a lonely church; and to my right were the tiled roofs of Santillana del Mar. Spain has seemingly boundless reserves of beauty.

I arrived at the museum with 20 minutes to spare (of course). This was hardly a problem, since the neo-cave comprises only a part of the display. There are dioramas of ancient peoples, skulls of ancestral species, piles of stone tools, and smaller replicas of cave art. Not bad for three euros—a modest price which includes the neo-cave, too. I particularly liked the examples of shapes made on the cave wall by blowing pigment against a hand, thus creating a reverse hand-print. There is something elemental about this gesture, allowing us to shake hands with someone from a different epoch. Perhaps all culture is rooted in the attempt to cheat death—sometimes literally, as with weapons and medicine, and sometimes figuratively, as with art. These cave-dwellers lived short and difficult lives compared to us; but will we leave any art that survives half so long?


Finally it was time for me to visit the neo-cave.  I joined a small group of waiting tourists, while a placid employee scanned our tickets. Finally, like the heavy gates to an ancient city, the doors of the neo-cave slid open. I could scarcely have been more excited if the caves had been real.

A single footpath leads down through the neo-cave, into the main chamber, and out again. Some introductory panels of information are posted along the way; and a glass screen projects a cave-dwelling family into the artificial cave—the Jetsons meet the Flintstones. All of this is got through in five minutes. The rest of the time is spent gazing up at the ceiling of the main chamber. Photos are not allowed, which is likely a good thing, since the combination of lighting, angle, and surface texture would make it difficult to capture the chamber. In any case, the paintings are reproductions anyway, so why reproduce them once over?

The main chamber consists of a roughly square space with a low, uneven ceiling, which has been covered with paintings. Most of these consist of hooved animals, most prominently bison. These are executed using charcoal and red ochre. The round bodies of the bison crowd around each other, sometimes overlapping, and conform to the bumpy, bulging surface of the cave. As a rough estimate, the average size of these figures is three feet across; and there must be several dozen individual figures. As is inevitable with prehistoric art, many mysteries remain as to the origin and function of these paintings. We know that they were completed during the last ice age, before the cave was sealed by a rockslide 13,000 years ago; but beyond that there is a wide range of possible dates. We may safely surmise that the bison were prey animals, and tentatively guess that these paintings were involved in some kind of ritual to ensure plentiful food. But we do not know if they were painted all at once—perhaps by a few brilliant painters—or over the course of generations, perhaps even used successively by distinct cultural groups. However we may guess, we do not know what these paintings meant to their creators. We cannot even rule out the possibility that they were made by neanderthals, not humans.

The neo-cave is lit up by discrete LED lights in the built into the floors, walls, and ceilings. It is tastefully done; but no electric light can replicate how these caves must have looked when seen by firelight. In the weak, quivering glow of the flames, these bison may have been terrifying apparitions, seeming to run and dance in the unsteady light. Given the location of these paintings and the light-sources available to people at the times, it seems unlikely that the creators saw them the way that we are inclined to: as works of visual art, to be contemplated for their great aesthetic beauty. But that does not mean that we are not free to view them this way. The bison are somehow both stylized and realistic. They represent the lumbering form of the animal—powerful, meaty, muscular—with relatively few, bold strokes, reducing the animals to their most essential features. Yet this does not render them to caricature, but turns them into elemental monsters, like fire or rain. Clearly these artists had carefully observed real bison, and fully understood the animals’ essential role in their survival.


After I emerged from the neo-cave, blinking and exhausted, I was left with that sense of empty purposelessness that accompanies the doing of any long-awaited thing. Now what? I strolled around the museum some more, but I had already had my fill of prehistory museums in Santander. Then the idea struck me to see if I could find the entrance of the cave.

This is very easy to do, for the cave stands within five minutes of the museum compound. You cannot get very close, since it is closed off with an ample fence (I bet vandals and thrill-seekers occasionally try to break in); and in any case, there is not much to see, just a little doorway covered with a barred gate. It was hard to believe that beyond that small portal lay one of the most remarkable finds in the history of art.

After being sealed by a rockslide around 13,000 years ago, the cave became a natural time capsule. Apparently the cave’s entrance had become revealed by the 19th century, since by then it was visited by locals. One of these locals was Marcellino Sanz de Sautuola, a well-to-do Spaniard who both happened to own the land and have an interest in archaeology—a fortunate coincidence. After being led into the cave by his young daughter and realizing the importance of the paintings, Sautuolo cooperated on the original publication announcing their existence. Sadly, academics dismissed his claim of the paintings’ great antiquity, and he died before the truth was realized—an unfortunate coincidence.


Now I was absolutely famished, so I descended the Altamira hill back to Santillana del Mar, once more passing through the delicious countryside. Contrary to what you might expect, Santillana del Mar is not actually on the sea, only somewhat near it (15 minutes by car). I had assumed that there was another Santillana somewhere in Spain, but I cannot find any, which leaves me wondering why they thought it necessary to add “del Mar” to their name. In any case, this pueblo is routinely included in lists of beautiful Spanish villages, and for good reason. Long before the Altamira caves were discovered, it was a stopping point on the Camino de Santiago, which meant that a fair amount of monied pilgrims travelled through these streets. The result is an extremely handsome village, well worth visiting even if you do not, for some insane reason, visit the Altamira site.


For lunch, I went to a restaurant whose name I unfortunately did not write down. It was one of the best meals I have had in Spain. I sat on a balcony overlooking some of the surrounding countryside, drinking an ice-cold red wine, with a brash, fruity flavor. Because I was alone, and had ordered the daily menu, they gave me a full bottle of wine all to myself (which I mercifully decided not to finish). For the main course I was served cocido montañés, the typical stew of Cantabria. Now, many regions of Spain have their own type of stew; and they are all broadly similar, consisting of beans and cured meat. This particular variety is made with white beans and collard greens, making it somewhat lighter than other cocidos. With wine, cocido, a salad, and a slice of cake in my belly, I waddled back to the bus stop to return to Santander.

I left Cantabria thinking of the mysterious power of shelter. The cramped church underneath the cathedral, the air raid shelter underneath the street, and the caves of Altamira—all of them created a similar emotional atmosphere, at once safe and unsafe. These spaces protect us from what is outside; and yet the claustrophobic darkness within is unnerving, and even frightening. A Jungian might say the visitor delves into a deeper layer of the unconscious, while a Freudian might be content by pointing out that caves remind us of a mother’s womb. Leaving psychoanalyzing to one side, I will only point out that, thousands of years ago, our ancestors were driven into caves to hide from the elements and to make contact with spirits; and now, thousands of years later, we are making caves for the same reasons—to hide and to pray.

[See real cave entrance, story of their discovery, eating in town

Review: Almagest

Review: Almagest

The Almagest: Introduction to the Mathematics of the HeavensThe Almagest: Introduction to the Mathematics of the Heavens by Ptolemy

… it is not fitting even to judge what is simple in itself in heavenly things on the basis of things that seem to be simple among us.

In my abysmal ignorance, I had for years assumed that tracking the orbits of the sun and planets would be straightforward. All you needed was a starting location, a direction, and the daily speed—and, with some simple arithmetic and a bit of graph paper, it would be clear as day. Attempting to read Ptolemy has revealed the magnitude of my error. Charting the heavenly bodies is a deviously complicated affair; and Ptolemy’s solution must rank as one of the greatest intellectual accomplishments of antiquity—fully comparable with the great scientific achievements of European Enlightenment. Indeed, Otto Neugebauer, the preeminent scholar of ancient astronomy, went so far as to say:

One can perfectly well understand the ‘Principia’ without much knowledge of earlier astronomy but one cannot read a single chapter in Copernicus or Kepler without a thorough knowledge of Ptolemy’s “Almagest”. Up to Newton all astronomy consists in modifications, however ingenious, of Hellenistic astronomy.

With more hope than sense, I cracked open my copy of The Great Books of the Western World, which has a full translation of the Almagest in the 16th volume. Immediately repulsed by the text, I then acquired a students’ edition of the book published by the Green Lion Press. This proved to be an excellent choice. Through introductions, preliminaries, footnotes, and appendices—not to mention generous omissions—this edition attempts to make Ptolemy accessible to a diligent college student. Even so, for someone with my background to attain a thorough knowledge of this text, he would still require months of dedicated study with a teacher as a guide. For the text is difficult in numerous ways.

Most obviously, this book is full of mathematical proofs and calculations, which are not exactly my strong suit. Ptolemy’s mathematical language—relying on the Greek geometrical method—will be unfamiliar to students who have not read some Euclid; and even if it is familiar, it proves cumbrous for the sorts of calculations demanded by the subject. To make matters worse, Ptolemy employs the sexagesimal system (based on multiples of 60) for fractions; so his numbers all must be converted into our decimals for calculation. What is more, even the names of the months Ptolemy uses are different, bearing their Egyptian names (Thoth, Phaöphi, Athur, etc.), since Ptolemy was an Alexandrian Greek. Yet even if we put these technical obstacles to the side, we are left with Ptolemy’s oddly infelicitous prose, which the translator describes thus:

In general, there is a sort of opacity, even awkwardness, to Ptolemy’s writing, especially when he is providing a larger frame for a topic or presenting a philosophical discussion.

Thus, even in the non-technical parts of the book, Ptolemy’s writing tends to be headache-inducing. All this combines for form an unremitting slog. So since my interest in this book was amateurish, I skimmed and skipped liberally. Yet this text is so rich that, even proceeding in such a dilettantish fashion, I managed to learn a great deal.

Ptolemy’s Almagest, like Euclid’s Elements, proved so comprehensive and conclusive when it was published that it rendered nearly all subsequent astronomical work obsolete or superfluous. For this reason, we know little about Ptolemy’s predecessors, since there was little point in preserving their work after Ptolemy summed it up in such magnificent fashion. As a result it is unclear how much of this book is original and how much is simply adapted. As Ptolemy himself admits, he owes a substantial debt to the astronomer Hipparchus, who lived around 200 years earlier. Yet it seems that Ptolemy originated the novel way of accounting for the planets’ position and speed, which he puts forth in later books.

Ptolemy begins by explaining the method by which he will measure chords; this leads him to construct one of the most precise trigonometric tables from antiquity. Later, Ptolemy goes on to produce several proofs of spherical trigonometry, which allows him to measure distances on the inside of a sphere, making this book an important source for Greek trigonometry as well as astronomy. Ptolemy also employs Menelaus’ Theorem, which also uses the fixed proportions of a triangle to establish ratios. From this I see that triangles are marvelously useful shapes, since they are the only shape which is rigid—that is, the angles cannot be altered without also changing the ratio of the sides, and vice versa. This is also, by the way, what makes triangles such strong structural components.

Ptolemy gets down to business in analyzing the sun’s motion. This is tricky for several reasons. For one, the sun does not travel parallel to the “fixed stars” (so called because the stars do not position change relative to one another), but rather at an angle, which Ptolemy calculates to be around 23 degrees. We now know this is due to earth’s axial tilt, but for Ptolemy is was the obliquity of the ecliptic. Also, the angle that the sun travels through the sky is determined by one’s latitude; this also determines the seasonal shifts in day-length; and during these shifts, the sun rises on different points on the horizon. To add to these already daunting variables, the sun also shifts in speed during the course of the year. And finally, Ptolemy had to factor in that the procession of the equinoxes—the ecliptic’s gradual westward motion from year to year.

The planets turn out to be even more complex. For they all exhibit anomalies in their orbits which entail further complications. Venus, for example, not only speeds up and slows down, but also seems to go forwards and backwards along its orbit. This leads Ptolemy to the adoption of epicylces—little circles which travel along the greater circle, called the “deferent,” of the planet’s orbit. But to preserve the circular motion of the deferent, Ptolemy must place the center (called the “eccentric”) away from earth. Then, Ptolemy introduces another imaginary circle, around which the planet travels with constant velocity: and the center of this is called the “equant.” Thus the planet’s motion was circular around one point (the eccentric) and constant around another (the equant), neither of which coincide with earth. In addition to all this, the orbit of Venus is not exactly parallel with the sun’s orbit, but tilted, and its tilt wobbles throughout the year. For Ptolemy to account for all this using only the most primitive instruments and without the use of calculus or analytic geometry is an extraordinary feat of patience, vision, and drudgery.

Even after writing all this, I am not giving a fair picture of the scope of Ptolemy’s achievement. This book also includes an extensive star catalogue, with the location and brightness of over one thousand stars. He argues strongly for earth’s sphericity and even offers a calculation of earth’s diameter (which was 28% too small). Ptolemy also calculates the distance from the earth to the moon, using the lunar parallax (the difference in the moon’s appearance when seen from different positions on earth), which comes out the quite accurate figure of 59 earth radii. And all of this is set forth in dry, sometimes baffling prose, accompanied by pages of proofs and tables. One can see why later generations of astronomers thought there was little to add to Ptolemy’s achievement, and why Arabic translators dubbed it “the greatest” (from which we get the English name).

A direct acquaintance with Ptolemy belies his popular image as a metaphysical pseudo-scientist, foolishly clinging to a geocentric model, using ad-hoc epicycles to account for deviations in his theories. To the contrary, Ptolemy scarcely ever touches on metaphysical or philosophical arguments, preferring to stay in the precise world of figures and proofs. And if science consists in predicting phenomena, then Ptolemy’s system was clearly the best scientific theory around for its range and accuracy. Indeed, a waggish philosopher might dismiss the whole question of whether the sun or the earth was at the “center” as entirely metaphysical (is it falsifiable?). Certainly it was not mere prejudice that kept Ptolemy’s system alive.

Admittedly, Ptolemy does occasionally include airy metaphysical statements:

We propose to demonstrate that, just as for the sun and moon, all the apparent anomalistic motions of the five planets are produced through uniform, circular motions; these are proper to the nature of what is divine, but foreign to disorder and variability.

Yet notions of perfection seem hard to justify, even within Ptolemy’s own theory. For the combined motion of the deferent and the epicycle do not make a circle, but a wavy shape called an epitrochoid. And the complex world of interlocking, overlapping, slanted circles—centered on imaginary points, riddled with deviations and anomalies—hardly fits the stereotypical image of an orderly Ptolemaic world.

It must be said that Ptolemy’s system, however comprehensive, does leave some questions tantalizingly unanswered. For example, why do Mercury and Venus stay within a definite distance from the sun, and travel along at the same average speed as the sun? And why are the anomalies of the “outer planets” (Mars, Jupiter, Saturn) sometimes related to the sun’s motion, and sometimes not? All this is very easy to explain in a heliocentric model, but rather baffling in a geocentric one; and Ptolemy does not even attempt an explanation. Even so, I think any reader of this volume must come to the conclusion that this is a massive achievement—and a lasting testament to the heights of brilliance and obscurity that a single mind can reach.

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Review: Life on the Mississippi

Review: Life on the Mississippi

Life on the MississippiLife on the Mississippi by Mark Twain

My rating: 3 of 5 stars

And, mind you, emotions are among the toughest things in the world to manufacture out of whole cloth; it is easier to manufacture seven facts than one emotion.

This is an awkward book to review, since it consists of so many, varied sections. Yet it can be neatly divided between the first third and the remaining portion. After a few brief chapters about the mighty river and its history, the beginning section focuses on Twain’s young days as a steersman aboard Mississippi River steamboats. These are easily the best pages. As evinced by the Huckleberry Finn stories, Twain had a marvelous way of writing from a child’s perspective, naively learning to navigate the world. What is more, Twain does an excellent job in illustrating the extensive knowledge necessary to effectively pilot a steamboat—memorizing hundreds of landmarks, learning how to gauge speed and depth, and dealing with difficult coworkers.

The second section is a meandering account of a voyage he took two decades after leaving the steamboat business, when he was an accomplished author. At this point he was already so famous he had to adopt a pseudonym. Here he pauses so often to lose himself in tributary wanderings that the narrative breaks down into a vaguely connected series of anecdotes, most of which seem obviously inflated or simply fictional. Though there is much to amuse in this section, I found myself growing increasingly restless and bored as I continued on, eager for the end. Though I did not dislike this book as much as I did A Connecticut Yankee, I nevertheless felt that the joke had gone stale and that Twain was merely filling up space.

My reactions to Twain tend to shift violently. Again, in the beginning section of this work, when he is writing from the perspective of his younger self, his writing is energetic and witty and wide-eyed. But when he dons the cap of a raconteur, I tend to find his stories mechanical and dull. His account of the Pilots’ Association is an excellent example of this—proceeding in predictable steps to the inevitable conclusion. And when he shifts away from humor, the results can be pretty grim. His flat-footed tall tale of the man who sought revenge for his murdered family—a mix of the ghoulish and the sentimental—is an excellent example of this.

Even with these faults and lapses, this book is an unforgettable portrait of a time and place that are gone for good, written by an indefatigably mordant pen.

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Review: The New Organon

Review: The New Organon

The New OrganonThe New Organon by Francis Bacon

My rating: 4 of 5 stars

Since I’ve lately read Aristotle’s original, I thought I’d go ahead and read Bacon’s New Organon. The title more or less says it all. For this book is an attempt to recast the method of the sciences in a better mold. Whereas Aristotle spends pages and pages enumerating the various types of syllogisms, Bacon dismisses it all with one wave of the hand—away with such scholarly nonsense! Because Aristotle is so single-mindedly deductive, his scientific research came to naught; or, as Bacon puts it, “Aristotle, who made his natural philosophy a mere bond servant to his logic, thereby [rendered] it contentious and well-nigh useless.”

What is needed is not deduction—which draws trivial conclusions form absurd premises—but induction. More specifically, what is needed is a great deal of experiments, the results of which the careful scientist can sort into air-tight conclusions. Down with the syllogism; up with experiment. Down with the schoolmen; up with the scientists.

In my (admittedly snotty) review of Bacon’s Essays, I remarked that he would have done better to have written a work entirely in aphorisms. Little did I know that Bacon did just that, and it is this book. Whatever Bacon’s defects were as a politician or a philosopher, Bacon is the undisputed master of the pithy, punchy maxim. In fact, his writing style can be almost sickening, so dense is it with aphorism, so rich is it with metaphor, so replete is it with compressed thought.

In the first part of his New Organon all of the defects of Bacon’s style are absent, and all of his strengths are present in full force. Indeed, if this work consisted of only the first part, it would have merited five stars, for it is a tour de force. Bacon systematically goes through all of the errors the human mind is prone to when investigating nature, leaving no stone unturned and no vices unexamined, damning them all in epigram after epigram. The reader hardly has time to catch his breath from one astonishing insight, when Bacon is on to another.

Among these insights are, of course, Bacon’s famous four idols. We have the Idol of the Tribe, which consist of the errors humans are wont to make by virtue of their humanity. For our eyes, our ears, and our very minds distort reality in a systematic way—something earlier philosophers had, so far as I know, neglected to account for. We have then the Idols of the Cave, which are the foibles of the individual person, over and above the common limitations of our species. Of these may include certain pet theories, preferences, accidents of background, peculiarities of taste. And then finally we have the Idols of the Market Place, which are caused by the deceptive nature of language and words, as well as the Idols of the Theater, which consists of the various dogmas present in the universities and schools.

Bacon also displays a remarkable insight into psychology. He points out that humans are pattern-seeking animals, which leads us to sometimes see patterns which aren’t there: “The human understanding is of its own nature prone to suppose the existence of more order and regularity in the world than it finds.” Bacon also draws the distinction, made so memorable in Isaiah Berlin’s essay, between foxes and hedgehogs: “… some minds are stronger and apter to mark the differences of things, others to mark their resemblances.” Bacon also notes, in terms no psychologist could fault, a description of confirmation bias:

The human understanding when it has once adopted an opinion (either as being the received opinion or as being agreeable to itself) draws all things else to support and agree with it. And though there be a greater number and weight of instances to be found on the other side, or else by some distinction sets aside and rejects, in order that by this great and pernicious predetermination the authority of its former conclusions may remain inviolate.

Part two, on the other hand, is a tedious, rambling affair, which makes the patient reader almost forget the greatness of the first half. Here, Bacon moves on from condemning the errors of others to setting up his own system. In his opinion, scientific enquiry is a simple matter of tabulation: make a table of every situation in which a given phenomenon is always found, and then make a table of every situation in which a given phenomenon is never found; finally, make a table of every situation in which said phenomenon is sometimes found, shake well, and out comes your answer.

The modern reader will not recognize the scientific method in this process. For we now know that Bacon’s induction is not sufficient. (Though, he does use his method to draw an accurate conclusion about the nature of heat: “Heat is a motion, expansive, restrained, and acting in its strife upon the smaller particles of bodies.”) What Bacon describes is more or less what we’d now call ‘natural history’, a gathering up of facts and a noting of regularities. But the scientific method proper requires the framing of hypotheses. The hypothesis is key, because it determines what facts need to be collected, and what relationship those facts will have with the theory in question. Otherwise, the buzzing world of facts is too lush and fecund to tabulate; there are simply too many facts. Furthermore, Bacon makes the somewhat naïve—though excusable, I think—assumption that a fact is simply a fact, whereas we now know that facts are basically meaningless unless contextualized; and, in science, it is the theory in question which contextualizes said facts.

The importance of hypotheses also makes deduction far more important than Bacon acknowledges. For the aspiring experimentalist must often go through a long chain of deductive reasoning before he can determine what experiment should be performed in order to test a theory. In short, science relies on both deductive and inductive methods, and the relationship of theory to data is far more intertwined than Bacon apparently thinks. (As a side note, I’d also like to point out that Bacon wasn’t much of a scientist himself; he brings up the Copernican view of the heliocentric solar system many times, only to dismiss it as ridiculous, and also seems curiously unaware of the other scientific advances of his day.)

In a review of David Hume’s Enquiry Concerning the Principles of Morals, I somewhat impertinently remarked that the English love examples—or, to use a more English word, instances. I hope not to offend any English readers, but Bacon confirms me in this prejudice—for the vast bulk of this work is a tedious enumeration of twenty-seven (yes, that’s almost thirty) types of ‘instances’ to be found in nature. Needless to say, this long and dry list of the different sorts of instances makes for both dull reading and bad philosophy, for I doubt any scientist in the history of the world ever made progress by sorting his results into one of Bacon’s categories.

So the brilliant, brash, and brazen beginning of this book fizzles out into pedantry that, ironically enough, rivals even Aristotle’s original Organon. So, to repeat myself, the title of this book more or less says it all.

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Review: Organon (Aristotle)

Review: Organon (Aristotle)

OrganonOrganon by Aristotle

My rating: 3 of 5 stars

Aristotle continues to provoke conflicting reactions in me. I am always torn between realizing his tremendous originality and historical importance, and suffering from his extraordinary dullness. This book exemplifies both sides of the coin. Seeing a man single-handedly create the field of logic, ex nihilo, is tremendous; yet reading through these treatises could put a coffee-addict in a coma.

I am not insensitive to the appeals of philosophy. Far from it; I think reading philosophy is thrilling. Some of my most acute aesthetic experiences have been had contemplating some philosopher’s idea. Yet I have never had this reaction to Aristotle’s writings. Part of this is due to his formidable difficulty; another part, to the nature of the works (which, I must constantly remind myself, are lecture-notes).

Nevertheless, Aristotle had a prosaic mind; even when faced with the most abstract phenomena in the universe, his first reaction is to start parceling everything into neat categories, and to go on making lists and explanations of these categories. He does make logical arguments, but they are often brief, and almost as often unsatisfactory. Much of the time the student is faced with the dreary task of working his way through Aristotle’s system, simply because it is his system, and not because it is empirically or logically compelling.

(Every time I write a review for Aristotle, it comes out so disappointed. Let me try to be more positive.)

My favorite piece in this was the Posterior Analytics, which is a brilliant treatise on epistemology, logic, and metaphysics. Aristotle succinctly presents an entire theory of knowledge, and it’s incomparably more rigorous and detailed than anything Plato could have produced. I also particularly liked the Topics, as there we see Aristotle as a seasoned debater, in addition to a bumbling professor. Of course, there is much of strictly philosophic interest in this work as well; a particularly memorable problem is that of the future naval-battle.

For me, Aristotle is at his best when he is discussing the acquisition of knowledge. For Aristotle, whatever his faults, more perfectly embodied the love of knowledge than any other thinker in history. He wanted to know all; and, considering his historical limitations, he came damn near close. Us poor moderns have to content ourselves with either a mastery of one tiny slice of reality, or a dilettante acquaintance with all of it; Aristotle had the whole world at his fingertips.

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Review: Autobiography (Darwin)

Review: Autobiography (Darwin)

The Autobiography of Charles Darwin, 1809–82The Autobiography of Charles Darwin, 1809–82 by Charles Darwin

My rating: 4 of 5 stars

I have attempted to write the following account of myself, as if I were a dead man in another world looking back at my own life. Nor have I found this difficult, for life is nearly over with me. I have taken no pains about my style of writing.

This is the quintessential scientific autobiography, a brief and charming book that Darwin wrote “for nearly an hour on most afternoons” for a little over two months. Originally published in 1887—five years after the naturalist’s death—it was somewhat censored, the more controversial religious opinions being taken out. It was only in 1958, to celebrate the centennial of The Origin of Species, that the full version was restored, edited by one of Darwin’s granddaughters, Nora Barlow.

The religious opinions that Darwin expresses are, nowadays, not enough to raise eyebrows. In short, his travels and his research slowly eroded his faith until all that remained was an untroubled agnosticism. What is interesting is that Darwin attributes to his loss of faith his further loss of sensitivity to music and to grand natural scenes. Apparently, in later life he found himself unable to experience the sublime. His scientific work also caused him to lose his appreciation for music, pictures, and poetry, which he heartily regrets: “My mind seems to have become a kind of machine for grinding general laws out of large collections of facts,” he says, and attributes to this the fact that “for many years I cannot endure to read a line of poetry.”

The most striking and lovable of Darwin’s qualities is his humility. He notes his lack of facility with foreign languages (which partially caused him to refuse Marx’s offer to dedicate Kapital to him), his terrible ear for music, his difficulty with writing, his incompetence in mathematics, and repeatedly laments his lack of higher aesthetic sensitivities. His explanation for his great scientific breakthrough is merely a talent for observation and dogged persistence. He even ends the book by saying: “With such moderate abilities as I possess, it is truly surprising that thus I should have influenced to a considerable extent the beliefs of scientific men on some important point.” It is remarkable that such a modest and retiring man should have stirred up one of the greatest revolutions in Western thought. Few thinkers have been more averse to controversy.

This little book also offers some reflection on the development of his theory—with the oft-quoted paragraph about reading Malthus—as well as several good portraits of contemporary thinkers. But the autobiography is not nearly as full as one might expect, since Darwin skips over his voyage on the Beagle (he had already written an excellent book about it) and since the second half of his life was extremely uneventful. For Darwin developed a mysterious ailment that kept his mostly house-bound, so much so that he did not even go to his father’s funeral. The explanation eluded doctors in his time and has resisted firm diagnosis ever since. But the consensus seems to be that it was at least in part psychological. It did give Darwin a convenient excuse to avoid society and focus on his work.

The final portrait which emerges is that of a scrupulous, methodical, honest, plainspoken, diffident, and level-headed fellow. It is easy to imagine him as a retiring uncle or a reserved high school teacher. That such a man, through a combination of genius and circumstance—and do not forget that he almost did not go on that famous voyage—could scandalize the public and make a fundamental contribution to our picture of the universe, is perhaps the greatest argument that ever was against the eccentric genius trope.

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Touching Tuscany: Florence

Touching Tuscany: Florence

Marie-Henri Bayle, who is better known by his pseudonym, Stendhal, visited Florence in the year 1817. He reports being so strongly affected by the art and the tombs that he became dizzy and nearly fainted. The term ‘Stendhal syndrome’ has since entered popular parlance, referring to lightheadedness induced by powerful art. If any city in the world is beautiful enough to endanger one’s health, it is most certainly Florence.

I imagine Stendhal riding through the Italian countryside on horseback, or being pulled in a leisurely carriage, giving the author time to observe the city’s surroundings and to savor its distant profile as he came near. The modern traveler seldom has such an experience. My first sight of the city was of the Firenze train station, whose cavernous interior, supported by metal girders and filled with tourists and ticket machines, was just as bland and anonymous as any other train station. We pay a price for the convenience of rapid transport.

Exactly 200 years after Stendhal fainted in Florence, I arrived early in the morning, having come from Pisa, where I was staying. Though it is admittedly inconvenient to take a train into Florence, I recommend this procedure to anyone traveling on a budget. Flights to and from Pisa are very cheap; and Pisa itself is far more economical than Florence. The trains run frequently between the two cities, and the ride takes around an hour. For my part I appreciated the chance to glimpse the Tuscan countryside through the train’s window: a bucolic tapestry of rolling green and brown hills, patched with farms and dotted with towns.

One day is all I had in Florence—absurd, I know—so I had to use my time effectively. My first stop was the Galleria dell’Accademia di Firenze, the museum famous for being the home of Michelangelo’s David. It does not look like very much from the street, so I almost missed the entrance. I was afraid that, due to the statue’s fame, I would have to wait in a dreadful line to get in; but perhaps because it was still early in the day, I was inside in minutes.

Once inside, a long hall opens up to reveal, standing at the far end under a brightly lit dome, the iconic form of the Biblical hero. My first reaction was surprise at its size. I had imagined the statue to be slightly larger than life-sized; but it is fully 17 feet tall—roughly three times larger than life—and stands on a pedestal which adds to its grandeur. I tried to examine some of the other paintings and statues on display, thinking it would be wise to leave David to the end. But I was so entranced by the statue that I soon gave up and went straight over to admire it.


I was reminded of a trip I had taken when I was a teenager to see the Statue of Liberty. Since I had seen the iconic statue thousands of times in photographs, I assumed that it would be underwhelming to see it up close. Yet I found that, once confronted with the behemoth, I could not turn away; I was drawn to it as with a magnetic force. Michelangelo’s David had the exact same effect on me. My eyes were fixed to the statue. Gazing at it, I felt my body tingle with a strange, excited energy. All the sleepiness of the morning was swept away; all my travel anxieties were quieted. The statue filled up my consciousness with a thrilling sensation of heroic beauty. Its effect is so powerful that it seems beguilingly new when seen in person, despite the overexposure it suffers in popular media.

Even more than other iconic works of art, Michelangelo’s David brings to mind the epithet “perfect.” The face, stance, and body are so convincingly conceived that we cannot imagine Michelangelo making any other choice. A well-known story, related by Giorgio Vasari (the famous art historian), tells how the politician Soderini criticized the statue’s nose for being too fat:

Michelangelo, noticing that the Gonfalonier was standing beneath the giant and that from where he was he could not see the figure properly, to satisfy him climbed on the scaffolding by the shoulders, seized hold of a chisel in his left hand, together with some of the marble dust lying on the planks, and as he tapped lightly with the chisel let the dust fall little by little, without altering anything. Then he looked down at the Gonfalonier, who had stopped to watch, and said: ‘Now look at it.’

To which Soderini replied: “Ah, that’s much better.”

This story is delightful in part because it captures how final, inalterable, and complete is the statue’s form—so perfect that any perceived flaw must be a mistaken apprehension. However, close inspection does reveal some deviations. The statue’s hands are noticeably too big, most obviously the right hand—which reminds me of a puppy who has yet to grow into his paws. The figure’s head is also, you will notice, too big for its slender body. Indeed if we saw a flesh-and-blood man who matched this statue’s form, I think we would be more shocked than impressed.

It is also worth noting that the statue is not exactly a convincing representation of the Biblical David. For one, the sling is so de-emphasized—just a barely visible line going over his shoulder and behind his back—that it is easy to overlook completely. And why would David be going into battle completely nude? Besides, it seems downright incongruous to make David, the famous giant-slayer, into a giant himself—a towering muscular warrior. Earlier representations of David, such as Donatello’s, had portrayed him as an impish boy; Michelangelo deviates from this tradition so far in his statue that the story is almost entirely forgotten as we gaze upon the work.


Yet, like any work of great art, what would normally be defects become, in Michelangelo’s statue, perfections. Nobody sees that glorious right hand, massively curling around the minuscule sling, and wishes it were otherwise. Nobody sees the towering muscular figure and wishes it were reduced to the stature of a boy. Nobody, in short, wishes the statue were anything other than what it is.

And yet, what is it? And why does this statue make such a deep, lasting impression? It is tempting to consider the David as something like the Venus de Milo, an ideal representation of human form. Yet, as I have pointed out, the statue is not anatomically correct—and quite intentionally so, since Michelangelo was not the man to make such an elementary mistake. And in any case the David’s muscular body, though impressive, does not differentiate it from one hundred other idealized nudes.

The viewer’s eyes can seldom pause on the statue’s torso, however fine, but inevitably stray up to the statue’s face. There we encounter something wholly unlike the serene, placid, empty expression of ancient statues. Rather, we find a face full of character—confident, defiant, supreme. The anonymous perfection of the ancient world—statues which unite the qualities of many into one ideal being—has become the individual perfection of the High Renaissance, the completeness of the single man.

As we are told in countless books, the Renaissance was a time when the mind of Europe shook off its sense of being powerless in the hands of divine forces, and developed a self-confidence in the power of humanity—and more than humanity in general, confidence in a few, select, great men. The ultimate expression of this occurred during the High Renaissance, when eminent artists were not merely regarded as brilliant craftsmen or genius creators, but in the words of Giorgio Vasari “mortal gods,” who strode about the earth like colossi, reshaping unformed chaos into perfect form like God Himself.

Everything about the David bespeaks this sense of power. His stance is the perfect combination of stability and mobility. He is rooted to the spot, and yet his gentle lean shows how easily he may shift himself. (This stance, which looks so natural in the statue, is actually quite difficult to reproduce—I’ve tried.) Even more than his muscles or his stance, however, the statue’s oversized head and hands are what give it the sense of force. For it is exactly these organs—giving us our ability to conceive the world differently, and to manipulate it into our prefered forms—that makes humans special, which makes us into “mortal gods.” The David is thus a symbol of humanity’s ability to subjugate matter to mind, to dominate the world with our will.

It is humbling to learn that Michelangelo completed this statue while he was still in his twenties. The original commission was for a statue to adorn the top of Florence’s cathedral; but since the work is obviously much too big to be hoisted up so high (it took three days to move it just a few blocks), a committee had to decide on a new location. Eventually it was agreed to put it in the plaza outside the Palazzo Vecchio, where it stayed until 1873, when it was finally moved into this museum in order to protect it from the elements. A copy now resides in the square—which, though apparently identical, fails completely to make the same impression as the original. Why this should be so is not something I can easily explain. The slight deviations in form and color are apparently enough to totally rid the statue of its mesmerizing majesty. A master’s touch is not so easily replicated.

Though there is nothing to compare to Michelangelo’s masterpiece, the Galleria dell’Accademia has a fine collection that is worth visiting on its own merits. Of particular note are the series of Prisoners originally sculpted by Michelangelo for Pope Julius II’s unrealized tomb. The most famous of these unfinished sculptures, the Dying Slave, is one of the prizes of the Louvre.


The pieces in Florence are, by comparison, rough and unformed—mere suggestions in stone. And yet I think they possess an eloquence all their own, providing snapshots of Michelangelo midway in the process of creation. The human forms emerge from the stone—the twisted bodies at once languid and dolorous, as if suffering from a nightmare. And like a dream they are themselves confused and only half-real. When the visitor compares these rough limbs, trapped in marble, to the smooth skin and living frame of the David, she can sense the tremendous act of imagination required to create these works—seeing the finished whole buried within unformed chaos, choosing the true alternative from infinite possibilities.

To me, this is the great theme in all of Michelangelo’s works: the act of creation which can make us into “mortal gods.” It was he, after all, who gave us the most poignant image of divine creation in Western art, on the roof of the Sistine Chapel.

The rest of the museum has some excellent paintings from the late gothic and the early Renaissance, but what most sticks out in my memory is the room full of sculptures by Lorenzo Bartolini. These are all plaster works, and range from busts, to funerary monuments, to friezes, to full-size sculptures. Though their technical execution is impressive, what impresses more is simply the proliferation of works on display—every wall and surface is covered, and there is hardly space for the visitor to walk through. I must admit, however, that the final effect of all this is of a frigid academic correctness.


Now it was time to see something of the city. Florence has a well-preserved historic center and maintains the look and feel of a medieval city. The narrow streets are not, however, so chaotic and claustrophobic as other old European cities I have visited, such as Toledo, making it a very pleasant city to stroll about in. But I only had a day—less, in fact—so I was in that rushed, anxious state of mind of having far too much to do in too little time. Aimless strolls and meditative people-watching were beyond me.

Soon I arrived in the Piazza della Signoria, the heart of the city. This iconic square is presided over by the Palazzo Vecchio, Florence’s city hall. This building has been the capital building of the city for hundreds of years, and has been called various names over its history, mostly corresponding to which political power was ascendant—Popolo, Priori, Signoria, Ducale. Nowadays it is simply called “old”—perhaps to acknowledging the power of time, which rules us all. It is an extremely attractive structure. The brown, square body of the building flowers into a decorative battlement, whose crenellated walls hang out over the edge. Stretching high up above is the clock tower, which mimics the main structure in its blooming parapet. Its slender form reminds me of a swan’s neck, and gives the whole building a lovely gentleness.

Note the David and Bandinelli’s Hercules and Cacus in the foreground

This building has been at the center of Florence’s history—and all its many factional disputes and power squabbles—for hundreds of years. It was also the scene of one of the most famous art contests in history. Leonardo da Vinci and the much younger Michelangelo Buonarroti (who disliked one another) were both commissioned to paint vast panoramas of battles from Florentine history. Both of them prepared full-sized preliminary cartoons that were hung in the Palazzo Vecchio for all to see and admire. Giorgio Vasari and Benvenuto Cellini both singled out these works for their surpassing excellence, the latter even saying: “So long as they remained intact, they were the school of the world.” Unfortunately, neither of these works survived: Leonardo’s shoddy paint deteriorated, and Michelangelo never even got around to painting it. The only survivors are some partial copies made while they were extant. Nowadays the spot they would have occupied is covered by paintings by Vasari, which few people care for.

The inside of the building is, of course, richly decorated; and it is one of my many regrets of my visit that I did not have time to go inside. But I was on the clock, and had to prioritize.


At one end of this square is one of the many treasures of Florence: the Loggia del Lanzi. This is a covered area, open to the public, filled with sculptures—a miniature, open-air museum. Two of my favorite sculptures on display were created by Jean Boulogne, a Flemish mannerist sculptor better known by his Italianized name Giambologna. One of these depicts Hercules fighting the centaur Nessus. The hero has the beast by the hair, and is bending its back painfully over his knee. The writhing, almost insect-like form of the centaur—prostrate and helpless—contrasts wonderfully with Hercules, who bends his body like a Roman athlete in preparation to strike the fatal blow.


Even more impressive is Giambologna’s Rape of the Sabine Women. The name hardly explains the action of the work (who is the man crouching underneath?), which is to be expected, since Giambologna originally crafted this as a demonstration of his prowess and only came up with the name afterwards. It is a sculptural tour de force, with no true front or back, no beginning or end. The writhing bodies twist upwards, revealing themselves in different aspects as the viewer walks around the work. The final effect is brilliant—pressing upwards with a desperate energy, seeming to stretch towards the sky. The work has proven very popular and is much reproduced; just recently I spotted a copy in the gardens of Versailles.

Yet the undoubted star of this group of sculptures is Benvenuto Cellini’s Perseus. Now, I admit I am prone to being partial to Cellini, since I read and loved his autobiography (see link above). In that book he describes the strain of constructing the statue:

The labour was more than I could stand; yet I forced myself to strain every nerve and muscle. To increase my anxieties, the workshop took fire, and we were afraid lest the roof should fall upon our heads; while, from the garden, such a storm of wind and rain kept blowing in, that it perceptibly cooled the furnace. … Battling thus with these untoward circumstances for several hours, and exerting myself beyond even the measure of my powerful constitution, and a sudden fever, of the utmost possible intensity, attacked me.


This was not the end of Cellini’s troubles, however. He was using a lost-wax technique to cast the statue out of one solid piece of bronze—something that was extremely novel and risky in Cellini’s age. After retiring to bed to recover from his sudden fever, and tossing and turning there for two hours, he was called back by an assistant who told him that the bronze was “caking,” which meant that the fire wasn’t hot enough to melt it. Cellini solved this by adding oak logs to the fire. But then the fire got so hot that the furnace exploded, forcing Cellini to pour the molten metal into the cast before it boiled out. But he found that the high temperature had burnt away the alloyed metals, thus preventing the bronze from pouring properly. He solved this crisis by throwing in his pewter dishes and cutlery, whose addition gave the metal the correct consistency. From this chaos his Perseus was born.

Cellini was a goldsmith, not a sculptor, by training; and his background helps to explain the peculiar excellence of his sculpture. The statue does not awe with its monumental grandeur, but rather delights in its fine detail. The base of the sculpture (which he designed as well) is as delicate as Cellini’s salt cellar in Vienna, and forms an integral part of the work. The statue itself is no less detailed: the viewer can almost smell the entrails dripping from Medusa’s severed head. This grisly detail is matched by the limp, crumpled, and beheaded body of Medusa laying underfoot; and all this combines to make Cellini’s Perseus a much more strikingly violent statue than we are accustomed to seeing. The realism makes the striding Greek hero, with his winged sandals and helmet, look both glorious and menacing; he has done a great deed but has also bathed himself in blood.

The sculptures in the Loggia del Lanzi are not the only ones to be seen in the Piazza. I have already mentioned the copy of Michelangelo’s David, which stands in the original position. Nearby is Baccio Bandinelli’s statue of Hercules and Cacus. The victorious hero holds the fire-breathing monster by the hair, his other hand clutching a club. What most sticks out for comment is Hercules’ gigantic frame; every inch of his skin is rippling with bulging muscles. The statue was famously mocked by Cellini (who was a rival for patronage and so not exactly a fair judge), who said “his sprawling shoulders are like the two pommels of an ass’ pack-saddle; his breasts and his the muscles of the body are not portrayed from a man, but from a big sack full of melons set upright against the wall.” And indeed, his skin does look unnaturally bumpy—especially his back. But the final impression is effective: conveying invincible physical strength.

Another prominent feature of the Piazza is the Fountain of Neptune, designed by Bartolomeo Ammannati. Unfortunately, however, I was unable to see the fountain, since it is undergoing restoration. It has been the repeated target of vandalism, and so nowadays it is covered by a thick scaffolding. Even Florence cannot be perfect.

Now it was time to go to Florence’s other famous square: the Piazza del Duomo, where the visitor can find Florence’s iconic cathedral. (Though the word “cattedrale” exists in Italian, the word “duomo” is commonly used to designate cathedrals. I had assumed it meant “dome” but I was wrong; it derives from the Latin word for house, “domus,” as in “house of God.”)

If any building in Florence is capable of inducing Stendhal syndrome, it is this. The cathedral is magnificent. The exterior of the building is a sublime work of abstract decoration, constructed using differently colored marble from various parts of Italy. It took centuries to complete, and must have cost a fortune. When combined with its decorative paintings, statues, and friezes, along with its monumental size and noble form, its harmonious geometrical arrangement, the impression is similar to that created by the interior of St. Peter’s in the Vatican—and, indeed, many Italian churches—an overwhelming sense of aesthetic pleasure, delightful on every scale. There is a wonderful brilliance to Italian architecture that, even if it does not reach the profundity of the gothic, compensates with its pure visual joy.


I waited on line to take a walk inside, which did not take half so long as I expected. Compared with its glorious façade, the inside is something of a let down, being surprisingly unadorned. There is, however, a famous painting of Dante by Domenico di Michelino, in which the Florentine poet stands before the city of Florence and gestures towards Hell, Purgatory, and Heaven in the background. This is but one of the many tributes that Florence paid to Dante posthumously, after its infamous banishment of the poet during his lifetime. There is also a 24-hour clock decorated by Paolo Uccello, whom Vasari criticizes in his Lives for dedicating his time to useless technical problems of perspective. Uccello was also responsible for the funerary monument to Sir John Hawkwood, an English mercenary. Yet the most memorable work is the decoration on the inside of the massive dome, completed by none other than Giorgio Vasari (who had help), depicting the Last Judgment. From the ground the viewer cannot see the details very well, but the various figures combine to make a harmonious image.


This dome is, of course, the most famous element of the cathedral. At the time it was built, it was an engineering feat without parallel. Its architect, Filippo Brunelleschi, studied several surviving Roman domes, such as the Pantheon, in order to conceive it; but he was at an engineering disadvantage to the Romans, since the formula for concrete had long been lost. Thus Brunelleschi was forced to use brick as a substitute lightweight material. His designs were so radical at the time that he had a difficult time getting the authorities to believe him. For one thing, since he realized that scaffolding would require an exorbitant amount of wood, he created a design that could be constructed without it. To his contemporaries, this sounded like madness. When he was asked to reveal his plans (for he had many rivals, and had to compete to gain creative control) Brunelleschi was unwilling to do so, and instead responded with a challenge:

… he suggested to the other masters, both the foreigners and the Florentines, that whoever could make an egg stand on end on a flat piece of marble should build the cupola, since this would show how intelligent each man was. So an egg was procured and the artists in turn tried to make it stand on end; but they were all unsuccessful. Then Filippo was asked to do so, and taking the egg graciously he cracked its bottom on the marble and made it stay upright. The others complained that they could have done as much, and laughing at them Filippo retorted that they would also have known how to vault the cupola if they had seen his model or plans.

This was not the end of his troubles, however. The commission, responding to a rival faction, soon appointed the artist Lorenzo Ghiberti to be Brunelleschi’s partner. Yet Ghiberti had little idea of the architect’s plans and no relevant experience. This greatly irked Brunelleschi, since he would have to share the glory with somebody who contributed nothing. Thus to reveal his partner’s incompetence, Brunelleschi pretended to be sick and unable to work; and since Ghiberti could not direct the work himself, the project came to a standstill. This made it sufficiently obvious that Brunelleschi was the driving force behind the construction.

The final result is glorious. Octagonal rather than circular, the dome has two shells, inner and outer, and is crowned with a lantern that is accessible via a stairwell in the dome itself. I admit that I am baffled by how Brunelleschi accomplished this feat. Without a wooden support, how did he keep the bricks in place as the mortar dried? It seems impossible. And how did he transport the bricks up so high without scaffolding? In addition to his architectural innovations, Brunelleschi also created influential contraptions to hoist and move the building materials; and it is possible that the young Leonardo da Vinci saw some of these, which would have obviously appealed to the young omnivore.

Nowadays a statue of Brunelleschi, by Luigi Pampaloni, stands in the plaza, a compass one hand and his plans in the other, the architect gazing anxiously up towards his creation. He was, without doubt, one of the great geniuses of the Italian Renaissance, and his dome remains one of history’s great examples of the combination of science and art.

Standing next door to the cathedral is its bell-tower, called Giotto’s Campanile since it owes its gothic design to that iconic Italian painter. Its colorful marble exterior, covered in decorations and sculptures, matches that of the cathedral; yet its vertical design is more obviously gothic in origin. Facing the cathedral is Florence’s baptistery, the Baptistery of St. John, where none other than Dante was dunked into the faith. Having just seen the sparse baptistery in Pisa, I did not feel inclined to go inside; but now I regret it, seeing that the building’s roof is decorated with a beautiful Romanesque mosaic.

The most famous element of the baptistery is, however, on the outside: the Gates of Paradise. These are monumental doors designed by Lorenzo Ghiberti, aforementioned as Brunelleschi’s unwelcome partner. He may have not been much of an architect, but he was a brilliant sculptor. He received the commision to make the doors after winning a famous competition, in which all the best Florentine artists participated. Here is the story from Vasari’s Life:

Altogether there were thirty-four judges, each one an expert in his particular art, and although opinions varied considerably, some of them liking the style of one man and some that of another, they all agreed none the less that Filippo Brunelleschi and Lorenzo di Bartoluccio had composed and finished their scenes better, and with a richer variety of figures, than had Donatello, even though his also showed great qualities of design. The figures in Jacopo della Querci’a scene were good, but they lacked delicacy despite all the care and design that had gone into them. Francesco di Valdambrino had made some good heads and his scene was well finished, but the composition was confused. …. Only the scene which Lorenzo offered as a specimen … was absolutely perfect in every detail: the whole work had design, and was very well composed; the finely posed figures showed the individuality of his style and were made with elegance and grace; and the scene was finished so carefully that it seemed to have been breathed into shape rather than cast with iron tools.

(Donatello did not actually participate in this competition, as he was too young at the time.)

The original doors have been moved into the Duomo Museum for restoration. What stands in the baptistery now is a modern copy. Nevertheless it is a stunning work, shimmering with gold and covered with detail. Upon seeing the exuberance of microscopic detail and delicate craftsmanship, one is not surprised to learn that the door took over twenty years to make. It was, however, somewhat difficult to appreciate, since it is removed with a fence and is usually surrounded by a crowd of onlookers. Ideally one would be able to get close and examine the door panel by panel. Its name was given it by Michelangelo several decades later, who, when asked his opinion of the doors, said they were fit to serve as the entrance to paradise; and Vasari seconded the opinion by calling the doors “perfect in every particular, the finest masterpiece in the world.”

Now it was time for another museum. I was saving the Uffizi for last, since it is open relatively late (until 18:50). Instead I went to the Bargello. This is an excellent art museum (if it were in any other city it would be more well-known) housed in the oldest civic building still standing in Florence. It is a somewhat severe structure, with high crenellated walls that make it look like a fortress, which was once occupied by the chief of police (“bargello” in Italian) and used for executions. Nowadays its medieval courtyard and expansive rooms are used for far more pacific purposes.


I had little expectations from this museum, so I was delighted to find several masterpieces that I had heard of before. One of these was yet another work by Michelangelo, his Bacchus. The statue was apparently made to emulate classical works; and for my part Michelangelo accomplished his task all too well. Though expertly made, with a convincingly off-center pose suggestive of drunkenness, the statue’s final effect is somewhat unpleasant. This is due, I think, to the antique face, which is stiff and inexpressive—hardly even human. Nevertheless I think it is astounding the degree to which the young artist recaptured the spirit of Greco-Roman art, especially considering how far beyond it Michelangelo could go.

Also on display are the panels used to judge of the competition for the baptistery doors. The two finalists, Brunelleschi and Ghiberti, both created a panel depicting the sacrifice of Isaac. It is fascinating to see how these two masters interpreted this traditional scene differently. For my part I can see why Ghiberti’s work was preferred. His figures are more supple and dramatic than Brunelleschi’s, whose seem stiff and unnatural by comparison. Another gem is Giambologna’s Mercury, one more of his much-copied figures. The extraordinary lightness, balance, and grace of the statue does justice to the fleet-footed messenger god.

Cellini is also represented here, for the museum has a small bronze model for his statue of Perseus, as well as the original base of the statue (I believe the one outside is a copy). I was even more delighted to find Gian Lorenzo Bernini’s bust of Costanza Bonarelli, the wife of one of his rich patrons, a woman with whom the artist fell madly in love. The intensity of his passion is easily visible in the work, which portrays his beloved with electrifying realness, his muse wearing an expression somewhere between ferocity and tenderness—the strange space is where all love affairs reside.


Yet my favorite pieces were found in the large hall on the first floor (second floor for Americans). Here can be found some of Donatello’s greatest works. Two statues of David are on display, an early one in marble and a later one in bronze. Of these the second is by far the greater. This was the first free-standing bronze statue made in Europe since antiquity. Here the Hebrew king is depicted nude, in a pose that can only described as sassy. Indeed, as many have remarked, the young warrior is astonishingly feminine, which have prompted some commentators to see it as intentionally homoerotic. Certainly, the solemnities of religion or the glories of battle do not come to mind when viewing the statue. One is instead drawn in by the beauty of the androgynous figure—his smooth skin, relaxed pose, and oversized hat and sword. The severed head of Goliath lying at his feet seems like an afterthought. Less beguilingly ambiguous, yet just as masterful, is the artist’s St. George, whose heroic pose and gaze prefigure the power displayed in Michelangelo’s David.


In this same room is yet another famous statue of David in Florence, this one by Andrea del Verrocchio. Here David is portrayed as even younger than in Donatello’s version, a boy in his early teens. The sensuality of Donatello is entirely absent from this version; yet Verrocchio maintains the impish defiance of the lithe figure. The boy is very handsome, which has caused some to speculate that Verrocchio modeled the work after his young pupil Leonardo da Vinci, known for his physical beauty. Apart from its aesthetic appeal, the statue is valuable for revealing the development of the Italian Renaissance. In Donatello’s we see the triumph of humanism and realism, in Verrocchio’s (made a generation later) the dominance of refinement, elegance, and delicacy, and in Michelangelo’s (made another generation later) the monumental grandeur of the High Renaissance.

Indeed, I would say that the Bargello’s collection, aside from its intrinsic worth, is valuable for its ability to reveal the development of Florence’s artists, both historically and biographically. It is one of the many jewels of the city.

But now I could not put it off any longer. I had to go see the greatest art museum on the Italian peninsula: the Uffizi.

The building of the Uffizi Gallery was designed by none other than Giorgio Vasari, who has already featured so prominently in this post. While Vasari may not have excelled in any field, he was certainly adept in many. The original idea was to make new government offices (hence the name “Uffizi”), but from the start (during the 16th century) the Medici rulers used at least a part of the building to display some of their massive art collection. As such, the Uffizi is one of the oldest museums in Europe, though it did not officially become a public museum until the 18th century, when the Medici family donated their art collection to the people of Florence. Nowadays it is the most-visited museum in Italy, and for good reason.

Vasari built a loggia, or an open courtyard, into his design; and this is now where visitors line up to buy a ticket, surrounded by street vendors selling their watercolors, posters, and other art paraphernalia, and heavily-armed military men look around with menaces and machine guns. In the 19th century sculptors added statues of famous Florentines into the walls of this courtyard; and the effect is a powerful reminder of how crucial this small city—with a population of just 70,000 during the High Renaissance—has been to Europe’s cultural history. Aside from great artists such as Benvenuto Cellini, Leonardo da Vinci, and Michelangelo, Florence has given us great writers such as Dante, Petrarch, and Boccaccio, and great thinkers like Machiavelli and Galileo. Imagine how different European history would be without these men! If brilliance were just the product of genetic chance, then it would boggle the mind that so many geniuses were born at around the same place and time; it seems that Florentine culture contained a vital spark that set these minds afire. If only we could figure out how to reproduce this cultural vitality.


After examining the eminent Florentines, I took my place on the line. I was sandwiched between American families. In general I dislike overhearing conversations. For every interesting tidbit there are nine stupidities. It is not that people are so foolish—at least, not so many of them—but that, when speaking freely among friends, almost everyone utters banalities, absurdities, or frankly foolish things at an alarming rate. The mind, when unchecked, generates a near-constant stream of nonsense. That is just the way we are built. This is why I so appreciate traveling alone in a foreign country. Without other people around to provoke me, and when all the ambient conversation is unintelligible, my mind calms down into a blank silence. Then, I can at least pretend that I am not an average dullard.

But, as I said, I was sandwiched between two American families; so that despite my earphones in and an audiobook playing (it was Bleak House) I could not help overhearing some of what was said. The majority was the usual sort of bickering and complaining that goes on during any family vacation—impatient whining, microscopic arguments, and so on. But at some point the families noticed each other, and started up a conversation, I suppose to pass the time as the line slowly inched forward. I learned that one group was from Tennessee, the other from Texas, and both had the accent to prove it. I remember hearing one of them say, “Ah, ya’ll are southerners, too. Ya’ll get it. Those Northerners look down on us.” And I must admit that it is true, at least as far as New Yorkers are concerned: we are very sure of our cultural superiority. Living in Europe has not helped to erase this tendency in myself.

Finally, after much waiting and more complaining from the Americans—the anxious impatience that people display is what really makes waiting in lines terrible—I entered the iconic gallery.

One of the Uffizi’s best qualities is its layout. A single, unbroken path can take the visitor from the start of the gallery to its end, in a satisfying chronological sequence. This, by the way, is one of the primary disadvantages of enormous collections such as the Louvre or the Metropolitan: the visitor must wander around, double back, scan a map; and even after all that, there is a very good chance of missing something. Not so in the Uffizi. An ornate hallway leads along the interior of the building—overlooking the aforementioned courtyard—filled with busts and sculptures. Leading outwards from the hallways are a series of rooms filled with paintings, giving the visitor a panoramic view of the Renaissance.


As always with museums, I am at serious risk of losing myself in descriptions of artworks, swelling this post beyond its already bloated proportions. To begin, I will only mention a few exemplary works. There is work by that celebrated founder of the Renaissance, Giotto: The Madonna Enthroned. At a glance it is clear that Giotto was still very much working within the gothic tradition; yet the symmetrical composition, realistic drapery of the clothing, and voluminous bodies show that Giotto had pushed art towards realism. This is especially apparent if we compare Giotto’s work with that of his (reputed) master, Cimabue, who also has a painting of the enthroned Virgin on display. Although Cimabue’s is excellent in its own way, it certainly seems stiff and stylized next to Giotto.

The Uffizi also has Gentile de Fabrio’s famous Adoration of the Magi, one of the high points of gothic art. It is a busy composition, with a multitude of figures arranged without respect for perspective. A further departure from naturalism are the costumes, which are plainly of the Renaissance and not of the ancient near east. Nevertheless it is a beautiful work—harmoniously arranged and full of tantalizing detail.


Skipping ahead a few centuries, the Uffizi also has the most iconic work of the mannerist period: Parmigianino’s Madonna with the Long Neck. The title more or less says it all. The painting seems to break, and very deliberately, all of the strictures of Renaissance art. The titular Virgin is flagrantly misproportioned: as in a gothic work, she is notably taller than everyone who surrounds her, and of course her neck is swan-like in its extension. Likewise, the infant Jesus appears massive; and in his sprawled pose on the Virgin’s lap, I cannot help thinking that the poor babe has had too much to drink. The work is glaringly unsymmetrical, with all the attendant angels crammed to one side; on the other, a prophet holding a scroll appears so ludicrously tiny that we fear the Madonna may squash him underfoot. For my part I think it is a beautiful painting, although it completely fails to evoke anything resembling religious sentiments.

Caravaggio also has some notable works on display. One is his imagined portrait of Bacchus, who reclines in a white robe, appropriately surrounded by grapes and wine. The final effect is not of classical grace, however, as Caravaggio’s realism transforms the god into a smug and self-satisfied boy. There is also a painting of Medusa’s severed head by the painter, which quite rivals Cellini for ghastliness. His most powerful work, however, must be his Sacrifice of Isaac. As is often remarked, Caravaggio had a genius for turning Biblical scenes—represented in highly stylized images for centuries—into strikingly realistic works. The detail that most distinguished this painting is Isaac’s face, distorted with fear and desolation—exactly how one would imagine a son to feel who was about to be killed by his own father.

The Uffizi also has an impressive collection of works from artists across the seas and beyond the alps. There are paintings by the Spanish triumvirate, El Greco, Goya, and Velazquez (an excellent self-portrait). Dürer, van Dyck, van der Weyden, and Rembrandt are also in attendance. I should also not neglect to mention some of the wonderful statues on display. In one room the sons and daughters of Niobe are displayed, all distressed and in agony due to Artemis and Apollo’s arrows. (Niobe boasted that she was superior to the goddess Leto, because she had more sons and daughters, and accordingly suffered divine punishment.) There are busts of famous Romans, such as Seneca and Marcus Aurelius. One niche contains a finely sculpted wild boar, of ancient date. Another pair of statues depict a mythological figure (Prometheus?) bound and hanging by his hands, no doubt suffering divine justice, which was very harsh back in those days.


I go on and on, and have not yet gotten to the stars of the Renaissance. Though not a Florentine, Raphael de Urbino is welcomed into the collection with his Madonna of the Goldfinch. As in many Raphael works, a very pretty Madonna sits in a lush field, while the infant Jesus and John the Baptist play at her knees (this time, cradling a goldfinch). The cool colors and symmetrical composition create the typical Raphael effect: a soothing, delightful harmony. There is also a version of Raphael’s iconic portrait of Julius II; long believe to be the original, nowadays that title is given to a version in the National Gallery, London.


Never one to be shown up, Michelangelo also contributes a version of the holy family, the Doni Tondo. This is actually the only finished and mature panel painting by that master which survives. (Two lesser works are kept at the aforementioned National Gallery.) The colors are extremely vibrant and bright, which is partially due to Michelangelo’s voluminous style, using stark contrasts in color to create a statuesque effect. As is often remarked, the great artist was first and foremost a sculptor, and his mature paintings look like an attempt to create sculptures in pigment. While I love the monumental grandeur of the painting, I must admit that I miss the bucolic sweetness of Raphael; and the nude figures in the background (which scholars have struggled to explain) only make matters worse. Michelangelo was not an artist for small scales.


I have cheated somewhat by viewing the gallery out of order, so as to discuss its two most paintings last: Sandro Botticelli’s Birth of Venus and Primavera. They are both in the same room, surrounded by other works by the Florentine master.

The Birth of Venus is just as stunning in person as I expected it to be. Few images in the history of Western art are comparably famous. We have seen it so many times that the painting has become an integral part of our visual culture. And yet, when you examine the painting, you will see that it is odd in several respects. First, like Michelangelo’s David, Botticelli’s Venus is conspicuously misproportioned: her long neck and sloping shoulders are even reminiscent of Parmigianino’s swan-like Madonna. Besides this, her stance, so apparently relaxed, would be impossible for a real person to hold. Noting these deviations reminds us that it is partly the effect of familiarity that we accept these images as “realistic” depictions of ideal beauty. We are so used to the image of David and Venus that our brains do not even scrutinize them.

The paintings attract crowds

Another oddity is that Botticelli obscures the narrative of the painting through the arrangement of his figures. Venus is supposed to be blown from the sea to the shore, where the hora (a minor goddess) is waiting to robe her. Yet all the figures are on the same, two-dimensional plane; and Venus’s gaze (as well as her conch shell) is unnaturally oriented perpendicularly towards the viewer rather than towards her destination. Indeed, the longer the painting is gazed at, the further from reality it appears. The female companion of the wind god, Zephyr, is knotted around his body in an impossible posture; the hora’s feet are levitating off the ground; and a consistent light source is difficult to identify. This is not the stereotypical realism of the Renaissance.

The paintings irrealism may partly be explained by noting Botticelli’s classical sources. He based the pose of Venus on an ancient Roman copy of a classical Greek statue, of Venus modestly covering herself—an idealized depiction of the female form. Botticelli may also have seen Greek vase paintings, which would explain the two-dimensional orientation of this work, as well as its unnatural orientation. Yet to these ancient influences Botticelli combines the emotional frankness of gothic paintings with the technical sophistication of the Renaissance. The result is a work so original that it can hardly be grasped on its own terms.

The final result is supremely convincing: the cool blues contrasting with the warm greens, the symmetrical composition of the zephyr and the mona, and the supreme beauty of the newly-born Venus. For my part, no image of the divine feminine is more convincing than Botticelli’s Venus—her graceful face, lithely bending body, flowing hair, playful modesty, and knowing smile. All the statues of Venus that have survived from antiquity seem like petrified dolls in comparison. The more I look at the painting, the more enchanting I find it. Botticelli achieves something quite unlike what we expect from the Renaissance—a deeply otherworldly work, symbolizing the harmonies of the natural world, the fertility of nature, and the profound mystery of creation.

The Birth of Venus, though daringly innovative, does not present a great challenge to the would-be art historian. But Botticelli’s other masterpiece certainly does: Primavera. This is another  visually arresting work, although it does lack something of the triumphant harmony of The Birth. Yet it makes up for this with its mystery; for nobody seems quite sure what Botticelli was trying to represent.


Eight figures stand in an orange grove. Clearly identifiable are the Three Graces dancing in a circle. Beside them, Mercury (wearing his winged sandals) is poking at a cloud, looking rather intrigued. In the center is a woman normally identified as Venus (though I don’t know why); and above her Cupid, blindfolded, aims his little bow, apparently at the Three Graces (which does not make good mythological sense). To the right of Venus is the personification of Spring, dressed in a floral dress, busy gathering flowers. Here we instantly recognize the enchanting face of Venus from The Birth. To her right, a woman is being abducted by a flying man: This latter is the god of wind, zephyr (also in The Birth, although here he is blue); and the pursued woman is Clovis, a nymph whom he carries off and marries, which magically transforms her into the goddess of Spring. This suggests that the painting should be seen as a narrative from right to left, with the abduction immediately leading to Spring, at Clovis’ left. But the story falls apart from there.

As in The Birth, here all the figures more or less occupy the same two-dimensional plane. Admittedly, Venus is higher up on the panel, which would normally indicate depth; but this is disrupted by Venus’ size—she is, if anything, bigger than the other figures. Botticelli had a genius for creating beautiful faces—classical in their symmetry, and yet possessing a sweet simplicity I normally associate with medieval painting—with which he endows each of his figures (except Cupid). The background, too, is remarkably lush: full of different species of plant and flower, a botanical cornucopia.

As far as interpretation goes, it is easy to see that Botticelli wanted to suggest the fertility and beauty of Spring. The viewer can also discern a general sequence, with springtime beginning at the right with wind and ending with Mercury banishing the clouds. But beyond this, many questions remain—the exact identities of the Graces, why Cupid is aiming his arrow at one of them, their symbolic relationship with Mercury and Spring, and so on—which makes this painting, among other things, a great gift to art historians around the world. Scholars would be out of work if every painting were easy to interpret.

You may be interested to learn that these paintings have only fairly recently come into artistic vogue. Vasari hardly pauses to mention The Birth and Primavera in his short (barely 10 page) biography of Botticelli, half of which is taken up with disapproving anecdotes about how the painter squandered his talents in later life. For centuries Botticelli was neglected and ignored. His personal style—idealized, stylized, figurative—was difficult to accommodate with popular views of the Renaissance, and so he received scant attention. It was partly due to the Pre-Raphaelites, a group of painters, poets, and critics devoted to the Early Renaissance, that his renown increased. Nowadays, The Birth of Venus is scarcely less famous than the Sistine Chapel, which shows how fickle a thing is fame.

The majority of Botticelli’s works were not of mythological subjects, of course, but of Christian ones; and many of these are on display too. What is striking is that Botticelli used the same face—unmistakably pretty and graceful—for his Virgins as for his Venus. Did he use the same female model throughout his working life, or was the iconic face his own invention? Partly as a result of this, his works can be identified at a glance. Though the two above-mentioned works are undoubtedly his masterpieces, I enjoyed all of his paintings; they are suffused with a refreshing sweetness that never fails to charm me.

I left the Uffizi as it was about to close and daylight was on the wane. With little time to spare, I made my way to my next destination: the Ponte Vecchio, or old bridge. This is by far the most famous bridge to span the river Arno, which it does at its narrowest point. Like the Ponte Rialto in Venice, the Roman Bridge in Córdoba, and the Charles Bridge in Prague, the Ponte Vecchio is bound to be flooded with tourists on any given day. There is not much of a view from the bridge in any case, since it is boxed in by little stalls for jewelers, goldsmiths, and souvenir shops, making it a kind of miniature mall. One notable feature is the Vasari corridor—designed by Vasari, of cours—a covered walkway that extends from the Palazzo Vecchio, through the Uffizi, over the Ponte Vecchio, and on to the Palazzo Pitti on the other side of the river. It was designed so that the Grand Duke could walk from his residence to the seat of government with ease and safety.


The corridor was damaged in 1993 when a car-bomb exploded near the Uffizi gallery, killing five people and destroying some works of art. The Sicilian Mafia detonated several of these car bombs around Italy, in an attempt to retaliate against the Italian government for its measures against the organization. There are few things more evil than blowing up a museum.

After crossing the bridge I trekked up the hill to the Piazzale Michelangelo. The walk up was very pleasant, taking me alongside rose gardens under a tree-shaded path. I was somewhat disappointed with the square itself, however: it little more than a vast, open parking lot, filled with tourists and stands selling paraphernalia. The only exception to this is the bronze copy of Michelangelo’s David, which similarly fails to recapture any of the magic of the original, not least because of its sickly green color. But the Michelangelo Square is nevertheless one of the great spots in Florence, because of the incomparable view of the city it offers.


Standing there, the entire old center is laid out before you. The river, crossed by the Ponte Vecchio, frames the bottom of the picture; and the rolling brown hills and mountains of Tuscany extend into the distance. The town lays flat in the valley, and the brightly-painted buildings are covered in rust-colored tiled roofs. Two buildings break the monotony: the Palazzo Vecchio and the Cathedral, which stand proudly over their surroundings. The sheer scale of Brunelleschi’s dome—by far the largest structure in the city—can be grasped from this distance. The view is one of the most picturesque views of a city I have ever seen, showing that the city of art is itself a work of brilliance.

Now I was running out of time. So I descended the hill, crossed back over the Ponte Vecchio, and went to wander around the city one last time before I took the train back to Pisa. I had had an incredibly full day, and could had seen what I most wanted to see. Yet even the fullest day in Florence cannot but leave the visitor full of regrets. What I most regret are the basilicas I missed. There is San Miniato al Monte, a beautiful Romanesque structure atop a hill, near the Michelangelo Square. Then there is the Basilica of San Lorenzo, a massive earth-colored building (it served as a cathedral before the Duomo) that became the burial-place for the Medici family, whose patronage played such an important role in the artistic life of Florence. Nextdoor is the Laurentian Library, one of Michelangelo’s most celebrated works of architecture. But my keenest regret is not visiting the Basilica di Santa Croce, a lovely church that is known as the Temple of Italian Glories. It was here that Stendhal had his famous fit of aesthetic pleasure, as he was overwhelmed by being near the tombs of Machiavelli, Galileo, and Michelangelo.

I only got to see this basilica from the outside, unfortunately, for it was closed for the day. Nextdoor is a statue of Dante, Florence’s most famous banished son, who is buried far away in Ravenna. Now that I had seen Florence, I could understand why Dante was so bitter about his banishment. It is one of the great cities of the world.


Images of Córdoba

Images of Córdoba

A couple months ago I took a quick trip down to Córdoba. I had gone before, but this time around I had a new camera. Luckily for me, very little skill is needed to take nice photos in Córdoba. It is a thoroughly pretty city; and the Andalusian sun lights up every shape and makes every color glow. Here are some of the pictures I took.

(If you would like to more about the city of Córdoba, you can see my post—now with updated pictures.)

My first goal was to photograph the statues of all three Cordoban philosophers: Maimonides, Averroes, and Seneca:


Next I wanted to get photos of Córdoba’s Mezquita, the Great Mosque of the Spanish Moors:


The mihrab, which marks the qibla, the direction of Mecca
Religious juxtaposition

After the Christians conquered Córdoba, they fortunately did not destroy this wonderful piece of architecture. But they did modify it. Most controversially, a Renaissance-style cathedral—with a chorus, nave, and altar—was built into the middle of the old mosque. For my part, though I regret the destruction of a part of the historic building, I think the effect is wonderful:


I also saw something new on this trip. As you may know, one of Córdoba’s most famous attractions are its patios, which are decorated with flowers every May as part of a city-wide competition. Visitors can enter these patios for free and can vote for their favorites. This charming custom has been added to UNESCO’s list of Intangible Cultural Heritage in 2012, and is now more popular than ever.

Unfortunately for me, I visited after the competition had wrapped up. But the museum of the Palacio de Viana—an old aristocratic residence—has a year-long display of Cordobese patios. I highly recommend a visit.



One need not pay to enter a monument to be surrounded by beauty in Córdoba, however, as the well-preserved city center is itself a monument:


And here is the Roman bridge, with the Mezquita in the distance:


Though I missed the patios, I did make it in time for Córdoba’s annual festival. The cities were filled with horses pulling carts filled with men and women in elaborate costumes. The men wore suits with broad-brimmed hats, and the women wore frilly, brightly colored dresses. Outside of the center an amusement park had been set up—creating an odd juxtaposition between the traditional Cordobese costumes and the Coney Island atmosphere.




Cordoba_dressesAs I hope you can see, Córdoba is one of the loveliest cities in a country full of conspicuously lovely cities. I highly recommend a visit

Review: The Structure of Scientific Revolutions

Review: The Structure of Scientific Revolutions

The Structure of Scientific RevolutionsThe Structure of Scientific Revolutions by Thomas S. Kuhn

My rating: 5 of 5 stars

Observation and experience can and must drastically restrict the range of admissible scientific belief, else there would be no science. But they cannot alone determine a particular body of such belief. An apparently arbitrary element, compounded of personal and historical accident, is always a formative ingredient of the beliefs espoused by a given scientific community at a given time.

This is one of those wonderfully rich classics, touching on many disparate fields and putting forward ideas that have become permanent fixtures of our mental furniture. Kuhn synthesizes insights from history, sociology, psychology, and philosophy into a novel conception of science—one which, despite seemingly nobody agreeing with it, has become remarkably influential. Indeed, this book made such an impact that the contemporary reader may have difficulty seeing why it was so controversial in the first place.

Kuhn’s fundamental conception is of the paradigm. A paradigm is a research program that defines a discipline, perhaps briefly, perhaps for centuries. This is a not only a dominant theory, but a set of experimental methodologies, ontological commitments, and shared assumptions about standards of evidence and explanation. These paradigms usually trace their existence to a breakthrough work, such as Newton’s Principia or Lavoisier’s Elements; and they persist until the research program is thrown into crisis through stubborn anomalies (phenomena that cannot be accounted for within the theory). At this point a new paradigm may arise and replace the old one, such as the switch from Newton’s to Einstein’s system.

Though Kuhn is often spoken of as responding to Popper, I believe his book is really aimed at undermining the old positivistic conception of science: where science consists of a body of verified statements, and discoveries and innovations cause this body of statements to gradually grow. What this view leaves out is the interconnection and interdependence between these beliefs, and the reciprocal relationship between theory and observation. Our background orients our vision, telling us where to look and what to look for; and we naturally do our best to integrate a new phenomenon into our preexisting web of beliefs. Thus we may extend, refine, and elaborate our vision of the world without undermining any of our fundamental theories. This is what Kuhn describes as “normal science.”

During a period of “normal science” it may be true that scientific knowledge gradually accumulates. But when the dominant paradigm reaches a crisis, and the community finds itself unable to accommodate certain persistent observations, a new paradigm may take over. This cannot be described as a mere quantitative increase in knowledge, but is a qualitative shift in vision. New terms are introduced, older ones redefined; previous discoveries are reinterpreted and given a new meaning; and in general the web of connections between facts and theories is expanded and rearranged. This is Kuhn’s famous “paradigm shift.” And since the new paradigm so reorients our vision, it will be impossible to directly compare it with the older one; it will be as if practitioners from the two paradigms speak different languages or inhabit different worlds.

This scandalized some, and delighted others, and for the same reason: that Kuhn seemed to be arguing that scientific knowledge is socially solipsistic. That is to say that scientific “truth” was only true because it was given credence by the scientific community. Thus no paradigm can be said to be objectively “better” than another, and science cannot be said to really “advance.” Science was reduced to a series of fashionable ideas.

Scientists were understandably peeved by the notion, and social scientists concomitantly delighted, since it meant their discipline was at the crux of scientific knowledge. But Kuhn repeatedly denied being a relativist, and I think the text bears him out. It must be said, however, that Kuhn does not guard against this relativistic interpretation of his work as much as, in retrospect, he should have. I believe this was because Kuhn’s primary aim was to undermine the positivistic, gradualist account of science—which was fairly universally held in the past—and not to replace it with a fully worked-out theory of scientific progress himself. (And this is ironic since Kuhn himself argues that an old paradigm is never abandoned until a new paradigm takes its place.)

Though Kuhn does say a good deal about this, I think he could have emphasized more strongly the ways that paradigms contribute positively to reliable scientific knowledge. For we simply cannot look on the world as neutral observers; and even if we could, we would not be any the wiser for it. The very process of learning involves limiting possibilities. This is literally what happens to our brains as we grow up: the confused mass of neural connections is pruned, leaving only the ones which have proven useful in our environment. If our brains did not quickly and efficiently analyze environmental stimuli into familiar categories, we could hardly survive a day. The world would be a swirling, jumbled chaos.

Reducing ambiguities is so important to our survival that I think one of the primary functions of human culture is to further eliminate possibilities. For humans, being born with considerable behavioral flexibility, must learn to become inflexible, so to speak, in order to live effectively in a group. All communication presupposes a large degree of agreement within members of a community; and since we are born lacking this, we must be taught fairly rigid sets of assumptions in order to create the necessary accord. In science this process is performed in a much more formalized way, but nevertheless its end is the same: to allow communication and cooperation via a shared language and a shared view of the world.

Yet this is no argument for epistemological relativism, any more than the existence of incompatible moral systems is an argument for moral relativism. While people commonly call themselves cultural relativists when it comes to morals, few people are really willing to argue that, say, unprovoked violence is morally praiseworthy in certain situations. What people mean by calling themselves relativists is that they are pluralists: they acknowledge that incompatible social arrangements can nevertheless be equally ethical. Whether a society has private property or holds everything in common, whether it is monogamous or polygamous, whether burping is considered polite or rude—these may vary, and yet create coherent, mutually incompatible, ethical systems. Furthermore, acknowledging the possibility of equally valid ethical systems also does not rule out the possibility of moral progress, as any given ethical system may contain flaws (such as refusing to respect certain categories of people) that can be corrected over time.

I believe that Kuhn would argue that scientific cultures may be thought of in the same pluralistic way: paradigms can be improved, and incompatible paradigms can nevertheless both have some validity. Acknowledging this does not force one to abandon the concept of “knowledge,” any more than acknowledging cultural differences in etiquette forces one to abandon the concept of “politeness.”

Thus accepting Kuhn’s position does not force one to embrace epistemological relativism—or, at least not the strong variety, which reduces knowledge merely to widespread belief. I would go further, and argue that Kuhn’s account of science—or at least elements of his account—can be made to articulate even with the system of his reputed nemesis, Karl Popper. For both conceptions have the scientist beginning, not with observations and facts, but with certain arbitrary assumptions and expectations. This may sound unpromising; but these assumptions and expectations, by orienting our vision, allow us to realize when we are mistaken, and to revise our theories. The Baconian inductivist or the logical positivist, by beginning with an raw mass of data, has little idea how to make sense of it and thus no basis upon which to judge whether an observation is anomalous or not.

This is not where the resemblance ends. According to both Kuhn and Popper (though the former is describing while the second is prescribing), when we are revising our theories we should if possible modify or discard the least fundamental part, while leaving the underlying paradigm unchanged. This is Kuhn’s “normal science.” So when irregularities were observed in Uranus’ orbit, the scientists could have either discarded Newton’s theories (fundamental to the discipline) or the theory that Uranus was the furthest planet in the solar system (a superficial fact); obviously the latter was preferable, and this led to the discovery of Neptune. Science could not survive if scientists too willingly overturned the discoveries and theories of their discipline. A certain amount of stubbornness is a virtue in learning.

Obviously, the two thinkers also disagree about much. One issue is whether two paradigms can be directly compared or definitively tested. Popper envisions conclusive experiments whose outcome can unambiguously decide whether one paradigm or another is to be preferred. There are some difficulties to this view, however, which Kuhn points out. One is that different paradigms may attach very different importance to certain phenomena. Thus for Galileo (to use Kuhn’s example) a pendulum is a prime exemplar of motion, while to an Aristotelian a pendulum is a highly complex secondary phenomenon, unfit to demonstrate the fundamental properties of motion. Another difficulty in comparing theories is that terms may be defined differently. Einstein said that massive objects bend space, but Newtonian space is not a thing at all and so cannot be bent.

Granting the difficulties of comparing different paradigms, I nevertheless think that Kuhn is mistaken in his insistence that they are as separate as two languages. I believe his argument rests, in part, on his conceiving of a paradigm as beginning with definitions of fundamental terms (such as “space” or “time”) which are circular (such as “time is that measured by clocks,” etc.); so that comparing two paradigms would be like comparing Euclidian and non-Euclidian geometry to see which is more “true,” though both are equally true to their own axioms (while mutually incompatible). Yet such terms in science do not merely define, but denote phenomena in our experience. Thus (to continue the example) while Euclidian and non-Euclidian geometries may both be equally valid according to their premises, they may not be equally valid according to how they describe our experience.

Kuhn’s response to this would be, I believe, that we cannot have neutral experiences, but all our observations are already theory-laden. While this is true, it is also true that theory does not totally determine our vision; and clever experimenters can often, I believe, devise tests that can differentiate between paradigms to most practitioners’ satisfaction. Nevertheless, as both Kuhn and Popper would admit, the decision to abandon one theory for another can never be a wholly rational affair, since there is no way of telling whether the old paradigm could, with sufficient ingenuity, be made to accommodate the anomalous data; and in any case a strange phenomena can always be tabled as a perplexing but unimportant deviation for future researchers to tackle. This is how an Aristotelian would view Galileo’s pendulum, I believe.

Yet this fact—that there can be no objective, fool-proof criteria for switching paradigms—is no reason to despair. We are not prophets; every decision we take involves risk that it will not pan out; and in this respect science is no different. What makes science special is not that it is purely rational or wholly objective, but that our guesses are systematically checked against our experience and debated within a community of dedicated inquirers. All knowledge contains an imaginative and thus an arbitrary element; but this does not mean that anything goes. To use a comparison, a painter working on a portrait will have to make innumerable little decisions during her work; and yet—provided the painter is working within a tradition that values literal realism—her work will be judged, not for the taste displayed, but for the perceived accuracy. Just so, science is not different from other cultural realms in lacking arbitrary elements, but in the shared values that determine how the final result is judged.

I think that Kuhn would assent to this; and I think it was only the widespread belief that science was as objective, asocial, and unimaginative as a camera taking a photograph that led him to emphasize the social and arbitrary aspects of science so strongly. This is why, contrary to his expectations, so many people read his work as advocating total relativism.

It should be said, however, that Kuhn’s position does alter how we normally think of “truth.” In this I also find him strikingly close to his reputed nemesis, Popper. For here is the Austrian philosopher on the quest for truth:

Science never pursues the illusory aim of making its answers final, or even probable. Its advance is, rather, towards the infinite yet attainable aim of ever discovering new, deeper, and more general problems, and of subjecting its ever tentative answers to ever renewed and ever more rigorous tests.

And here is what his American counterpart has to say:

Later scientific theories are better than earlier ones for solving puzzles in the often quite different environments to which they are applied. That is not a relativist’s position, and it displays the sense in which I am a convinced believer in scientific progress.

Here is another juxtaposition. Popper says:

Science is not a system of certain, or well-established, statements; nor is it a system which steadily advances towards a state of finality. Our science is not knowledge (episteme): it can never claim to have attained truth, or even a substitute for it, such as probability. … We do not know: we can only guess. And our guesses are guided by the unscientific, the metaphysical (though biologically explicable) faith in laws, in regularities which we can uncover—discover.

And Kuhn:

One often hears that successive theories grow ever closer to, or approximate more and more closely to, the truth… Perhaps there is some other way of salvaging the notion of ‘truth’ for application to whole theories, but this one will not do. There is, I think, no theory-independent way to reconstruct phrases like ‘really there’; the notion of a match between the ontology of a theory and its ‘real’ counterpart in nature now seems to me illusive in principle.

Though there are important differences, to me it is striking how similar their accounts of scientific progress are: the ever-increasing expansion of problems, or puzzles, that the scientist may investigate. And both thinkers are careful to point out that this expansion cannot be understood as an approach towards an ultimate “true” explanation of everything, and I think their reasons for saying so are related. For since Popper begins with theories, and Kuhn with paradigms—both of which stem from the imagination of scientists—their accounts of knowledge can never be wholly “objective,” but must contain an aforementioned arbitrary element. This necessarily leaves open the possibility that an incompatible theory may yet do an equal or better job in making sense of an observation, or that a heretofore undiscovered phenomenon may violate the theory. And this being so, we can never say that we have reached an “ultimate” explanation, where our theory can be taken as a perfect mirror of reality.

I do not think this notion jeopardizes the scientific enterprise. To the contrary, I think that science is distinguished from older, metaphysical sorts of enquiry in that it is always open-ended, and makes no claim to possessing absolute “truth.” It is this very corrigibility of science that is its strength.

This review has already gone on for far too long, and much of it has been spent riding my own hobby-horse without evaluating the book. Yet I think it is a testament to Kuhn’s work that it is still so rich and suggestive, even after many of its insights have been absorbed into the culture. Though I have tried to defend Kuhn from accusations of relativism or undermining science, anyone must admit that this book has many flaws. One is Kuhn’s firm line between “normal” science and paradigm shifts. In his model, the first consists of mere puzzle-solving while the second involves a radical break with the past. But I think experience does not bear out this hard dichotomy; discoveries and innovations may be revolutionary to different degrees, which I think undermines Kuhn’s picture of science evolving as a punctuated equilibrium.

Another weakness of Kuhn’s work is that it does not do justice to the way that empirical discoveries may cause unanticipated theoretical revolutions. In his model, major theoretical innovations are the products of brilliant practitioners who see the field in a new way. But this does not accurately describe what happened when, say, DNA was discovered. Watson and Crick worked within the known chemical paradigm, and operated like proper Popperians in brainstorming and eliminating possibilities based on the evidence. And yet the discovery of DNA’s double helix, while not overturning any major theoretical paradigms, nevertheless had such far-reaching implications that it caused a revolution in the field. Kuhn has little to say about events like this, which shows that his model is overly simplistic.

I must end here, after thrashing about ineffectually in multiple disciples in which I am not even the rankest amateur. What I hoped to re-capture in this review was the intellectual excitement I felt while reading this little volume. In somewhat dry (though not technical) academic prose, Kuhn caused a revolution that still forceful enough to make me dizzy.

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