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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