Review: A Manual of Greek Mathematics

A Manual of Greek Mathematics by Thomas L. Heath

My rating: 4 of 5 stars

In the case of mathematics, it is the Greek contribution which it is most essential to know, for it was the Greeks who first made mathematics a science.

As a supplement to my interest in the history of science, I figured that I ought to take a look into the history of mathematics, since the two are quite intimately related. This naturally led me to the Greeks and to Sir Thomas L. Heath, who remains the most noteworthy translator, divulgator, and commentator in English eighty years after his death. This book is likely the best single volume you can get on the subject, as it covers all of the major mathematicians in some detail while giving a complete overview.

It is also reasonably accessible (“reasonably” being the operative word). Certainly it is no work of popular math in the modern sense; it is not pleasure reading, and Heath assumes a certain amount of knowledge on the reader’s part. A thorough knowledge of algebra and geometry is assumed, and a few words in ancient Greek are not translated. What is more, large sections of the book are essentially extended summaries and explications of Greek treatises, which makes them almost impossible to read without the original text alongside. Personally I would certainly have appreciated more spoon-feeding, as it was quite difficult for me to prevent my eyes from glazing over.

The book is divided primarily by subject-matter and secondarily by chronology. Heath introduces us to notation, fractions, and techniques of calculation, and then on to arithmetic. Geometry, of course, dominates the book, as it was the primarily form of Greek mathematical thought. Heath summarizes the contributions to geometry by Pythagoras and his followers, and the scattered mathematicians we know of in the years between Thales and Euclid. Once Euclid appears, he writes his famous Elements, which encapsulates the entire subject and which rendered many previous works obsolete. After Euclid we come to the divine Archimedes and the great Apollonius, who put the capstone on the tradition. Ptolemy (among others) made great advances in trigonometry, while Diophantus made strides in algebra (as well as inspired Fermat).

Heath’s account of these mathematicians is largely internal, meaning that he is focused on the growth of their ideas rather than anything external to the science. Reading this convinced me—as if further evidence was needed—that I do not have the moral fiber or intellectual temper to appreciate mathematics. Heath writes admiringly of the works of Euclid and Archimedes, finding them not only brilliant but beautiful. While I can normally appreciate the brilliance, the beauty normally escapes me. Ratios, volumes, lines, and equations simply do not make my heart beat.

Indeed, the questions that I find most fascinating are those that are hardly touched upon in this book. Most important, perhaps, is this: What aspect of a culture or a society is conducive to the development of pure mathematics? Though claims of Greek specialness or superiority seem antiqued at best nowadays, it is true that the Greeks made outstanding contributions to science and math; while the Roman contribution to those fields—at least on the theoretical side—is close to nil. The mathematics of Ancient Egypt amount to techniques for practical calculations. Admittedly, as Otto Neugebauer wrote about in his Exact Sciences of Antiquity, the Babylonians had quite advanced mathematics, allowing them to solve complex polynomials; they also had impressive tabulations of the heavenly motions.

Even so, it was the Greeks who created science and math in the modern sense, by focusing on generality. That is, rather than collect data or develop techniques for specific problems, the Greeks were intent on proving theorems that would hold in every case. This also characterizes their philosophy and science: a rigorous search after an absolute truth. This cultural orientation towards the truth in the most general, absolute form seems quite historically special. It arose in one fairly limited area, and lasted for only a few centuries. Most striking is the Greek disdain of the practical—something that runs from Pythagoras, through Plato, to Archimedes.

Of the top of my head, here are some possible factors for this cultural development. The Greek economy was based on slavery, so that citizens often could afford to disdain the practical. What is more, the Greek political model was based on the city-state—a small, close-knit community with limited expansionist aims and thus with limited need for great infrastructure or novel weapons. The relative lack of economic, political, or military pressure perhaps freed intellectuals to pursue wholly theoretical projects, with standards that arose from pure logic rather than necessity. Maybe this seems plausible; but I am sure many other societies fit this description, not just the Greeks. The development of culture is something that we do not fully understand, to say the least.

This has taken me quite far afield. In sum, this book is an excellent place to start—either by itself, or as a companion to the original Greek works—if you are interested in learning something about this astounding intellectual tradition. That the Greeks could get so far using geometry alone—that is, without variables or equations—is a testament to human genius and persistence.

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Quotes & Commentary #68: Bryson

“It’s remarkable that bad things don’t happen more often. According to one estimate reported by Ed Yong in the Atlantic, the number of viruses in birds and mammals that have the potential to leap the species barrier and infect us may be as high as 800,000. That is a lot of potential danger.”

—Bill Bryson

This past Christmas, my mother gave me Bill Bryson’s new book on the human body as a present. It was an excellent gift: I spent half my Christmas break totally absorbed in it. The book is fascinating for several reasons. For one, there is an awful lot that most of us do not know about our own bodies—which itself is funny to think about. But perhaps we are better off not knowing, since the book also highlights how many things could potentially go wrong in the intricate functioning of our mortal frames. The existence of life is a miracle in its own right; and the existence of highly complex life—such as us (or so we like to flatter ourselves)—is a miracle of exponential proportions. So many things have to go right in order for you and me to be here.

That means it is easy for things to go wrong. And a viral infection—when malicious genetic code hijacks our cells—is one way that this marvelous process can get disrupted. One of the best chapters in Bryson’s book is on diseases. When I read the chapter, not too long ago, it seemed to be mainly about things from the distant past that used to menace our species. Bryson discusses typhoid and typhus, smallpox and ebola, and of course the Spanish flu of 1918. Most of these illnesses strike us nowadays as historical curiosities, rendered obsolete by the invention of vaccines and effective antibiotics. But Bryson sounds a note of warning in the chapter that now seems quite prescient. He quotes Michael Kinch, a specialist on drug discovery of Washington University, as saying:

The fact is, we are really no better prepared for a bad outbreak than we were when Spanish flu killed tens of millions of people a hundred years ago. The reason we haven’t had another experience like that isn’t because we have been especially vigilant. It’s because we have been lucky.

I vividly remember reading that passage, and scoffing. Surely, I thought, we must be far better prepared than they were back in 1918, when medicine and technology were so comparatively primitive. I was wrong. Bryson deserves kudos for his writing, as this current crisis has completely borne out his warnings. We are in far more danger than we like to think, and we are basically not prepared for it.

One rather stunning fact—stunning because we so rarely think of it—is how many people normally die from the seasonal flu. In the United States alone, it is between 30-40,000 per year, and that number gets much bigger during particularly bad years. According to Bryson’s book, in the 2017-18 flu season, upwards of 80,000 people died of the flu. These numbers are stunning, especially considering the massive international response that is already underway to slow the spread of this new coronavirus, which has so far taken far fewer lives. Perhaps we should always be practising social distancing…

The primary issue, at the moment, is essentially this: our society was not built to handle large-scale infectious diseases with fatality rates significantly higher than the seasonal flu. We do not have enough hospital beds, nurses, doctors, respirators, masks, or anything else. Our entire way of life—hanging out in bars, going to concerts, flying from country to country—is premised on being largely free from dangerous infectious diseases. We really did not know how lucky we were. Our situation was highly anomalous in human history, and it will take months before we can return to it.

What is most frustrating, for me, is the degree to which the situation is out of my hands. Everyone craves a sense of control. In a crisis, we want to know what we can do to protect ourselves, or to contribute to a common cause. Right now, these actions are rather humble: wash your hands, stay at home as much as possible, self-isolate if you show symptoms. This is all well and good; but we naturally want to know what is the scale of the danger and how long this immense disruption will last.

At this point, the information available is far from clear. The more articles I read, the more contradictory the information seems. Some are predicting infection rates of up to 80% of the population, while others predict 20%. Some predict that the disease will turn out to be less deadly than it seems, while others are predicting a complete global disruption lasting for months. It also seems unclear (to me, at least) whether children are effective vectors of the virus. Judging from the school closures, many believe yes; but I also have read that there is little available evidence.

Our best tool in fighting pandemics are vaccines. But unfortunately vaccines can take quite a long time to develop. It is not as easy as I (naively) thought. Many trials must be performed to ensure that the vaccine is effective and safe for the general population, and this takes time: months and months. If we cannot immunize ourselves artificially, then, the only possibility is to develop a herd-immunity the hard way: by getting the disease itself. This is a frightening prospect. That route would entail a great deal of suffering and death. But how long can we wait in our homes? In short, I am unclear how we are going to get out of this mess.

Meanwhile, I am fairly stuck in my little apartment in Madrid, one of the new epicenters of the virus. We have only had three days of isolation, and it is not so bad thus far. I began an exercise routine that I can do in my room, and my brother and I have been cooking a lot of hearty meals. But I really cannot see how everyone will be able to keep this up for the long-term, either economically or psychologically. Without extraordinary government measures, I do not think that people could stay in their homes much longer than one month without a great many people facing serious financial strain. Even in the best case scenario, the consequences for the economy seem quite grave. And this is putting aside the social pressure to resume normal life, which will increase from day to day.

At present, I swerve wildly from optimism to pessimism. What I want most of all is a return to normalcy. Never has my old life seemed so desirable! The strangest thing about this crisis is that it went from trivial to serious so quickly. Everyone seems to have been caught unawares. But even Bill Bryson—a popular writer with no specialized training—was able to see potential danger once he looked into the research. If only our experts had been as intelligent and as anxious as he.

Review: Winesburg, Ohio

Winesburg, Ohio by Sherwood Anderson

My rating: 3 of 5 stars

This book did not conform to my expectations, and this is often a cause of bitterness with me. I opened Winesburg, Ohio thinking that it would be a series of carefully-plotted, intersecting short stories illustrating the reality of small-town life in America. And I was excited for this hypothetical book, since it seemed like a wonderful concept. But Anderson had quite different ideas, and his were far less to my taste.

For one, the stories in Winesburg, Ohio have very little in the way of plot, and so they can hardly weave an intricate tapestry. The effect is not that of a carefully worked-out machine, but if a simple accumulation. What is more, this is hardly a work of realism in any meaningful sense. Anderson is not one for sensory details, nor for social analysis; his world is composed of individual souls residing in a shadowy world. The stories could have taken place just as easily in Winesburg as in Warsaw, since Anderson’s fundamental concern is something much more universal.

The insistent message of these stories is that people are bound up within themselves, their inner passions shut off from the world, and they have little idea how to rectify their situation. Thus, the stories follow a characteristic pattern: The protagonist’s frustrated dreams and desires are narrated, and then a crisis follows in which the character tries, unsuccessfully, to disburden herself of this frustration. This usually takes the form of a frantic encounter with George Willard, the young town reporter. The story ends as soon as the crisis is shown to be unsuccessful.

I have many criticisms of these stories. Anderson is as guilty as any author can be of telling and not showing. His stories consist almost entirely of narration. What is worse, I often found the narration unsuccessful, as Anderson seems allergic to the use of vivid, concrete details. We are never in the moment with a character, never able to watch a scene unfold in our mind’s eye. Someone extremely sympathetic to Anderson’s style may argue that this creatures a distance between the reader and the story which mirrors the emotional distance between Anderson’s characters. In my case, however, the result was often apathy or bemusement.

As an example of his style, consider this passage:

There was something biting and forbidding in the character of Kate Swift. Everyone felt it. In the schoolroom she was silent, cold, and stern, and yet in an odd way very close to her pupils. Once in a long while something seemed to have come over her and she was happy. All of the children in the schoolroom felt the effect of her happiness. For a time they did not work but sat back in their chairs and looked at her.

This passage is characteristic in its almost total lack of sensory information. Indeed it seems intentionally vague: “in an odd way,” “something came over her,” “felt the effect”—these phrases suggest that Anderson himself was not interested in really picturing to himself how this strange scene could actually play out. It also shows a kind of curious anti-realism when it comes to describing human behavior. As somebody who has worked as a teacher, I can scarcely imagine the reaction of young pupils to a mysteriously happy teacher being to simply look at her. Has Anderson ever been around a child?

Of course, an author is under no obligation to describe people as behaving realistically. Nevertheless, I think that this oddity is symptomatic of one of the paradoxes in these short stories: though they are about the innermost struggles of different individuals, Anderson seems rather uninterested in his characters as individuals. The persons in this book can hardly be called individuals, in fact, but are mere points of tension. They have problems but no personalities, and once their crisis is over they have no further interest. The way that Anderson writes dialogue is particularly infelicitous—unnatural to the point that it must have been intentional, but which nevertheless struck me as jarring. Luckily, there is not much of it.

What perhaps struck me most about these stories is how strongly they reminded me of a lot of contemporary writing. The idea that we are all silently suffering, or that, in Anderson’s own words, “everyone in the world is Christ and they are all crucified”—and, most importantly, that emotional expression will fix this problem—this strikes me as a profoundly limited worldview. For my part, I do not think that emotional connection alone is enough to solve any problem, unless it is supplemented by a thoughtful empathy—the ability to see humans in the round and not as simply balls of frustrated passions.

Indeed, as Lionel Trilling argues in his excellent essay on Anderson, the paradox of this philosophy is that it can lead to a world just as cold and brutal as one of repressed desires. And yet, this is an idea that I encounter again and again: that all we need is emotional expression. Expression is easy, however, while understanding is infinitely more difficult.

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Review: The Works of Archimedes

The Works of Archimedes by Archimedes

My rating: 5 of 5 stars

In fact, how many theorems in geometry which have seemed at first impracticable are in time successfully worked out!

Many of the most influential and ingenious books ever written possess the strange quality of being simultaneously exhilarating and quite boring. Unless you are among that rare class of people who enjoy a mathematical demonstration more than a symphony, this book will likely possess this odd duality. I admit this is the case for me. Reading this book was a constant exercise in fighting the tendency for my eyes to glaze over. But I am happy to report that it is worth the trouble.

Archimedes lived in the 3rd century BCE, somewhat after Euclid, in Syracuse on the island of Sicily. Apart from this, not much else can be said with certainty about the man. But he is the subject of many memorable stories. Everybody knows, for example, the story of his taking a bath and then running through the streets naked, shouting “Eureka!” We also hear of Archimedes using levers to move massive boats, and claiming that he could move the whole earth if he just had a place to stand on. Even his death is the subject of legend. After keeping the invading Romans at bay using ingenious weapons—catapults, cranes, and even mirrors to set ships afire—Archimedes was killed by a Roman soldier, too preoccupied with a mathematical problem to care for his own well-being.

True or not, good stories tend to accumulate around figures who are worthy of our attention. And Archimedes is certainly worthy. Archimedes did not leave us any extended works, but instead a collection of treatises on several topics. The central concern in these different works—the keystone to Archimedes’s method—is measurement. Archimedes set his brilliant mind to measuring things that many have concerned impossible to reckon. His work, then, is an almost literal demonstration of the human mind’s ability to scan, delimit, and calculate things far outside the scope of our experience.

As a simple example of this, Archimedes established the ratios between the surface areas and volumes of spheres and cylinders—an accomplishment the mathematician was so proud of that he apparently asked for it to be inscribed on his tombstone. Cicero describes coming across this tombstone in a dilapidated state, so perhaps this story is true. Archimedes also set to work on giving an accurate estimation of the value of pi, which he accomplished by inscribing and circumscribing 96-sided polygons around a circle, and calculating their perimeters. If this sounds relatively simple to you, keep in mind that Archimedes was operating without variables or equations, in the wholly-geometrical style of the Greeks.

Archimedes’s works on conoids, spheroids, and spirals show a similar preoccupation with measurement. What all of these figures have in common is, of course, that they are composed of curved lines. How to calculate the areas contained by such figures is not at all obvious. To do so, Archimedes had to invent a procedure that was essentially equivalent to the modern integral calculus. That is, Archimedes used a method of exhaustion, inscribing and circumscribing ever-more figures composed of straight lines, until an arbitrarily small gap remained between his approximations and what he was attempting to measure. To employ such a method in an age before analytic geometry had even been invented is, I think, an accomplishment difficult to fully appreciate. When the calculus was finally invented, about two thousand years later, it was by men who were “standing on the shoulders of giants.” In his time, Archimedes had few shoulders to stand on.

The most literal example of Archimedes’s concern with measurement is his short work, The Sand Reckoner. In this, he attempts to calculate the number of grains of sand that would be needed to fill up the whole universe. We owe to this bizarre little exercise our knowledge of Aristarchus of Samos, the ancient astronomer who argued that the sun is positioned at the center of the universe. Archimedes mentions Aristarchus because a heliocentric universe would have to be considerably bigger than a geocentric one (since there is no parallax observed of the stars); and Archimedes wanted to calculate the biggest universe possible. He arrives at a number is quite literally astronomical. The point of the exercise, however, is not in the specific number arrived at, but in formulating a way of writing very large numbers. (This was not easy in the ancient Greek numeral system.) Thus, we partly owe to Archimedes our concept of orders of magnitude.

Archimedes’s contributions to natural science are just as significant as his work in pure mathematics. Indeed, one can make the case that Archimedes is the originator of our entire approach to the natural sciences; since it was he who most convincingly demonstrated that physical relationships could be described in purely mathematical form. In his work on levers, for example, Archimedes shows how the center of gravity can be found, and how simple principles can explain the mechanical operation of counterbalancing weights. Contrast this with the approach taken by Aristotle in his Physics, who uses wholly qualitative descriptions and categories to give a causal explanation of physical motion. Archimedes, by contrast, pays no attention to cause whatever, but describes the physical relationship in quantitative terms. This is the exact approach taken by Galileo and Newton.

Arguably, the greatest masterpiece in this collection is On Floating Bodies. Here, Archimedes describes a physical relationship that still bears his name: the relationship of density and shape to buoyancy. While everyone knows thpe story of Archimedes and the crown, it is possible that Archimedes’s attention was turned to this problem while working on the design for an enormous ship, the Syracusia, built to be given as a present to Ptolemy III of Egypt. This would explain Book II, which is devoted to finding the resting position of several different parabolas (more or less the shape of a ship’s hull) in a fluid. The mathematical analysis is truly stunning—so very far beyond what any of his contemporaries were capable of that it can seem even eerie in its sophistication. Even today, it would take a skilled physicist to calculate how a given parabola would rest when placed in a fluid. To do so in ancient times was simply extraordinary.

Typical of ancient Greek mathematics, the results in Archimedes’s works are given in such a way that it is difficult to tell how he originally arrived at these conclusions. Surely, he did not follow the steps of the final proof as it is presented. But then how did he do it? This question was answered quite unexpectedly, with the discovery of the Archimedes Palimpsest in the early 1900s. This was a medieval prayer book that contained the remains of two previously unknown works of Archimedes. (Parchment was so expensive that scribes often scraped old books off to write new ones; but the faded impression of the original work is still visible on the manuscript.) One of these works was the Ostomachion, a collection of different shapes that can be recombined to form a square in thousands of different ways (and it was the task of the mathematician to determine how many).

The other was the Method, which is Archimedes’s account of how he made his geometrical discoveries. Apparently, he did so by clever use of weights and balances, imagining how different shapes could be made to balance one another. His method of exhaustion was also a crucial component, since it allowed Archimedes to calculate the areas of irregular shapes. A proper Greek, Archimedes considered mechanical means to be intellectually unsatisfactory, and so re-cast the results obtained using this method into pure geometrical form for his other treatises. If it were not for the serendipitous discovery of this manuscript, and the dedicated work of many scholars, this insight into his method would have been forever lost to history.

As I hope you can see, Archimedes was a genius among geniuses, a thinker of the rarest caliber. His works are exhilarating demonstrations of the power of the human mind. And yet, they are also—let us admit it—not the most exciting things to read, at least for most of us mere mortals. Speaking for myself, I would need a patient expert as a guide if I wanted to understand any of these works in detail. Even then, it would be hard work. Indeed, I have to admit that, on the whole, I find mathematicians to be a strange group. For the life of me I cannot get excited about the ratio of a sphere to a cylinder—something that Archimedes saw as the culmination of his entire life.

Archimedes is the very embodiment of the man absorbed in impractical pursuits—so obsessed with the world of spirals and curves that he could not even avoid a real sword thrust his way. And yet, if subsequent history has shown anything, it is that these apparently impractical, frigid, and abstract pursuits can reveal deep truths about the universe we live in—much deeper than the high-flown speculations of our philosophers. I think this lesson is worth suffering through a little boredom.

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Review: The Ambassadors

The Ambassadors by Henry James

My rating: 4 of 5 stars

He had spoken in the tone of talk for talks sake, and yet with an obscure truth lurking in the loose folds…

One would think that, of all the people living on this good green earth, I would be especially prone to loving this particular work of literature. After all, it is about a young American who moved to Europe, fell in love, and then resisted his family’s entreaties to come back and make more money. If you know anything about me, you will know that this has a special resonance. I am also, as it happens, a lover of fancy prose and classic novels. Clearly, in my case, the book’s prospects were extremely favorable.

It is with mild surprise, then, that I report that my feelings are mixed. This is not a novel that one can easily love. It is, rather, a product of James’s infamous late style, which divided critics at the time and has continued to do so ever since. There are many ways to characterize this style—dense, laborious, obscure—but I think that the keynote here is vague. Both in his descriptive passages and his dialogue, James maintains a kind of studious vagueness that can be either delightful or infuriating, depending on your mood and taste. In everything from his sentence structure, to his dialogue, to his descriptions, to his plotting—vagueness reigns.

To indulge in highfalutin terminology, I would say that this is an aesthetic triumph at the expense of humanistic value.

First, the triumph. James, at his best, achieves something like that achieved by the impressionist painters. The strokes of his pen are suggestive rather than illustrative. He asks much of the reader; and this means that the reader becomes an active part of the story. Virtually nothing—not the book’s resolution, nor the personality of the major characters, nor even the meaning of some knotty sentences—is unambiguous, which means that each reader can make the book her own. In other words, James’s late style is quite like the Ostomachion of Archimedes: a set of puzzle pieces that can be assembled in a myriad of ways.

I say that this is an aesthetic triumph because James achieves an effect that is unique, distinctive, novel, and demanding. He creates, in other words, his own aesthetic realm. The cageyness, the uncertainty, the self-referential quirks of this book—we can clearly see, in retrospect, that James was paving the way for literary modernism. And like much of modernism, I think that this aesthetic triumph comes at a great cost to humanistic value.

To simplify matter somewhat, you can describe this loss at the emphasis of form over content. The novels of Dickens, Dostoyevsky, Elliot, Tolstoy—say what you will about them, but they have an awful lot of content. Putting aside whatever explicit messages these novels may carry, they introduce us to concrete places, to remarkable individuals, to unforgettable stories. They capture, in other words, a human reality; and in so doing they help us to come to grips with life itself. Now, do not get me wrong: all of these authors also have aesthetic merits. If they did not, they would not be artists at all—merely columnists. My point is that their artistic style was entirely compatible with a definite view of the world, a view that is communicated in their works. This I call their humanistic value.

My main criticism of this book, then, is that James’s remarkable aesthetic sense overpowered whatever message he wished to transmit. Based on a straightforward reading, the intended message is this: American culture is narrow and materialistic, and it leads people to give up enjoyment for superficial, conventional reasons. We are, thus, presented with a cast of characters who embody this difference. Strether and Chad are exquisitely sensitive to the charms of Europe, and improve under its influence; while other Americans, such as Waymarsh, insistently stay within their narrow horizons.

The problem is, again, the vagueness. James is insistently vague on every detail. How exactly is life in Europe more liberating than life in America? And how exactly have Strether or Chad improved? These may seem like superficial questions, but the entire weight of the plot hinges on them. We cannot come to any moral conclusion without knowing the details. Indeed, James is so impressionistic in his portrayal of the main characters that we can hardly come to any conclusions at all. Do we even like these people? Even the ending is veiled in vagueness. Will Chad return to America? And why does Strether decide to return? And is his return a failure, or a success, or what? It is simply impossible to answer these questions.

Perhaps I would have been able to stomach all of these irresolutions if I had absolutely adored James’s style. But I do not. Indeed, I confess to finding James’s prose quite ugly—laborious, convoluted, and dry. There is hardly a passage in this book that one can read aloud without sounding like an alien. The following is entirely typical:

Nothing could have been odder than Strether’s sense of himself as at that moment launched in something of which the sense would be quite disconnected from the sense of his past and which was literally beginning there and then. It has begun in fact already upstairs and before the dressing-glass that struck him as blocking further, so strangely, the dimness of the window of his dull bedroom; begun with a sharper survey of the elements of Appearance than he had for a long time been moved to make.

A few sentences of this may be fine; but pages of it are painful. Granted, James is capable of quite lovely writing. I was enchanted, for example, by his description near the end, of Strether’s venture into the French countryside. Yet, all too often, the book is like this passage: opaque. His dialogue is only slightly better—readable, and yet still plagued by the strained and unnatural cadences of James’s prose. Besides this, James’s characters have the same tendency to vagueness as James himself, and never spell out what they mean.

Obviously this will come down to taste. I like things to be clear and unambiguous. That is my taste. James clearly did not agree. That I liked this book in spite of this divergence is a testament to James’s aesthetic power. He was an artist in the highest sense of the word.

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Review: Don Juan

Don Juan by Lord Byron

My rating: 4 of 5 stars

Let us have wine and woman, mirth and laughter,
Sermons and soda water the day after.

The legend of Don Juan appears to be one of the most productive stories in all of literature. After its first setting by Tirso de Molina—still a classic of the Spanish stage—it has been adapted innumerable times. Molière’s powerful version may be the most famous for the theater, and Mozart’s opera is considered to be among the greatest works of music even sounded. After speaking in French verse and singing in mellifluous Italian, the infamous seducer of Seville lived on—though much altered—to speak iambic pentameter in Lord Byron’s comedic epic.

Nonetheless, Lord Byron’s use of the legend is free to the point that it may as well have been discarded entirely. The protagonist is, indeed, an attractive young man from Seville with a formidable sexual appetite. Byron’s Juan, however, is usually the seducee rather than the seducer. He does not lie to get his way, he does not have a wisecracking servant, he does not kill the fathers of his victims, and he does not meet his end at the hands of a living statue. There is none of that here. Instead, Don Juan is an attractive young boy with a good heart who runs into a lot of trouble, mainly because every woman who sees him wants him. It is a pleasant twist on an old tale.

Though a member of the Romantic age, Byron does not strike me as a Romantic poet. His poetry is witty, snappy, sharp, irreverent, and lean. There is nothing sentimental, meditative, or wistful in this long poem. Indeed, the verse is so prose-like that it is hardly even poetical. His most obvious literary forebear is not Milton or Donne, but Pope—another witty versifier. It seems strange, then, that of all the great English Romantic poets, it was Byron who was arguably the most famous and influential. Perhaps tastes did not change as much as we are prone to believe.

This epic poem has a loose and baggy structure. That is to say that it is full of holes and an awful lot of wind blows through it. Byron appears to have begun with a fairly concrete idea in mind, and the first three or four cantos are brilliant fun. Soon thereafter the poem falls apart, however—dissolving into an endlessly long aside, in which the main action is lost. The poem ceases to be the comic epic of Don Juan and instead becomes a vehicle for Byron’s own endless editorializing. This is still mostly worth reading, for Byron’s wit if not for his logic, but it is not exactly a work of high art.

Poor Don Juan is left in the lurch, and never does get to meet his final end—whatever that may have been. Byron met his own end before he could give one to Don Juan. If not for that, this poem may have gone on for twenty cantos more. But at the rate the story was progressing in the final cantos, twenty more may not even have been enough to bring this sprawling story to a satisfying conclusion. So let us be thankful for what we have. The parts that are weak are readable, and the parts that are strong are delightful.

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Review: the Martian Chronicles

Crónicas marcianas by Ray Bradbury

My rating: 4 of 5 stars

I am not sure that I am in the best position to judge this short story collection, since the circumstances of my reading it were far from optimal. I downloaded the audio version to pass the time on a long drive, and I decided on the Spanish translation since my co-pilot would have fallen asleep otherwise. I soon discovered that listening to a foreign-language book while navigating mountain roads is not conducive to careful appreciation (or careful driving).

This is much closer to a short-story collection than to a conventional novel, but Bradbury blurred the lines a bit by adding some connecting passages to his stories (originally published separately). It is really only the setting and a vague sense of chronology that connects the separate chapters. And despite his post-facto additions, Bradbury did not achieve full consistency in his Martian world. This is not a problem, however, since I think the inconsistency adds to the stories rather than detracts. The final effect is much like an episodic TV show, which can invent itself anew with each iteration.

Bradbury has become known as a science-fiction writer; and yet these stories may be more accurately described as “anti-science fiction.” He has little interest in the details of technology, cosmology, or space travel, and even less interest in making his stories plausible or realistic. Indeed, Bradbury is not merely uninterested, but positively worried about what the future may bring. For Bradbury, Mars is not the fourth planet from the sun—with its own moons, its unique geology, its practical challenges—but a kind of parallel world where his fears can play out. Much like The Twilight Zone, these stories have one consistent message: “Be careful what you wish for.” Where other people saw the dawning of the space age, Bradbury saw only an extension of human idiocy beyond the clouds.

Arguably, this is quite a conservative message—anti-science, anti-technology, anti-change—but it also resonated with me. I remember being a little kid and contemplating the wonders that the future would bring: flying cars, tourism to the moon, miracle cures. Nowadays, this mood of optimism seems very distant. New technologies, rather than filling us with wonder, are prompting second-thoughts: automation that reduces job opportunities, face-recognition technology that only extends the surveillance state, or the unknown threat of artificial intelligence. And when I think of space travel, rather than imagining the next glorious phase of humanity’s ascent, two buffoons come to mind: Elon Musk (with his SpaceX) and Donald Trump (with his Space Force).

Well, I do not want to get too gloomy in a book review. My point is that Bradbury’s stories may indeed contain a valuable lesson: be careful what you wish for.

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Review: Bullshit Jobs

Bullshit Jobs: A Theory by David Graeber

My rating: 5 of 5 stars

Economies around the world have, increasingly, become vast engines for producing nonsense.

Reading this was cathartic. Like so many people, I, too, have experienced the suffering that is a useless job—a job that not only lacks any real benefit to society, but which also does not even benefit the company. (Lucky for me, I am now a teacher, which, for all its unpleasant aspects, almost never feels useless.) Even though I got a lot of reading and writing done on the job, the feeling of total futility eventually drove me half-crazy. So it felt liberating to read an entire book about this phenomenon.

But let me take a step back and explain the book. In 2013 Graeber published an article in STRIKE! magazine (a fairly obscure publication) about bullshit jobs, and it immediately went viral. This book is basically an articulation, elaboration, and defense of the points in that short article. Graeber notes that Keynes predicted the rise of automation to cause a startling reduction in the work-week. Yet this has not occurred. Many economists explain this by pointing to the rise of the so-called “service” industry. But this would seem to imply that we have switched from factory-work to making lattes for one another, or giving each other massages. As Graeber shows, this is hardly the case: the number of people in such jobs has remained fairly constant. What has grown, rather, is a vast edifice of managerial and administrative work.

Anyone familiar with the academic world will instantly recognize this. Universities have come to be dominated by a top-heavy administrative structure, and faculty have been forced to spend ever-increasing amounts of time on bureaucratic nonsense. The same is true in the medical field, or so I hear. Really, the story is the same everywhere: an increasingly arcane hierarchy of administrators, leading to byzantine networks of paperwork—all of it ostensibly for improving quality, and yet manifestly distracting from the real work. This kind of ritualistic box-ticking is only one of the types of bullshit jobs that Graeber investigates. Also included are flunkies (subordinates whose only role is to make superiors feel important), goons (jobs which arise from a kind of arms race, such as marketing agents or corporate lawyers), and duct tapers (who are hired to patch over an easily-fixed problem).

Obviously, one could argue all day about the typology of useless jobs. One could also argue about which jobs, if any, are useless. It must be said that Graeber’s reliance on subjective experience of his informants does introduce a worrisome element of capricious judgment. Besides this, some might say that the free market can never give rise to useless jobs, since such things would be obviously detrimental to a company’s profits. But one need only read through the many testimonies collected by Graeber to be convinced that, yes, some jobs really ought not to exist. According to surveys, around 40% of workers report that they believe their own jobs to be useless—so useless that they could vanish tomorrow without anyone minding. To pick just one of Graeber’s examples: a man works for a subcontractor of a subcontractor of a contractor for the German military, whose job is to fill out the paperwork necessary to allow somebody to move their desk from one room to another room. I do not think this is necessary.

But this raises the obvious question: If so many jobs are really useless, why do they exist? One might understand this happening in the government, but this is precisely the sort of thing that the private sector should be immune from. Well, Graeber is an anthropologist, not an economist, and so his explanations are social and cultural. He cites several factors. There is a huge amount of political pressure, from the left and the right, to create more jobs. This is natural, since being out of work means being poor, or worse. More than that, we have culturally internalized the institution of “work” to the extent that our jobs are the primary source of meaning in many people’s lives, even if they ultimately are disagreeable. Indeed, Graeber believes it is just the unpleasantness of work that makes it a source of value in our culture, as it becomes a type of ennobling suffering.

Graeber also notes the usefulness of useless jobs to the upper classes. For one, they keep people endlessly busy; and, what is more, well-paying, white-collar jobs—even useless ones—make their holders identify with the interests of the upper class. The economy then becomes a kind of engine for distributing favors and resources down an elaborate chain of command. Graeber coins the term “managerial feudalism” for this arrangement: the return of the medieval obsession with ranks mirrored by the modern penchant for inflated job titles. Now, my brief summary does not do justice to Graeber’s writing. Nevertheless, it is here where one wishes most for an economist to contribute to the argument. For even if there are forces countervailing the pressures of profit, the economy is still running on manifestly capitalist lines. So how could a sort of inefficient feudalism exist in this context?

Another point that Graeber examines is the relative pay of people with useful and useless employment. The obvious trend is that jobs which have undeniable social value—like nurses and teachers—are paid less, while jobs that have questionable or even negative social value—such as “creative vice presidents” and corporate lobbyists—are richly rewarded. Now, I do not think you need to be an idealist to see this situation as undesirable. Graeber explains this tendency by analyzing the culture of work (specifically, that useful employment is supposed to be its own reward, while useless employment requires incentives), but again one craves an economic explanation. (This, by the way, is one of the frustrations of social science: that the different disciplines operate with incompatibly different premises and methodologies.)

For my part, my own experience, combined with the many testimonies and statistics in this book, is enough to convince me that some jobs are really bullshit—even from the limited standpoint of a company’s profit. And I think that Graeber may be correct in searching for a cultural and political, rather than a strictly “economic,” explanation. After all, we humans are not exactly renowned for our rational economies. But for my part, I think he may have underestimated the role that corporate mergers have played in vastly reducing competition—and, thus, the pressure to eliminate useless jobs.

While all of this deserves analysis and debate, I think that this book is valuable if only for raising serious questions about the institution of work itself. The more that I read about history, the more I have come to see our modern ritual of work as strange and aberrant. The idea that we would all go to work five days a week, eight hours a day, year after year—regardless of whether we are making cars or filling out forms, and regardless of how much work there is on any given day—would have struck people in nearly any other place and time as bizarre.

To me, it just seems backwards to use a cookie-cutter schedule for every task (from lawyer to salesman), and then expect every member of society to adopt this basic template or risk abject poverty. Considering that the economy requires a certain level of employment to function, and that the current social safety net could not support a large number of unemployed people anyway, perhaps it should come as no surprise that we are plagued by dummy jobs. And if you think about it, it would be an amazing coincidence if the economy—through all the structural and technological changes of the previous century—always needed between 90 to 95 percent of the working population at any given time.

Graeber’s proposed solution to this problem is Universal Basic Income—providing every person with a regular paycheck, sufficient to cover the necessities of life. Personally I think that this is a wonderful idea, and one which could greatly alleviate many of our social ills. Unfortunately, in the United States, at least, UBI seems just as likely as paid maternity leave. But whatever the means, I think it is high time to change our attitude towards work. We spend enormous amounts of time doing things we do not want to do, and, what is worse, things which often do not need to be done. What fuels this is a kind of masochistic work ethic, defining our worth by our ability to do things that we do not want to do. This ethic has so pervaded our culture that, in America at least, we take it for granted that everything from health care to our self-respect should depend on our jobs.

One of Graeber’s most interesting points is that the phenomenon of useless jobs may reveal that we are using a flawed conception of human nature. One would think that being paid to do little or nothing would be the height of happiness. But most people in useless jobs report profound feelings of unease and distress. Again, my own experience testifies to this. Though I had little work, and was paid decently, I often found myself miserable, even beside myself with a strange mixture of boredom and anxiety. Graeber has a long section on this, but basically it comes down to the way that useless work undermines our sense of agency in the world. There is a reason the gods punished Sisyphus that way. As Dostoyevsky said, having humans perform an unpleasant, uninteresting, and totally worthless task might be the most profound form of torture. In my own case, it gave me a very unsettling feeling of dissociation, as if I really could not control my own actions.

So if we build our economy on the assumption that humans, left to themselves, will choose to get the maximum reward for the least benefit, we may be building on false premises. I think that Graeber is right, and that people generally prefer feeling like they are doing something useful. This is why I think we ought not to fear that Universal Basic Income, or a drastic reduction in working hours, would lead to a society of lazy idlers. In any case, people bored at home may do something more worthwhile than people bored at work, who mostly seem to go on social media. (Graeber notes that the rise in social media use coincides with the rise of useless employment. Certainly it was true in my case, that useless employment led naturally to spending huge amounts of time on Facebook.)

This summary does not do justice to the full contents of the book. Graeber is a sharp writer and an agile thinker. Not only is he the first to really hone in on this strange aspect of the modern world, but he does so within a wide perspective. To give just a few more examples, he connects the rise of bullshit jobs with the slowdown in scientific progress and the decline in quality of Hollywood movies. Perhaps Graeber’s political identity as an anarchist helps him to avoid the basic narratives of both the left and the right, and to develop strikingly original opinions about social problems. While I am not anarchist myself, I think the institution of work deserves far more questioning and criticism. We have accepted work as the bedrock of society and the foundations of our lives’ meanings, and yet most of us do not particularly like it. If I could wax utopian for a moment, I would imagine a movement devoted to the creation of a society of leisure. I would even work for it.

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Review: The Myth of Sisyphus

The Myth of Sisyphus and Other Essays by Albert Camus

My rating: 4 of 5 stars

I still vividly remember my writing class in my first semester of college. Our professor was a lover of paradoxes. She had us read Kafka and Borges, whom none of us could understand. And she had a habit of asking impossible questions—such as “What does it mean to be infinitely finite?”—and savoring the uncomfortable silences that followed. Once, she even scared us half to death by asking one of these questions, and than yelping like a banshee half a minute later. Quite a good professor.

The final section of this iconic essay was among the readings she had us read. Of course I did not understand a word of it. I was no where near mature enough to wrap my mind around the idea of absurdism. The “meaning of life” was not a problem for me at that time. Surrounded as I was by thousands of potential friends and girlfriends—free for the first time in my life to do as I pleased—such a confrontation with nihilism was beyond the horizons of my mental life.

This was not the case four years later, when I graduated college with thousands of dollars in debt, confronted with the possibility of deciding “Who I Wanted to Be.” Probably I should have read this book at that time, when I could so keenly feel the weight of life’s pointlessness. Or maybe I should have read it a year later, when I was working in an office job. Humankind has seldom plunged deeper into the void than in entry-level positions.

I mention this biographical background because I think this book should likely not be read during a time of relative stability and contentedness, such as I am in now. We seldom pause to ponder the “meaning of life” when we are enjoying ourselves. The problem of “philosophical suicide” is not a problem at all on beautiful summer days. It is only a problem on cold, rainy Tuesday nights, in the few minutes of mental calm between work, chores, sleep, and work the next day. Unfortunately, such Tuesdays come all too often in this world of ours.

My point is simply that I would have enjoyed this essay far more under more propitious circumstances. Albert Camus’s style is well-calculated to please: a winsome mixture of anecdote, philosophy, literary criticism, and poetry. Certainly it is a relief after dragging my way through Sartre’s tortured syntax and cumbersome verbiage. Camus, by contrast, is concise and stylish. My only reservation is that, for all his accessibility, Camus is not perfectly clear. I say this from the perspective of somebody trying to read his essay as a philosophical work. All philosophy consists in argument; and in order to accept or reject an argument, one must use clearly defined terms. With Camus, however, I was never quite sure what his criteria were for considering something absurd or meaningful—his two central categories.

This is perhaps the wrong way to read Camus. What he was trying to create was arguably more in the tradition of wisdom literature than formal philosophy. From this perspective, the essay is somewhat more satisfying. However, here too I found Camus somewhat lacking. One extracts more piquant lessons in the art of life from Montaigne or La Rochefoucauld than from Camus. Where Camus excels these authors is not in wisdom per se, but in capturing a certain mood, a mood peculiar to modern times: being intellectually and spiritually adrift. After all of the traditional systems belief which underpinned life have crumbled, it is the crushing realization that one is unable to justify anything, even life itself. In this peculiar vein, Camus is difficult to beat.

Even so, I wonder if this iconic essay adds anything essential to that famous remark of Pascal: “Man is only a reed, the weakest in nature, but he is a thinking reed.” Camus’s Sisyphus is the twin brother of Pascal’s thinking reed—the plaything of an indifferent universe, and yet dignified by his consciousness. In his more despairing moments, Pascal may have been quite as horrified by the vast spectacle of an indifferent cosmos as Camus: “The eternal silence of these infinite spaces frightens me.” The essential difference between these two men is not their realization of humanity’s insignificance, but their reactions. Pascal seeks to escape this conclusion any way he can, bolstering his faith with every fallacious argument under the sun. Camus was innovative in his insistence that we must calmly accept this situation, taking it as a starting point and not as a depressing conclusion.

My main criticism with this essay is that, if life has no inherent meaning, and the universe is nothing but a cold expanse, this throws the question of the “meaning of life” back upon each individual. Answering that question definitively, for every person, becomes de facto impossible. But, again, perhaps Camus is not trying to prove anything universal. Rather, his essay is a sort of invitation to abandon the traditional justifications of life, and to focus, as Camus himself did, on the smaller joys—sunlight, the sea, travel. The rest of the essays in this collection may be seen in that light, as enlarging upon Camus’s omnivorous curiosity for his surroundings.

What bothers me is that I do not agree with Camus’s opening assertion: I do not think the most pressing question is whether we should all just commit suicide. To the contrary, once this question is decided in the negative, it opens up a world of far more interesting issues.

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Review: Coriolanus

Coriolanus by William Shakespeare

My rating: 3 of 5 stars

In my review of Plutarch’s Lives, I noted the stark difference between that ancient author’s conception of personality, and our own. For Plutarch, character was static and definable—an essence that is manifested in every decision and remark of a given person. Compare this with Montaigne’s or Shakespeare’s portrayal of personality: fluctuating, contradictory, infinitely deep, and ever fugitive. To borrow a metaphor from Oswald Spengler, the Plutarchian self is statuesque, while the Shakespearian self is more like a work of music. The first is a self-contained whole, while the second is abstract, fleeting, and morphs through time.

It is fascinating, therefore, to see Shakespeare handle a story right out of Plutarch. Shakespeare adapts his art to the subject-matter, and creates a character in Caius Marcius Coriolanus that is remarkably opaque. I say “remarkably” because Shakespeare had just finished with his five greatest tragedies, each of which has a character notable for its depth. Caius Marcius, by contrast, is a man almost in the Plutarchian mode: with a enumerable list of vices and virtues, who acts and speaks predictably, with little self-reflection. Next to Hamlet, Iago, or Macbeth, the Roman general seems almost childlike in his restriction.

Like Julius Caesar, this play is interesting for a certain amount of moral ambiguity. It is difficult to side with any of the major players. The plebeians of Rome are certainly not a mindless rabble, but they are somewhat vain and narrow-minded, not to mention easily influenced by empty words. Coriolanus himself is a superb soldier but ill-suited to anything else, whose capital vice is not exactly pride, but a certain smallness of mind. His mother, Volumnia, is scarcely less warlike than her son. Even if her counsels are good, it is difficult to see the mother-son relationship as perfectly healthy. She comes across, rather, as a kind of Roman helicopter mom, bringing up her son to be a killing machine for the glory of the state.

For me, the tragedy was not quite successful, simply because Coriolanus was such an unsympathetic protagonist—belligerent, scornful, reactionary, and often a great fool. It is a testament to Shakespeare’s art that he is not altogether hateful. As Harold Bloom says, this play is technically brilliant: in its pacing, language, and plotting. Shakespeare was certainly a professional. But if you come to Shakespeare seeking grand personalities, the work is a barren field.

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Lotz in Translation

Saving the world—one long, pretentious blog post at a time.

Tag: Book