Review: A Manual of Greek Mathematics

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.



View all my reviews

Review: Winesburg, Ohio

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.

View all my reviews

Review: The Works of Archimedes

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.



View all my reviews

Review: The Ambassadors

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.

View all my reviews

Review: A Room of One’s Own

Review: A Room of One’s Own

A Room of One’s Own by Virginia Woolf

My rating: 5 of 5 stars

This book is quite wholly unlike what I expected it to be. Judging from its reputation, I expected a fiery tract, an impassioned plea, a manifesto. But this is, rather, an exquisitely calm, delicate, and delightful work of writing. Considering that these adjectives also serve to describe Woolf’s fiction, maybe I should not be so surprised after all. Woolf was above all a writer; and it is the extraordinarily fine quality of its writing that makes this essay a classic work.

Woolf’s fundamental argument is simple: Writing literature requires education, experience, time, privacy, and independence. Historically, women lacked access to all of these things; so it should be expected that there are comparatively few classic women writers. Woolf regards this as a shame—not because of the human suffering involved, but because of the aesthetic privation. Women simply write differently than men, Woolf thinks, and by depriving women of the means to write, we are depriving ourselves of a wholly different sort of literature. Thus, Woolf frames women’s emancipation in rather materialistic terms (“a room of one’s own and 500 pounds a year”), and gives an ultimately aesthetic ground for doing so. It is a curious argument.

For any lovers of reading (and I assume there are lots of us here), it is compelling to think of the many poems, plays, and novels that were never written because huge portions of the population were deprived of the appropriate means to write them. Woolf brings this out with the famous example of Judith Shakespeare, the Bard’s equally talented sister who was never able to write a word.

As poignant as this example is, however, ultimately I do not think it is wise to ground an argument for women’s emancipation along aesthetic lines. If the premise to Woolf’s argument were correct, then we should be simply swimming in masterpieces nowadays. Yet I frankly doubt that the 2020s will, in 100 years, be considered a better decade for literature than the 1920s. After all, Woolf herself lived in the 1920s—and I doubt we can match her.

In any case, I do not think this essay stands or falls on the merit of Woolf’s arguments alone. Better yet, I do not think it should be evaluated as an argument at all. It is, rather, a sort of literary clarion call; and if it has inspired even one woman to take up the pen, then I think it has accomplished its purpose. Personally, I found the writing so intoxicatingly good, and Woolf’s sense of aesthetic value so overpowering, that I was myself driven back to the writing desk. Lucky for me, I have a room of my own, too—though it is rather small.



View all my reviews

Review: Don Juan

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.



View all my reviews

Review: Economics (Great Courses)

Review: Economics (Great Courses)

Economics by Timothy Taylor

My rating: 4 of 5 stars

Economics is one subject that causes me perpetual unease. Everybody cares about the economy, of course, and everybody argues about how it should be structured and managed. Imposing terminology is thrown around, graphs and statistics are wheeled out, and yet the situation always seems quite unclear to me. So I was pleased when Timothy Taylor framed his lectures, not as the gospel truth of economics, but as an introduction to the language of economics. Learning this language is essential if you would like to take part in this endless societal argument.

Considering the restraints of time and of format, I think that Taylor deserves praise for these lectures. In 18 hours, he manages to cover all of the major topics of micro- and macro-economics—supply and demand, price curves, government regulation, fiscal policy, etc.—in an accessible but not overly simplistic style. Further, Taylor is an engaging speaker whose enthusiasm for a potentially dreary subject helps to alleviate the dryness. Someone has got to get excited about interest rates, I suppose.

A major shortcoming of these lectures is that they were recorded in 2005, just before the enormous financial crash. Surely, a new edition is called for. Considering how much time has passed, however, I think that these lectures have held up remarkably well. For the most part, the major disagreements and issues in economics do not seem to have changed very much. Everything is here—healthcare costs, financial crashes, trade wars, deficits—which is probably not a reason to celebrate.

If Taylor can be criticized, I think it should be for inserting too many of his own views into these lectures. Some degree of editorializing is inevitable in any academic course, I think. But Taylor is quite an opinionated guide, and never hesitates to advocate for his pet policies. Admittedly this did make the lectures more interesting at times; but it also undermined Taylor’s insistence that economics is merely a way of thinking rather than a specific doctrine. To the contrary, these lectures contain very specific presumptions about and prescriptions for a successful society (hint: it is all about a free market).

Speaking more generally, it is frustrating for me the degree to which the social sciences inhabit parallel worlds. Not only do anthropology, psychology, and economics study different sorts of phenomena, but they make very different assumptions about human behavior—which often contradict one another. I was acutely aware of this while listening to these lectures, since I was concurrently reading psychologist Daniel Kahneman’s Thinking, Fast and Slow, which argues that the rational agent model of economic actors is fundamentally flawed. Meanwhile, my brother is reading anthropologist David Graebner’s book about the many different (non-capitalist) ways that economic activity has been carried out throughout time and across space.

Compared to psychology and anthropology, economics can seem worrisomely abstract to me—too content to rest its conclusions on untested assumptions and a priori principles. In these lectures, for example, I would have appreciated more case studies of historical examples in lieu of theoretical explanations. This would have illustrated the concepts’ usefulness far more effectively, I think.

But I am drifting off topic. As a painless introduction to economics, these lectures do an admirable job. It is a fascinating discipline with much to teach us. I am glad to have a break for now, though. A dismal science indeed.



View all my reviews

Review: Thinking, Fast and Slow

Review: Thinking, Fast and Slow

Thinking, Fast and Slow by Daniel Kahneman

My rating: 5 of 5 stars

Nothing in life is as important as you think it is when you are thinking about it.

I think this book is mistitled. For years, I assumed that it was some kind of self-help book about when to trust your gut and when to trust your head, and thus I put off reading it. But Thinking, Fast and Slow is nothing of the sort. As I finally discovered when the book was gifted to me (the ecstatic blurbs in the front pages were the first clue), this book is the summary of Daniel Kahneman’s study of cognitive errors. The book should probably be called: Thinking, Just Not Very Well.

Granted, my initial impression had a grain of truth. Kahneman’s main focus is on what we sometimes call our gut. This is the “fast thinking” of the title, otherwise known as our intuition. Unlike many books on the market, which describe the wonders of human intuition and judgment, Kahneman’s primary focus was on how our intuition can systematically fail to draw correct conclusions. So you might say that this is a book about all of the reasons you should distrust your gut.

Every researcher of the mind seems to divide it up into different hypothetical entities. For Freud it was the conscious and unconscious, while for Kahneman there are simply System 1 and System 2. The former is responsible for fast thinking—intuition, gut feelings—and the second is responsible for slow thinking—deliberative thought, using your head. System 2, while admirably thorough and logical, is also effortful and sluggish. Trying any unfamiliar mental task (such as mental arithmetic) can convince you of this. Thus, we must rely on our fast-acting System 1 for most of any given day.

System 1 generates answers to questions without any experience of conscious deliberation. Most often these answers are reasonable, such as when answering the question “What you like a hamburger?” (Answer: yes). But, as Kahneman demonstrates, there are many situations in which the answer that springs suddenly to mind is demonstrably false. This would not be a problem if our conscious System 2 detected these falsehoods. Yet our default position is to simply go with our intuition unless we have a strong reason to believe our intuition is misleading. Unfortunately, the brain has no warning system to tell you that your gut feeling is apt to be unreliable. You can call these sorts of situations “cognitive illusions.”

A common theme in these cognitive illusions is a failure of our intuition to deal with statistical information. We are good at thinking in terms of causes and comparisons, but situations involving chance throw us off. As an example, imagine a man who is shy, quiet, and orderly. Is he more likely to be a librarian or a farmer? Now consider the answer that springs to mind (librarian, I assume): how was it generated? Your mind compared the description to the stereotype of a librarian, and made the judgment. But this judgment did not take into account the fact that there are many times more farmers than male librarians.

Another example of this failure of intuition is the mind’s tendency to generate causal stories to explain random statistical noise. A famous example of this is the “hot hand” in basketball: interpreting a streak of successful shots as due to the player being especially focused, rather than simply as a result a luck. (Although subsequent research has shown that there was something to the idea, after all. So maybe we should not lament too much about our intuitions!) Another well-known example is the tendency for traders to attribute their success or failure in the stock market to skill, while Kahneman demonstrated that the rankings of a group of traders from year to year had no correlation at all. The basic point is that we are generally hesitant to attribute something to chance, and instead invent causal stories that “explain” the variation.

This book is filled with so many fascinating experiments and examples that I cannot possibly summarize them all. Suffice to say that the results are convincing, not only because of the weight of evidence, but mainly because Kahneman is usually able to demonstrate the principle at work on the reader. Our intuitive reactions are remarkably similar, apparently, and I found that I normally reacted to his questions in the way that he predicted. If you are apt to believe that you are a rational person (as I am) it can be quite depressing.

After establishing the groundwork, Kahneman sets his sights on the neighboring discipline of economics. Conventional economic theory presupposes rational actors who are able to weigh risks and to act in accordance with their desires. But, as Kahneman found, this does hold with actual people. Not only do real humans act irrationally, but real humans deviate from the expected predictions of the rational agent model systematically. This means that we humans are (to borrow a phrase from another book in this vein) predictably irrational. Our folly is consistent.

One major finding is that people are loss-averse. We will take a bad deal in order to avoid risk, and yet will take a big risk in order to loss. This behavior seems to be motivated by an intense fear of regret, and it is the cause of a certain amount of conservatism, not only in economics, but in life. If an action turns out badly, we tend to regret it more of it was an exceptional rather than a routine act (picking up a hitchhiker rather than driving to work, for example), and so people shy away from abnormal options that carry uncertainty.

Yet, logically speaking, there is no reason to regret a special action more than a customary one, just as there is no reason to weigh losses so much more heavily than gains. Of course, there is good evolutionary logic for these tendencies. In a dangerous environment, losing a gamble could mean losing your life, so it is best to stay to the tried-and-true. But in an economic context, this strategy is not usually optimal.

The last section of the book was the most interesting of all, at least from a philosophical perspective. Kahneman investigates how our memories systematically misrepresent our experiences, which can cause a huge divergence between experienced happiness and remembered joy. Basically, when it comes to memory, intensity matters more than duration, and the peaks and ends of experiences matter more than their averages. The same applies with pain: We may remember one experience as less painful than another just because the pain was mild when it ended. And yet, in terms of measured pain per minute, the first experience may actually have included more experiential suffering.

As a result of this, our evaluations of life satisfaction can often have very little to do with our real, experiential well being. This presents us with something of a paradox, since we often do things, not for how much joy they will bring us in the moment, but for the nice memory they will create. Think about this: How much money would you spend on a vacation if you knew that every trace of the experience would be wiped out as soon as the vacation ended, including photos and even your memories? The answer for most people is not much, if anything at all. This is why so many people (myself included) frantically take photos on their vacations: the vacation is oriented toward a future remembering-self. But perhaps it is just as well that humans were made this way. If I made my decisions based on what was most pleasant to do in the moment, I doubt I would have made my way through Kant.

This is just a short summary of the book, which certainly does not do justice to the richness of Kahneman’s many insights, examples, and arguments. What can I possibly add? Well, I think I should begin with my few criticisms. Now, it is always possible to criticize the details of psychological experiments—they are artificial, they mainly use college students, etc. But considering the logistical restraints of doing research, I thought that Kahneman’s experiments were all quite expertly done, with the relevant variables controlled and additional work performed to check for competing explanations. So I cannot fault this.

What bothered me, rather, was that Kahneman was profuse in diagnosing cognitive errors, but somewhat reticent when it came to the practical ramifications of these conclusions, or to strategies to mitigate these errors. He does offer some consequences and suggestions, but these are few and far between. Of course, doing this is not his job, so perhaps it is unfair to expect anything of the kind from Kahneman. Still, if anyone is equipped to help us deal with our mental quagmires, he is the man.

This is a slight criticism. A more serious shortcoming was that his model of the mind fails to account for a ubiquitous experience: boredom. According to Kahneman’s rough sketch, System 1 is pleased by familiarity, and System 2 is only activated (begrudgingly, and without much relish) for unfamiliar challenges. Yet there are times when familiarity can be crushing and when novel challenges can be wonderfully refreshing. The situation must be more subtle: I would guess that we are most happy with moderately challenging tasks that take place against a familiar background. In any case, I think that Kahneman overstated our intellectual laziness.

Pop psychology—if this book can be put under that category—is a genre I dip into occasionally. Though there is a lot of divergence in emphasis and terminology, the consensus is arguably more striking. Most authors seem to agree that our conscious mind is rather impotent compared to all of the subconscious control exerted by our brains. Kahneman’s work in the realm of judgments closely parallels Johathan Haidt’s work in morals: that our conscious mind mostly just passively accepts verdicts handed up from our mental netherworld. Indeed, arguably this was Freud’s fundamental message, too. Yet it is so contrary to all of our conscious experiences (as, indeed, it must be) that it still manages to be slightly disturbing.

Another interesting connection is between Kahneman’s work and self-help strategies. It struck me that these cognitive errors are quite directly related to Cognitive Behavioral Therapy, which largely consists of getting patients to spot their own mental distortions (most of which are due to our mind’s weakness with statistics) and correct them. And Kahneman’s work on experiential and remembered well being has obvious relevance to the mindfulness movement—strategies for switching our attention from our remembering to our experiencing “self.” As you can see from these connections, Kahneman’s research is awfully rich.

Though perhaps not as amazing as the blurbs would have you believe, I cannot help but conclude that this is a thoroughly excellent book. Kahneman gathers many different strands of research together into a satisfying whole. Who would have thought that a book about all the ways that I am foolish would make me feel so wise?



View all my reviews

Review: the Martian Chronicles

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.



View all my reviews

Review: The Wright Brothers

Review: The Wright Brothers

The Wright Brothers by David McCullough

My rating: 4 of 5 stars


When you open a McCullough book you know what to expect: fine prose, strong storytelling, and inspiring stories of American heroes. That is his domain, and he is the master of it. This book about the Wright brothers exemplifies all of these virtues in just over 300 pages. The audio book in particular, narrated by McCullough himself—whose folksy and yet erudite speaking voice encapsulates his ethos—is perhaps the most concentrated form of McCullough that you can imbibe.

Like many people, I was surprised at how little I knew about the Wrights. My hazy impression of their story was thus: The brothers were eccentric bike mechanics who, through a series of trial and error, managed to make some primitive flying machines, devices that could putter a few hundred feet and lift a few dozen feet off the ground. This is quite wrong. The Wrights approached the problem of flight with remarkable dedication and care. They read all the scientific literature they could find; and they performed careful experiments, documenting each step of the way. Their final product was not just some clumsy motor-powered kite, but a sophisticated machine capable of crossing the English channel and flying over the Eiffel Tower. Their creative vision was matched only by their persistence and perfectionism.

The story of the Wrights is legitimately inspiring. Having no special resources, no roadmap, no background, no support, they were able to succeed where so many other famous and wealthy inventors failed. They endured countless setbacks, both in the research and development of their craft and then in achieving recognition for their accomplishments. But in the end, two modest men from Ohio profoundly changed human life. It is a testament to their tenacity as much as to their intelligence.

It is difficult to criticize McCullough, because he does so perfectly what he sets out to do: show us how people in ordinary circumstances accomplish extraordinary things. But of course, this requires minimizing or even ignoring many aspects of a story that would attract other writers. One prominent example of this is the Wrights’ personalities. McCullough portrays them as dignified and diligent, representatives of an old-fashioned work ethic, unconcerned with fame or fortune. But in the hands of another biographer, the Wrights might not come across as so perfectly admirable. To me, they seemed curiously aloof, distant, and even repressed. The fact that Orville flew into a rage when his sister got married, for example, seems to be worth more investigation than McCullough is willing to give it. He dismisses the long estrangement as one of Orville’s “moods.”

Reading McCullough is a bit strange in today’s political climate. He was never concerned with being cutting-edge; but now more than ever he feels distinctly like a holdover from another era. As is commonly observed, American life has become deeply divided; so McCullough’s mission—to write about universally admirable Americans—seems especially quixotic. Yet McCullough’s reputation appears to have survived the late polarization relatively intact. And I think that is a good thing. True, it is wise to be wary of national mythologizers. But for the life of me I cannot find anything to trouble my conscience or divide the nation in the figures of Wilbur and Orville Wright.



View all my reviews