Review: Maxwell’s Treatise on Electricity and Magnetism

Maxwell’s Treatise on Electricity and Magnetism: The Central Argument by Howard J. Fisher

My rating: 4 of 5 stars

Most good books lend themselves to be read on many levels. One can read them superficially, merely for momentary pleasure, or study them deeply, working your way slowly through their contents. For the most part, I try to chart a middle path through these two extremes, doing my best to understand what I’m reading—at least on a basic level—without getting bogged down in academic study.

However, some books simply do not lend themselves to that approach, and this is one of them. One can skim over the mathematical proofs in, say, Newton’s Principia and still get a fairly good idea of what the book is about. But in Maxwell’s magnum opus, the math is what does the talking. Indeed, by the midway point I was so desperate—feeling guilty, lazy, and stupid for understanding so little of what I was reading—that I decided to turn to an old ally, Kahn Academy. There, I went through all of the videos on electricity and magnetism, and learned a great deal. (The last time I had any formal instruction on the subject was in my sophomore year of high school, and I doubt I understand much back then.)

But I found, when I picked up the book again, that even this Hail Mary would not save me from the perdition of Maxwell’s writing. Indeed, as I had already bought the heavily annotated student’s edition (with copious notes by Howard J. Fisher), it seemed that I had used up all of my lifelines, and simply had to content myself with only the most superficial reading of this important book.

What follows, then, is probably as valuable as a review of Hamlet by somebody with an elementary level of English. Here I goes.

Now, as I mentioned, the version I picked up is meant for students. Thus, it is heavily abridged and, often, so full of explanatory footnotes that the original text is crowded out.

For what it’s worth, even if you do have the mathematical and scientific chops to handle Maxwell’s tome, I would recommend either this version or something similar. The original is famous for being rather unfocused and overlong. After all, this book was not meant to be Maxwell’s Origin of Species—a text devoted to propounding a radical new theory. Maxwell had already set forth his most revolutionary insights—most notably in the paper “A Dynamical Theory of the Electromagnetic Field,” in 1865—several years before this book was published. Instead, this was meant as a kind of definitive textbook on the subject, to be studied by university students, telegram technicians, and other specialists. Thus, there are long sections in which he rehashed old theories which would be of limited interest to any modern reader.

This edition attempts to pare down the original, leaving only what Fisher considers to be the “central argument”—that is, the material leading directly to Maxwell’s signature breakthroughs. These would be, first, his four famous eponymous equations and, second, the electromagnetic theory of light.

Regarding the former, as you may know, Maxwell did not actually formulate his equations in the form which modern students encounter them. It was one of Maxwell’s followers, Oliver Heaviside, who put the equations into their definitive form. Instead, Maxwell puts forward twelve equations, which use the now-defunct quaternion notation rather than vector calculus. This makes Maxwell’s presentation seem rather foreign, even to those less ignorant than myself. What is more, Maxwell has a liking for using Gothic letters as symbols in his equations, which gives them a doubly strange appearance.

More generally, I think even a mathematically literate reader will have some trouble following significant portions of this book, if only because Maxwell’s mathematical language seems clunky and dated. In my version, for example, Fisher is continually translating Maxwell’s operations into more familiar forms (which, admittedly, I still did not follow).

As I had recently made my way through an (abridged) version of Faraday’s epochal Experimental Researches in Electricity, I was most interested in the sections in which Maxwell reflects on his predecessor’s work. He is extremely laudatory of the English physicist and is quite generous in giving credit for developing this new way of examining electricity.

And, indeed, if I have any way of understanding Maxwell, it is only through the lens of Faraday. At first glance, the devoted experimentalist with no mathematical schooling seems to have little in common with the visionary theorist who prefers numbers to words. And yet, as I’m sure Maxwell would agree, they were bound together by a new vision of the cosmos. In a nutshell, and said very imprecisely, I think their insight was to see energy rather than matter as fundamental.

In the Newtonian view that preceded Maxwell, the world was composed of matter—indeed, even light was supposed to be made up of little corpuscles. This matter traveled in straight lines and attracted other matter in straight lines. This Newtonian view was embodied in, say, Ampère’s earlier theory of electromagnetism.

And yet this view always sat uncomfortably with Faraday, who instead saw the curving lines of the magnetic field as the fundamental reality, rather than one piece of matter attracting another via “action at a distance.” Indeed, Faraday’s brilliant experiment involving the shifting of light via a magnet got him tantalizingly close to the central insight of Maxwell’s life: the unification of light with electromagnetic radiation.

Faraday is one fount of Maxwell’s inspiration. Yet if Maxwell has a mathematical predecessor, it is Joseph-Louis Lagrange, whose work comprises a culminating chapter in this book. Lagrange arguably developed the math that Faraday had been striving toward from another direction. For in Lagrangian mechanics, rather than thinking of forces being exerted by physical objects, one thinks of the energies in the system—the object in question merely following the path of least resistance through the fields of energy around it.

It was Maxwell’s great insight to see how the work of Faraday and Lagrange—among many, many other brilliant scientists—fit together to form one complete account of electricity and magnetism. It is a theory in which fields of energy take precedence over particles, indeed in which the world around us is filled with vibrations in luminiferous ether. And while some parts of Maxwell’s theory (notably the ether) have not survived to the present day, his basic insight was so sound and so significant that, as Richard Feynman said, his discovery constitutes one of the major turning points in human history. You certainly wouldn’t be reading this review without it. Thus, Maxwell’s name stands beside Newton’s and Einstein’s as one of the greatest physicists of all time—even if his book is completely opaque to people like me.

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Review: The Emperor of All Maladies

The Emperor of All Maladies: A Biography of Cancer by Siddhartha Mukherjee

My rating: 5 of 5 stars

I do not consider myself a superstitious person—not even remotely—but somehow I felt a deep reluctance to pick up this book. It may have taken us a long time to figure out the germ theory of diseases, yet the psychology of contagion runs deep. I had the irrational fear that even learning about cancer would somehow unleash it into my life.

But turning away from frightful things is not a good way to live. And, anyway, even though there is a lot of sadness in this book, and a lot to stoke your fears (perhaps it is best to avoid if you have a tendency toward hypochondria), but this is basically a story of innovation.

Mukherjee moves through surgery, radiation therapy, chemotherapy, cancer prevention, and modern targeted drugs, showing how each arose and developed in response to different sorts of cancer and out of the science and technology of the moment. It is a vast story, which includes the development of anasthesia and antibiotics, the discovery of genes and chromosomes, the first research into radioactivity, and the campaign against smoking. To use the obvious metaphor, it is a war waged on multiple fronts.

The challenges are manifold. I had naively thought that all cancer was basically the same disease, with its subtypes just minor variations. But it turns out that there is enormous genetic and chemical variety among cancers, so that a treatment effective for one may do little for another. Indeed, even for a single type—breast cancer, say—treatment can be unpredictable. This is what makes the story of doctor’s attempt to treat the disease so riveting, as it feels like a battle between two equally wily antagonists. At several points in this history, doctors attempt extreme cures—radical surgeries, or nearly fatal doses of chemotherapy—only to be defeated. Meanwhile, the victories can be as modest as a remission of just a few months.

It is probably best not to philosophize about a fatal disease, but there does seem to be a lot of irony in our quest to defeat cancer. For one, it has only become so prevalent in the modern period, because we have started living so long. Its appearance as the great killer, then, is a kind of perverse mark of progress. Further, there is the irony of trying to fight what is, in essence, a corrupted version of ourselves—a group of renegade cells which have figured out how to replicate and survive even better than our own body. There is great scope for metaphor here, but if there is a moral to cancer then I don’t think it is a simple one.

Mukherjee does an admirable job weaving a potentially chaotic and depressing story into something coherent and even hopeful. Though the book is composed of history, science, and his own experience as a doctor, these different threads reinforce one another rather than clash. The clinical anecdotes are sparing—just enough to connect the past to the present—and his thumbnail explanations of science are lucid and illuminating. But, most important, despite the many tragic deaths which litter these pages, the final impression is of how much can be accomplished when a researcher’s diligence, a doctor’s pledge to save life, and a patient’s will to live work together, generation after generation.

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Review: Faraday’s Experimental Researches in Electricity

Faraday’s Experimental Researches in Electricity: Guide to a first reading by Michael Faraday

My rating: 4 of 5 stars

In the first volume of Robert Caro’s biography of Lyndon Johnson, there is a fantastic chapter about what life in the Texas Hill Country was like before electricity arrived. Every basic task was substantially more difficult: water had to be carried in buckets, clothes had to be washed by hand, water had to be boiled over an open fire, milk and eggs had to be refrigerated in ice cellars, and on and on. When power finally did arrive to this rural area—thanks in large part to Johnson’s work—it transformed daily life in a matter of years. Johnson was considered a hero, and rightly so.

But if Lyndon Johnson deserves ample praise for having helped bring electricity to his district, what does Michael Faraday deserve? For it was Faraday who first discovered the principles of the electric motor and the electric generator. If not for him, the harsh conditions described by Caro—a life of ceaseless toil, barely eking out a living—might be not just confined to a rural area in Texas, but the general condition of our species. Faraday was, in short, a historical figure of supreme importance, and his work represents a turning point in human history.

Knowing this, it is shocking to see just how humble and, in many ways, how simple his work actually was. The tools at his disposal seem, to the modern reader, almost laughably primitive. Whereas modern physicists are using a city’s worth of power to accelerate particles down a track kilometers long, Faraday was fiddling with wires and bar magnets and compasses. And yet, with such simple tools at his disposal, and with scarcely any formal education—indeed, hardly knowing any math beyond basic algebra—Faraday made contributions to physics comparable to Newton or Einstein.

The format of this book is simple. It is not, like the Principia, a unified work conceived as a final theory. Rather, Faraday reached his conclusions slowly, over years of experimental work; and this book is a reflection of his process. Starting in 1821, Faraday began publishing accounts of his experiments in the Philosophical Transactions of the Royal Society. These papers were eventually collected and published in three separate volumes, in 1839, 1844, and 1855, consisting of 29 “series” of experiments in total.

Before I go any further, I should note that I did not make my way through all three of these volumes. Rather, I bought a condensed and annotated version published by Green Lion Press and edited by Howard Fisher. Frankly, I do not have the patience or interest to fight my way through 1,500 of the original, and I doubt many others do either. I also very much appreciated Fisher’s introductory essays, without which I think I would have been quite lost (and I often was, anyway).

Remarkably, Faraday maintains a numbering system for his paragraphs throughout, so that he can refer to earlier paragraphs of previous series as easily as one might cite the Bible. This is a simple device, but it does help to reveal the unity that underpins the apparently disorganized quality of this work, as it shows how Faraday was continually returning to the same questions and refining his answers.

I have already mentioned that Faraday was unversed in mathematics. And this makes him fairly unique in the field of physics, in which equations are sometimes elevated to a level that equates math with reality. However, the more one reads of his work, the more one comes to see that, even if he eschewed quantitative reasoning, Faraday was an extremely precise thinker. Part of this is his use of diagrams, which for Faraday almost take on the role of equations in summarizing complex relationships. He is also very sensitive to language, and is constantly trying to choose words that do not carry any inappropriate theoretical baggage.

Just because this book is written in good old-fashioned English, however, does not make it easy. Often, Faraday is responding to dead controversies and in general is using both language and theories that seem strange to the modern reader. To pick a simple example, static electricity is referred to as “ordinary” electricity, since this was the most commonly encountered electricity in Faraday’s day. What is more, Faraday very often must describe a detailed experimental apparatus or procedure, and I very often found myself totally unable to picture what was going on.

Here is a fairly typical example:

A ray of light issuing from an Argand lamp, was polarized in a horizontal plane by reflexion from a surface of glass, and the polarized ray passed through a Nichol’s eye-piece revolving on a horizontal axis, so as to be easily examined by the latter. Between the polarizing mirror and the eye-piece two powerful electro-magnetic poles were arranged, being either the poles of a horse-shoe magnet, or the contrary poles of two cylinder magnets; they were separated from each other about 2 inches in the direction of the line of the ray, and so placed, that, if on the same side of the polarized ray, it might pass near them; or if on contrary sides, it might go between them, its direction being always parallel, or nearly so, to the magnetic lines of force.

I don’t know about you, but I find this to be extremely exhausting.

Not all of the book was so dense, however. I particularly enjoyed the fifteenth series, which basically consisted of Faraday and his assistants putting their hands in a tank and getting an electric eel to shock them. Science was indeed simpler back then.

But the final impression is of Faraday’s remarkable theoretical vision. Although he is an extremely concrete thinker—couching even his most speculative remarks in terms of experiments—he nevertheless succeeded in probing some highly abstract questions. Beginning with the relationship between electricity and magnetism, he goes on to consider the relationship of force to matter, to light, and even to empty space.

His work is, in short, a model for science, showing how careful observation and the judicious use of imagination can revolutionize our understanding of the natural world. Compared to the baroque mathematical models of string theorists—whose theories have yet to receive any confirmation from experiment—Faraday’s approach is refreshing indeed.

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(Cover image is Faraday’s labs in the Royal Institution; photo taken from Wikimedia Commons; uploaded by AnaConvTrans.)

Review: Wonderful Life

Wonderful Life: The Burgess Shale and the Nature of History by Stephen Jay Gould

My rating: 3 of 5 stars

This book is a headache-inducing mixture of contrary qualities. My emotions swung wildly as I read, from pleasure to exasperation, from wonder to annoyance.

The subject of the book is fascinating. Gould here sets out to tell the story of the Burgess Shale, a site discovered in 1909 by Charles Walcott in the Canadian Rockies. Owing to unusual conditions (an underwater mudslide, 500 million years ago) fossils of thousands of ancient organisms were preserved in excellent condition—not only the typical hard parts that survive fossilization, but their soft tissue as well. This was an unprecedented and highly significant find, as it provided a kind of snapshot of life shortly after the famous Cambrian Explosion (when macroscopic animals suddenly become common in the fossil record).

Amazingly, though the importance of the find was widely understood, most of the specimens collected remained unanalyzed and poorly understood for decades. Their discoverer, Walcott, published a few preliminary studies but nothing of significant depth. It was not until the 1970s that a team of researchers—Harry Blackmore Whittington, Derek Briggs, and Simon Conway Morris—started reinvestigating these samplings and publishing long monographs on their findings. Their research and conclusions form the core of Gould’s book.

It is when Gould is describing the story of the shale’s discovery, and especially when he is describing how the scientists went about their work, that he is at his absolute best. And I think he deserves all the praise in the world for this. Few books for the general public, if any, take the reader so intimately into the process of paleontological research—collecting specimens, dissecting samples, debating taxonomies. What is more, Gould manages to make a book about fossilized worms into absolutely gripping reading. There were times when I felt my heart swell with admiration for these scientists hunched over a microscope, scratching through the exoskeleton of some three-inch creature in order to write a 100-page monograph to be read by a handful of experts. This is no small accomplishment for an author.

Where Gould falters, for me, is in the interpretation he gives to this story. Gould argues that the Burgess fossils completely overturn our notions of evolution and constitute a breakthrough comparable with Darwin’s theory. He bases this grandiose claim on the amount of taxonomic diversity encountered within the samples. Now, when Walcott first analyzed the fossils, he classified the animals as members of modern groups. But when Whittington, Briggs, and Conway Morris re-examined these fossils, they found a great many organisms that did not fit into any modern classification.

From this, Gould draws two conclusions. First, he asserts that this was a particularly fertile time for evolution; and he bases this claim on the large variation present in the fossils. Second, he makes the grander claim that the large number of viable organisms whose descendants did not survive to the present day proves that the history of life is highly contingent.

Now, let me explain why both of these claims are frustrating.

For one, there is a perfectly obvious reason why the Cambrian period could have involved more evolutionary “experimentation” than the present day. This is that, when organisms are first evolving to occupy previously unoccupied niches—as the first macroscopic animals were doing—there would be comparatively less environmental pressure to do so in the most efficient possible way. The first freely swimming animal, for example, did not need to swim faster than any other animal trying to eat it. Gould himself eventually gets around to this explanation, though he seems not entirely satisfied with it.

But the other—and even more obvious—explanation is that these animals are only more varied in a limited sense. As Gould himself admits, modern animals occupy more varied environments and exhibit a far large range of sizes and behaviors. What the Burgess animals possess is taxonomic variety—requiring the creation of new phyla, families, or orders to accommodate them into our filing cabinets. However, what he fails to mention is that this is exactly what one should expect from such ancient fossils. Our taxonomic categories were developed to classify modern animals, so why should they apply neatly to animals living half a billion years ago?

I think this point deserves further elaboration. Our modern categories were purposefully defined using the traits which remain invariable over the largest number of extant species. They would be useless otherwise. It is thus nonsensical when Gould wonders why there should arise so many new phyla in the Cambrian, but not today. This is like wondering why there are so many strange words in Chaucer but not the newspaper. In other words, the huge taxonomic variation Gould discusses is largely an artifact of our own categories and not an actual property of the animals themselves. A foreign language does not have an objectively more complex vocabulary just because there are more unfamiliar words in it.

Ironically, some of the taxonomic weirdness that Gould discusses has since been revised away, as the “radical” interpretations of Whittington, Briggs, and Conway Morris were themselves re-interpreted, placing many animals in more familiar categories. To take just one example, the Burgess animals hallucigenia is here presented as a truly nightmarish creature which walks on spikes and has tentacles sticking out of its back. Most concerning of all, it has a formless blob for a head! This animal was, understandably, at first given its own genus; but it has since been recognized as a lobopodian when a more accurate reconstruction was hit upon. (It turns out that the spikes are on its back and are not its legs; and that its head is, in fact, not a formless blob.)

Of course, Gould can hardly be blamed for basing his book on outdated science. After all, it was published over 30 years ago. But I do think that Gould, of all people, should have known that interpretations of fossil remains are frequently contested and revised, so it seems unwise of him to have based such grandiose conclusions on such a shaky foundation.

Now for Gould’s second claim, that the Burgess fossils prove that the history of based on chance—or, in his words, “decimation by lottery.” He repeatedly states that no modern scientist, if transported back in time, could have selected which lineages would survive to the present day or would end in extinction, since there is no obvious anatomical flaw in the extinct lineages. And he argues that this proves chance, not superiority, determined evolutionary survival.

This strikes me as a completely bizarre argument, since I am not sure who Gould is even arguing against. What scientist believes they could pick out evolutionary winners and losers 500 million years from now? Or even 500 years from now? Virtually every organism is well-adapted to its environment. If you traveled to the previous ice age, could you find an anatomical flaw in the woolly mammoth? I doubt it. But does this prove that extinction is totally random? Hardly.

Indeed, Gould eventually admits that even he himself does not believe that extinction is a truly random process (though this makes his use of the term “lottery” rather puzzling). Instead, he adopts the wholly conventional view that extinction occurs when the environment changes too quickly for a species to adapt, and that the species which do survive environmental shifts are able to do so because of traits they evolved under different circumstances.

In other words, yes, luck is a factor in evolutionary survival. Indeed, considering that evolution is a physical process, one could argue that it is completely a matter of luck which species survive or perish. In a general sense, luck determines whether an asteroid will hit, whether an invasive species will outcompete you, or whether hairless primates will destroy your habitat. But what biologist would deny that? It strikes me that the only people who seriously object to this do so for religious reasons, seeing the evolution of human life as something pre-ordained or divinely guided. Yet Gould acts as if he is arguing against the dominant view in his field.

To sum up, Gould is grandly making a non-controversial point using evidence that does not even prove his point. The burgess fauna were not necessarily more varied than today’s; and even if they were, that would not prove that evolution is random.

I am sorry to be writing such a critical review of this book. It just seemed such a shame that such a great story could be weighed down by so much unnecessary intellectual baggage. If this had simply been an exploration of the Burgess fauna it would have been delightful. Indeed, though perhaps outdated, the many illustrations of ancient creatures are still charming to contemplate. And though I found the book quite frustrating, if read in the right spirit, I still think it is wonderfully educational about the process of science—though, perhaps not in the manner it intended to be.

(Cover photo a reconstruction of hallucigenia by Martin R. Smith and Jean-Bernard Caron. Taken from Wikimedia Commons, CC BY-SA 4.0.)

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Review: Why We Sleep

Why We Sleep: Unlocking the Power of Sleep and Dreams by Matthew Walker

My rating: 5 of 5 stars

I first heard of this book from Michael Pollan’s short work on caffeine. There, he calls Why We Sleep (to paraphrase) one of the most disturbing books he had read in a while. This caught my attention. How could a book on sleep be disturbing?

From the first page of this book, I knew why. The author, Matthew Walker, is essentially diagnosing a major health crisis that is going on in front of our drooping, baggy eyes—namely, the crisis of insufficient sleep. According to Walker, virtually everything we do—how we work, how we relax, how we seek entertainment—is disruptive of sleep. And he has plenty of studies to show that, when you do not sleep enough, there are serious consequences.

In addition to the familiar cognitive impairments of bad sleep (inability to focus, lack of energy, wild mood swings), there are the long-term health risks, such as the increased likelihood to develop cancer, heart disease, or diabetes. More unfortunate still, there does not seem to be any way of getting around the familiar recommendation of eight hours of sleep per night. We cannot get by with less, and we cannot make it up on the weekend.

Indeed, the news gets worse and worse. Even moderate amounts of alcohol and caffeine can gravely affect sleep (and marijuana, too—sorry); and sleeping pills may do more harm than good. Our phones, tablets, and computers—even our indoor lights—wreak additional damage by throwing off our natural diurnal rhythms. So this pretty much eliminates all of my nightly plans.

What it comes down to, says Walker, is a cultural disrespect for sleep. I am certainly guilty of this. I have always taken pride in using the opportunity of a plane, train, or bus ride to read a book rather than to nod off, and felt secretly superior to those dozing around me. More generally, sleeping is often equated with laziness. Waking up after midday is a moral failing; taking a nap on the job is a fireable offense; and going to bed early is socially questionable. Further, many people—especially in the business world—take pride in their ability to get by on few hours of sleep. Wakefulness is productiveness. But this prejudice is, Walker contends, based on ignorance of the real value of sleep.

Sleep is a biologically basic process. All mammals, birds, and reptiles, some fish, and even insects have been observed in a sleep-like state. Lack of sleep can not only be harmful, but fatal. Some gruesome rat experiments have shown this, as does the rare disease, Fatal Familial Insomnia, in which the brain becomes incapable of generating sleep—which is inevitably fatal. Sleep is just as basic a need as food. And as you might expect from such a basic need, it is hard-wired into our evolution. Indeed, two distinct types of sleep have evolved, which accomplish different purposes: REM and (creatively named) non-REM.

As you may know, the REM stands for “rapid eye movement,” which is when we experience vivid dreams; and it alone accomplishes many things. In addition to fostering creativity by forging novel links between memories, REM sleep apparently keeps us sane (people experimentally deprived of REM sleep for long enough experience symptoms of psychosis). Non-REM is, perhaps, the more restful sort, when new memories are moved from temporary storage to a more permanent location. The two sleep types thus work together and come at predictable moments in the night: deep non-REM sleep early on, and REM closer to the time we wake up. (Short sleep thus selectively cuts down our REM sleep time.)

Walker explains the science because he wants to drive home the importance of sleep—not a luxury, or an indulgence, but a survival mechanism designed by natural selection. With this basic point in hand, Walker goes on to make several social criticisms, and at times the book almost becomes a polemic.

Take driving, for example. Everybody knows that driving drunk is dangerous and irresponsible. But Walker cites studies showing that drowsy driving is, if anything, even more dangerous. When you are sleep deprived, your brain can drift off into what are called “micro-sleeps,” which last just a couple seconds. This is quite enough time to get into a serious car crash. And this is common. Over the Christmas break, everybody I mentioned this to had a story about falling asleep behind the wheel. It has happened to me, too—a thoroughly alarming experience, which thankfully did not result in a crash. Considering this, I cannot help but agree with Walker this issue is just as deserving of public awareness campaigns as inebriated driving.

Walker is also highly critical of how the medical community treats sleep. For one, most general physicians have little training when it comes to sleep, and so are apt to prescribe sleeping pills to patients with insomnia. Unfortunately, sleeping pills merely sedate the brain without generating natural sleep, and so do not really solve the problem. Another issue is that of doctors’ timetables. From residency on, doctors are often expected to work inhumanly long shifts, even though evidence shows that sleep-deprived doctors are less effective by every measure. Another issue is patient sleep. Although sleep is highly conducive to healing, hospitals often present hostile sleep conditions (loud noise, bright lights, poorly scheduled tests), especially in the ICU, which actively impedes recuperation.

Last but not least, Walker contends that many (though not all!) children diagnosed with mental disorders, like ADHD, may really be suffering from a sleep problem, as insufficient sleep can cause many of the same symptoms (lack of focus, lack of emotional control, etc.). This neatly dovetails with another issue: schools. According to Walker, every person has a natural sleep-schedule, and teenagers tend to have a later one than adults. When teenagers are expected to get to class by eight o’clock or earlier, therefore, we are making it impossible for them to adequately sleep, in the same way most adults would not be able to adapt to a job that began at six in the morning. As a result, many teenagers are chronically under-slept. No wonder that they are so considerate and polite.

This certainly resonates with my experience. Not only did my high school start early, but most of the musical extra-curriculars took place in the hour before regular classes. This meant that I had to arrive by quarter to eight, while I hardly ever went to bed before midnight (often much later). Unsurprisingly, I was a zombie for most of my morning classes. It is easy for me, then, to concur with Walker in proclaiming these early start times for high schools to be illogical and counterproductive. Thankfully this message seems to be slowly sinking in, and some schools have begun pushing back their schedules.

This review, long as it is, hardly does justice to the content of this book. Not only has Matthew Walker written an excellent work of popular science, but he has written a quietly revolutionary work. After all, our society would really look quite different if we took our need to sleep as seriously as we took our need to eat. The world Walkers imagines is certainly a more relaxed and humane one (though, it must be said, perhaps a bit puritanical in its strictures). Imagine, for example, a world when napping during work was encouraged and when start times were flexible. Imagine getting a deduction on your health insurance for sleeping enough. A boy can dream.

There was only one moment in which I doubted the good Walker. In 2015, a study was released that tracked the sleep of three hunter-gatherer groups, and found that they slept, on average, slightly less than seven hours, rather than the expected eight. This seems to undermine Walker’s contention that the modern world is uniquely inimical to sleep. He counters that the study may only show that these hunter-gatherers are also not sleeping enough. But this seems like rather weak tea after telling us of the evils of coffee, alarm clocks, and LED lights. If those free of modern temptations can’t do it right, what hope do we have? Perhaps we are doomed. Even so, I think all of us could benefit by treating our shuteye with a little more respect. Speaking of which, it is already past my bedtime.
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A fellow reviewer on Goodreads, Siddhartha, recommended an article written by the blogger Alexey Guzey that examines the first chapter of Matthew Walker’s book in depth, purporting to find many factual errors. I think it is worth going over Guzey’s points.

First, he notes that, while Walkers claims that longer sleep leads to longer life, in reality studies show a kind of U-curve, where both short and long sleep times are associated with higher mortality. Walker addresses this later on, but defends his position by stating that diseases and comorbidities often lead people to sleep more. Guzey counters that some diseases actually make people sleep less. In any case, Walker’s argument does seem fairly week to me in the absence of evidence that these longer sleep times are certainly caused by diseases. (Also it seems like circular reasoning to assert that anyone sleeping significantly longer than 8 hours must have some sort of disease. Were they presumably under-sleeping before, causing an illness that pushed them into over-sleeping?)

Guzey’s next points out that it is untrue that a good night’s sleep is always beneficial, since sleep deprivation is used as a therapy for depression. Now, to me these seems like nit-picking. One can still say it is almost always beneficial. True, Walker does discount the potential benefits of sleep deprivation therapy without much thought, but that is still a minor point since Walker is not a psychologist.

Guzey’s third point is also somewhat unfair. He points out that it is far from certain that the lack of sleep is what kills victims of Fatal Familial Insomnia. Yes, Walker uses Fatal Familial Insomnia to bolster his claim that lack of sleep is fatal, but he does admit (later on) that it is impossible to say that the lack of sleep is what actually kills in the disease, since victims suffer extensive brain damage. But Walker bases his assertion of the mortality of sleep loss on some (rather cruel) rat studies. Admittedly, we are not rats.

Another of Guzey’s criticisms is that, while Walkers is quite insistent on the eight-hour number, the National Sleep Foundation actually recommends anywhere between seven and nine hours. (And though Walkers invokes the WHO, the World Health Organization has not actually issued sleep recommendations.) This is certainly a legimitate critique of the book, since somebody who sleeps seven hours is actually within the normal range, even though they would get the impression from Walker’s book that they are underslept and at risk.

Several other factual errors Guzey point out are quite valid. It does seem true that, contrary to Walker, the WHO has not declared any sleep loss epidemic in industrialized nations. This is a serious error in itself. Guzey also calls into question whether those in the industrialized world really are getting less sleep now than people did 100 years ago. This claim, in my opinions, does deserves far more scrutiny. True, late night work emails and LED screens are recent inventions. But working on a farm or a factory is hardly more forgiving or flexible. And, again, if hunter-gatherers aren’t sleeping more than we are, perhaps the evidence of a recent sleep loss epidemic is not so strong after all.

Not having done any research myself, I can only give my two cents. I did get the strong impression that Walker consistently emphasized the most potentially dire consequences and examples of sleep loss. And, honestly, I really hope that Walker’s prophecies of doom are somewhat exaggerated, since obtaining perfect sleep while going to work, having a decent social life, keeping up with a hobby or two (not to mention the pressures of raising children—not that I have any) seems close to hopeless.

Even after all of this, I do think that this book is an important corrective to our current cultural disregard of sleep. Thank you for your time.

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Review: Mosquito

Mosquito: A Natural History of Our Most Persistent and Deadly Foe by Andrew Spielman

My rating: 4 of 5 stars

This is a thoroughly fascinating book about one of my least favorite things in the world. And I am one of the lucky ones. Even when those around me are getting eaten alive, I am normally spared the worst of the mosquito onslaught, for reasons that are largely elusive. Indeed, when I was an undergraduate studying in Kenya, one of my classmates did a small study on us, counting our bites and trying to see if they correlated with blood-type or other variables like perfume or shampoo. Since all of us had the same schedule, it seemed a promising study. But, alas, no insight was gained, though I was surprised to find that some of us had well over 60 bites, while I had less than 10.

Yet mosquitoes are more than annoyances; they are major vectors of disease, as I was reminded of daily when I took my malaria prophylactic. And after giving the reader some basic facts of mosquito biology, the book switches focus to disease control. There was much I did not know. For example, I had no idea that malaria was once present in New Jersey and New York, until aggressive government policies in the early 1900s eliminated the scourge. Similarly, I had no notion of the role that the Tennessee Valley Authority had in freeing America’s south from the malarial menace, largely by destroying mosquito nesting sites.

I also learned more about the story of Yellow Fever in the Americas. Though it may seem obvious to us nowadays that a disease can be transmitted by a mosquito bite, this was quite a controversial claim in the year 1900. It took careful work by a team of doctors in Cuba to prove that mosquitoes, not blood or bile, communicated the illness. This insight quickly led to the program of insect control that was instrumental in the building of the Panama Canal—a project that had proven impossible for the French, who labored under ignorance of the disease’s cause, and had to abandon the project as thousands of workers succumbed.

The authors of the book also have much to say on the subject of DDT. Having only read Rachel Carson’s Silent Spring, I had only been exposed to the argument against this popular pesticide. But Spielman and D’Antonio make a good case that, when used responsibly, the potential benefits of DMT far outweighs its health risks. Unfortunately, the pesticide was used to such a huge extent during the anti-malaria wars of the 1950s that it has lost much of its efficacy via accumulated resistance in mosquito populations. Spielman (the book’s entomologist) believes that this effort was ill-conceived, since it aimed for the impossible goal of total vector elimination, and it only resulted in the blunting of DDT, our most powerful weapon (not to mention decreased resistance in the human population from temporary reduction in malaria rates).

Malaria remains a major problem in vast areas of the world. We do not have an effective vaccine, and the plasmodium which causes the disease can evolve in response to drug treatments in just the same way that mosquitoes can evolve in response to DDT. And while those in temperate climates may be inclined to view it as a distant concern, this may soon prove not to be the case, as global warning expands the range of malaria-carrying mosquitoes northward. For my part, I think we are due for another big anti-malaria push, this time using smarter methods. But like the mosquito itself, the malaria parasite is one of our oldest enemies, having evolved with us for millions of years; so it may not be easy.

The authors close with a modern example of a tropical disease making it to a temperate zone: the 1999 West Nile outbreak in the New York City region. Surprisingly, I can remember this, even though I was only eight years old at the time. My mother told me that I had to stay inside on a beautiful summer night because they were spraying for mosquitoes. Soon, the helicopter came roaring by, dusting the area with insecticide. My brother remembers the entire playground in his Kindergarten being covered in a tarp to avoid getting sprayed. Such efforts did not succeed to eliminate West Nile in the United States, and now it circulates in the local bird and mosquito populations, closely monitored.

If the current pandemic helps to spur us to more aggressive public health measures, then I think mosquito control should be close to the top of the agenda. As Spielman himself notes, the mosquito does not serve any crucial functions in ecosystems—not as pollinators or even as prey—and are the most significant animal vectors of disease on the planet. Indeed, the mosquito is so perfectly useless and so perfectly dreadful that you wonder how anyone can maintain their faith in an almighty and infinitely loving God when faced with such a horrid product of blind evolution. They really are awful little things. And though we can never hope to eliminate them entirely, there is hope that we can break the chain of disease transmission long enough to at least make their bites mere itchy annoyances rather than a harbinger of doom.

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Review: The Great Influenza

The Great Influenza: The Story of the Deadliest Pandemic in History by John M. Barry

My rating: 4 of 5 stars

People write about war. They write about the Holocaust. They write about the horrors that people inflict on people. Apparently they forget the horrors that nature inflicts on people, the horrors that make humans least significant.

Like so many people nowadays, I have been scrambling to wrap my mind around the current pandemic. This led me, naturally, to the last major worldwide outbreak: the 1918 influenza. I have a distant connection to this disease. My great-grandfather (after whom I was named) was drafted out of Cornell’s veterinary school to work as a nurse in a temporary hospital set up for flu victims. I read the letters he sent to his mother, describing the experience.

John Barry’s account of this virulent flu is sobering to say the least. In a matter of months, the flu spread across the world and caused between 50 and 100 million deaths. More American soldiers died from this flu than from the entire Vietnam War. In most places the mortality rate hovered around two percent, but it struck much more fiercely elsewhere. In the Fiji Islands, 14 percent of its population succumbed; in Western Samoa, twenty-two percent; and in Labrador, a third of the population died. And because the disease mainly struck young people—people in their twenties and thirties—thousands were left orphans.

Barry’s book is not, however, simply a record of deaths. He sets the historical scene by giving a brief overview of contemporary medicine. In the early 1900s, modern medicine was just coming into its own. After centuries in which it was thought that bad air (“miasma”) caused illness, and in which bleeding was the most popular “cure,” researchers were beginning to discover viruses and bacteria, and were beginning to understand how the immune system combats these germs. Major public health initiatives were just getting underway. The John Hopkins School of Public Health had been founded, and the Rockefeller Institute was making new types of research possible. It was not the Dark Ages.

The other major piece of historical context is, of course, the First World War. Undoubtedly this played a major role in the epidemic. Not only did troop movements help to spread the disease, but press censorship virtually guaranteed that communities were unprepared. Barry notes how newspapers all across the country consistently downplayed the danger, which ironically only further increased panic. (The pandemic is sometimes called the “Spanish flu,” because the press in neutral Spain was uncensored, and so reported freely on the disease.) The war effort overrode all of the warnings of disease experts; and by the time the disease struck many communities, most of the available doctors and nurses had been sent to the military.

Barry’s narration mainly focuses on the United States. Partly this is because this is where he believes the disease originated (there are several competing theories), partly this is because the disease’s impact in Europe was overshadowed by the war, and partly this is simply because of the amount of easily available sources. I did wish he had spent more time on other countries—especially on India, which suffered horribly. The sections on science—both on the history of science, and summarizing what we know now about flu viruses—were in general quite strong. What was lacking, for me, were sections on the cultural impact of the disease.

But perhaps there are not so many. As Barry notes, no major novelist of the time—Hemingway, Fitzgerald, Lawrence—mentioned the pandemic in their works. I have noticed the same thing myself. I cannot recall a single mention of this flue in biographies and autobiographies of people who lived through the pandemic, such as John Maynard Keynes or even John D. Rockefeller (who personally funded research on the disease). This is perhaps understandable in Europe, where the deaths from the pandemic were swallowed up in news of the war; but it seems odd elsewhere. What is more, the pandemic did not seem to exacerbate existing racial or class tensions. In many ways the virus seems to have swept through communities and then disappeared from memory.

(Barry does have one fairly controversial claim in the book: that Woodrow Wilson contracted the flu while negotiating the treaty of Versailles, and that it caused him to capitulate to Clemenceau’s demands. If this is true, it would be a major historical consequence.)

It is illuminating to compare the 1918 pandemic to the current crisis. There are many similarities. Both are caused by easily transmissible viruses, and both spread around the world. The H1N1 flu virus and the SARS-CoV-2 virus both infect the respiratory system, causing fever, coughing, and in severe cases pneumonia and ARDS (acute respiratory distress syndrome). In both cases, no vaccine is available and no known treatment is effective. As in 1918, doctors are turning desperately to other therapies and medicines—those developed for other, unrelated diseases like malaria—and as in 1918, researchers are publishing at a frantic pace, with no time for peer review. Police are again wearing masks, hospitals are again overrun, and officials are struggling to catch up with the progress of the virus.

But of course, there are many important differences, too. One is the disease itself. The 1918 flu was almost certainly worse than the novel coronavirus. It was more deadly in general, and it killed younger people in far greater numbers—which resulted in a much bigger dip in life expectancy. (Young people died because their immune systems overreacted in what is called a “cytokine storm.”) The H1N1 flu also had a far shorter incubation period. This meant that the gap between infection and the first symptoms was short—often within 24 hours—and patients deteriorated far more quickly. Barry describes people being struck down within mere hours of showing their first symptoms. The challenge of the SARS-CoV-2 virus, however, is the very long incubation period—potentially up to two weeks—in which people may be infectious and yet not show symptoms. This makes it very difficult to keep track of who has it.

The explanation for this difference lies in the nature of the virus. A virus is basically a free-floating piece of genetic code incased in a protein shell. It needs to highjack animal cells in order to reproduce; and it infiltrates cells using proteins that link up with structures on the cells’ surface. Once inside, the virus begins to replicate until the cell literally bursts, spilling virus into adjacent cells, which in turn get infected, and which in turn burst. Each burst can release thousands of copies. The rate at which the virus replicates within the cells determine the incubation period (between first infection and first symptoms), and coronaviruses replicate significantly more slowly in animal cells, thus explaining the slower onset of symptoms. Their greater speed also means that flu viruses change faster, undergoing antigenic drift and antigenic shift, meaning that new strains of the virus are inevitable. The novel coronavirus is (likely) more stable.

Another potential difference is seasonality. Flu viruses come in seasonal waves. The 1918 virus struck first in spring, receded in summer, and then returned in autumn and one last time in the winter of 1919. Every wave hit very quickly—and then left just as quickly. Most cities experienced a sharp drop-off in cases after about six weeks of the first patients. The seasonality of the 1918 flu was partly a result of the genetic drift just mentioned, as the different waves of this flu were all at least subtly different strains of the virus. Atmospheric conditions—humidity and temperature—also presumably make some difference in the flu virus’s spread. COVID-19 may exhibit a very different pattern. It may, perhaps, be less affected by atmospheric conditions; and if it mutates and reproduces more slowly, it may linger around for one long wave rather than several short ones. This is just my speculation.

Well, so much for the virus. How about us? The world has changed a lot since 1918. However, not all of those changes have made us better prepared. Fast and cheap air travel allowed the virus to spread more quickly. And economic globalization did not help, either, as both medicines and medical equipment are often produced overseas and then imported, thus rendering countries more vulnerable to supply-chain disruption than in the past. As we witness countries and states compete for supplies, this vulnerability is very apparent.

But of course we have many advantages, too. Many of the deaths caused by the flu and the coronavirus are not from the virus infection itself, but because the virus renders us vulnerable to secondary infections by bacteria, causing pneumonia. Antibiotics (which did not exist in 1918) can save many lives. Another advantage is medical care. The most severe patients of both epidemics were struck with ARDS, a condition with an almost 100% mortality rate for those who do not receive intensive medical care (using a ventilator machine). In 1918 they were able to administer oxygen, but far less effectively than we can. Even so, even with the best intensive care, the survival rate of ARDS is between 40-60%. And our ability to administer intensive care is quite limited. The ventilator shortage has become a global emergency in itself, as hospitals are overrun.

Medical science has also advanced considerably. Now we can isolate the virus (which they could not do in 1918), test individuals for it, and work on a vaccine. However, testing has so far been unable to keep up with the virus. And the most optimistic estimate of an available vaccine is in a year. Arguably a much bigger advantage is information technology. The press is not censored—so citizens have a much better idea of the risks involved—and experts can communicate with each other in real time. We can coordinate large-scale societal responses to the pandemic, and can potentially even use technology to track individual cases. As we come to better understand the virus, we will be able to use more sophisticated statistical methods to understand its progress. None of this was possible in 1918.

One thing that we will have to contend with—something that is hardly even mentioned in Barry’s book—is the economic toll that this virus will take. Even in the ugliest days of the 1918 pandemic, governments did not require businesses or restaurants to close. War preparations went on unabated. (In 1918, after years of slaughter and at the height of the war, life was simply cheaper than it is now.) Our societal response will likely mitigate the health crisis but will create a secondary economic crisis that may ultimately be more difficult to solve. The solutions to this crisis could be our most lasting legacies. Already Spain’s government is talking of adopting universal basic income. Though of course it is far too early to predict anything with confidence.

Comparisons with 1918 are partly depressing, and partly uplifting. Depressing, because we knew this was possible and did not prepare. Depressing, because so many governments have gone through the same cycle of early denial and disorganized response as they did back then. Uplifting, because we do know much more than we did. Uplifting, because—after our early fumbles—we are finally coordinating as a global community to deal with the crisis. Perhaps most uplifting of all, despite some ugly stories here and there, the crisis has revealed a basic sense of solidarity in the face of a universal threat. Hopefully, unlike 1918, we will not do our best to forget about this one.

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Review: Deadliest Enemy

Deadliest Enemy: Our War Against Killer Germs by Michael T. Osterholm

My rating: 5 of 5 stars

This is a critical point in history. Time is running out to prepare for the next pandemic. We must act now with decisiveness and purpose. Someday, after the next pandemic has come and gone, a commission much like the 9/11 Commission will be charged with determining how well government, business, and public health leaders prepared the world for the catastrophe when they had clear warning. What will be the verdict?

If I had read this book in more normal circumstances, I do not know how I would have responded. Perhaps I would have been slightly unnerved, but I think I would have been able to sleep soundly by dismissing most of it as alarmist. In fact, I did just this a few months ago, when I read Bill Bryson’s book on the body, and scoffed at his claim that another 1918-style pandemic was easily possible. Nowadays, however, reading this book is more depressing than anything. Those in the field saw this crisis coming from miles away, but few of us listened. The epidemiological community must feel rather like Cassandras right about now: uttering prophecies that nobody pays any attention to.

(As Osterholm was responsible for most of the ideas in this book, and as it is written from his perspective, I will refer to him as the author in this review.)

This book attempted to be the Silent Spring for infectious diseases. That it did not succeed in doing so is attributable just as much to human nature as to the book itself. Limiting the use of pesticides is fairly easy and relatively painless for most of us. But mobilizing the political will necessary to prepare for health crises in the hypothetical future—preparations that would involve a great deal of money and many institutional changes—is not such an easy sell, especially since we had been lulled into a false sense of security. As is the case with climate change, the dangers seemed so remote and theoretical that for most of us it was difficult to even imagine them.

After witnessing what this new coronavirus has done to our entire way of life in a few short weeks, I was quite disposed to take Osterholm seriously. And I think the entire content of the book—not just the warnings about a potential pandemic—are valuable. Osterholm turns his attention to a wide array of threats: Zika, AIDS, Yellow Fever, Typhoid, Malaria, Ebola, MERS. We are vulnerable on many fronts, and we are generally not doing much to prepare.

One example are the many diseases that are transmitted by mosquito bites. As modern transportation has introduced disease-carrying mosquitos into ever-more parts of the world, and global warming expands the geographic range of mosquitos, this will be an increasing concern. (Silent Spring may, ironically, have contributed to this problem.) Another worry is bio-terrorism. Now that we can see how paralyzing even a moderately lethal virus can be, imagine the damage could be inflicted by a genetically-modified virus. And the technology to edit genes is becoming cheaper by the year. We have already experienced bio-terrorism in the US on a relatively small scale with the 2001 anthrax attacks. This is just a taste of what is possible. According to Osterholm, a mere kilogram of the anthrax bacteria could potentially kill more than an atomic bomb. And it would be far cheaper to acquire.

But these are not even the biggest threats. According to Osterholm, we face two virtual certainties: another flu pandemic, and the imminent ineffectiveness of antibiotics.

The latter is quite terrifying to consider. Antibiotics are not easy to discover, and our arsenal is limited. Meanwhile, bacteria constantly evolve in response to environmental pressures, including to the use of antibiotics. It is inevitable that resistance to available antibiotics will increase; and this could have a profound effect on modern medicine. Even routine operations like knee-replacements would be unsafe if we did not have effective antibiotics. Slight injures—a scratch in the garden from a rose-bush—could result in amputations or even deaths. And yet, antibiotics continue to be widely prescribed for ailments they cannot treat, and given indiscriminately to livestock, which only accelerates the impending bacterial resistance.

The other major threat (as we are learning) is a pandemic. Now, Osterholm was not precisely correct in predicting the cause of the next pandemic, since he thought it would be a flu virus (though he does have a good chapter on coronaviruses, and in any case a flu pandemic is still just as possible). But he is certainly correct in identifying our many structural weaknesses. He notes our lack of stockpiles and correctly predicts a shortage in protective gear, face masks, and ventilators in the event of a pandemic. And though medical science has advanced a lot since 1918, in many ways we are even more vulnerable than we were back then, most notably because of our supply chains. Since so many of our medicines and medical equipment—among other things—are produced overseas, shortages are inevitable if trade is disrupted.

Osterholm is quite illuminating in his discussion of pharmaceutical companies and their incentives. As private businesses, they have little to gain by investing in preventative vaccines or in new antibiotics. In the former case, this is because vaccines have to undergo thorough testing and pass FDA approval, requiring millions in investment, only to face the prospect of uncertain demand once the vaccine hits the market. The case of SARS is instructive. After the disease was identified in 2002, companies rushed to make a vaccine; but when SARS receded, interest in the vaccine disappeared and pharmaceutical companies, cutting their losses, stopped work on the vaccine. We still do not have one.

The incentive system is just as ineffective when it comes to antibiotics. Finding new antibiotics is costly; and since there are currently many cheap antibiotics on the market, a new patented antibiotic probably would not turn a large profit. Besides, effective antibiotic stewardship requires that we use them sparingly, thus further limiting profit potential. Drug companies have much more to gain by creating products that would require continuous use, such as for chronic conditions. Letting the free market decide which drugs get developed, therefore, is not the wisest decision. Osterholm advocates the same approach as taken by government in weapons contracts, wherein the government essentially guarantees payment for any product that meets specifications.

Osterholm’s most ambitious idea for government funding is for a new universal flu vaccine. The flu vaccine we are all familiar with is based on old technology, and can only provide protection from a few strains of flu. Scientists essentially must guess what sort of flu will be circulating in a year; and they must do so every year. But Osterholm thinks that there is good reason to believe that a universal flu vaccine is possible, and recommends we devote at least as much money to such a vaccine as we devote to AIDS research. This seems very sensible to me, since the next pandemic will likely enough come from a flu virus.

I am summarizing Osterholm’s book, but I do not think I am doing justice to its emotional power. Now that I am living through the events that Osterholm predicts (in surprising detail), I feel a strange mixture of outrage and fear: outrage that governments did not listen when they had time, and fear that we will repeat the same mistakes when this current crisis is over. I cannot help but be reminded of another situation in which we comfortably ignore the dire warning of scientists: climate change. My biggest hope for the current crisis, then, is that afterwards we will be more willing to heed the warnings of these nerds in lab coats.

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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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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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Lotz in Translation

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

Category: Science & Math