A Mathematician’s Apology (Modern Library Nonfiction #87)

(This is the fourteenth entry in The Modern Library Nonfiction Challenge, an ambitious project to read and write about the Modern Library Nonfiction books from #100 to #1. There is also The Modern Library Reading Challenge, a fiction-based counterpart to this list. Previous entry: Six Easy Pieces.)

mlnf87Clocking in at a mere ninety pages in very large type, G.H. Hardy’s A Mathematician’s Apology is that rare canapé plucked from a small salver between all the other three-course meals and marathon banquets in the Modern Library series. It is a book so modest that you could probably read it in its entirety while waiting for the latest Windows 10 update to install. And what a bleak and despondent volume it turned out to be! I read the book twice and, each time I finished the book, I wanted to seek out some chalk-scrawling magician and offer a hug.

G.H. Hardy was a robust mathematician just over the age of sixty who had made some serious contributions to number theory and population genetics. He was a cricket-loving man who had brought the Indian autodidact Srinivasa Ramanujan to academic prominence by personally vouching for and mentoring him. You would think that a highly accomplished dude who went about the world with such bountiful and generous energies would be able to ride out his eccentric enthusiasm into his autumn years. But in 1939, Hardy survived a heart attack and felt that he was as useless as an ashtray on a motorcycle, possessing nothing much in the way of nimble acumen or originality. So he decided to memorialize his depressing thoughts about “useful” contributions to knowledge in A Mathematician’s Apology (in one of the book’s most stupendous understatements, Hardy observed that “my apology is bound to be to some extent egotistical”), and asked whether mathematics, the field that he had entered into because he “wanted to beat other boys, and this seemed to be the way in which I could do so most decisively,” was worthwhile.

You can probably guess how it all turned out:

It is indeed rather astonishing how little practical value scientific knowledge has for ordinary man, how dull and commonplace such of it as has value is, and how its value seems almost to vary inversely to reputed utility….We live either by rule of thumb or other people’s professional knowledge.

If only Hardy could have lived about sixty more years to discover the 21st century thinker’s parasitic relationship to Google and Wikipedia! The question is whether Hardy is right to be this cynical. While snidely observing “It is quite true that most people can do nothing well,” he isn’t a total sourpuss. He writes, “A man’s first duty, a young man’s at any rate, is to be ambitious,” and points out that ambition has been “the driving force behind nearly all the best work of the world.” What he fails to see, however, is that youthful ambition, whether in a writer or a scientist, often morphs into a set of routines that become second-nature. At a certain point, a person becomes comfortable enough with himself to simply go on with his work, quietly evolving, where the ambition becomes more covert and subconscious and mysterious.

Hardy never quite confronts what it is about youth that frightens him, but he is driven by a need to justify his work and his existence, pointing to two reasons for why people do what they do: (1) they work at something because they know they can do it well and (2) they work at something because a particular vocation or specialty came their way. But this seems too pat and Gladwellian to be a persuasive dichotomy. It doesn’t really account for the journey we all must face over why one does something, which generally includes the vital people you meet at certain places in your life who point you down certain directions. Either they recognize some talent in you and give you a leg up or they are smart and generous enough to recognize that one essential part of human duty is to help others find their way, to seek out your people — ideally a group of eclectic and vastly differing perspectives — and to work with each other to do the best damn work and live the best damn lives you can. Because what’s the point of geeking out about Fermat’s “two squares” theorem, which really is, as Hardy observes, a nifty mathematical axiom of pure beauty, if you can’t share it with others?

But let’s return to Hardy’s fixation on youth. Hardy makes the claim that “mathematics, more than any other art or science, is a young man’s game,” yet this staggering statement is easily debunked by such late bloomers as prime number ninja Zhang Yitang and Andrew Wiles solving Fermat’s Last Theorem at the age of 41. Even in Hardy’s own time, Henri Poincaré was making innovations to topology and Lorentz transformations well into middle age. (And Hardy explicitly references Poincaré in § 26 of his Apology. So it’s not like he didn’t know!) Perhaps some of the more recent late life contributions have much to do with forty now being the new thirty (or even the new twenty among a certain Jaguar-buying midlife crisis type) and many men in Hardy’s time believing themselves to be superannuated in body and soul around the age of thirty-five, but it does point to the likelihood that Hardy’s sentiments were less the result of serious thinking and more the result of crippling depression.

Where Richard Feynman saw chess as a happy metaphor for the universe, “a great game played by the gods” in which we humans are mere observers who “do not know what the rules of the game are,” merely allowed to watch the playing (and yet find marvel in this all the same), Hardy believed that any chess problem was “simply an exercise in pure mathematics…and everyone who calls a problem ‘beautiful’ is applauding mathematical beauty, even if is a beauty of a comparatively lowly kind.” Hardy was so sour that he compared a chess problem to a newspaper puzzle, claiming that it merely offered an “intellectual kick” for the clueless educated rabble. As someone who enjoys solving the Sunday New York Times crossword in full and a good chess game (it’s the street players I have learned the most from; for they often have the boldest and most original moves), I can’t really argue against Hardy’s claim that such pastimes are “trivial” or “unimportant” in the grand scheme of things. But Hardy seems unable to remember the possibly apocryphal tale of Archimedes discovering gradual displacement while in the bathtub or the more reliable story of Otto Loewi’s dream leading the great Nobel-winning physiologist to discover that nervous impulses arose from electrical transmissions. Great minds often need to be restfully thinking or active on other fronts in order to come up with significant innovations. And while Hardy may claim that “no chess problem has ever affected the development of scientific thought,” I feel compelled to note Pythagoras played the lyre (and even inspired a form of tuning), Newton had his meandering apple moment, and Einstein enjoyed hiking and sailing. These were undoubtedly “trivial” practices by Hardy’s austere standards, but would these great men have given us their contributions if they hadn’t had such downtime?

It’s a bit gobsmacking that Hardy never mentions how Loewi was fired up by his dreams. He seems only to see value in Morpheus’s prophecies if they are dark and melancholic:

I can remember Bertrand Russell telling me of a horrible dream. He was in the top floor of the University Library, about A.D. 2100. A library assistant was going round the shelves carrying an enormous bucket, taking down book after book, glancing at them, restoring them to the shelves or dumping them into the bucket. At last he came to three large volumes which Russell could recognize as the last surviving copy of Principia mathematica. He took down one of the volumes, turned over a few pages, seemed puzzled for a moment by the curious symbolism, closed the volume, balanced it in his hand and hesitated….

One of an author’s worst nightmares is to have his work rendered instantly obsolescent not long after his death, even though there is a very strong likelihood that, in about 150 years, few people will care about the majority of books published today. (Hell, few people care about anything I have to write today, much less this insane Modern Library project. There is a high probability that I will be dead in five decades and that nobody will read the many millions of words or listen to the countless hours of radio I have put out into the universe. It may seem pessimistic to consider this salient truth, but, if anything, it motivates me to make as much as I can in the time I have, which I suppose is an egotistical and foolishly optimistic approach. But what else can one do? Deposit one’s head in the sand, smoke endless bowls of pot, wolf down giant bags of Cheetos, and binge-watch insipid television that will also not be remembered?) You can either accept this reality and reach the few people you can and find happiness and gratitude in doing so. Or you can deny the clear fact that your ego is getting in the way of your achievements, embracing supererogatory anxieties and forcing you to spend too much time feeling needlessly morose.

I suppose that in articulating this common neurosis, Hardy is performing a service. He seems to relish “mathematical fame,” which he calls “one of the soundest and steadiest of investments.” Yet fame is a piss-poor reason to go about making art or formulating theorems. Most of the contributions to human advancement are rendered invisible. These are often small yet subtly influential rivulets that unknowingly pass into the great river that future generations will wade in. We fight for virtues and rigor and intelligence and truth and justice and fairness and equality because this will be the legacy that our children and grandchildren will latch onto. And we often make unknowing waves. Would we, for example, be enjoying Hamilton today if Lin-Manuel Miranda’s school bus driver had not drilled him with Geto Boys lyrics? And if we capitulate those standards, if we gainsay the “trivial” inspirations that cause others to offer their greatness, then we say to the next generation, who are probably not going to be listening to us, that fat, drunk, and stupid is the absolute way to go through life, son.

A chair may be a collection of whirling electrons, or an idea in the mind of God: each of these accounts of it may have its merits, but neither conforms at all closely to the suggestions of common sense.

This is Hardy suggesting some church and state-like separation between pure and applied mathematics. He sees physics as fitting into some idealistic philosophy while identifying pure mathematics as “a rock on which all idealism flounders.” But might not one fully inhabit common sense if the chair exists in some continuum beyond this either-or proposition? Is not the chair’s perceptive totality worth pursuing?

It is at this point in the book where Hardy’s argument really heads south and he makes an astonishingly wrongheaded claim, one that he could not have entirely foreseen, noting that “Real mathematics has no effects on war.” This was only a few years before Los Alamos was to prove him wrong. And that’s not all:

It can be maintained that modern warfare is less horrible than the warfare of pre-scientific times; that bombs are probably more merciful than bayonets; that lachrymatory gas and mustard gas are perhaps the most humane weapons yet devised by military science; and that the orthodox view rests solely on loose-thinking sentimentalism.

Oh Hardy! Hiroshima, Nagasaki, Agent Orange, Nick Ut’s famous napalm girl photo from Vietnam, Saddam Hussein’s chemical gas massacre in Halabja, the use of Sarin-spreading rockets in Syria. Not merciful. Not humane. And nothing to be sentimental about!

Nevertheless, I was grateful to argue with this book on my second read, which occurred a little more than two weeks after the shocking 2016 presidential election. I had thought myself largely divested of hope and optimism, with the barrage of headlines and frightening appointments (and even Trump’s most recent Taiwan call) doing nothing to summon my natural spirits. But Hardy did force me to engage with his points. And his book, while possessing many flawed arguments, is nevertheless a fascinating insight into a man who gave up: a worthwhile and emotionally true Rorschach test you may wish to try if you need to remind yourself why you’re still doing what you’re doing.

Next Up: Tobias Wolff’s This Boy’s Life!

Bullies (FYE #6)


Bullying is the most common form of violence in America and often carries into adulthood. Every day, more than 160,000 students stay home from school because they fear being bullied. This week, we discuss bullying at length. Poet Shane Koyczan uncovers the dark beginnings of “To This Day,” a poem abut bullying that went unexpectedly viral. We talk with Emily Bazelon, author of Sticks and Stones, to learn more about the bullying phenomenon. Dr. William Copeland reveals how bullying’s long-term effects extend into adulthood and discusses an unprecedented study that followed 1,420 kids from North Carolina for twenty years. Distinguished author James Lasdun tells us how a relentless student cyberstalked him and refuses to stop to this very day. And we find out how an innocent girl with progeria was relentlessly tortured by cyberbullies who reviled her for no good reason at all.


As if Broken Bones Hurt More

Shane Koyczan read his poem, “To This Day,” over a video that was animated by volunteers. The video became a YouTube sensation, racking up five million views in a week. But before Koyczan had poetry, there was the daily hell at school in which he was singled out for being different. Now that the bully’s reach has extended beyond the classroom, Koyczan discusses how conversation and compassion are invaluable tools against the hate and meanness. (Beginning to 5:46)


More Than Sticks and Stones

Emily Bazelon, author of Sticks and Stones and senior editor at Slate, reveals how Swedish psychologist Dan Olweus has developed an anti-bullying program in place within many of America’s schools right now. But how can kids stick up for themselves? And what of school principals who believe that putting the bully and the victim in the same room to talk out the problem? And with so many other national problems, why should we care about bullying? (5:46 to 12:10)


The Long-Term Effects of Bullying

In late February, JAMA Psychiatry published a report revealing how the long-term effects of bullying stretched into adulthood. In an unprecedented undertaking, 1,420 kids from Western North Carolina were asked about bullying at various points in their life over a twenty-year period by a group of psychologists. For subjects who had been bullied in school, depression and anxiety continued into their twenties. We talked to Dr. William Copeland, the lead researcher, to learn what this means for those who past, present, and future children. (12:10 to 25:02)


On Being Cyberstalked

James Lasdun is a heralded poet, a celebrated novelist, and a distinguished and generous teacher of creative writing. But when a former student started sending him emails, Lasdun’s quiet life turned into a nightmare. His new memoir, Give Me Everything You Have, chronicles the ongoing horror. (25:02 to 53:24)


The Princess and the Trolls

Adalia Rose is a five-year-old girl suffering from progeria. She lives in a modest apartment with her single mother. But Adelia’s harmless videos became a dark magnet for trolls. We chat with Camille Dodero, who wrote a lengthy investigative piece for Gawker, about why the trolls found the prospect of picking on an innocent girl so funny and reveal how high-profile cyberbullying feeds into another American sickness. (53:24 to end)

Loops for this program were provided by The Psychotropic Circle and Martin Minor. Follow Your Ears Theme (licensed) by Mark Allaway.

Follow Your Ears #6: Bullies (Download MP3)

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Jonah Lehrer: A Malcolm Gladwell for the Mind

As the terrible news of Andrew Koenig’s suicide and Michael Blosil leaping to his death, both after long depressive bouts, emerged over the weekend, the New York Times Sunday Magazine had aided and abetted Jonah Lehrer’s continued slide into unhelpful Gladwellian generalizations by publishing his sloppy and insensitive article claiming that depression really isn’t that bad. Lehrer, an alleged bright young thing who found his own tipping point with How We Decide, appears to have cadged nuanced examples from such thoughtful books as Kay Redfield Jamison’s Touched with Fire and Daniel L. Schachter’s The Seven Sins of Memory, proving quite eager to cherrypick tendentious bits for a facile sudoku puzzle, or perhaps print’s answer to a “fair and balanced” FOX News segment, rather than a thoughtful consideration.

Lehrer attempts to establish a precedent with Charles Darwin’s mental health: a troubling task, given that the great evolutionist kicked the bucket around 130 years ago and, thus, didn’t exactly have the benefit of psychiatric professionals watching over his bunk, much less a DSM-IV manual. Lehrer suggests that the “fits” and “uncomfortable palpitation of the heart” that Darwin referenced in his letters represented depression. While it’s difficult to diagnose a mental condition in such a postmortem manner, John Bowlby’s helpful book, Charles Darwin: A New Life, has collected various efforts to pinpoint what Darwin was suffering from. And Bowlby’s results tell a different story. Darwin, who was very careful to consult the top medical authorities of his time, described his “uncomfortable palpitation” in a letter to J.S. Henslow on September 1837, when he was hard at work making sense of his data after the Beagle had landed back. In 1974, Sir George Pickering made an analysis of Darwin’s symptoms from these shards and attributed this state to Da Costa’s Syndrome, more commonly known as hyperventillation. Da Costa’s is most certainly unpleasant, but it is not depression. Dorland’s Medical Dictionary describes Da Costa’s as “a manifestation of an anxiety disorder, with the physical symptoms being a reaction to something perceived to be dangerous or otherwise a threat to the person, causing autonomic responses or hyperventilation.” (Emphasis added.) This diagnosis was backed up, as Bowlby notes, by Sir Hedley Atkins and Professor A.W. Woodruff.

Later in his book, Bowbly suggests that Darwin may have suffered from fairly severe depression during the months of April and September 1865 — which corroborates the “hysterical crying” that Lehrer eagerly collects and that Darwin conveyed to his doctor. But where Bowbly is careful to note that the “hysterical crying” leading to depression is a speculation based merely on a phrase and an anecdote conveyed by Darwin’s son, Leonard, Lehrer conflates both Darwin’s “hysterical crying” and Bowlby’s other non-depression examples into depression. Furthermore, Lehrer fails to note that the reason that Darwin was “not able to do anything one day out of three” (as he noted in a letter to Joseph Dalton Hooker on March 28, 1849) was because, as Darwin noted, his father had died the previous November. (Lehrer does note Darwin’s grief following the death of his ten-year-old daughter and proudly observes that the DSM manual specifies that the diagnosis of grief-related depressive disorder “is grief caused by bereavement, as long as the grief doesn’t last longer than two months.” But David H. Barlow’s Anxiety and Its Disorders cites a 1989 study*, which points out that “it is not uncommon for some individuals to grieve for a year or longer” and observes that some people may need longer than two months to escape severe incapacitating grief. A major depressive disorder may not necessarily be the result after two months of grief. In other words, the human mind is not necessarily an Easy-Bake oven.)

The basis for Lehrer’s thesis — that Darwin conquered the totality of his apparent “depression” to “succeed in science” and that his “depression” was “a clarifying force, focusing the mind on its most essential problems” — is predicated on a willful misreading of the primary sources, one that apparently eluded the indolent army of Times fact checkers, who only had to consult Bowlby’s more equitable analysis. This was irresponsible assembly from Lehrer: bad and inappropriate badinage intended to back up a sensational headline and convey Darwin as a falsely triumphant poster boy for severe depression. But depression is a deadly disorder, a condition that requires a less specious summary.

Lehrer later cites David Foster Wallace’s short story, “The Depressed Person,” as a qualifying example for how the depressive mind remains in a “recursive loop of woe.” One may find comparisons between DFW’s real depression and the details contained in the story. But the story, written in third person and loaded with clinical details, might also be read as something which depicts the regular world’s failure to comprehend inner torment. Prescriptive analysis may very well apply to patterns of behavior, but fiction is an altogether different measure.

It is doubtful that DFW ever intended his story to be some smoking gun for lazy cognitive science, as Lehrer insists that it is, when Lehrer declares that those with “ruminative tendencies” are more likely to be depressed. Daniel L. Schachter’s The Seven Sins of Memory, a book that Lehrer appears to have relied upon for the Susan Nolen-Hoeksema example, pointed out that people “who focus obsessively on their current negative moods and past negative events, are at a special risk for becoming trapped in such destructive self-perpetuating cycles.” But what of those who are ruminating after a positive mood or after positive events? The danger of using a phrase like “ruminative tendencies” is that it discounts Nolen-Hoeksema’s clear distinction between dysphoric subjects inclined to ruminate (and feel worse) and “nondysphoric subjects [who] would show no effects of either the rumination or distraction inductions on their moods.” Perhaps by warning his readership of “ruminative tendencies,” Lehrer is encouraging them not to ruminate and therefore become mildly depressed about Lehrer’s dim findings. Lehrer is right, however, about the Loma Prieta earthquake data (also found in the Schachter book). But his failure to distinguish between the dysphoric and nondysphoric perpetuates a convenient generalization rather than an article hoping to contend with conditional realities.

Near the end of his piece, Lehrer confesses that the criticisms against the analytic-rumination hypothesis are often responded to “by acknowledging that depression is a vast continuum, a catch-all term for a spectrum of symptoms.” Well, if only he had told us this at the head of the article before leading us down a rabbit hole. He later writes, “It’s too soon to judge the analytic-rumination hypothesis.” Well, it wasn’t too soon to speculate on Darwin’s letters (not all the result of depression) or David Foster Wallace’s inner psychological state, as reflected through a story.

Lehrer also brings up Joe Forgas’s experiments at a Sydney stationery store, whereby Forgas hoped to get his subjects to remember trinkets. He played different music to match the weather. Wet weather made the subjects sad, and the sadness made the subjects more attentive. But in a Financial Times article written by Stephen Pincock, Forgas was careful to note “that any benefits that he has found apply only to the passing mood or emotion of sadness, rather than the devastating illness that is severe, clinical depression.” Once again, Lehrer neglects to mention this scientific proviso, leading readers to conclude that Forgas’s results are more related to depression.

It’s also important to note that the Paul Andrews study Lehrer relies on, which drew an interesting correlation between negative mood and improved analysis, defines “depressive affect” as “an emotion characterized by negative effect and low arousal.” This is a fundamentally different metric from outright depression, which Andrews’s study is clear to specify. But Lehrer confuses the two terms and retreats back to his clumsy Darwin metaphor of “embrac[ing] the tonic of despair.”

I don’t doubt that Lehrer wished to point out how depressive affect, or modest negative feelings, need not translate into a crippling existence. But his distressing conflation of “depressive affect” and “depression,” and his insistence that even a modest negative feeling might be categorized as depression, may very well suggest to readers that hard-case depressives in serious need of care and treatment might do without these essential long-term remedies. As someone who has offered assistance to friends living with this very real condition, I find Lehrer’s willingness to lump every sad behavioral pattern into “depression” truly shocking. I’m also greatly concerned that the New York Times — the ostensible paper of record — has failed to fact-check the selected studies, thus misleading readers into believing that depression is always a “clarifying force.” Depression, as Andrews attempted to convey to Lehrer, is “a very delicate subject.” Andrew did not wish to say anything reckless for the record. It’s just too bad that Lehrer did.

* Jacobs, Hansen, Berkman, Kasi & Ostfield (1989). Depressions of bereavement. Comprehensive Psychiatry, 30(3), 218-224