Great Expectations and Supermen

Dickens, Nietzsche, and the science of a better life

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One of the most memorable scenes of Great Expectations, as illustrated in the original 1861 text

Pip, of Dickens’s Great Expectations, was set to have a normal childhood and to lead a happy existence, albeit a humble one, until Estella came along. He had a job ready for him in Joe’s forge; he had a father-figure, a mentor, and a friend, in Joe; he had a faithful friend, even a prospective romantic companion, in Biddy. He took happiness even from—indeed, only from—the simplest of things.

For example, in their nightly eating of bread and butter by the hearth, Pip and Joe shared in an amusing ritual.

In our already-mentioned freemasonry as fellow-sufferers, and in his good-natured companionship with me, it was our evening habit to compare the way we bit through our slices, by silently holding them up to each other’s admiration now and then,—which stimulated us to new exertions.

They did all this while trying to avoid the wrath of Pip’s tyrannical older sister. The reader comes to look back with fondness on a time when avoiding Mrs. Joe’s temper was the greatest of Pip’s troubles.

Everything changes when Pip meets Estella, the gorgeous but ice-hearted daughter of Miss. Havisham, a reclusive, mysterious old rich woman, at a mansion in the nice part of town.

Over a game of beggar my neighbor: “He calls the knaves Jacks, this boy!” said Estella with disdain, before our first game was out. “And what coarse hands he has! And what thick boots!”

Back home, Pip broods over his hands and his boots.

I took the opportunity of being alone in the courtyard to look at my coarse hands and my common boots. My opinion of those accessories was not favorable. They had never troubled me before, but they troubled me now, as vulgar appendages. I determined to ask Joe why he had ever taught me to call those picture-cards Jacks, which ought to be called knaves. I wished Joe had been rather more genteelly brought up, and then I should have been so too.

Thus begins Pip’s obsession with becoming a “gentleman”. He’d like to wear the finest clothes; to become literate and read the best books; to associate with the most refined of people. Life in the kitchen and forge was good enough for Pip, until it wasn’t.

Yet when Pip comes into a fortune and starts a new life in London, all is not always splendid. Worse than his daily troubles and trifles is the fact that his once-easygoing relationship between Joe becomes stilted and forced. Back in rural Kent, now-gentlemanly Pip has dinner with his uncultivated companions:

Soon afterwards, Biddy, Joe, and I, had a cold dinner together; but we dined in the best parlor, not in the old kitchen, and Joe was so exceedingly particular what he did with his knife and fork and the saltcellar and what not, that there was great restraint upon us.

And their easygoing relationship of the past seems distant and inaccessible.

“Mr. and Mrs. Hubble might like to see you in your new gen-teel figure too, Pip,” said Joe, industriously cutting his bread, with his cheese on it, in the palm of his left hand, and glancing at my untasted supper as if he thought of the time when we used to compare slices.

Despite all the frills of life with London’s upper crust, Pip can’t help but wonder at times, “with a weariness on my spirits, that I should have been happier and better if I had never seen Miss Havisham’s face, and had risen to manhood content to be partners with Joe in the honest old forge.”

Great Expectations gives rise to a question I myself have considered quite a bit: is it necessarily better to eat better food, to see better plays, and to dine with people who have better manners? Or might one rationally opt to gain pleasure from baser sources? If a college student gains as much pleasure from Burger King as a chef does from French haute cuisine, is not the student better off in this regard? Is Pip wise to pursue a life of excellence, at the expense of the simple things which once gave him pleasure? Continue reading

The Valley

This article is part of a series on Complex Algebraic Geometry. See also:
1. The Hardest Conjecture; 2. The Valley; 3. A Mathematical Daydream

“I see a massive valley before me. The only question is… Should I cross it?”

This is how, about three years ago, and living in Moscow, I posed to a friend the dilemma of whether I should attend graduate school for math.

The analogy held up well. I often envisioned my progress through the program in terms of the same imposing valley. “The brambles are getting so thick, at this depth, that the light which once flowed liberally from the surface is becoming damp and attenuated,” I once thought, as I entered the later stages of the notorious first-year program in algebra and analysis. “I’m so far from charted land that I’m encountering species wholly unknown to the outside world,” I thought later, during my second year – as I first began to encounter Hodge Theory – envisioning passing into a dark forest where marvelous, strange creatures chirped and glowed.

Once in while I’d perceive myself on an unexpected trail towards a promising discovery. “It’s as if I’ve glimpsed light on the other side much earlier than I had anticipated,” I’d think.

The analogy seems to have lost some of its power now. I’ve made my way to the other side, sure. But much of the valley remains unexplored – by me or by anyone else. Continue reading

The Hardest Conjecture

This article is part of a series on Complex Algebraic Geometry. See also:
1. The Hardest Conjecture; 2. The Valley; 3. A Mathematical Daydream

Among the so-called Millenium Prize Problems – seven notoriously difficult mathematical problems, each open for decades, and each now carrying, courtesy of the Clay Mathematics Institute, a million-dollar prize – Kieth J. Devlin places the Hodge Conjecture last. “[A]n author should delay as long as possible introducing anything is likely to make his reader give up in despair,” Devlin writes in his book, The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of our Time. “There is no… path even to the problem’s front door.”

The Hodge Conjecture fascinated me even before I began studying mathematics. Its sheer inscrutability surely played a role. I sensed, behind the incomprehensible words and symbols of its Wikipedia page, a bafflingly deep, and coherent, world. I had to understand.

The problem’s formidability was only partly to blame. This world – which I envisioned – was not just expansive, but beautiful. I perceived, there, something like Dante’s “music of the heavenly spheres”.

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French artist Gustave Doré’s depictions of Dante’s Paradise.

My graduate study has taken me into a field of math relatively close to that which the Hodge Conjecture occupies. As I’ve explored the rich foothills of this towering mountain, its peak has become even more stunning and mysterious.

I will try to explain the conjecture to this blog’s lay readers. Continue reading

Characteristic Classes

This story is part of a series entitled Leaving Mathematics. See also:
1. The Baltimore Snowstorm; 2. The Italian School; 3. Characteristic Classes

Rainer noticed the pattern halfway through July. He had constructed smooth surfaces in a certain four-dimensional smooth algebraic variety, using the Chern classes of vector bundles. He noticed that he could anticipate these surfaces’ Hodge numbers. “This seems to amount virtually to something like a non-existence result,” he wrote, later that day, in an email to a junior faculty member at another school.

Rainer soon sank into a deep depression. “I go full days without saying a single word,” he told Diego, over the phone. Continue reading

Ruminations

Jalāl ad-Dīn Rumi informs math and life.

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A page from Rumi’s Mathnawi.

“It’s very perverse, what you’re doing,” Professor Vyacheslav Shokurov said, one afternoon in his office chair, with a skepticism characteristic of the mathematician. “One usually begins with examples – examples not treatable by the existing theory. One then develops new theory.”

Shokurov peered at me for an instant, and then lifted his hands from his lap. “But you’ve developed the theory first. And now you go looking for examples.”

My mathematical research had been stalled for about two weeks, for exactly this reason. Continue reading

A Fragile Truth

My four-week psychiatry rotation at Western State Hospital landed smack in the middle of peak general election season. And, oddly enough, these two experiences have yielded remarkable similarities. In both cases, I have been forced to entertain various versions of the truth.

Many of the patients here at Western State are psychotic. Our known and stated goal, then, is to return these patients to reality-based thinking. Only then might they qualify for discharge. This exercise has presented philosophical challenges. Certainly, sometimes, our job is easy. One of our patients, who signs her forms as Michelle Obama Prince Harry Elizabeth Queen Zealand, communicates with Russia, Germany, Berlin, Jerusalem, East Germany, West Germany, South Germany, and Russia, by radio, television, and satellite, including the satellite in the backyard of her palace, which she built, and in which we currently reside. Another patient, though, gave me pause. Continue reading

Demons Within

If only Nicolas Winding Refn were as intent on my liking his films as I was.

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The first few scenes of Neon Demon offer the richness of experience that, as it seems, only Nicolas Winding Refn is capable of delivering. The protagonist (Elle Fanning), a gorgeous aspiring model from small-town Georgia, glides wide-eyed through the streets of LA in a red Mustang, driven by her new (and soon-to-be-ex-) boyfriend. America’s Next Top Model, after crossing America’s Former Top Model, comes home to a puma, prowling about her thrashed motel room. A haggard-looking Keanu Reeves strides out of the dingy, blue-lit motel lobby to smoke a cigarette in the red light of the Motel 6 sign. Indeed, this was quite something. Was Neon Demon going to be what Only God Forgives never was—the movie that could rival Drive?

Continue reading