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A Chemical Dependency 

And a mathematical romance: Oliver Sacks and Edwin A. Abbott

Wednesday, Feb 20 2002

Despite being published in the opening years of the 21st century, Oliver Sacks’ new book belongs more truly with the literature of the 19th. Where in the past Sacks has trained his eye on the psychic landscapes of his patients, the subject of Uncle Tungsten: Memories of a Chemical Boyhood is himself, or more specifically the extraordinary years between the ages of 10 and 14, during which he re-enacted in his home laboratory the history of chemistry in its formative era. And what a splendid re-enactment it was!

From his initial attraction to minerals -- a colossal spearlike cluster of stibnite, gleaming dark cubes of galena -- the precocious child is drawn into a love affair with the elements, coming to know each one like an intimate friend. There are the alkaline metals, including sodium, potassium, calcium and barium, that dissolve in liquid ammonia to produce a deep-blue solution “the very color of Heaven”; phosphorus, the devil‘s element, which magically bursts into flame upon contact with water; and tungsten, one of the “noble metals,” which, along with gold and silver, resists corrosion and can be drawn into the finest of wires.

Sacks’ acquaintanceship with the elements is not the cold knowledge of theory, but the tactile intimacy that emerges from handling, precipitating, dissolving, roasting, fusing and reacting each individual substance. It is the glorious particularities of each element that bring this book scintillatingly to life. That, and the life itself, which harks back so resolutely to a predigital age. There is nothing virtual here.

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Those who have admired Sacks‘ penetrating portraits over the years will not be disappointed by the light he now sheds on his own painful past. Across that life lies a monumental shadow. Like thousands of other English children at the height of the London Blitz, Oliver and his brother Michael were sent away to the countryside, ostensibly for their own safety. In the Sacks boys’ case, it is hard to imagine that London could have been less dangerous than the hellhole in which Oliver would pass three Dickensian years, where, he tells us, he was beaten almost daily and often starved. On returning home (his faith in God, family and life shaken to the core), Oliver retreated into the realm of science. When brother Michael went briefly mad, Sacks tells us with unflinching honesty, he drowned out his sibling‘s ravings by burrowing further into his books.

While the elements with their idiosyncratic characteristics provide the bedrock of Sacks’ new universe, he craves more: What are the underlying principles that determine these properties -- their boiling point, specific heat, hardness, conductivity? Over the course of four years, assisted by his preternaturally scientific family (particularly his beloved Uncle Dave, owner of a light-bulb factory and thus fondly known as the titular Tungsten), Sacks recapitulates many of the great experiments in the history of chemistry, gradually learning from firsthand experience the inner mysteries of matter.

The culmination of this self-propelled apprenticeship is Oliver‘s grasp of the periodic table, that mythic symbolic ordering of the entire atomic realm. Sacks presents his awakening to the beauty of Mendeleev’s table as nothing less than a revelation of some divine cosmic order. One cannot but feel that in his own way he has visited Paradise.

But at the age of 14, of his own free will, Oliver Sacks leaves his Eden. After the joys of personal discovery, he is now subjected to the deathly curriculum of high school science; moreover, his knowledge of chemistry has advanced to the point where he must enter the 20th century, the age of quantum mechanics. For all its power, quantum mechanics throws a blanket over reality, muffling atomic action in what physicist John Wheeler has termed “a great cloud of unknowing.” At this stage of history, chemistry reaches a turning point, forking sharply away from the tactile, hands-on tradition that young Oliver so enjoyed. For Sacks then, this is, finally, a story of Paradise lost.

If Uncle Tungsten is a kind of love letter to all things chemical, Edwin Abbott‘s Flatland is a self-described mathematical romance; both offer the reader a visceral, almost ecstatic, experience. In the tradition of Lewis Carroll, of whom Abbott was a contemporary, Flatland is one of that singular era’s most charmingly peculiar tales, and is now being reissued by Perseus in a handsome annotated edition.

Penned over the summer of 1884, Flatland recounts the story of one A. Square, a humble quadrilateral living in a two-dimensional world. Just as Immanuel Kant was convinced of the logical necessity of our three-dimensional world, so Abbott‘s Square is convinced of the inevitability of his own planar universe. But our polygonal hero has his mind blown apart when a mysterious visitor from “Spaceland” wrenches him into the ineffable realm of Solids. Under the guidance of Lord Sphere -- a geometrical Virgil to Square’s Dante -- he is vouchsafed a view of a hitherto unsuspected third dimension, an immeasurable Paradise wherein he is shown the perfected version of his own humble form: a Cube.

Why stop at three dimensions, Square now inquires, why not proceed onward to the fourth -- surely this is only the beginning of an endless succession? “In that blessed region of Four Dimensions, shall we linger on the threshold of the Fifth, and not enter therein? Ah, no!,” says Square. “Let us rather resolve that our ambition shall soar with our corporeal ascent. Then, yielding to our intellectual onset, the gates of the Sixth Dimension shall fly open; after that a Seventh, and then an Eighth . . .”

Written two decades before Einstein introduced the idea of a physically real fourth dimension with his Special Theory of Relativity, Flatland belongs to the rare genre of mathematical fiction, that esoteric cousin to science fiction. To Abbott‘s classic tale, English mathematician Ian Stewart now adds a new layer of interpretation. As Martin Gardner famously embellished Alice’s Adventures in Wonderland, so Stewart excavates the strata of scientific, mathematical and sociological context in which Abbott‘s tale is embedded. One of the signal achievements of 19th-century mathematics was the discovery of non-Euclidean and higher-dimensional geometries -- this was the golden age of topology. As Stewart notes, talk of a fourth dimension captivated the imagination of Victorians, many of whom saw in this mathematical construct a new space for the spirit.

Stewart nicely explicates the mathematical ideas underlying Flatland, and provides a wealth of information on its literary progeny, such as A.K. Dewdney’s The Planiverse. (Stewart himself wrote a sequel, Flatterland.) Perhaps most intriguing, Stewart reveals the sociological dimension to Abbott‘s work. From the beginning, some readers of Flatland have been troubled by the apparently misogynistic treatment of females in this laminar world: Where men span the polygonal spectrum from triangles and squares to hexagons and circles, women are that lowliest of beings, straight lines. Consisting of just a single side, they are without rational form. The consequences are devastating, for having no area whatever, they literally possess no inner life, and hence no mind.

Rather than endorse the chauvinism such reductionism implies, Abbott intended to lampoon it. Stewart reveals Abbott’s long-standing interest, as headmaster at one of London‘s top schools, in reforming women’s education. Victorian social hierarchies and hypocritical mores were indeed a chief target of Abbott‘s satire, and in the final tragic fall of A. Square we can all recognize the plight of the revolutionary who dares to speak out against prevailing orthodoxy. For just as Oliver Sacks has to exit his Eden, so Abbott’s Square is ultimately cast out of his higher-dimensional heaven. Here too we have the bittersweet victory of Paradise glimpsed but finally denied.

It has been said that the duty of art is “to enchant the conceptual landscape.” With Oliver Sacks‘ peregrinations through Mendeleev’s garden and A. Square‘s travels in hyperreality, we witness the power of science also to enchant. On the one hand with chemistry, on the other hand with mathematics, Sacks and AbbottStewart traffic not in the instrumental power of their science, but in its ability to amaze. So rich in texture yet light in spirit, these books propel us without sentiment into the realm of the fantastic.

  • And a mathematical romance: Oliver Sacks and Edwin A. Abbott

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