The One State and Its Discontents

May 22, 1999

Boof Review
Philip J. Davis

We. By Yevgeny Zamyatin, translated from the Russian by Mirra Ginsburg
Avon Books, New York, 1987, paperback, 232 pages, $5.99.

I am no fan of sci-fi. On the printed page I abhor it. I very rarely go to sci-fi movies. Should I run into it on TV, I turn it off. How is it then that I am writing a review of a book that is almost eighty years old and has been classified both as sci-fi and as "early dystopia," a book I knew nothing about until a few weeks ago?

Answer: Its existence was mentioned to me by a correspondent who pointed out that the book had a significant mathematical underlay. Add to this the fact that when I checked out early assessments of We, including that of the translator and a 1946 review by the famous George Orwell, I found that practically nothing was said about this underlay.

Aficionados of sci-fi say that We is one of the classics of the genre. It is discussed in courses in sci-fi and Russian fantasy. It's been made into a play. Be that as it may, I found We simultaneously boring and fascinating. It bored me insofar as various elements of the society postulated by Zamyatin have, alas, been closely realized, perhaps overrealized, not only in literature and film, but also in actuality in this terrible century. And as we go about our daily business, all of us have internalized these elements; the specter of Big Brother or regimentation by Big Government keeps emerging in one form or another. We accept losses of privacy and of other freedoms and think it a slight price for additional bits of convenience or security.

We fascinated me insofar as its setting is one of the first literary dystopias. (It predates both Huxley's Brave New World and Orwell's 1984.) Written before Stalin or Hitler, its prescience is remarkable. And it implies the existence of dystopic elements in mathematical thinking.

For all that mathematicians have always constituted a very small minority within society, they have taken a number of lumps from perceptive critics. The nature of the lumps has depended on time, place, and what the mathematicians were perceived as doing.

In antiquity, say in the second century AD, a mathematician might have known all of Euclid and Archimedes, but he functioned primarily as an astrologer. At that time, in fact, the word "mathematician" was often used to designate an astrologer. Although accepted and regularly practiced by numerous excellent mathematicians well into Kepler's day, astrology always lived under a cloud of skepticism. Early blasts against it included the book Against the Astrologers (c. 180-190), by Sextus Empiricus. The book begins with the sentence "The task before us is to inquire concerning astrology or the 'Mathematical Art' " and ends well satisfied that the author has "brought forth many valid objections" against this Chaldean doctrine "which is without substance." The laws of Diocletian (245-313) proscribed the practice of astrology. Saint Augustine practiced it as a young man and blasted away against it in later life.

Moving quickly to the 18th century, we find several differing views about mathematicians. In 1726, Dean Jonathan Swift published Gulliver's Travels, now regarded primarily as a children's book and published for them in bowdlerized and abridged editions. But Swift intended Gulliver as a sharp satire on the whole of contemporary society. One group he laces into is the Royal Society---its astronomers, physicists, and mathematicians. And he castigates the mathematicians for living in the clouds (the flying island Laputa), where, totally self-absorbed, they see everything through the needle's-eye of mathematics:

"If they would, for example, praise the Beauty of a Woman, or any other animal, they describe it by Rhombs, Circles, Parallelograms, Ellipses, and other Geometrical Terms."

"Although they are dexterous enough upon a Piece of Paper, in the Management of the Rule, the Pencil, and the Divider, yet in the common actions and Behaviour of Life, I have not seen a more clumsy, awkward and unhandy People, nor so slow and perplexed upon all other subjects, except those of Mathematicks and Music." (Gulliver, Part Three, Chapter Two.)

In 1734, Bishop George Berkeley published The Analyst, or a Discourse addressed to an Infidel Mathematician. Largely concerned with the lack of proper foundations for the calculus (he called infinitesimals "ghosts of departed quantities"), Berkeley's criticism still resonates in the mathematical world. Think of "nonstandard analysis" with its "hyperreal numbers"; or consider the opposite view, that continuous mathematics is passť and discrete mathematics now rules the roost.

Berkeley also deplored the tendency of educated men to defer to the decisions of mathematicians "where they [i.e., the mathematicians] have no right to decide. That is one short way of making Infidels, I am credibly informed."

Thus, mathematics endured complaints that its applications to individuals were false, that its study was pursued out of vain curiosity, that its internal reasoning was inadequate. And throughout the 20th century, beginning with We, we have been faced with the claim that mathematics has elements that can lead to societal dystopia. Incidentally, the word "dystopia" is only now entering English dictionaries; I take it to mean a community that promises a paradise and delivers a hell on earth.

A word about the author. Yevgeny I. Zamyatin (1884-1937) had training and experience as a naval architect and hence was not ignorant of mathematics. His main work, though, was as a writer of satiric novels and essays. Initially a Bolshevik, he was a rebel and a heretic during the Tsarist regime as well as after the Russian Revolution. He was both exiled and jailed. In 1931, with the help of Maxim Gorky, he got permission from Stalin to leave Russia, and he lived for the remainder of his life in Paris. His writing was translated and made available all over the world, but not in Russia.

Writing in the early 1920s, Zamyatin imagines in We a 26th-century society, created after a 200-year war that destroyed most of the world's population. "One State" is the name of the glassed-in colony described in We. Freedom is restricted, for freedom and happiness are incompatible. ("When a man's freedom is reduced to zero, he commits no crimes.") The daily activities of the inhabitants, including sex, are strictly programmed and monitored, if not by direct bugging, then by the issuance of chits.

People are called numbers and are identified by numbers (by the way, do you have your ID with you?). One State is set up with mathematical perfection and was created "to integrate completely the colossal equation of the universe." Ethical questions are reduced to mathematics (shades of Leibnitz) and are no longer a matter of individual choice. Irrational numbers and imaginary numbers are used to symbolize the tension between what can and what cannot exist when projected onto the human sphere.

"The Benefactor," re-elected continually as enforcer, is paradoxically at once "average" and absolutely vital to the repressive operation of One State. "The Guardians" are everywhere poised to pick off the disgruntled, or those who drink or smoke (cf. electronic surveillance). The rebellious, those who are out of line, are diagnosed as suffering from a condition called "imagination." They have their imaginations removed by a newly invented machine that does brain washing. If this procedure is not effective, they might have to be liquidated---literally reduced to a pool of water---by an earlier machine known as "The Guillotine."

There seems to be a world out there beyond "The Wall" (familiar?) that surrounds this coercive Paradise, but of course "Beyond the Wall" is forbidden territory. It is interesting that apart from the machines used to zap refractory personalities, Zamyatin is not much interested in dreaming up technological miracles of the future. His sentences are short and his prose is crisp; dialog is often broken off in mid-sentence, adding a substantial note of sinister ambiguity. Mathematical terms and allusions permeate the entire text.

So much for the background. What's the story line? Our hero (perhaps the dupe) is D-503, a mathematician who is engaged in designing some kind of flying vehicle known as "The Integral." Apart from his technological skills, he's your average guy. D-503 falls in love (bad, bad) with the heroine, I-330. It turns out that I-330 is a rebel and a member of an opposition group. D-503 goes along with this for a while, but apprehensively.

Zamyatin writes the following "socio-math" dialog between D-503 (He) and I-330 (She):

He: "Don't you realize that what you're planning is revolution?"
She: "Of course it's revolution. Why is this absurd?"
He: "It's absurd because there can be no revolution. Because our revolution was the final one. And there can be no others. Everyone knows this. . . ."
She: "My dear---you are a mathematician. More---you are a philosopher, a mathematical philosopher. Well then, name me the final number."
He: "What do you mean . . . what final number?"
She: "Well, the final, the ultimate, the largest number."
He: "But that's preposterous. . . . How can there be a final number?"
She: "Then how can there be a final revolution?"

I think this scene mocks the words of the communist anthem, "The Internationale" (France, 1871, various translations):

"It is our last and decisive battle
The Internationale will save the human race."

In reading this dialog, I was gratified to learn that Zamyatin agrees with me in deploring apocalyptic visions: the last struggle, the end of days, the final word, the TOEs (Theories of Everything).

As might be expected, the activities of D-503 are detected, and he is confronted by The Benefactor in a terrifying scene. D-503 has his imagination removed, after which he has no option but to break down and betray I-330 (cf. the "banality of evil" as described by Hannah Arendt in Eichmann in Jerusalem).

In one of the last pages, the reader will find, advanced in the service of defending One State, a "proof" of the impossibility of infinity (still a topic of discussion by philosophers of mathematics today).

Astrology is a failed piece of applied mathematics. Jonathan Swift described to a T the personality of many contemporary mathematicians. I'm sure the reader can name names. Bishop Berkeley commented wisely on the tendency of mathematicians to think of themselves as shoemakers who create shoes that fit no one's feet. Yevgeny Zamyatin's message that one had better watch the mind set of mathematics as it plays out in social policy is as incisive today as it was when he wrote the book.

Philip J. Davis, professor emeritus of applied mathematics at Brown University, is an independent writer, scholar, and lecturer. He lives in Providence, Rhode Island.

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