In Search of Infinity
by N. Ya. Vilenkin, translated by Abe Shenitzer
1.
It's hard to translate Russian mathematics books into English. I did it for a living for nearly 30 years, and you can trust me in this.
In fact it's hard to translate anything at all from Russian into English. (I could go further: It's hard to translate anything at all into English. Can we leave that for another day, though?)
Don't think about difficulties like a bizarre alphabet or unfamiliar words. You quickly learn to get past those things. And don't pay any mind to fatuous people who claim that "translation is fundamentally impossible." They are just enjoying the buzzing sound between their ears. Proofs that people can translate from language to language are almost too common to mention. Here's a good one: Folks like me have been doing it for millennia.
One thing that makes translating from Russian to English (RU-EN) such a challenge is that these two languages differ so greatly in structure. In a certain sense, for example, English "agglutinates," that is, we form new expressions by chaining words together. Not the way German speakers do, by literally butt-jointing the words to make compounds like Dampf + Schiff = Dampfschiff (steamship) and Dampfschiff + Fahrt = Dampfschifffahrt (steam navigation), but by making a string of free-standing nouns into one term: Admiralty brass propeller shaft. This habit goes a long way back into our history, and it's related to another key fact about English: Word order matters. A brass Admiralty is not the same as Admiralty brass. Order is one of the ways we state relationships.
Russian speakers don't mash words together to make compounds. (Probably they do it more now than a century ago. The Russian language is more in contact with English and other languages than it used to be, and some features naturally rub off. But no one would describe Russian as agglutinating.) Instead, they follow a conservative set of rules in expressing relationships. The most frequent kind of relationship between two nouns is the one expressed by the use of the genitive case, which has to do with association or belonging: kollegi Markova, the colleagues of Markov or Markov's colleagues; karandash Ivana, the pencil of Ivan or Ivan's pencil.
(To understand how I am rendering Russian text in this English-language web page, see the table at right.)
Well, I don't mean to turn this into a dissertation, let alone one on Slavic linguistics. But think this way: Every relationship that's expressed in a Russian text, whether through the genitive case or in any other way, has to be expressed in a "native" way in English. Sometimes that means using an "of" phrase, sometimes creating a multiword compound, sometimes working harder to understand what the writer said. It just depends. Very often this process is not straightforward; a phrase like "the axis of the shaft of the motor of the lifting apparatus of the drum" may signal that the translator has comprehended but hasn't succeeded in turning the real Russian into real English.
And several other features of Russian don't align with features of English. We have a complicated set of verb tenses: "By the time you have tied your shoes, I shall have rounded the track." Russian uses simpler tenses but has a feature called "aspect" that makes the sentences "Dickens wrote novels" and "Dickens wrote Barnaby Rudge" use different though related verbs (Dikkens pisal romany, Dikkens napisal «Barnabi Radzh».). Links between words don't depend on the words falling near each other, because grammatical case relates sentence parts separated by as much as a clause or two. I could go on. My point is that you don't learn the alphabet, buy a dictionary and hang out your shingle as a RU-EN translator.
2.
Translating math texts isn't easy either, even for mathematicians. Again, it isn't a matter of strange fonts and symbols or twisted-looking vocabulary, but of two specialized languages.
(A quick, tendentious note about people who "know Russian": Some of them will make very fine translators, but the transition is not automatic or even simple. Every text is about something. Just as you wouldn't claim to know English and therefore be able to sit down and write an article about Greek-American enclaves in the South, you must not claim that knowing Russian enables you to translate an article about Armenian offshore oil production.)
Math isn't the only field to create its own idiom. A couple of decades ago, a team at the University of Montreal studied many disciplines, seeking cases where automatic translation might be feasible. For automatic translation to work in Canada, they needed to identify an activity where English-speaking professionals communicate in a highly stylized and unambiguous language and so do French-speaking professionals. The UM group discovered that aircraft maintenance manuals were a pretty good example, but broadcast weather bulletins were even better. "It will rain in Sherbrooke" always comes out the same way in English and always comes out the same way in French, and similarly for blasts of Arctic cold, subtropical cyclones and snow up to the second-story windows. The automatic translation project had a striking success.
But while mathematicians do use standard expressions--having first agreed on their meanings--that isn't all they write. If a paper just consisted of "If" (formula) "then" (formula) "so that we can infer" (formula), sure, you could think about automating the process. It's never that simple, though. Math articles, unlike weather reports, contain background, narrative and conclusions. And a translator who knows nothing at all about the field can become disoriented and incoherent within a sentence or two. That's why editors prefer to assign math translation projects to mathematicians, and likewise in physics, engineering, business administration and many other disciplines.
What's more, there are "ethnic" differences in the style of writing. In German, a formula is a noun; it has to be either a subject or an object. In American math, it isn't too uncommon to see the "=" sign in a formula treated as a verb, and a formula can take the place of a whole clause. The translator has to know when this kind of substitution is allowable and when it will make the author look like an idiot.
If you are, as I am, a failed mathematician, you are in for a spell of brutally hard study at the beginning of a project. You must learn how the local math language sounds--keeping in mind that algebraists and number theorists speak distinct dialects--and ditto for some remote math language. You must push your understanding to the very limit and a little way beyond, and you must run down every possible reference. All math translation is hard.
3.
So we come to RU-EN math translation. Now mathematics, as an academic pursuit, is a subject one writes about in formal Russian. There is no set limit on the length and complexity of sentences. Subjects are repeated in full every time, not shortened for easy flow. Verbs run chiefly to passive voice. (In fact Russian doesn't have a proper passive voice, so official Russian uses a mock-passive made from an active verb. "X was added to Y" is expressed with the same words as "We added X to Y" and "They added X to Y." The practice would be confusing enough even without intermixed statements like "Smith and Jones did this computation in 1957. They added X to Y.")
Turgidity is at a premium. Fluency counts for nothing, and conciseness--to judge by results--is abhorred. You may say this is true in English as well, but it isn't so. Prose about math is hard to understand, but that's because what it is about is hard to understand. Learn the math, and the text surrounding it becomes crystal-clear and even graceful. Formal English writing can tolerate ponderousness but doesn't seek it. The Russian sentence just rumbles along, sans people, sans copulas, sans everything. You're lucky if it turns out to mean something.
One of the ways a translator checks terminology and reasoning is to compare the original text with work on which it is based. Chasing references is a vital part of the project. I've seen many instances, though, where the author says a formula comes from such-and-such a source, but the expression cited does not resemble what the author has written. Somewhere in the chain of transmission, the formula has been integrated or differentiated or expanded in series or the notation has been inverted. Maybe the original formula applied to the sex of chickens, and the author changed it all around because he wanted to calculate the number of first-magnitude stars in a cluster. Such a practice makes it extra-hard to validate the translation, and Russian mathematicians are the worst in this respect.
4.
Naum Yakovlevich Vilenkin's book V poiskakh beskonechnosti came out sometime before 1995; internal evidence--specifically the author's application of Marxist-Leninist theory, his citation of Engels as an authority on mathematicians and Sin, and his identification of some practitioners as Soviet mathematicians--suggests that the book dates back before 1991.
As of 1995, when this translation appeared, Abe Shenitzer was a member of the Department of Mathematics & Statistics of York University in Ontario.
Shenitzer's approach to this text--more of a history with illustrative arguments than a full-blown theoretical treatment--was to create a translation that can be traced back to Vilenkin's words rather than a "literary" translation that reads as if composed in English. This is by far the most frequent choice of translators in math and many other disciplines.
The original, in turn, seems to have occupied a register just a bit below that of standard formal Russian. The abstract describes it as a "popular" work, and while most of the text runs in the approved stiff manner, it does contain outbreaks of whimsy and personal response.
Vilenkin says his aim is to review the story of concepts of infinity in both math and physics, from antiquity to the present, and to provide the reader with background for understanding what happens next. He begins with drawings on the walls of caves and brings his narrative down to at least the middle of the 20th century. He gives more detail and adopts a somewhat more critical stance than you might expect to see in a popular math book in our country, if there were a popular math book in our country.
It's always useful to see familiar ideas from a new angle, and as far as Westerners are concerned at least, we get that from Vilenkin. The notion of infinity, in some sense, is very old: Poets in India and Central Asia referred to "boundless" spaces and "numberless" things. Zeno's arguments about divisibility (Achilles' steps never stop getting shorter) can be recast as statements about infinity. But there have been ages when mathematics explicitly ruled out any reasoning based on boundlessness or indefinitely small quantities, and even Newton and Leibniz, when they invented calculus, went beyond what was conservatively allowed at the time. (The "infinitesimal" is a quantity that is capable of diminishing forever; if it got so small and no smaller, it wouldn't be infinitesimal, and your calculus would just be arithmetic.)
As a presumably Soviet writer, Vilenkin needs to note that Aristotle characterized Zeno of Alea as "the founder of dialectic." His chapters on the 20th century spend more ink on Soviet "schools" of mathematics, and their B-list members, than I thought was possible. And of course there's Engels weighing in on the shakiness of mathematics when it divorces itself from the material world:
When variable magnitudes entered mathematics and when their variability was extended to the infinitely small and infinitely large, then mathematics, usually so very moral, perpetrated the Fall. . . . The virgin state of absolute meaningfulness . . . belonged to the past. (page 134)
Given the original text and the strategic choices Shenitzer made, this book almost could not have been done any better. As a long-time RU-EN science and math translator, I imagine I can see through the translation to the original, and what I see at both levels is the same. The author's jokes are undoubtedly as funny in English as they are in Russian, and his arguments are rendered with exemplary clarity. Nobody should hold that Vilenkin is a great stylist, but the style he exhibits in his writing, Shenitzer reflects in his translation.
I say "almost" only because of a deeply held feeling, which I express as an axiom: Any Translator Can Improve Any Translation. Yes, I can improve this work, and I'll give you an example: A scientist is reported as "obtaining" a letter from Albert Einstein. Instead, he "received" or "got" the letter. Same word in Russian, poluchil. There, I improved it. But in making that claim, I don't mean that In Search of Infinity is not excellent already. It is a fine piece of the translator's art.
5.
I can't say why, but Vilenkin's book has no peer as a remedy for insomnia. It contains two paragraphs so fast-acting that I still don't know how they end.
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