May 16, 2007

Zero in Russia


The answer to the question - "how did a pre-Petrine Russian express the notion of zero as a number, in writing and in speech?" - is supersimple: it didn't. The Greeks had no zero, the Romans had no zero, the Russians had no zero as long as they used their variant of Greek numeration.

Zero appears as placeholder in Hindu-Arabic numerals; it is first TREATED as number in using HA numerals for calculation (6-0=6); it is first RECOGNIZED as a number extremely late... the Flemish mathematician Simon Stevin at the end of the 16th century announced that the ONE is the same numerically as all other numbers, and called zero "the root of number." So it's not a number even here. Pascal thinks you're dumb if you don't understand that 0-4=0. One could do all sorts of incredible things in math before coming up with the notion of zero as a number.

Russians used the abacus to calculate - no one ever calculated in Slavic numerals because, like Greek and even Roman numerals, they are not intended for calculation but for setting down results. If your numeration or calculation has no place for zero, you won't understand why there should be a numeral that points to absence of number.

Zero entered Muscovy in the early- or mid-seventeenth century when introduction of HA numerals allowed for calculating on paper. Zero was called tsifra from the Arabic word for empty (sifr) and Medieval / Renaissance Latin for zero (cifra), which gave English both "zero" and "cipher." In Russian, already in the 17th century the word for zero started referring to all HA numerals (tsifry), also arithmetic (tsifir') and code (tsifir'). (Same denotative spread as in Latin, by the way.) I read in, I think, A. P. Iushkevich that in the 17th century the HA zero was also called "on" or "onik," like the letter O, which in Slavic numeration stands for 70.

Anyway, before the seventeenth century there really is nothing in any way like the concept of zero in Russia. And, of course, the concept of number at this point includes only natural numbers, nothing more.

Eugene Ostashevsky
NYU


I seem to remember an article on this subject by Simonov, the leading specialist on early Russian mathematical manuscripts, but I can't find it. For some discussion of this see ch. 2 of A. P. Iushkevich, Istoriia matematiki v Rossii, M. 1968. Also L.L. Kutina, Formirovanie iazyka russkoi nauki, M.,1964, pp. 14-20.

There are several coins, manuscripts and printed books of Russian origin in the seventeenth century which use or give lists of modern 'hindu-arabic' numerals, and Russian traders and officials in the Posolskii prikaz must certainly have been familiar with western numerals, so the concept must have been known and understood, at least by some.

Russian alphabetical numerals did not in fact need a zero since every number ending in zero in modern notation had a letter to designate it: e.g. k= 20. These could be modified by a preceding or subscript oblique line with two cross bars to produce thousands, and various kinds of circle round the letter for larger multiples of 1000. Arithmetical calculation was perfectly possible in this system as it had been for the Greeks from whom it was taken.

The earliest words for zero are recorded from the end of the 17th century and early eighteenth century - on, onik (i.e. the name of the latter o) in Peter I notebook (1688) and Kopievskii, later tsifra and nul'.

Emeritus Professor W. F. Ryan FBA, FSA
Warburg Institute
(School of Advanced Study, University of London)

Tags: math
Like this post? Get a weekly email digest + member-only deals

Some of Our Books

Life Stories: Original Fiction By Russian Authors

Life Stories: Original Fiction By Russian Authors

The Life Stories collection is a nice introduction to contemporary Russian fiction: many of the 19 authors featured here have won major Russian literary prizes and/or become bestsellers. These are life-affirming stories of love, family, hope, rebirth, mystery and imagination, masterfully translated by some of the best Russian-English translators working today. The selections reassert the power of Russian literature to affect readers of all cultures in profound and lasting ways. Best of all, 100% of the profits from the sale of this book are going to benefit Russian hospice—not-for-profit care for fellow human beings who are nearing the end of their own life stories.
A Taste of Russia

A Taste of Russia

The definitive modern cookbook on Russian cuisine has been totally updated and redesigned in a 30th Anniversary Edition. Layering superbly researched recipes with informative essays on the dishes' rich historical and cultural context, A Taste of Russia includes over 200 recipes on everything from borshch to blini, from Salmon Coulibiac to Beef Stew with Rum, from Marinated Mushrooms to Walnut-honey Filled Pies. A Taste of Russia shows off the best that Russian cooking has to offer. Full of great quotes from Russian literature about Russian food and designed in a convenient wide format that stays open during use.
Bears in the Caviar

Bears in the Caviar

Bears in the Caviar is a hilarious and insightful memoir by a diplomat who was “present at the creation” of US-Soviet relations. Charles Thayer headed off to Russia in 1933, calculating that if he could just learn Russian and be on the spot when the US and USSR established relations, he could make himself indispensable and start a career in the foreign service. Remarkably, he pulled it of.
Tolstoy Bilingual

Tolstoy Bilingual

This compact, yet surprisingly broad look at the life and work of Tolstoy spans from one of his earliest stories to one of his last, looking at works that made him famous and others that made him notorious. 
The Frogs Who Begged for a Tsar (bilingual)

The Frogs Who Begged for a Tsar (bilingual)

The fables of Ivan Krylov are rich fonts of Russian cultural wisdom and experience – reading and understanding them is vital to grasping the Russian worldview. This new edition of 62 of Krylov’s tales presents them side-by-side in English and Russian. The wonderfully lyrical translations by Lydia Razran Stone are accompanied by original, whimsical color illustrations by Katya Korobkina.
Fish: A History of One Migration

Fish: A History of One Migration

This mesmerizing novel from one of Russia’s most important modern authors traces the life journey of a selfless Russian everywoman. In the wake of the Soviet breakup, inexorable forces drag Vera across the breadth of the Russian empire. Facing a relentless onslaught of human and social trials, she swims against the current of life, countering adversity and pain with compassion and hope, in many ways personifying Mother Russia’s torment and resilience amid the Soviet disintegration.
At the Circus (bilingual)

At the Circus (bilingual)

This wonderful novella by Alexander Kuprin tells the story of the wrestler Arbuzov and his battle against a renowned American wrestler. Rich in detail and characterization, At the Circus brims with excitement and life. You can smell the sawdust in the big top, see the vivid and colorful characters, sense the tension build as Arbuzov readies to face off against the American.
93 Untranslatable Russian Words

93 Untranslatable Russian Words

Every language has concepts, ideas, words and idioms that are nearly impossible to translate into another language. This book looks at nearly 100 such Russian words and offers paths to their understanding and translation by way of examples from literature and everyday life. Difficult to translate words and concepts are introduced with dictionary definitions, then elucidated with citations from literature, speech and prose, helping the student of Russian comprehend the word/concept in context.
Woe From Wit (bilingual)

Woe From Wit (bilingual)

One of the most famous works of Russian literature, the four-act comedy in verse Woe from Wit skewers staid, nineteenth century Russian society, and it positively teems with “winged phrases” that are essential colloquialisms for students of Russian and Russian culture.
Faith & Humor: Notes from Muscovy

Faith & Humor: Notes from Muscovy

A book that dares to explore the humanity of priests and pilgrims, saints and sinners, Faith & Humor has been both a runaway bestseller in Russia and the focus of heated controversy – as often happens when a thoughtful writer takes on sacred cows. The stories, aphorisms, anecdotes, dialogues and adventures in this volume comprise an encyclopedia of modern Russian Orthodoxy, and thereby of Russian life.

About Us

Russian Life is a publication of a 30-year-young, award-winning publishing house that creates a bimonthly magazine, books, maps, and other products for Russophiles the world over.

Latest Posts

Our Contacts

Russian Life
73 Main Street, Suite 402
Montpelier VT 05602

802-223-4955