Zero - Biography of a Dangerous Idea

Title: Zero – The Biography of a Dangerous Idea
Author: Charles Seife
Publisher: Souvenir Press 2005 (First published 2000)
ISBN: 0-285-63594-8
Pages: 230

A very good book on the origins and development of the idea of zero in mathematics, physics and other exact sciences. The book is well researched and written in a witty and lucid style, emanating the confidence of the author. The book spans three millenia about the subject matter it handles, but the huge span of time is rapidly shrunk into a moment by the mellow narrating style. When historical information are described, the time honoured voice of a historian is heard; while mathematical concepts are portrayed, the erudite voice of a seasoned mathematician is audible behind the lines. The book is a superb one on the face of the fact that so many aspects of human knowledge are condensed into a few hundreds of pages in a way relished by any class of readers. Mathematicians and lay people alike get impressed by the book and I am sure that a book of such a fine stature is very difficult to come by easily in the near future.

Babylonians and Mayans used zero in their maths. The Mayans calendar had starting month with the number zero and on every month, the days started from zero, instead of one as is the case now. The first day of the month was Zip. The next day was 1 Zip, the following day was 2 Zip and so forth, until they reached 19 Zip. The next day was the seating of Zotz’ – 0 Zotz’ followed by 1 Zotz’ and so forth. Each month had 20 days, numbered 0 through 19. While the Greek thinkers abhorred the concept of zero, its philosophy was also devoid of the idea. The Greeks in fact relayed this aversion to zero from the earlier Egyptian civilisation. Since the West based their foundations on Greeks, particularly Aristotle till the Renaissance, zero didn’t percolate to Europe. Absence of zero ensured the lack of the concept of infinity, as they are both complementary. The famous Zeno’s paradox about the race between Achilles and a tortoise is a case in point. Unless calculus and convergent series are not invoked, it is not possible to solve the Zeno’s paradox. In fact, the world waited about 1500 years to solve the issue once and for all, till Newton and Leibniz established calculus as a firm edifice on the palace of mathematics in the 17^th century C.E. The author gives the clearest explanation of Zeno’s paradox and how it could be solved. A detailed explanation of Zeno’s paradox may be looked up in the Wikipedia. Suffice it to say that the limit is 2, which is the point at which Achilles crosses the tortoise.

Archimedes used the concept of limits to calculate the area of a parabola, by drawing infinitesimal triangles and rectangles inside it and summing up their areas. The great scientist, mathematician and thinker lived in an era when the Greek sun was about to be eclipsed by the superpower, Rome. Even though Rome’s sway extended over a huge span of land in the ancient period, it was bereft of any mathematical thinking. Archimedes was killed by a Roman soldier when he failed to answer his queries properly and the act is spoken in jest as the greatest contribution of Rome to mathematics. Christianity spread its wings in Europe and Rome faded away. The early Christians cherished the ideals of Aristotle and Greek thinkers and based their theology on it. Zero had no place in it. A good description of the development of our present calendar is given. Christian monks took upon them the task of devising means for the reckoning of days. “Easter was a drifting holiday, so every few generations a monk was drafted to calculate the dates when Easter would fall for the next hundred years. Dionysius Exiguus was one of these monks. In the sixth century, the pope, John I, asked him to extend the Easter tables. While translating and recalculating the tables, Dionysius did a little research on the side; he realized that he could figure out just when Jesus Christ was born. After chugging through a bit of math, he decided that the current year was the 525^th year since the birth of Christ.” (p.54). There was no year zero in the calendar.

Such a close start (in those times) was found to be difficult for astronomers and they wanted to start counting the days from an earlier period. The fixing of the date was quite arbitrary and was fixed on January 1, 4713 BC by the scholar Joseph Scaliger in 1583. His Julian date (named after his father, Julius) became the standard way to refer to astronomical events, because it avoided all the weirdness caused by calendars that were constantly under construction.

After this discussion, the author goes to Eastern civilizations to trace out the history of zero. He says that the concept was carried from Babylon to India by the invasion of Alexander the Great. But this assertion is marked by contrast with his earlier comments that Greeks didn’t encourage the ideas about zero. How could Alexander, himself a Greek, carry a concept which he thought clearly to be a fallacy, into a land whose north-western fringe only he could bring under his banner? It is quite probable that the idea spontaneously emerged in India at that time. Indian philosophy was based on duality, as did most of the eastern civilisations. As with the yin and yang of the Far East and Zoroaster’s dualism of good and evil in the Near East, creation and destruction were intermingled in Hinduism” (p.64). “Sometime around the fifth century AD, Indian mathematicians changed their style of numbering; they moved from a Greek-like system to a Babylonian-style one. An important difference between the Babylonian style was that Indian numbers were base-10 instead of base-60. Our numbers evolved from the symbols that the Indians used; by rights they should be called Indian numerals rather than Arabic ones” (p.67).

Seife then explains how the word zero originated. “The Indian name for zero was sunya, meaning empty, which the Arabs turned into sifr. When some western scholars described the new number to their colleagues, they turned sifr into a Latin-sounding word, yielding zephirus, which is the root of our word zero. Other western mathematicians didn’t change the word so heavily and called zero cifra, which became cipher. Zero was so important to the new set of numbers that people started calling all numbers ciphers, which gave the French their term chiffre, digit.” (p.73). Fibonacci, in the 12^th century introduced the Arabic numerals into Italy based on his contacts in North Africa where Arab culture flourished. However, the prevailing monarchs received the idea with some trepidation. Many kingdoms banned its use, citing that these numbers were easily alterable. The book then goes on to the Renaissance and the development of calculus. Another major step was taken in the time of Georg Cantor. The book is a little cumbersome at this stage, when his contributions are discussed. Zero appears prominently in modern physical theories like quantum mechanics and relativity. An extensive discussion is given.

A disproportionate amount of space is allotted to physical theories than they warranted in the present frame of study. Since the book was about zero and its development, the innards of quantum mechanics need not be described in too large a detail. This is the only drawback which can be pointed against the book. After he reached the modern age, Seife seems to have lost the sense of direction and to fill pages, he unnecessarily dwelt on relativity and how it developed in the 20^th century.

The book is adorned with many clear illustrations and diagrms which clarify the point fully. The description is often very witty. An extract from the footnote on page 54 goes like this, “One dating system had the year 1 based upon the founding of the city of Rome, and the other was based on the accession of the emperor Dioclitian. To the Christian monk, the birth of his Saviour was a more important event than the foundation of a city that had been sacked by Vandals and Goths a few times – or, for that matter, the beginning of the reign of an emperor who had an unfortunate penchant for maintaining his menagerie of exotic animals on a diet of Christians”.

The book is highly recommended.

Rating: 4 Star