| The Origin of Zero |
| A slightly mathematical vignette for Sonja |
| Bent E. Petersen - May 9, 1998 |
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Our system for representing numbers has its roots in the system used by the Babylonians about 4000 years ago. Their system was base 60, or perhaps a combination of base 60 and base 10, and was a positional or place-value system, that is, the relative position of a digit enters into determining its value. In our system we multiply by successive powers of 10 as we move to the left - the Babylonian used powers of 60.
The Babylonian system was ambiguous though because it lacked a symbol for 0. Occasionally a space was used to mark a missing digit, but trailing spaces were not used (and would be difficult to detect). In addition multiple successive spaces would be difficult to detect accurately. The Babylonians relied on context to resolve the ambiguity.
In a later period, 600 BC to 300 AD, a symbol for zero was introduced, but it was not used as a trailing zero. Thus one could not really distinguish 3600, 60, 1, 1/60, and so on, except by relying on the context.
The Egyptians, around 1650 BC and earlier developed a base 10 system, but it was nonpositional. One can view such a system as additive. For example, if "1" is the symbol for one and "A" is the symbol for ten, then twelve can in principle be written as 11A, A11 or 1A1. Of course the Egyptians did have a preferred order for writing their symbols.
Egyptian number representation was also distinguished by an elaborate scheme for representing fractions by unit fractions, that is, sums of reciprocals of integers.
| An interesting feature of Egyptian mathematics was the use of the concept of an unknown quantity to be determined by solving an equation. The unknown was typically called "hau" or "aha". It is very difficult not to jump to the obvious conclusion here! | Aha! |
The Greeks had a system for representing numbers for everyday arithmetic. This system used 27 letters to represent numbers in a nonpositional decimal system. That is, there was a symbol for each of the numbers 1, 2, 3, .., 9, 10, 20, 30, ..., 90, 100, 200, 300, ..., 900. As in the Egyptian system, the order of the symbols made no difference to the value (and there was no zero).
The decimal systems and positional systems are quite ancient. The union of the two, together with a fully functional zero digit, is quite recent however. Perhaps around 300 AD the Hindus introduced a fully functional zero in a decimal positional system. They called their zero "sunja". It means empty space. When the notion spread to Baghdad perhaps around 600 AD the named shifted to the Arabic "sifr" which again means empty space. In Medieval Latin it became "ciphra". The Latin entered Middle English as "siphre" which eventually became "cypher" in English and "cipher" in American.
This Hindu-Arabic system of representing numbers made its way into Europe by various means. There are traces of it as early as 976 AD in Spain. The person who deserves the credit though for introducing the system into Europe is Leonardo of Pisa, better know as Fibonacci, who wrote a popular text, Liber Abaci, in 1202. This text introduced Europeans to much of the mathematics preserved or developed by the Arabs, and in particular, to the Hindu-Arabic number representation system.
The word "ciphra" also evolved to signify the whole decimal positional number system. To this day integers are referred to as "cyphers" in English, though the usage is not common in American. With "ciphra" taking on a new more general meaning, a word derived from it, the Medieval Latin "zephirum" or "zepharino", came to be used to denote zero. This word eventually entered English as "zero".
In Medieval Europe some communities banned the positional number system. The bankers of Florence, for example, were forbidden in 1299, to use Hindu-Arabic numerals. Instead they had to use Roman numerals. Thus the more convenient Hindu-Arabic numbers had to be used secretly. As a result "ciphra" came to mean a secret code, a usage that continues in English. The resolution of a code is of course "deciphering" - a very popular word in modern English.
Let's return to the ancient Hindus. They originally used a dot to represent zero, but later used a small circle. Old manuscripts containing integers of large magnitude must have contained an impressive number of dots. At least one poet, perhaps influenced by a mathematical manuscript, was led to refer to the stars metamorphically as "sunya bindu" which means "zero dots".
| So now with the considerable weight of centuries of historical authority, and with a large dose of poetic license to enhance the truth and to mangle the pronunciation of the ancient Hindi, I can tell my granddaughter Sonja that the stars in the sky are "sonja dots!" I think she will be pleased. |  |
| Sonja 1997 |
Morris Kline, Mathematical Thought from Ancient to Modern Times, Oxford Univ. Press, New York, 1972.
Dirk J. Struik, A Concise History of Mathematics, 3rd ed., Dover Publications, New York, 1967.
Robert K. Logan, The Alphabet Effect: The Impact of the Phonetic Alphabet on the Development of Western Civilization, St. Martin's Press, New York, 1986.
Disclaimer: This article is a vignette with a vaguely mathematical content. It is intended to amuse and to entice. It is not a scholarly paper. If you seriously want to know more or to question what is here, then search the expert literature.
Copyright © 1998 Bent E. Petersen. This document may be used, copied and distributed freely, entire and intact, for any purpose, but may not be altered. If you want to improve on it, which can certainly be done, then please write your own.
No claim of historical veracity is made, quite the contrary.
Last updated Thursday, April 10, 2003
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