Explorations in Mathematics: The Origins and Use of Zero

Investigating the History of the Origin of Zero

The concept of zero in today's world is taken for granted and it plays a role in mathematics particularly in number theory but this was not always so. From archeological digs somewhere around 30,000 years ago man began making markings which some scientists attribute as a count. Of what those primitive people were counting is unknown.

This hub, and several which will follow it will investigate the beginnings and history of zero.

One and Many

In the beginning of mathematics there appeared to be only a distinction between one and many. Over time as language became more sophisticated the idea of counting numbers was formed. One and many evolved into one, two and many followed by one,two, three........and many. There are tribes today, the Siriona Indians of Bolivia and the Yanoama people of Brazil which still have no words for anything greater than three except the word "many".

Binary Counting

For certain tribes which are not limited in their counting., that is they do understand the concept of more than one and less than "many" they may still be linguistically limited in expressing a count. The Bacairi count by a binary system. "One" is followed by "two", then "two" and "one, then "two" and "two", etc.

Counting in the Egyptian Book of the Dead

In the Book of the Dead, the soul must know the number of his fingers and be able to recite a counting rhyme to satisfy Aqen, the ferryman.

Counting Was Essential to Enter the Netherworld

In the Book of the Dead no one is allowed to enter the Netherword "who does not know the number of his fingers"
In the Book of the Dead no one is allowed to enter the Netherword "who does not know the number of his fingers"

The Egyptians Prospered Without the Concept of Zero

Consider the construction of the pyramids. The Egyptians may not have been theoretical geometers but their building techniques were flawless. Written record indicate that they had a sophisticated means of recording numbers. They were able to work with geometry in building and had the ability not only to survey but also do complex mathematics to compute volumes without the need for zero.

Roman Numerals

Roman numerals were used for counting and although extremely cumbersome in calculations it was possible to do arithmetic operations. There is however no symbol for zero.
Roman numerals were used for counting and although extremely cumbersome in calculations it was possible to do arithmetic operations. There is however no symbol for zero.

The Babylonians Create A Symbol for Zero

The Greeks developed a system of numbers similar to that of Egypt. They adopted the practical knowledge of Geometry of the Egyptians as well and perfected in a theoretical mathematical system. They system of writing number although originally similar to that of Egypt later evolved into one of distinct letters representing numbers. However, there was no zero.

It was the Babylonians who created the symbol for zero. Their system of counting was different from the other ancient cultures which generally had adopted a base-10 system. In may seem strange as to how this came about in a culture whose number system is sexagesimal (based on 60, but then consider our culture 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day).

They system of counting is based on only two symbols: a simple mark, a wedge, to indicate 1 and a double wedge to indicate 10. They aggregated these symbols to represent anything from the value of 1 to that of 59.

As a result of having only two symbols: they had multiple meanings. A single wedge could take on a variety of meanings: 1 60, 120, etc.etc.


Babylonian Representation of Numbers

The Babylonian system of counting was relied on a sexagesimal base. Zero evolved as a symbol or placeholder for the beginning of the next set of 60.
The Babylonian system of counting was relied on a sexagesimal base. Zero evolved as a symbol or placeholder for the beginning of the next set of 60.

Babylonian Numeric Inscription is a Translation of an Abacus

Many ancient cultures had "counting machines", what today we ould refer to as an abacus. Adding on an abacus is a simple process of moving stone or beads for one side to the other of a row. When there are no more stones to move on a certain row, the stones or beads are returned to the starting position in that row and a stone in the next higher row is advanced.

An Abacus

The use of a "counting machine" or abacus has been pervasive in many cultures throughout the ages. This is an example of an 18th Century English model.
The use of a "counting machine" or abacus has been pervasive in many cultures throughout the ages. This is an example of an 18th Century English model.

The Problem Dealing With Inscribing the Data

The problem was not that the Babylonians had not developed a symbol for sixty. The problem was that one could distinguish 60 from 120 and so forth on an abacus, but this concet is meaningless on a clay tablet. There was no way of known what that symbol meant. There "work around" was to use a new symbol a set of wedges to repent in writng the "empty space" in the abacus after the calculation was complete.

In Our Next Installment......

"nothing Comes of Nothing" we will discuss the rejection and superstition which surrounded zero for a very, very long time.

Even Today People Resort to Simple Tally Systems

Even today in sophisticated societies people use tallies. Generally the counting is by five reminiscent of finger counting.
Even today in sophisticated societies people use tallies. Generally the counting is by five reminiscent of finger counting.

Sources and For Further Reading

Boyle, David (2001). The Sum of Our Discontent: How Numbers Make Us Irrational. New York: Texere. ISBN 1-58799-060-1.

Niven, Ivan, Zuckerman, Herbert S., and Montgomery, Hugh L. (1991) An Introduction to the Theory of Numbers. 5th Edition. ISBN 0-47162546-9.

Seife, Charles (2000). Zero: The Biography of a Dangerous Idea .New York: Penguin Books. ISBN 0-670-88457-X.



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