The history of zero
The numeral zero is one of history's most important inventions
The numeral zero is one of the most significant inventions in human history. Early numeral systems worked for basic counting, but they were awkward and inadequate for complex operations like multiplication, division, and advanced arithmetic. Concepts such as calculus couldn’t even be conceived using these early systems.
Zero revolutionized mathematics, enabling advanced algebra, calculus, exponential numbers, and more. Computers, nuclear physics, space exploration, modern statistics, and all the innovations derived from advanced mathematics rely on the numeral zero.
The Development of Zero
The history of zero is long and intricate, with different cultures inventing it at different times. The Hindu-Arabic numeral system, which we use today (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), includes zero as both a number and a placeholder. This system, through positional notation, enables us to express numbers like 10, 100, or 203, where zero serves as a place marker.
Without zero, numbers become difficult to express and manipulate. Adding a zero to 100 gives 1000, simplifying calculations like dividing by 10 and representing large numbers. We take these conveniences for granted today, but this wasn’t always the case.
Numeral Systems Before Zero
Early numeral systems had no symbol or even concept for zero. Many required a unique symbol for every new base number, such as 10, 20, 30, etc. This created unwieldy, complicated numerals and made division and calculation challenging.
Consider trying to subtract 103 from 1,504 in a system like Roman numerals (MDIV - CIII). This calculation is messy compared to the ease of using the decimal system.
The earliest numeral system, used by the Sumerians, lacked a marker for zero. Without zero, the number ‘11’ could represent 11, 101, 1,001, or 10,001. Zero resolves this ambiguity.
The Babylonians, who inherited the Sumerian system, began using a space to indicate the absence of a number, a primitive form of zero. For example:
11 (no space between the one symbols) = eleven
1 1 (one space between the one symbols) = one hundred one
1 1 (two spaces between the ones) = one thousand one
However, spaces alone were problematic because it was often unclear how many spaces were between symbols.
The Babylonians eventually invented a placeholder symbol to mark these spaces, effectively serving the same function as zero in their system.
Other Cultures' Contributions
Several early cultures independently invented their own placeholder symbols. The Mayans used a shell-like symbol, while the Khmer people used a dot. The earliest known use of a zero symbol as a decimal figure comes from Khmer numerals, dating back to 683 AD.
However, these early systems still didn’t consistently use their zero or placeholder symbol after numerals. Without this consistency, it was still unclear whether a numeral represented 11, 110, 1,100, or even 11,000.
Counting devices like the Inca Quipu, Asian rod counting boards, and the abacus utilized spaces or blank spots to denote nothing in a digit column, serving the same function as zero.
Zero as a concept and symbol
Zero began as a simple place marker but gradually developed into a full-fledged concept and number. While early cultures understood the idea of "nothing," the abstraction of "nothing as something" took much longer to develop.
Indian mathematicians were the first to fully understand zero as both a symbol and an idea, influenced by the Buddhist and Hindu philosophical focus on emptiness. The word "zero" comes from the Hindu term "sunyata," meaning nothingness.
Brahmagupta, an Indian mathematician and astronomer, further developed zero and formulated arithmetic rules involving it. He established the rules for reaching zero through addition and subtraction and laid the groundwork for operations with negative numbers. However, division by zero, an issue Brahmagupta couldn’t resolve, was addressed centuries later by Isaac Newton and Gottfried Leibniz.
The Spread of Zero to Europe
Zero took time to reach Europe. In the 8th century, Arabian sailors brought Brahmagupta’s work to Baghdad, where it was further developed by Arabian mathematicians. By 879 AD, zero had evolved into a small oval shape.
In the 12th century, Italian mathematician Fibonacci introduced zero and Hindu-Arabic numerals to Europe. This system replaced the abacus, the common tool for arithmetic, and soon spread across Europe, especially among accountants and bankers. Zero was crucial for balancing books and understanding financial accounts.
Resistance to Zero in Europe
Medieval European religious leaders resisted the use of zero, believing that if God represented everything, then nothingness (zero) must be linked to the devil. Despite such opposition, merchants often covertly used zero in their transactions.
Zero in Modern Science and Mathematics
French philosopher and mathematician René Descartes further advanced the concept of zero by introducing the Cartesian coordinate system, which uses zero (0,0) as the origin for graphing functions.
Though adding, subtracting, and multiplying by zero are straightforward, division by zero long puzzled mathematicians. Newton and Leibniz tackled this problem in the 1600s by inventing calculus. Calculus studies change over time, using concepts like limits as values approach zero. This breakthrough has been crucial for understanding motion, electricity, heat, light, and countless other phenomena. Calculus continues to be essential in fields ranging from physics to economics to computer science.
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David, Another thought provoking and educational writing by you! Thank you! Have you considered an article on the number 3 and possible connections with the metaphysical significance of the number 3 and the development of Christianity's Doctrine of the Trinity?