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The discovery of ‘zero’ and why it matters

Today it seems obvious and self-evident, but the existence of ‘zero’ escaped from the mathematicians’ and the philosophers’ imagination for centuries. It is not clear when it was first discovered (some might say invented), nor by whom, in part because its use has been subjected to many changes throughout centuries and also because it appeared in many parts of the world; either as an independent discovery or carried over from civilization to civilization. It is considered to be one the most important discoveries of human thought and without it mathematics would have stuck in 600 AD, with algebra not becoming able to find ways to expand into truly abstract ideas that would allow the use of negative numbers, whose usability had not been identified in antiquity.

While mathematicians started thinking about the concept of zero around 3,000 BC (and rejected it), it was not before 200-300 BC that the Babylonians used a symbol that evolved into what we now know as ‘zero’. The Babylonians changed the form of the symbol many times, from two parallel lines to these:

zero 1eng

In the time when mathematics was merely a method to count physical objects and solve problems of daily experience, there was no need for such a number. In order for someone to say he has “0 camels” he would just say “I don’t have camels”. There is already a large leap of reason from “5 camels” to “5 objects” and to the more abstract “5”. Moreover, the use of zero allowed us to think of mathematics as something abstract, and not only as a method to measure things.

First known depiction of zero as am indicator (two parallel lines), in the city-state Sumer of Mesopotamia, 5,000 years ago. (photo)
First known depiction of zero as am indicator (two parallel lines), in the city-state Sumer of Mesopotamia, 5,000 years ago. (photo)

Later, somewhere between 400 and 1200 AD, the concept of zero evolved, and it was accepted that it meant a number. If this belated reception of zero as a number still seems peculiar to you, consider that for a long time even ‘1’ wasn’t deemed to be a number. It was thought that a number of things had to mean many things at once. So, when there was 1 camel, there was just “a camel”. Only with the appearance of a second camel did the need to count them arrive.

The basic idea in the case of zero was the creation of a number for “nothing”. The important idea was the notion of a new kind of number, which would represent the specific idea of “nothing”.

Initially, zero was used as a punctuation mark, as an indicator, as a means to solve the problem of writing a number with many digits. Without zero, the number 2046 would be written as 246, as would the number 2460. Only using context could someone understand the difference. This is not as strange as it sounds. When, today, someone replies “Two and a half” to the question “How much for an ice-cream?” we understand “2.5 euros”, while the same answer to the question “What time is it?” means something completely different. Context makes all the difference. Here, the zero is not exactly used as a number yet, but as a mark showing us the meaning of whatever is written on paper. More accurately, the number 2046 means we have 2 thousands, 0 hundreds, 4 tens and 6 units.

The discovery of zero allowed us to also construct the negative numbers, which were also not needed for a period. There was no need to know about negative numbers when we were counting camels. Negative camels would mean debt in camels. Fibonacci, around 1,200 AD, allowed negative results in problems that preoccupied him concerning financial issues, and he interpreted them as debt or loss, instead of the profit that a positive number signifies.

An example of the use of zero in ancient Greek (bottom right corner) (photo)
An example of the use of zero in ancient Greek (bottom right corner) (photo)

The ancient Greeks, even though they made great progress in mathematics, used geometry as a basis for their theories. There was no need to think abstractly about numbers, as they counted lengths of lines and circumferences. So they did not think about ‘zero’ even as an indicator (as the Babylonians did before them). There were exceptions, like some astronomers and, later, Ptolemy in the 2nd century AD (in Almagest), who used the symbol “O”, but only as a punctuation mark.

The Indians adopted it, and in 7th century AD they made the first use of negative and decimal numbers, leading it to a more sophisticated form that is similar to the modern one. So, they used it both as a number, meaning a symbol that represents something (this “something”, here, is the “nothing”), and as an index. Some say it is the notion of nothingness (or insignificance) referred to in philosophical texts of the East that this umber was ascribed to. The word “shunya”, which meant “void”, “nothing”, something like “salvation”, is the word they used for the number ‘zero’. But it was the Arabs who evolved its usage developing algebra, and spread it during the ‘golden age of the Arabs’ (roughly between 8th and 12th century). The English word “zero” comes from the Arabic word “sifr”.

In the center of the image we can discern the number 270, exactly as we write it today. This is the first depiction of zero as a number, in the Ganesh temple, in the city Gwalior of India (9th century AD). (photo)
In the center of the image we can discern the number 270, exactly as we write it today. This is the first depiction of zero as a number, in the Ganesh temple, in the city Gwalior of India (9th century AD). (photo)

The adoption of zero in relation to the Arabic numbers that replaced the Latin ones, allowed for the quick and easy modern method of multiplication and division. Imagine the multiplication table in Latin numbers… But their spread was hindered by religious prejudice, as the Arabic numbers were considered too easy to manipulate in order to commit forgery or deception (the number 1 is easily transformed into the number 7) and the negative numbers (that would not be discovered without the zero) were deemed blasphemous by associating them to profit made from gambling and usury that creates debt. Besides, nothingness was identified with chaos and the void, elements of hell in the Christian tradition. The use of negative numbers was spread just in the 16th century AD.

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