Folha: ‘Before being a number, zero was a symbol of absence’
Reproduction of Marcelo Viana’s column in Folha de S. Paulo.
A journalist friend sent me an article by a young neuroscience researcher, Benjy Barnett, on a fascinating topic: on a neurological level, how does our brain represent the number zero? Behind this is the broader question of how the human mind understands nothingness, the absence of something. What happens in our brains when we look at a tree and realize that there are no birds in the branches? The answer is an important ingredient in understanding what constitutes human consciousness.
Zero is a separate number with a unique history. The numbers before it arose in response to two practical needs: counting and measuring. The first gave rise to arithmetic, the science of natural numbers (1, 2, 3…). The second gave rise to geometry, which relates to positive numbers, both rational (fractions) and irrational. None of them need zero. After all, as the English mathematician and philosopher Alfred Whitehead (1861 – 1947) pointed out, “nobody goes to the store to buy zero fish”.
The motivation for the concept of zero had a very different origin: the discovery of the positional method of numbering. The idea is brilliant: instead of using new symbols every time we need to represent larger and larger numbers, as the Egyptians, Greeks and Romans did, we now always use the same symbols (currently 0, 1, 2, …, 9) but allow them to take on different values depending on their position. For example, in the number 233, the digit 3 in the middle is worth thirty while the one on the right is worth three. As well as being economical, the positional system also revolutionized the calculation of operations – addition, multiplication and even radication – by putting them within everyone’s reach.
On the other hand, a difficulty arises when we come across numbers in which some position is empty: for example, 203 has no tens and 230 has no ones. In early positional systems, this type of situation was ignored, with both numbers being represented by 23, which was clearly unsatisfactory. A special symbol had to be created to signal empty positions!
This was first done in Sumer 5,000 years ago. But the symbol (0) we use today for this purpose dates back to the beginning of our era in India, where it was called “chunia” (“emptiness” or “nothingness”). At that time, it wasn’t yet considered a number: it was just a symbolic representation of absence (of units, tens, etc.). The new concept would only begin to be treated as a real number in the 7th century, when the Indian mathematician Brahmagupta (598-668) explained how to do operations with it. It arrived in Western Europe during the Middle Ages, at the hands of the Arabs, and was popularized by the “Book of the Abacus” by the Italian Leonardo Fibonacci (1170-1250). Fibonacci called it “zephirum”, from which we get our “zero”.
Read the full column on the Folha website.