The Power of Zero

Why do we count to ten? Because we have ten fingers*. That’s one of the things I learned recently which, when someone said it, made absolute sense. That’s why we have ten times table, and everything is broken down this way today … apart from binary 1’s and 0’s, which is probably because technologists only have one finger.

Talking of 1’s and 0’s, I hadn’t thought about it until listening to David McWilliams book about money that is was the invention of zero that changed everything in math, as we could now talk not just tens, but hundreds, thousands and more. Before, it was just M’s, X’s, C’s and L’s.

No-one used the number zero much until the seventh century. Then it started to be used in trade in India. The innovation of having a zero led to widespread usage around the Fertile Crescent of Northern Africa and the Middle East. Then, finally, it spread to Europe as trading markets were linked from East to West through Sicily.

It’s difficult to explain the power of zero, but the reason it became so integral to modern finance, economics and mathematics is thanks to a guy named Fibonacci, a trader from Pisa who wrote a book, Liber Abaci, about calculations way back in 1202. It was the first business book for merchants and bankers ever produced, as it explained how to use ledger systems, interest rates, the time value of money and, oh yes, the use of the number zero.

How did he learn all of this?

Well, Fibonacci’s father was Guglielmo, an Italian merchant and customs official. Guglielmo directed a trading post in Béjaïa in modern-day Algeria, and Fibonacci travelled with him as a young boy. It was here where he was educated and learned about the Hindu–Arabic numeral system using the power of zero which, at that time, was by traders from Europe and elsewhere. The use of zero to break-up numbers into bite-size chunks that could grow from zero to infinity was a massive breakthrough, and revolutionised how merchants traded. It led Europe out of the Dark Ages and into the Machiavellian Da Vincian Florentine world of the Renaissance.

Why?

Because zero allowed far more innovative trading using buying and selling than there had ever been before. The History Channel explains it well:

It might seem like an obvious piece of any numerical system, but the zero is a surprisingly recent development in human history. In fact, this ubiquitous symbol for “nothing” didn’t even find its way to Europe until as late as the 12th century.

Zero’s origins most likely date back to the “fertile crescent” of ancient Mesopotamia. Sumerian scribes used spaces to denote absences in number columns as early as 4,000 years ago, but the first recorded use of a zero-like symbol dates to sometime around the third century B.C. in ancient Babylon. The Babylonians employed a number system based around values of 60, and they developed a specific sign—two small wedges—to differentiate between magnitudes in the same way that modern decimal-based systems use zeros to distinguish between tenths, hundreds and thousandths. A similar type of symbol cropped up independently in the Americas sometime around A.D. 350, when the Mayans began using a zero marker in their calendars.

These early counting systems only saw the zero as a placeholder—not a number with its own unique value or properties. A full grasp of zero’s importance would not arrive until the seventh century A.D. in India. There, the mathematician Brahmagupta and others used small dots under numbers to show a zero placeholder, but they also viewed the zero as having a null value, called “sunya.” Brahmagupta was also the first to show that subtracting a number from itself results in zero.

From India, the zero made its way to China and back to the Middle East, where it was taken up by the mathematician Mohammed ibn-Musa al-Khowarizmi around 773. He studied and synthesized Indian arithmetic and showed how zero functioned in the system of formulas he called ‘al-jabr’—today known as algebra. By the 10th century, the zero had entered the Arabic numeral system in a form resembling the oval shape we use today.

The zero continued to migrate for another few centuries before finally reaching Europe sometime around the 1100s. Thinkers like the Italian mathematician Fibonacci helped introduce zero to the mainstream, and it later figured prominently in the work of Rene Descartes along with Sir Isaac Newton and Gottfried Leibniz’s invention of calculus. Since then, the concept of “nothing” has continued to play a role in the development of everything from physics and economics to engineering and computing.

In other words, without a zero, we wouldn’t have today’s world. There would be no banking or global trade. There would be no national and regional governments. There would be no air travel or space travel. There would just be no nothing, except a zero … which we hadn’t invented and that’s why it was called, pre-zero, the Dark Ages.

 

* Interestingly, the ancient Babylonians counted in units of sixty because it had clear composite numbers, which is why we have sixty seconds in a minute, sixty minutes in an hour and 360 degrees in a circle. Gawd knows why we have 24 hours in a day though.

** Although many say that India invented the zero, there are debates about this as the concept of zero has been independently discovered and developed by many ancient civilizations including the Mayans, Babylonians, Indians, and Chinese. However, the credit for the discovery of the number zero as a numerical digit is generally attributed to the ancient Indian mathematicians.