A brief history of numbers and counting, Part 2: Indian invention of zero was huge in development of math

Published: Monday, Aug. 6 2012 10:00 a.m. MDT

The most revolutionary advance in numbers since the Sumerians invented math: zero. (Shutterstock.com) The most revolutionary advance in numbers since the Sumerians invented math: zero. (Shutterstock.com)

Under the curious minds of the ancient Greeks, beginning with Pythagoras, who brought with him new concepts he learned during his time in Egypt, mathematics rose to a highly evolved level of theoretical mathematics, which ushered in a golden age of math.

But, the Greek’s role in mathematics ended, quite literally, with Archimedes, who was killed by a Roman soldier during the Siege of Syracuse in 212 BC. Under the rule of Rome, mathematics entered a dark age, and for a couple different reasons.

The main reason was that Romans simply weren’t interested in mathematics (they were more concerned with world domination), and secondly, because Roman numerals were so unwieldy, they couldn’t be used for anything more complicated than recording the results of calculations. Romans did all their calculating on a counting board, which was an early version of an abacus. And because of that Roman mathematics couldn’t, and didn’t, go far beyond adding and subtracting. Their use of numbers was good for nothing more than a simple counting system. The Romans' use of numbers was no more advanced than the notches on the Ishango Bone. There’s a good reason there are no famous Roman mathematicians.

The next big advance (and it was a huge advance) in the world of numbers and mathematics came around 500 AD in India. It would be the most revolutionary advance in numbers since the Sumerians invented math. The Indians invented an entirely new number: zero.

Under Hinduism, the Indians possessed concepts such as Nirvana and eternity. These are some very abstract concepts that need some abstract math to help describe them. Take for instance a Rajju. A Rajju is the distance that a deity can fly in a six-month period. Or a Palya, which is the length of time it would take to build a cube of lamb’s wool 10-km high if you were to lay one strand of lamb’s wool every century. Try expressing that idea with Roman numerals.

The Indians needed a way to express very large numbers, and so they created a method of counting that could deal with very large numbers. It was they who created a different symbol for every number from one to nine. They are known today as Arabic numerals, but they would more properly be called Indian numbers, since it was the Indians who invented them. The Indians have been using “Arabic” numbers them since about 500 BC.

Once zero was invented it transformed counting, and mathematics, in a way that would change the world. Zero is still considered India’s greatest contribution to the world. For the first time in human history the concept of nothing had a number.

Zero, by itself, wasn’t necessarily all that special. The magic happened when you paired it with other numbers. With the invention of zero the Indians gained the ability to make numbers infinitely large or infinitely small. And that enabled Indian scientists to advance far ahead of other civilizations that didn’t have zero, due to the extraordinary calculations that could me made with it. For example, Indian astronomers were centuries ahead of the Christian world. With the help of the very plastic and fluid Arabic numbers, Indian scientists worked out that the Earth spins on its axis, and that it moves around the sun, something that Copernicus wouldn’t figure out for another thousand years.

The next big advance in numbers, the invention of fractions, came in 762 AD in what is now Baghdad — and what was then Persia. The Persians were Muslims, and it was their adherence to the Koran and the teachings of Islam that led to the invention of fractions.

The Koran taught that possessions of the deceased had to be divided among their descendants. Unlike Christianity at the time, Islam — which was scarcely 100 years old at the time — divided belongings among women as well as men. But women got a lesser share. Working all of that out required fractions. But prior to 762 AD they didn’t have a system of mathematics sophisticated enough to do a very proper job. Enter Arabic numbers.

It’s not known for certain how Arabic numbers came to the Islamic world, but the most prevalent theory states that one day an ambassador from India arrived in Baghdad and presented the Kaliph with the greatest gift he could think of: Arabic numbers.

Using Arabic numbers Muslim mathematicians invented entirely new methods of mathematics. Beside just simple fractions they turned Arabic numbers into quadratic equations, and algebra, and these numeric breakthroughs enabled science, mathematics and astronomy to reach new levels in the Middle East.

By 1200 AD, Arabic numerals made their way to North Africa, and from there, thanks to the curious son of an Italian merchant, they would soon make their way to Europe.

Leonardo Pisano Bigollo, who would later be known as Fibonacci, had been raised using Roman numerals. He was first introduced to Arabic numbers in Algeria while traveling with his merchant father. Fibonacci became enthralled with this new method of counting, and its very practical and plastic abilities. He introduced Arabic numbers to Europe when he returned to Italy. In 1202 he published a book of mathematics called "Liber Abaci" and it was through that book that Europe was introduced to Arabic numbers.

The Roman numeral system was deeply entrenched in Europe, and it took awhile for the Arabic system to catch on. The name for zero in Italian was cipha, and it was regarded with such suspicion that it became the word for secret code: cipher. What finally caused the Arabic number system to catch on was good old-fashioned human greed, and a merchant class that could use it to quickly, easily and more precisely calculate interest on their goods and properties.

Prior to the Catholic Reformation, Christians weren’t allowed to charge interest on loans because the Catholic Church said it was a sin to do so. But after the Catholic Reformation charging interest was allowed and the merchant class quickly adopted the new Arabic system because interest could be calculated out to 12 decimal points, which worked to the advantage of the merchants. An abacus, the old system of counting under the Romans, could only calculate interest out to two decimal points.

From there, use of Arabic numbers spread to conquer the world.

The next big evolution in numbers came in Germany in 1679. German mathematician Gottfried Liebnitz invented a system of counting that used only ones and zeros; what would eventually be called the binary system. In the binary system ones stand for something, and zeros stand for nothing.

Liebnitz even went so far as to design a machine that would count in binary. The digital age, it seemed, had arrived. But — and this is big — though he designed his binary machine he never built it, and the world would have to wait another 265 years before one and zero would usher in the modern world.

The machine that would usher in the digital age was named Collosus, built in England in 1944, during World War II, as a code-breaking apparatus. Colossus was able to perform millions of rapid calculations, and with its help the Allies cracked numerous Nazi codes. Thanks to Collosus, Ally code-breakers often knew what the Germans said even before Hitler did. Some experts believe that Collosus may have shortened the war by as much as two years.

From there the binary system was adopted and used in every computer ever built. Computer code has literally made possible the Internet, space exploration and indeed modern life.

To read additional science stories by Steven Law go to www.curiosity101.com

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