Numbers who invented

Early humans in the Paleolithic age likely counted animals and other everyday objects by carving tally marks into cave walls, bones, wood or stone. Each tally mark stood for one and each fifth mark was scored through to help keep track. As early civilizations developed, they came up with different ways of writing down numbers.

Many of these systems, including Greek, Egyptian and Hebrew numerals, were essentially extensions of tally marks. The used a range of different symbols to represent larger values. For example, in the Ancient Egyptian system, a coiled rope represented and a water lily represented Each symbol was repeated as many times as necessary and all were added together, so under the Ancient Egyptian system, would be shown as three coiled ropes.

As the number of batteries in the line increased, so did their errors. They are learned, acquired through cultural and linguistic transmission. And if they are learned rather than inherited genetically, then it follows that they are not a component of the human mental hardware but are very much a part of our mental software—the feature of an app we ourselves have developed.

It comes indirectly from my work on languages in the Amazon. In the book, you talk at length about how our fascination with our hands—and five fingers on each—probably helped us invent numbers and from there we could use numbers to make other discoveries. So what came first—the numbers or the math? There are obviously patterns in nature. There are lots of patterns in nature, like pi, that are actually there.

These things are there regardless of whether or not we can consistently discriminate them. When we have numbers we can consistently discriminate them, and that allows us to find fascinating and useful patterns of nature that we would never be able to pick up on otherwise, without precision. Numbers are this really simple invention. These words that reify concepts are a cognitive tool.

Without them we seem to struggle differentiating seven from eight consistently; with them we can send someone to the moon. A lot of people think because math is so elaborate, and there are numbers that exist, they think these things are something you come to recognize.

Another interesting parallel is the connection between numbers and agriculture and trade. What came first there? I think the most likely scenario is one of coevolution. Marcus du Sautoy, a professor of mathematics at the University of Oxford, said, "Today we take it for granted that the concept of zero is used across the globe and is a key building block of the digital world. But the creation of zero as a number in its own right, which evolved from the placeholder dot symbol found in the Bakhshali manuscript, was one of the greatest breakthroughs in the history of mathematics.

The findings show how vibrant mathematics have been in the Indian sub-continent for centuries. Over the next few centuries, the concept of zero caught on in China and the Middle East. According to Nils-Bertil Wallin of YaleGlobal , by , zero reached Baghdad where it became part of the Arabic number system, which is based upon the Indian system. A Persian mathematician, Mohammed ibn-Musa al-Khowarizmi, suggested that a little circle should be used in calculations if no number appeared in the tens place.

The Arabs called this circle "sifr," or "empty. Al-Khowarizmi also developed quick methods for multiplying and dividing numbers, which are known as algorithms — a corruption of his name. Zero found its way to Europe through the Moorish conquest of Spain and was further developed by Italian mathematician Fibonacci, who used it to do equations without an abacus, then the most prevalent tool for doing arithmetic.

This development was highly popular among merchants, who used Fibonacci's equations involving zero to balance their books. Medieval religious leaders in Europe did not support the use of zero, van der Hoek said. They saw it as satanic. Everything that was not was of the devil," she said. Wallin points out that the Italian government was suspicious of Arabic numbers and outlawed the use of zero.