What came first — maths or written language?

For those who hate numbers, maths is an acronym for Mentally Agitated Teachers Harassing Students.

But that’s of course not the whole story. “I think we grow up thinking that maths is very dry and all about passing exams, when really maths is one of the proudest achievements of our cultural heritage. When you learn the context of mathematical discoveries and can learn its charms without fear of
failing an exam, a whole world opens up,” says Alex Bellos, author of Alex’s Adventures in Numberland — Dispatches from the Wonderful World of Mathematics. In this interview, he speaks to DNA on the world of numbers.

How old are numbers?
Well, it depends on what we mean by
numbers. If we mean the ability to realise that two things are different from one thing, this is as old as humans are. If we mean a system of words and symbols for numbers, then this is only about 8,000 years old and originated in Sumer — present day Iraq.

How did numbers emerge?
Numbers emerged as a way to count objects, say sheep. Originally objects would have been counted by tallying — so, if you have 50 sheep, you might need to make 50 marks; or have 50 pebbles, so you know how many sheep you have when you are not with the sheep. But the Sumerians then started to make clay marks, where symbols referred to particular numbers. This was much more convenient.

What I find amusing is that these number symbols were the first examples in western culture of a script. So it is perfectly fair to say that written language, and therefore literature, was a consequence of numbers. Books are here because of maths!

In the first chapter of your book, you talk about some Amazonian tribes who can count only till five. Can you elaborate?
In my book I wanted to explain ‘where numbers come from’ — culturally, psychologically and neurologically. What is this ‘number instinct’ that we have? Some of the most interesting research comes from studies of Amazon tribes who have only a few numbers in their languages. I looked at one tribe in particular — the Munduruku, who only have words for one, two, three, four and five. In fact, the word for five is the same as the word for ‘handful’.

The studies try to see how good the Munduruku are at certain tests to do with numbers and amounts. The results show that while the Munduruku are unable to use exact numbers, they have an ability to estimate rough amounts, which is as good as the westerners’. This would appear to show that you can have this ‘number sense’ even if you don’t have numbers.

How did the decimal number system evolve?
When you come up with a number system, one of the first things you need to do is choose a ‘base’. This is the term used to describe the groupings of numbers. We have a base of 10, or decimal
system, because we group our numbers in (groups of ) 10.

While this seems obvious, there are lots of other cultures in history — and some still in existence — who use bases other than 10. There seems to be a very obvious reason why we use base 10 — and that is because we have 10 fingers (including thumbs). So, when we learn to count using our fingers, it is natural to group numbers in 10s. (Or fives, or 20s. And 5, 10 and 20 are the most common bases used by humans). If we had only four fingers per hand, we would undoubtedly have had eight as base. And if we have only three, we would have had six as base!

Why is time counted in base 60 and not 10?
This is a legacy of the Babylonians, who had a base 60 system. No one knows why they had that base, because it seems a bit crazy. But there is one way that having 60 seconds in a minute and 60
minutes in an hour is advantageous than if we had 100 seconds in a minute and 100 minutes in an hour. This is to do with the divisibility of 60. It is possible to divide 60 into 2, 3, 4, 5 and 6. And it is very convenient to split the hour into halves, thirds, quarters, fifths and sixths. On the other hand, you can only divide 100 by 2, 4 and 5.

You write that in ancient India “coining words for large numbers was a scientific and a religious preoccupation.” What did you mean?
I write about the ancient Indian approach to numbers in comparison to the Greek approach of roughly the same time.

The Greeks never went beyond a ‘myriad’, or 10,000. Sanskrit, however, had the word koti, which means a crore, or 1,00,00,000. In the Lalitavistara
Sutra, Buddha lists a word that means 10 followed 421 zeros, which is many, many more atoms than there are in the entire universe.

The ancient Indians used these big numbers to do their astronomical and astrological calculations. With higher numbers, they could do better astronomy and Indian astronomy was indeed ahead of its time. The other aspect of higher and higher numbers is religious. It is a way of getting closer to the gods, or eternity... 

How did the concept of zero evolve?  
My interest in this is the link between the invention of zero — made in India, probably around 400CE — and the Buddhist/Hindu mystical idea of ‘nothingness’.

In the West, we didn’t invent zero. We thought of nothing as, literally, nothing. But in India the idea that nothing was something was already a religious conviction, which helped bring about the mathematical idea.

Sudoku, it seems, was originally invented in the US. The Japanese saw it and ran with it. Can you take us through the entire Sudoku story?
Sudoku was originally called Number Place, and was invented by an American puzzle enthusiast called Howard Garns about 30 years ago. It was hardly noticed. Then a Japanese puzzle magazine editor, Maki Kaji, revamped the puzzle, called it Sudoku, placed the given numbers in a symmetrical pattern, and in the early 80s put it in his Japanese magazine.

Some more people noticed but not that many, and only in Japan. Then, about a decade ago a retired Hong Kong judge, Wayne Gould, who was holidaying in Japan, saw it and after spending several years working out a programme to
generate Sudokus, told The Times in London about it. Within months, it was an international phenomenon.

Was the success of Sudoku partly due to its exotic sounding name?
Absolutely! Sudoku sounds much more exciting than Number Place. We have this myth in the west of superior Oriental wisdom.

Alex Bellos can be contacted at www.alexbellos.com or www.twitter.com/alexbellos