Appliance of Science: Where did numbers come from?

By Dr Naomi Lavelle

Seven-year-old Lile from Bray, Co Wicklow, has counting on her mind and she sent me this question. “Who made up numbers and when do they stop?” It seems numbers and some form of counting go back a long way.

Archaeologists have discovered bones with scratch marks on them, considered a primitive form of counting. These bones are about 150,000 years old.

No one person or civilisation made up numbers. Lots of different number systems have been created all over the world, throughout history. Many of these are no longer in use but some still remain.

The most commonly used number system today is called the Hindu Arabic number system. It uses just 10 symbols or digits to express any (rational) number imaginable. Those digits are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

This number system is called a base 10 system.

BASE SYSTEMS

Over the years there have been lots of base systems. The Romans developed a base 5 counting system. Aztecs used a base 20 system and the Babylonians used a base 60 system.

We have other base systems in use in our daily lives too, for example digital equipment, like our computers, use a base 2 system; coding and storing information using just zeros and ones.

We use a base 12 system for keeping time and measuring angles.

NUMERICAL HISTORY

How did we get from lines on bones to a base 10 system?

As cultures and societies advanced so too did their way of counting and thinking in numbers. You may not need too many numbers if you live in a cave, but once you start grouping together and building structures and civilisations then numbers become important.

Ancient Egyptians are known for the amazing structures they built, such as the pyramids. These structures show they had a well-developed number system; without such mathematics they would not have been able to accurately build the pyramids.

They used a base 10 system, with seven symbols.

The Romans used a system that had five symbols, making it more complex to express larger numbers. This system was dominant in many parts of Europe for over 500 years.

A major advance in modern mathematics was the invention of a symbol for zero and its use in calculations. Indian mathematicians are credited with developing it in the fifth century AD.

WHAT WOULD HAPPEN IF WE HAD NO NUMBERS

We need numbers for all our everyday living. However, it seems not everyone uses them. The Piaha are an indigenous Amazonian tribe and anthropologists have discovered they have no words for numbers.

WHEN DO NUMBERS STOP?

The answer is that they don’t. If you think about it, any number we can come up with, we can always add one. Numbers and counting are never ending.

However, we do like to give names to big numbers, like a million and a trillion.

One of the biggest numbers with a name is called a googolplex and if you wanted to write it you would write one, with 100 zeros after it. The company Google took its name from this.

A number called Graham’s number is said to be so enormous that there is not enough room in the universe to write it!