## NATURAL NUMBERS

##### Why are these numbers called Natural?

Image of Ishango bone, dated 20000 years back discovered in Congo, with three columns of notches and speculated to belong to a very advanced civilization.

The journey of the human species with Natural numbers is similar to a toddler learning to count. This story probably begins with our first ancestors in the African continent. Australopithecus, is considered to be our first ancestor because they were the first to walk on two legs. They would be the first to need counting. Four million years back the ecosystem around them in Africa started to dry up due to climate changes and the tree tops could not provide enough food. The weaker ones started to move out in search of food and slowly started to walk on two legs. This helped them to cover more distance and and also could sight danger. They became scavengers on the animals that also died in this drought. Here they had come back and communicate what they saw. Probably that was the first need for counting and they probably did that using their fingers.

Now meat eating developed their brains and also their bodies and 200,000 years ago saw the first of homosapiens. They started using stones and sticks for larger numbers though never counted and depended on the relative size. This is similar to many animals today and even human 3 year olds.

The next phase saw tally bones like Lembogo bone and Ishango bone. The Lembogo bone discovered today has 29 notches though it is broken on a side. It is speculated to be a tool for a woman monitoring her menstrual cycle and dated to around 40,000 years. The Ishango bone though seems to be a advanced tool from a village in the Congo and Uganda border. Three columns with notches still puzzle archeologist and mathematicians. Some feel it is from an advanced civilization and few believe it is just a random markings by someone.

Finally, after the last ice in 11,000 BC, man who was a hunter gatherer started to settle down along the banks of three major rivers, The Nile, The Euphrates-Tigris and Indus River after inventing agriculture and also taming animals. This helped some men to to focus on science and technology. They started to become ambitious and started building temples and step Pyramids. And here mathematics and numbers also had to catch up. Every one of these civilization started to develop large numeral systems.

Now these were all different from each other. The Egyptians had a primitive system which never had a place value. This meant that symbols were required for every power of 10 and they had to be repeated over to get the number. For eg. To get the number 1234, the symbol for 1000 was repeated once, 100 was repeated twice, 10 repeated thrice and the symbol for 1 repeated once.

Now the Babylonians had a far superior number system which was positional. They needed only two symbols. A line for 1 and wedge shaped symbol for 10. They had a base 60 number system and used these symbols to give apt value for different place values. This had so much of influence that we still use this base for calculation of Time and Angles in Geometry.

Though in the end of all this, these large numeral systems could only be used to represent numbers and could not be used to do arithmetic on paper. These civilizations used the Abacus for this and the oldest Abacus is dated to around 2400 BC in Babylonia though it was a rather primitive one. The drawback was that these arithmetic were done by the privileged and we had to wait for the discovery of Zero which would empower all and also revolutionaries mathematics.