COUNTING BEFORE NUMBERS
Mathematics is as old as human civilization. Mathematics and counting are much older than discovery of numbers. Mathematics originated because there was a need to:
1. measure areas of land
2. measure lunar cycles
3. measure cycle of flooding of rivers (Nile)
4. study various patterns
5. keep account of number of sheep (or animals)
6. keep account of loans
Mathematics originated thousands of years B.C. It is believed that human civilization started at the banks of river Nile. People started farming and found that after regular intervals the flooding of Nile takes place. Then the humans started keeping account of the duration/cycle of flooding of Nile. It was also found that moon changes its shape and full moon comes after regular intervals. Change of seasons etc. were another regular features from where the first calendar calculations started.
Siberian Shepherds realized that they need to keep account of their sheep, so that no sheep gets missing from the flock. It is easy to distinguish between 2 and 3 sheep/objects or between 3 and 4 sheep/objects. Even the animals have the sense of counting. Animals can also distinguish between 2 and 3 objects or 3 and 4 objects. For example, suppose there are 4 eggs in the nest of a bird and one goes missing then the bird will surely come to know and will start looking for the missing one. But if there are hundreds of eggs then it is impossible for a bird/animal to distinguish if one or two goes missing, it means that birds and animals have sense of counting but only upto certain extent. Similarly for Siberian Shepherds it was easy to distinguish if the number is less. But for a big flock of sheep Siberian Shepherds started keeping a track using one to one correspondence (which was later used by George Cantor to study size of infinity). Siberian Shepherds started putting one pebble for one sheep into an urn when the sheep goes for grazing. When the flock of sheep us to come back Shepherds use to throw one stone out of urn for each sheep and if they find that any stone is left in the urn at the end then it meant that those many sheep went missing. So this is how Siberian Shepherds use to count much before the discovery of numbers.
Since we can easily distinguish between the objects upto 4, this the reason that in bar gate method after putting four bars we put a gate so four bars and a gate means 5.
Later when human civilization developed and it was realized that the account of loans has to be kept. In early attempts records were kept by putting the bars on wooden sticks known as tally sticks, where number of bars represent the number of articles lent. Then the problem started coming, who will keep the tally stick (also known as stock), if the person who took the load keeps the stick then he may erase one or two bars and if the person who gave loan keeps it then he may add one or more lines. In order to avoid such problems These sticks were split in two so that the two sides to an agreement had a record of the situation when the loan was to be re paid then both parts of the sticks were matched.
It is believed that the word STOCK Exchange & bank STOCK originated from there only. The London fire or the burning of Parliament in 1834 was due to the fact that all the old bar sticks kept for official records were to be burnt and when the sticks kept in the parliament were burnt the wall of the Parliament caught fire and it burnt.
There was another way of keeping such records, pebbles use to be put into a soft clay jar where each pebble represent the article lent and after the transaction the soft clay jar was sealed and gets hardened. During repayment, the same vessel use to be broken and the repayment was done on the basis of number of pebbles in the clay jar.