Counting before numbers
數字(發明)前的計數
Before the invention of written numbers, people used many different ways to count things.
在數字發明之前,人們采用不同的方式來對東西計數。
At first, people used their fingers, and even their toes.
一開始,人們用他們的手指,連同自己的腳趾。
However, they could only count small numbers in this way.
然而,他們也只能指望這樣來計算小的數字。
After that, they began to make small marks on sticks and bones.
后來,他們開始用棍棒和骨頭制作一些小物件。
This helped them count bigger numbers.
這有助于依靠它們計算更大的數字。
They used them to count things like the days of the month, the amount of food and the number of animals they had.
他們依此來計算如每個月天數、他們擁有的食物和動物數量(那樣的數字)。
Then people began to use tokens made from clay or small stones.
再后來人們開始使用由粘土或小石塊做成小物件。
This helped them count even bigger numbers.
這可以用來計算更大的數字。
They often put the tokens on pieces of string so that they could carry them around easily.
他們通常會它們穿成串兒,以方便他們攜帶。
This developed into tools like the abacus.
這就發展成了如算盤的工具。
Finally, people began to develop systems of written marks to show different numbers,
最后,人們開始擴展文字系統,用來顯示不同的數字,
and this led to the Hindu-Arabic system (0-9).
于是產生了印度 - 阿拉伯數字(0-9)。
We are still using this system today.
直到今天,我們仍然在使用這套(數字)系統。