Finger counting-a computer that grows on the body

Before the germination of civilization, human ancestors did not have the concept of "number" in the vast virgin forest. They knew this tree and that tree, but they did not have the concept of which tree it came from or how many trees there were in a certain range.

When the ancestors gradually realized counting, it was initially limited to a very small number. They use specific parts of the body, such as nose for 1 and eyes or ears for 2. Before liberation, the cultural development of some ethnic groups in China was relatively slow. They can only count to 3 or 10 at most. After that, I couldn't count them. I just called them "duo". Abroad, some tribes in Australia, Papua New Guinea and Brazil do not use two or more numbers to define their names.

People are not good at counting by nature, and it is easy to subconsciously classify numbers above 3 as "many"

This is like, without conscious statistics, when one or two people say that you look good, you will remember that one or two people say that you look good. When three or four people say this, your impression must be: Many people say that I look good!

However, after all, human beings have to deal with a lot. In addition to eating and drinking Lazarus every day, ancestors gradually need to face simple statistical problems such as "how many prey were caught" and "how many people were there in the tribe". They began to use all parts of the body, and finally our protagonist-fingers appeared.

Every primitive tribe has a set of internal general rules. According to statistics, at least 900 different limb counting methods have been found in Papua New Guinea alone. One of them is like this. The number 1~27 is represented by 27 parts of the upper body. In our opinion, this is much more troublesome than using numbers directly.

Of course, fingers and toes are the most widely used and the oldest. One finger/toe 1, two hands 10, one person 20. Because of this, many nationalities have used decimal system in history. In Tibetan, the word "person" has the meaning of 20; In French, 80 is quatre-vingts (4 20 yuan) and 90 is quatre-vingt-dix (4 20 yuan plus 10).

Compared with toes, fingers are more convenient and vital (still in use today), which is the fundamental reason why humans use decimal counting by default.

Relatively simple finger counting, usually one hand represents one number and the other hand represents ten numbers, which can directly represent 1~99.

A little more advanced, you can use finger segmentation. One theory holds that the 12 knuckles of ancient Babylonians represented 1~ 12 with one hand, and the five fingers of the other hand represented 5 times of 1 ~ 12, thus representing 1~60. This corresponds to the sexagesimal way in which cuneiform characters record numbers.

At a higher level, all kinds of gestures formed by finger bending and knuckle direction can be used to represent larger numbers. A typical example is a set of finger counting methods compiled by Italian mathematician luca pacioli in 1494.

I have to sigh the wisdom of human beings. In an era without external tools, fingers can count to millions or even millions. Now we often use hands to represent numbers in our lives, but basically we only count from 1 to 10, then from 1 1 to 20, and there are some simple gestures to represent special numbers such as 6 and 8.

However, it is not uncommon to express numbers only with fingers. Nowadays, the sign language used by deaf people can express extremely rich meanings besides numbers. If you want to call a finger a computing tool, you should at least realize the computing function. Fingers can really do some simple calculations, plus mental arithmetic, which can not only add and subtract, but also multiply and divide. China had a mature method of "hand calculation" in ancient times. In his book Arithmetic Unity, Cheng Dawei, a mathematician in the Ming Dynasty, recorded in detail the "golden palm" algorithm invented by a businessman in Qin Jin [1], and the calculation was completed by pointing his right hand at the knuckles of his left hand.

It can be said that the algorithm is in hand, and I have it all over the world. When businessmen go out to talk about business, they hide their hands in their sleeves (at that time, the algorithm was a trade secret and could not be easily revealed), swallow gold in their sleeves, count with their fingers and make the accounts clear. There is a song saying:

Although "manual calculation" is convenient, the numerical range that can be calculated is limited after all, and it needs to be combined with complex mental calculation formulas. Now some math teachers are keen to develop finger speed algorithms for children, which are indeed faster and more reliable than pure mental arithmetic. They can be used to develop intelligence, but they have been brought to the limit in practical application. It is this limitation of fingers that urges human beings to get rid of the shackles of body parts and move towards more advanced computing tools step by step.