Physical counting, knot counting, track counting, etc. The counting method of primitive society shows how to check the number of sheep returning from grazing with pebbles at that time; Count the number of prey by tying rope; Record the fishing amount by carving on wood and so on.
Number of chips: each chip represents 1, or 10, or 100, and so on.
Quotient code count
Interpretation of symbols used to represent numbers in China, also known as grass code and quotient code.
Besides, zero is still zero
The business word 〡〢〣〤〥〦〧〨123290.
Corresponding figures
Quotient code: 〡〢〣〤〥〦〧〨〩.
Chinese characters: 1234567890
Words: 1234567890.
Arabia: 1 23455 6789 10
write
1, just write a vertical one;
2, two vertical: 〢
3, three vertical: 〣
This is a cross: 〤
5, written as 〥, in fact, it is just five words written hastily.
6, written as a dot plus a horizontal, one of which stands for 5: 〦.
7. Write a little and add two horizontal lines: 〧
8. One point plus three horizontal lines: 〨
9, written as "long" grass: 〩
Use examples
Ancient people used an abacus to count. The above point is like the next child on the abacus indicating five, so 〦 is six and 〧 is seven, which is easy to understand. It should be noted that when "〡〢〣" meet, the middle will become a horizontal line. Otherwise, "|||" will not know whether it is one hundred and eleven, three, twenty-one or twelve. If you say 2 134, you should write 〢〣〤 at the age of 32, and write 〣〣.
The real use of these symbols should be combined with the characteristics of vertical writing of ancient account books. Otherwise, look at one more number, the difference is too big, and it is generally recorded as two lines.
For example, if the price is 50.9 cents, you can write:
〥〩
▲
This ▲ stands for "corner", and its tip is generally placed below the middle of 〥 and 〩.
Another example: the price is 5 yuan and 80 cents, and you can write:
〥〨
●
This stands for "circle" and is generally placed below the middle of and.
For another example, if the price is 3,908 yuan, you can write:
〣〩0〨
a thousand
When you say 1000 words, you should put them under 〣, which may be due to different customs in different places. But it should be marked below (or below) the right of the first digit.
The concept of human numbers can be traced back to the Paleolithic Age, about tens of thousands or even hundreds of thousands of years ago. At that time, Neanderthals had to deal with numbers in the collective action of collecting food and catching prey, especially in the activities of distributing and exchanging surplus goods, they had to use numbers for simple operations.
The origin of decimal system
The earliest known numbers are some of the simplest natural numbers, such as 1, 2, 3, etc. With the passage of time, people can master more and more natural numbers, so the problem of how to write these numbers arises. Although different nationalities around the world choose their own different symbols to count, at first, almost all of them use a horizontal bar or a vertical bar (that is, "-"or "丨") to represent 1, and two horizontal bars or two vertical bars (that is, "=" or "∨") to represent 2, which means that for comparison, however, In order to simplify the counting method, people need to create a new symbol to represent a specific number. Many areas choose this specific number as 10, because a person has 10 fingers, and fingers are the earliest and most convenient counting tool for human beings, so decimal is produced. Subsequently, special numbers such as one hundred, one thousand and ten thousand were given special symbols, which made it more convenient to express large numbers in decimal.
In the history of human use of numbers, there have been five decimals, twelve decimals, hexadecimal, twenty decimals, and sexagesimal in some areas. Except for the minute and second units in the timing and counting angles, which still have traces of sexagesimal, other decimals have been replaced by decimals.
Although the carry system simplifies the representation of numbers, people have to constantly create new symbols to represent larger and larger numbers. How to express an arbitrarily large number with a limited number of symbols?
The writing of numerals in different areas of early human beings was quite different, but one thing was the same, that is, they all had "order", that is, writing was nothing more than from left to right, or from right to left, or from top to bottom. So the counting symbol has the concept of position. Each counting symbol itself represents several different sizes, and the same counting symbol is written in different positions, and its numerical size is also different, which is the origin of the numerical system. "The principle of ranking system is indeed a great event of world significance. This principle is not only a fundamental change in methods, but now we know that without it, any progress in arithmetic is impossible. " This sentence is a scientific historian Danzig's pertinent evaluation of the value system.
Ancient counting method
With the decimal system and the value system, ten independent symbols must be created, and they are independent in writing, so that the counting system is perfect.
Since the appearance of writing, many cradles of human civilization have almost had the carry system, but the value system only appeared in a few places, and a perfect counting system came into being very late.
The counting method of ancient Egypt more than 3000 years ago is as follows:
For example, 258 writing. This counting method is decimal, but there is no numerical system; As far as the above symbols are concerned, they can only represent 99999 at most, which is very troublesome to write. Now we can only use five symbols to represent the number 99999, but they use 45 symbols.
Babylonians in Cuba used the hexadecimal numerical system more than two thousand years ago. There are only two symbols to represent numbers, namely 1 and 10. Because they use the bit system, the symbols mean one bit 1, ten bits 60, hundreds 60×60, and so on. For example, the number 93, they wrote. However, because there is no zero symbol and the symbols of 1-9 are not independent of each other, it is easy to cause confusion. Babylonian characters are called "cuneiform" because they have no "paper" and "pen". The writing method is to write on the sticky clay tablet with a carving knife, and then dry or burn the written clay tablet, so that a solid clay tablet book can be preserved for a long time. Use a meat cleaver to carve symbols in one stroke, but only two strokes are needed.
The ancient Greeks' counting system was decimal, but there was no concept of value system. They drew a bar on it with 27 ancient Greek letters α, β and γ to represent numbers. The first nine letters stand for 1-9, the middle nine letters stand for 10-90, and the last nine letters stand for 100-900. In this way, the largest number can only represent 999. In order to represent larger numbers, they introduced a new counting symbol. This counting system is very complicated, but because no numerical system is introduced, there is no guarantee that any large number has a corresponding symbol.
More than two thousand years ago, the Mayans living in central North America created the only ancient writing in America, including digital symbols. They use ""for 1 and "-"for 5, for example 13. They have the concept of location system, but they use decimal system. The formation of this decimal system may be related to the fact that fingers and toes participate in counting at the same time, indicating that their history of wearing shoes is not long. A multi-bit counting method is that the high bit is lower than the low bit, such as 159 = 7× 20+ 19. Because of the value system, this counting system is quite advanced. Although the counting symbols are not independent, it is not easy to cause confusion by using hierarchical writing. However, Mayan culture lasted for more than 1000 years. In the 9th century, several big city-states here suddenly declined, and the culture was interrupted. The reason is still unknown.
Counting system in ancient China
China established a complete decimal system in Shang Dynasty more than 3000 years ago. The numerical symbols are as follows:
Since the invention of counting tools, China people's counting system has made great progress. During the Spring and Autumn Period and the Warring States Period more than 2,000 years ago, calculation and compilation were widely used in China. Calculation is a thin bamboo stick, and the number 1-9 is expressed in two ways:
Vertical type:
Horizontal style:
1 2 3 4 5 6 7 8 9
The representation of multi-digits is alternating vertically and horizontally, which avoids the confusion that may be caused by symbol independence. For example, the representation of 22837 is. So the ancient counting system in China is a typical decimal system.
The original meaning of "calculation" refers to calculation, the middle "grid" refers to several calculation chips on the table, the lower "grid" is the bracket, and the upper "&<1950; "Represents its material. The word "strategy" is synonymous with calculation and preparation, and ancient books called "twig as strategy", so operation, operation, strategy and calculation were synonymous in ancient times. In Sean's Historical Records, there is a saying that "winning or losing is a strategic plan thousands of miles away", which shows that military strategists at that time also used calculation and planning as a tool in their accounts before commanding a battle.
In fact, it is not important to adopt decimal system, but it is important to have the concept of value system. Babylonians and Mayans had the concept of value system, but it was not a decimal; Both ancient Egypt and ancient Greece were decimal, but there was no decimal. Only China was the first country to adopt the decimal system. Needham, a famous British historian of science, once said, "Without this decimal system, it is almost impossible to have our unified world now." Therefore, the creation of the decimal system is an indelible contribution made by the ancient people of China to the world.
The origin of "Arabic numerals"
At present, all countries and regions in the world widely adopt a unified decimal counting system, and its counting symbols 1, 2,3, …, 9,0 are called Arabic numerals. However, it is wrong to think that these ten numbers and this counting system were invented by Arabs. In fact, this invention should be attributed to Indians.
India began to use counting symbols around the 3rd century BC, and then gradually formed a decimal counting system, but it was not until the 6th century AD that the numerical system was adopted. India is an ancient civilization close to China. There are many cultural exchanges between the two countries in history. Therefore, the decimal counting system adopted by India in the 6th century may have been influenced by China.
In India in the 2nd-4th century A.D., the numbers on coins were written as follows:
There was no symbol of zero at that time. In the mathematical manuscripts around the 8th century AD, the writing of numbers evolved into:
Although the Indian decimal system may be influenced by China, they created ten independent symbols, which are an indispensable part of a perfect decimal system, especially the invention of the zero symbol, because for a long time, people did not regard zero as a number, so they did not specifically determine a symbol for it; But without the sign of zero, the counting system is defective. As for how to write digital symbols, it doesn't matter, as long as it doesn't cause confusion and is easy to write, of course, it's best to use strokes. Indians have basically done this.
After the 8th century, India's counting method was introduced to Arab countries, and Europeans learned this decimal system and corresponding numbers from Arabs. During the circulation of about 1000 years, the writing of numbers has changed so much that it finally evolved into a familiar form. Europeans see that these numbers come from Arabs, so they call them "Arabic numbers"; Since17th century, European mathematics has occupied a dominant position in the world, and all countries in the world have learned mathematics from it, including the name "Arabic numerals". As we all know, this title is a big misunderstanding in the history of world mathematics development.
The appearance of carry system and counting method laid the foundation of mathematics, while decimal system and Arabic numeral counting method are common all over the world because of their simplicity and science. They are not only the crystallization of human wisdom, but also the beginning of mathematical civilization. In every corner of the world, no matter adults or children, no matter what language they speak, Arabic numerals and decimal values are the same. Whether from children's early knowledge or scientists' complex mathematical operations, they are inseparable from the most basic Arabic numerals. It is inseparable from human life.