How did human beings discover and record natural numbers

How did human beings discover and record natural numbers

The birth of number
Mathematics, the father of natural science, originated from the great invention of natural numbers
A few years ago, in order to survive, the ancestors of human beings often lived together in groups. They worked together during the day to hunt wild animals, birds or collect fruit and potato food. At night, they lived in caves and shared the income from their work. In the long-term common work and life, they gradually came to the point where they had to say something, With the development of the content of labor, their language also developed, and finally surpassed the language of all other animals. One of the main signs is that language contains the color of arithmetic
Human beings first came up with the vague concept of "number". They returned from hunting, with or without prey, so they had two concepts of "have" and "nothing". For several days in a row, there was no animal to catch, so there was no meat to eat, and the concepts of "have" and "nothing" gradually deepened
Later, social life developed into tribes. Tribes are composed of families with few members. The so-called "you" can be divided into "one", "two", "three" and "many" (some tribes don't even have "three"), But he could not tell how many kinds of wild animals he had captured and how many kinds of trees he had seen. If he asked the witch doctor, he would make up some words to answer the question of "how many kinds" and recite them in a very meaningful way, Three fingers and arrows: "I'll have a deer. You'll have to give me three arrows." they didn't know arithmetic at that time
About 10000 years ago, the glacier retreated. Some stone age nomadic hunters started a new way of life in the mountains of the Middle East, farming. What kind of dates and seasons did they meet, Especially in the Nile Valley, the Tigris River and the Euphrates River Valley, when they developed more complicated agricultural society, they also encountered the problem of paying taxes. This requires that the number has a name. Moreover, the count must be more accurate. Only "one", "two", "three" and "more" are far from enough
Between and around the Tigris and Euphrates rivers is called Mesopotamia, where there was a culture, like Egyptian culture, which is one of the oldest in the world, But in the same way, they established the earliest system of writing natural numbers - marking on trees or stones to record the passing days
Later (especially after they settled in villages), they gradually used symbols instead of marks, that is, one symbol for one thing, two symbols for two things, and so on. This method of counting continued for a long time. About 5000 years ago, Egyptian priests had written numbers on a kind of grass paper made of reeds, The priests in Mesopotamia, on the other hand, wrote on soft clay boards. They still used single strokes to indicate "-" and other symbols to indicate "+" or larger natural numbers. They repeatedly used these single strokes and symbols to indicate the numbers they needed
In 1500 B.C., the Inca people (part of the Indian) in Peru, South America, were used to "count the number by tying a knot on the rope for each bunch of crops they received. The number of knots was used to record the harvest. The" knot "had the same function as the mark, and was also used to express the natural number. According to the records of the book of changes, the Chinese people in ancient times were also" rule by tying a knot. ", Later, it was changed to "Book deed", that is to use a knife to score on bamboo or wood. One stroke stands for "one". Until today, we Chinese people still use the word "Zheng" to count. Each stroke stands for "one". Of course, the word "Zheng" also contains the meaning of "every five into one"
Human beings are the product of animal evolution, and there was no concept of quantity at first. However, the developed human brain has reached a more rational and abstract level of understanding of the objective world. In this way, in the long life practice, due to the needs of keeping track of events and distributing daily necessities, the concept of number gradually came into being. For example, if one beast is captured, it is represented by a stone. Three animals are captured, It is said that the ancient Persian kings also used ropes to count the number of days when they were fighting. They used sharp tools to mark the bark or animal skin, or to count the number of days when they put a stick on the ground. These methods were used much more, Gradually formed the concept of number and notation
At first, the concept of number was 1, 2, 3, 4 no matter where it was Such a natural number begins, but the notation is the same size
Many of the ancient Roman wall clocks are still quite advanced
In fact, there are only seven symbols of Roman numerals: I (for 1), V (for 5), X (for 10), l (for 50), C (for 100), D (for 500) and m (for 1000). No matter how the positions of these seven symbols change, the numbers they represent are unchanged. They can represent any number according to the following rules:
1. Repetition times: a Roman numeral symbol repeated several times means several times of the number. For example: "III" means "3"; and "XXX" means "30"
2. Right plus left minus: a symbol representing a large number, with a symbol representing a small number attached to the right, means a large number plus a small number, such as "VI" for "6", "DC" for "600". A symbol representing a large number, with a symbol representing a small number attached to the left, means the number of large number minus a small number, such as "IV" for "4", "XL" for "40", "VD" for "495"
To add a line to a Roman numeral to indicate a thousand times that number. For example, "15000" means "15000" and "165000" means "165000"
Ancient China also attached great importance to counting symbols. The oldest oracle bone inscriptions and bell and tripod inscriptions all had counting symbols, but they were difficult to write and recognize. Later generations did not use them. In the spring and Autumn period and Warring States period, production developed rapidly. To meet this need, our ancestors created a very important calculation method -- calculation. The calculation chips were made of bamboo sticks, and also made of bone, It can be used for counting and operation. With the popularity of calculation, the pendulum method of calculation becomes the symbol of counting. There are two types of pendulum method of calculation, horizontal and vertical, which can represent the same number
It is clear from the fact that there is no "10" in the calculation figures that the calculation strictly follows the ten digit system from the beginning. A number with more than 9 digits must be entered into one digit. If the same number is placed in the hundreds, it will be hundreds, This method of calculation was very advanced at that time. Because the real use of decimal system in other parts of the world was at the end of the 6th century. But there was no "zero" in the calculation number, and when it came to "zero", there would be a vacancy. For example, "6708" could be expressed as "┴╥". If there was no "zero" in the number, it was easy to make mistakes, However, most people believe that the invention of the mathematical symbol "0" should be attributed to the Indians in the 6th century. They first used black dot (·) to represent zero, and then gradually became "0"
When it comes to the appearance of "0", it should be pointed out that the word "zero" appeared very early in ancient Chinese characters. However, at that time, it did not mean "nothing", but only "fragmentary" and "not much", such as "odd", "sporadic" and "odd". The idea of "105" is that there is another odd five beyond 100. With the introduction of Arabic numerals, "105" is exactly pronounced as "105", and "zero" corresponds to "0", "Zero" also has the meaning of "0"
If you observe carefully, you will find that there is no "0" in the Roman numeral. In fact, "0" was introduced into Rome in the 5th century. But the Pope was cruel and conservative. He did not allow any use of "0". A Roman scholar recorded some advantages and explanations about the use of "0" in his notes, so he was summoned by the Pope and executed the punishment of "Z ǎ n", so that he could no longer hold a pen to write
But no one can stop the emergence of "0". Now, "0" has become the most meaningful digital symbol. "0" can mean no or yes. For example, temperature 0 ℃ does not mean no temperature; "0" is the only neutral number between positive and negative numbers; the power of 0 of any number (except 0) is equal to 1; 0! = 1 (the factorial of zero is equal to 1)
In addition to the decimal system, in the early days of mathematics, there were many kinds of numeral system, such as pental system, binary system, ternary system, Sevens system, octal system, decimal system, hexadecimal system, twenties system, sixties system and so on. In the long-term application of real life, the decimal system finally gained the upper hand
The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0, which are commonly used in the world, are called Arabic numerals. In fact, they were the earliest used by ancient Indians. Later, Arabs integrated ancient Greek mathematics into their own mathematics, and spread this easy to write decimal notation throughout Europe, gradually evolving into today's Arabic numerals
The concept of number, the writing of number and the formation of decimal system are the results of human long-term practice
With the needs of production and life, it is found that it is far from enough to represent natural numbers. If five people divide four things in the distribution of hunting, how much should each person get? So scores are produced. The research on scores in China is more than 1400 years earlier than that in Europe! Natural numbers, fractions and zeros are generally called arithmetic numbers. Natural numbers are also called positive integers
With the development of society, people find that many quantities have opposite meanings, such as increase and decrease, advance and retreat, rise and fall, East and West. In order to express such quantities, negative numbers are produced. Positive integers, negative integers and zeros are collectively called integers. If positive and negative fractions are added, they are collectively called rational numbers, People find it much more convenient to calculate
However, in the process of digital development, an unpleasant thing happened. Let's go back to Greece 2500 years ago, where there was a Pythagorean School, which studied mathematics, science and philosophy. They believed that "number" is the origin of all things, dominating the whole nature and human society, This is the source of the world's beauty and harmony. By number, they mean integers. The appearance of fractions makes "numbers" not so complete. But fractions can be written as the ratio of two integers, so their belief has not wavered, It is found that there is no number that can be expressed by integer proportion. If this number is x, since the result of derivation is x2 = 2, he drew a square with side length of 1, and set the diagonal as X. according to Pythagorean theorem x2 = 12 + 12 = 2, it can be seen that the length of the diagonal of the square with side length of 1 is the number to be found, This number must exist. But what is it? How to express it? Hippassos and others were puzzled, and finally decided that it was a new number that they had never seen before. The emergence of this new number shocked the Pythagorean School and shaken the core of their philosophical thought