The decimal notation system includes two principles: decimal and decimal. Decimal stands for full decimal. Bit value means that the same number represents different values in different positions, such as three numbers 1 1, where 1 on the right represents 1 one in one bit and1in the middle represents1one in ten bits. This makes the extremely difficult integer representation and calculation so simple and easy, but when representing ten, each bit needs a sign zero to occupy a position; Only in this way can the symbol of 1 represent 10, otherwise the numbers will be easily confused. So that people often ignore its key role in the development of mathematics.
According to archaeological findings, the decimal system was invented by China people in 1400 BC, that is, in the middle of Shang Dynasty, that is to say, the decimal system was not invented when the Shang Dynasty was overthrown and established in Tang Dynasty. BC 1400. It's 3400 now.
At the latest in Shang Dynasty, China had adopted the decimal system. It can be seen from the Wen Tao and Oracle Bone Inscriptions in Shang Dynasty that we were able to record any natural number within 100,000 with thirteen numbers, such as one, two, three, four, five, six, seven, eight, nine, ten, hundred, thousand and ten thousand. Although the shapes of these numbers have changed in later generations and become the current writing methods, the notation has never been interrupted and has been used and improved day by day.
Decimal notation is the most advanced and scientific notation in the ancient world, which plays an inestimable role in the development of world science and culture. As Joseph Needham said, "Without this decimal system, it is impossible to have our unified world now." A batch of pottery was unearthed in F90 1 room in the late Yangshao period in Dadiwan, mainly including four pieces of clay trough-shaped slats, long-handled ear-twisting shovels with fine sand, clay single-ring ear dustpan, and mud-covered deep-belly cans. The volume of the strip disk is about 264.3 cubic centimeters; The natural texture volume of shovel paper is about 2650.7 cubic centimeters; The natural texture volume of basket paper is about 5288.4 cubic centimeters; The volume of the four deep belly tanks is about 26082.438+0 cubic centimeters. It can be seen that, except that the dustpan copy is twice as much as the shovel copy, the relationship between the other three pieces is ten times increasing. The discovery of these weights and measures also provides very valuable physical data for studying the origin of China's ancient decimal system. Although the notation of ancient Babylon had the significance of value system, it used hexadecimal and the calculation was very complicated.
Mozi also discussed the decimal system around 400 BC. China widely used decimal notation as early as Shang Dynasty, and Mozi was the first scientist to summarize and expound the concept of value system. He clearly pointed out that different digits have different values. For example, on the same number, one is less than five, while on different numbers, one can be greater than five. This is because in the same number (unit, tens, hundreds, thousands, etc.), five contains one, and when one is in a higher number, it in turn contains the invention of decimal, which is a great contribution of China to world civilization. As Needham said in the Mathematical Volume of the History of Science and Technology in China, "The number system of Shang Dynasty is more advanced and scientific than that of ancient Babylon and ancient Egypt at the same time", "Without this decimal system, it is almost impossible to have our unified world now".
There are several views about the origin of 0:
0 is an extremely important number symbol, and the concept of 0 thinking has existed in other regions for a long time.
According to historical records, the Mayans had a mathematical system called "the most brilliant product of human mind", and the Mayans (or their Omek ancestors) independently developed the concept of zero.
Maya civilization first invented the special font 0. In Mayan numerals, 0 is represented by a pictographic symbol like a shell. And uses a binary number system; This number is represented by a dot (-) as 1 and a bar (-) as 5. Inscriptions show that they sometimes use hundreds of millions.
The zero mentioned here is not the Arabic numeral 0 we use, but it should be the earliest digital symbol containing the concept of 0.
In ancient Egypt, as early as 2000 BC, some people used special symbols to record zeros in bookkeeping.
There are 0 seeds in ancient Babylonian literature. However, unlike now, the symbol of 0 is represented by spaces. For example, to represent 10 1, Babylon wrote 1 1.
The concept of 0 has a long history in China and has been recorded in many documents. In ancient China, counting chips was used for calculation. In counting chips and abacus, spaces were used to indicate 0. (However, in China's ancient knotting notation, "zero" appeared in the negation of "yes", indicating "no". ) 2700 years ago, in 700 BC, China was very mature in digital planning; Molecules are decimal position systems, which are similar to the decimal position systems in the world now. Because the calculation is a natural decimal system, the space in the early calculation only represents the concept of zero, and there is no symbol zero to represent it. In the 4th century BC, mathematicians in China explained the concepts of negative numbers and zero.
The Nine Chapters of Arithmetic in the 1 th century AD said: "The pros and cons are: the points of the same name, the benefits of different names, the negative ones, and the negative ones. Its synonyms are divided, the same name is beneficial, and there is no positive or negative. " Subtraction: When you meet numbers with the same sign, subtract their values; when you meet numbers with different signs, add their values. The difference between zero MINUS positive numbers is negative, and the difference between zero MINUS positive numbers is positive. " ) The concept of "Buru" in the above text is usually considered as zero by mathematical historians. (For the full text, see Wikipedia's "Nine Arithmetic Chapters". Even so, there was no symbol to represent zero at that time. There is no "zero" symbol at the beginning of digital calculation, and it will be empty when it meets "zero". For example, "6708" can be expressed as "┴〧〨" (because seven and eight have no corresponding symbols, quotient codes are used instead; After all, quotient codes are derived from arithmetic codes. Since 7 and 8 have no corresponding symbols, quotient codes are used instead. After all, quotient code comes from arithmetic code) "(Because seven has no corresponding symbol, Suzhou code is used instead; After all, Suzhou code is calculated. There is no "zero" in the number, so it is easy to make mistakes. So later, someone put the copper coins in the empty space to avoid making mistakes, which may be related to the appearance of the symbol "Ф".
It was not until the early 7th century in India that the great Indian mathematician Graf Magpuda first explained the nature of 0, that is, any number multiplied by 0 is 0, and any number can be obtained by adding or subtracting 0. Unfortunately, he didn't mention the example of calculating with the symbol of life position.
However, most people believe that the invention of the mathematical symbol "0" should be attributed to Indians in the 6th century. Indian civilization can be traced back to 2000 BC, but they didn't have mathematics before 800 BC. After about the 3rd century BC, numerical symbols appeared in India, typically Brahman numerals. The outstanding feature of Brahman number is that it gives each number of 1 to 9 a separate label, and there is no zero-sum and carry notation. They first used the black dot ""to represent zero, and then gradually became "O".
However, it is said that around 2500 BC, the symbol "0" was used in the Vedas, the oldest document of Brahmanism in India. At that time, zero indicated the vacancy in Indian Brahmanism (according to this statement, zero appeared in the negation of "being" in ancient China, meaning "nothing". You can also forget it). -I have doubts about the last paragraph, if it is true; So why did Indians still use black spots as a symbol of "zero" in the 6th century? As for when the dot became round, it is impossible to verify the exact time. (This book started in Zhan Jing, published in 7 18 AD, with a volume of 104 and a page of 1089, and translated nine Indian calendars; At that time, Indians' zeros were still black spots. Moreover, this statement feels the same as the knotting notation in ancient China. Zero appears in the negation of "you" and means "no".
Around the third century BC, the ancient Indians completed the invention of the digital symbol 1 to 9, but there was no "0" at this time. The "0" symbol appeared more than 1000 years after the Gupta dynasty in India invented the digital symbol 1 to 9. It was not round when it first appeared; It is represented by a black dot. As for when to turn from a point to a circle, the specific time is impossible to verify. Until 876 AD, people were in Gualior, India. Found a stone tablet engraved with the number "27o". This is also the earliest record of the symbol "0" found by people, but the symbol of this zero is a circle O smaller than zero; Nor is it like the modern symbol "0".
But if you say symbols, there are already spaces in China's calculation; Later, copper coins were used to represent the symbol of zero in calculation. Since then, copper coins have evolved into zero as a symbol of zero; Is a very normal thing. In 690; Wu Zetian promulgated "Handwriting of Zetian", in which one word is "é" (earlier than the Indian small circle symbol O 186); although
However, it didn't mean zero at that time. However, the early record of "Ф" in ancient mathematics in China is represented by "Ф", so that numbers can be distinguished. Because China had the habit of writing with a brush in ancient times, Lian Bi wrote with a brush; It is much more convenient to write Ф than Ф. The copper coin in the outer ring is the symbol of zero in calculation, so the symbol of zero gradually becomes "Ф" drawn counterclockwise; This is the appearance of China's zero symbol. The Ming calendar of Jin Dynasty 1 180 has numbers such as "403" and "309".
According to the research of Dr. Lee Yue Se, a famous British expert in the history of science, "0" originated from China and Indian culture, and it was the value system first used by China that promoted the emergence of zero. Indians created "0" under the influence of China's calculation and value system. China used decimal notation as early as 3000 years ago in Shang Dynasty. There are numbers such as "600 and 50 and 9 (659)" in Oracle Bone Inscriptions, and the decimal notation is clearly used. China Zhou Dynasty (65438 BC+0046 BC-256 BC) inherited the decimal system of Shang Dynasty and made remarkable progress. Decimal symbols include ten, hundred, thousand, ten and one hundred million, such as the bronze inscription in the Western Zhou Dynasty, "Cut the devil's side" ... captured 33,081 people ",and there are several digits, such as". Mozi also discussed the value system around 400 BC, thus increasing the decimal system that existed in Shang Dynasty. Decimal officially appeared in the record. Mozi was the first scientist to summarize and expound the concept of value system. He clearly pointed out that different digits have different values.
For example, on the same number, one is less than five, while on different numbers, one can be greater than five. This is because in the same number (unit, ten digits, hundred digits, thousand digits, etc.), five contains one, and when one is in a higher number, it also contains the invention of five, which is a great contribution of China to world civilization.
And how did a black spot in India become a symbol of zero? I wonder if there is any evidence of evolution. Moreover, there was no decimal system in ancient India, and China had the earliest decimal system in the world. Although ancient Egypt was decimal, there was no position system. Although Babylon has a warehouse system, Babylon is a 60-base system; Only China can satisfy ten at the same time.
Decimal numerical system derived from decimal system and position system. However, the earliest time when the symbol of "0" in China literature indicates "0" is also impossible to verify. In the Song Dynasty, Cai Shen's New Works of Jurisprudence (1135-1198) indicated the vacancy with a square "ai". The Ming calendar of Jin Dynasty 1 180 has numbers such as "403" and "309". In A.D. 1247, Qin used the symbol "zero" to represent the concept of zero in nine chapters of his works. There is a "0" image in question 14 of Ye Li's Circle Survey of the Sea Mirror (1248).
In short, the origin of zero is still inconclusive, but in any case, zero has a very strong vitality since its appearance, and it is now widely used in all fields of society.