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A perfect world is inseparable from numbers, which hide the laws between everything. Since ancient times, numbers have not only become tools for dealing with various affairs, but also reveal the laws of numbers, which reflects the rational ability, root and power of human beings in studying natural phenomena. Exploring the laws of numbers behind phenomena attracts great wise men. Euclid, Copernicus, Kepler, Descartes, Galileo, Pascal, Newton, Einstein and many other masters have built magnificent scientific buildings on the basis of exploring numbers: Euclid Geometry Building, Newton Classical Mechanics Building, Mendeleev Element Period Building, Darwin Evolution Building, Einstein's Relativity Space-time Building, Quantum Mechanics Building of Microphysics...

In the face of these magnificent scientific buildings, people not only admire these scientific masters, but also let us have a deeper understanding of what ancient Chinese Zhuangzi said: "the beauty of the original earth reaches the principle of all things." In this "beauty of the original earth" and "reaching the principle of all things," the law of number has always been the goal of human pursuit.

After the Renaissance, Arabic numeration, decimal fractions and logarithm appeared one after another, which became the three great inventions in the mathematical world. Their appearance promoted the emergence and development of modern mathematics. The logarithm is harder to discover intuitively, and therefore harder.

Laplace, the great French mathematician and astronomer of the 18th century, believed that the invention of logarithm "shortened the calculation time and extended the life of astronomers." In fact, the superiority of logarithm is far more than dealing with large amounts of data. In more fields, logarithm has more important applications.

Human thinking about logarithm originated very early. As early as 500 BC, Archimedes compared two series: One series is the multiplication of 10, which is 1, 10, 102, 103, 104,…, the other is 0, 1, 2, 3, 4,…On the surface, there is no direct relationship between the two series, but he found the internal relationship between them. The addition and subtraction of the second series can express the multiplication and division of the first series, for example, the addition of 1 and 2 corresponds to the square of 3 in 103 in the first series. He could have developed logarithmic relationships along these lines, but unfortunately he couldn't.

2000 years later, German mathematician Stifler noticed this again. He compared two other series, 0, 1, 2, 3, 4, 5,…and 1, 2, 4, 8, 16, 32,…. He found that the addition and subtraction operations in the former series corresponded to the multiplication and division operations in the latter series. For example, in the former series, 2 and 5 added together to make 7. In the latter series, the product of the corresponding terms 4 and 32, 128, is exactly 2 to the seventh power, and there is also an implicit logarithmic relationship between these two series. Following this line of thought, logarithmic relations may also be developed, but unfortunately the concept of fractional exponents was not perfected at that time, making it difficult to further expand this idea.

Archimedes and Stifler's discoveries opened the way for the establishment of logarithm, and the development of astronomy in the 15th and 16th centuries promoted the establishment of logarithm. During this period, huge and complex astronomical figures were placed in front of people.

Astronomers, for example, fret over the number crunches they have to dodge when calculating the relative positions of planets and their orbits by multiplying, dividing, raising, and squaring large amounts of data. The search for a simple way to reduce large numbers to decimals and replace multiplication and division with addition and subtraction became a demand for the beginning of the astronomical age, and this brilliant method was finally discovered by the English mathematician John Napier.

John Napier was born in Edinburgh, Scotland, in 1550. Little is known about his early life except for a letter from a local priest, Napier's uncle, to his father. The letter read,"God bless you, sir, send your son to school. You can send him to France. At home, he could not have received a good education, nor could he have adapted to this dangerous world. Sending him out would have given him better protection and might have done great things. I assure you, he will. Napier was only ten years old. Uncle's two judgments were correct. Napier was born when his father was only 16 years old and "could not be well educated at home." Later, Napier proved that he did make "great feats."

In 1565, Napier entered St Andrews University at the age of 16. Two years later, he fell in love with theology, but he didn't get a degree. He travelled to France, Italy and Holland before returning to his native Scotland. He devoted a great deal of time to theological studies, but he was also obsessed with mathematics, which was only a hobby for him.

Napier's "hobby" led him to important discoveries. Napier again noted the correspondence between arithmetical and geometric series, but he went further than Archimedes and Stiffey in finding a way to express the relationship. He discovered that the product relationship between every two numbers in the latter group corresponds to the sum of the two numbers in the former group, and if this correspondence is applied, multiplication and division can be replaced by addition and subtraction. In order to find this substitution relationship, he spent more than twenty years studying numbers, during which time he invented logarithm, also found formula memory for solving spherical trigonometry problems, invented the expression of trigonometric functions, and introduced decimal notation for fractions. Among them, the study of logarithm occupied more of his time.

In 1614 Napier published a book entitled The Wonderful Theorem of Logarithms, which discussed logarithmic operations and included a table of sine logarithm. At that time, there was no perfect symbol of exponent, and there was no concept of "bottom," which restricted Napier's logarithmic formula, but it can still be seen from this table that his mathematical ideas are superb.

Two years after the publication of the book Wonderful Logarithms, the book was translated from Latin into English and published again. In the foreword to the book Napier describes how he thought about his invention: "I found this method actually because the complexity of calculations bothered me too much. In multiplication, division, multiplication, and square root, I encountered a particularly large number of numbers. It was not that these numbers could not be counted, but that they were long and cumbersome and took up too much time. Sometimes errors are made in calculations. So I wanted to figure out a way to deal with these annoying roadblocks and obstacles. I have come up with many ways to do this, but the most effective one is logarithmic. "

Napier Invented a Copy of a Calculator Based on Logarithms In 1614, before the book was translated into English, an English mathematician, Clutter Briggs, was the first to react positively and immediately realized the importance of Napier's logarithm. In a letter to a friend dated March 10, 1615, he said,"Napier, the master of Markingston [Napier's estate in Sougara], admires me with his logarithm, and I wish I could see him this summer. Thank God, I have never seen a book that interests me so much. It's fascinating. "

Briggs really went to see Napier. He rode a four-day trek to Kingston, Scotland. On July 2, 1615, the two met, and this meeting became a key day in the development of logarithm. Briggs advised Napier to make the logarithm "base" at 10, i.e., 1 for 10, 2 for 100, or n for 10n. This key suggestion not only makes logarithm have the concept of "bottom," but also forms the logarithmic pattern with "bottom." Briggs also suggested that he construct logarithmic tables in this way. Unfortunately, Napier was in poor health and could not finish the job.

Napier died on April 4, 1617. This year Briggs published the world's first common logarithmic table with a "base" of 10, and then, in 1620, Professor Gante of Gladham College successfully produced the world's first logarithmic scale for practical calculation, thus beginning the great development of logarithmic research and practical use.

The discovery of logarithm caused great repercussions in the world. It was like a flood of open source. Within a century, it spread almost all over the world and quickly penetrated trade and astronomical research. Astronomers, in particular, took the discovery almost with rapture. Logarithms were an important computing tool before computers were invented. After several generations of mathematicians, the significance of logarithm has not only been a calculation technique, especially the development of logarithm based on natural number e, but also the inextricable relationship between logarithm and many fields has gradually been revealed.

Logarithms were an epoch-making discovery in mathematics that simplified the number procedure and reduced the complexity of solving problems. Logarithms have wide applications in natural science and technology. In mathematics, probability and statistics, the law of large numbers and fractals, physics, thermodynamics, entropy and chaos, computer science, logarithmic analysis and integrated logarithmic law, biology, spiral structure and microbial growth period, informatics, light information processing, econometrics, psychology, Higgs law of human cognition, even music and fine arts, For example, in the relationship between audio frequency and interval in music creation, logarithmic law is everywhere, and the development of logarithm has brought great impetus and development to astronomy, cosmology, radioelectronics, communication and other fields.

More importantly, through logarithmic studies, important scientific methods were recognized. The important role of induction and analogy can be seen from the development of logarithm. All things in the world have inherent relations. The task of science lies in revealing the internal relations and laws of these relations. Mathematics studies the quantitative relations among them, among which the most basic one is the corresponding relationship between two sets. The important research methods to find this relationship are induction and analogy.

The monument to Napier in St. Cuthbert's church Laplace once said: "Even in mathematics, induction and analogy are the principal tools for discovering truth. "The use of induction and analogy not only makes people see the rigor and strong logic of the internal structure of mathematics, but also the association between different expressions. This association is not accidental, it shows the strength of the internal logical structure of mathematics. It can make connections between seemingly unrelated things, find breakthroughs from seemingly untouchable things, make seemingly vague things clear and clear, and find a "walking stick" from this shore to the other shore. There is something interesting in the transformation between "banks" within mathematics. It can be said that wonderful logarithm is everywhere. Napier went down in history for this discovery, revealing this wonderful source.

Source: 365 Days in the History of Science, slightly deleted Author: Wei Fengwen Wu Yi Editor: Zhang Runxin This article comes from Weixin Official Accounts: Origin Reading (ID: tupyread), Author: Wei Fengwen, Wu Yi, Editor: Zhang Runxin

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