--Leibniz
(I)
G.W. Ieibnlz (1646-1716) was a German philosopher who deservedly became known as the "Master of All Trades".
Mathematics and philosophy were among the many fields in which Leibniz demonstrated his outstanding genius. He made outstanding contributions to law, management, history, literature, logic, etc., and will always be remembered for his outstanding achievements in these fields. It is not an exaggeration to describe Leibniz as an "all-rounder".
July 1, 1646, Leibniz was born in Leipzig, Germany. His grandfather had served in the Saxon government for three generations; his father was a professor of ethics at the University of Leipzig. Leibniz's youth was spent in an official family and in a strong academic atmosphere.
Leibniz lost his father when he was six, but his father's love of history had infected him. Although admitted to the Leipzig School, he taught himself largely by reading in his father's library, and by the age of 8 he had begun to study Latin and by 12 Greek, leading to an extensive reading of many classical books on history, literature and philosophy.
When he was 13, Leibniz took a particular interest in the logic course at his high school, and despite his teacher's discouragement, he tried to improve on Aristotle's philosophical categories.
In 1661, at the age of 15, Leibniz entered the University of Leipzig to study law. He kept up with the standard second-year humanities curriculum, which included philosophy, rhetoric, literature, history, mathematics, Latin, Greek, and Hebrew.In 1663, at the age of 17, Leibniz was honored for his remarkable philosophical treatise, "On the Metaphysical Controversy in Regard to the Principle of the Individual - on the "Doctrine of the Organism as a Whole," for which he received his bachelor's degree.
Leibniz needed to study at a higher college, such as a seminary, law school, or medical school, to get his doctorate. He chose law. But law didn't take up all of his time; he also read extensively in philosophy and studied math. For example, he spent the summer in Jena listening to Weil's lectures on mathematics, where he was exposed to neo-Pythagoreanism - the idea that number is the fundamental reality of the universe - as well as to a number of other "heretical" ideas.
In 1666, at the age of 20, Leibniz was well prepared for his doctorate in law, but the faculty in Leipzig refused to grant him the degree. Their public excuse was that he was too young and immature, but in reality they were irritated out of jealousy -- at the time, Leibniz possessed far more knowledge of the law than those of them put together!
So Leibniz transferred to the University of Altdorf outside Nuremberg, submitted his long-prepared doctoral dissertation, defended it, and was duly awarded his doctorate. The University of Altdorf also offered him a professorship, which he declined. He said he had other ambitions - he wanted to change his original intention of living a collegiate life and decided to devote himself more to the outside world.
1666 was the year of Newton's miracles -- the invention of calculus and the discovery of gravity; it was also the year of Leibniz's great work -- in his self-proclaimed "high school work", On Combinatorics. In his self-proclaimed "work for high school students," On Combinatorics, the 20-year-old attempted to create a universal method in which the correctness of all arguments could be reduced to a certain kind of calculation. At the same time, it is a universal language or script, during which symbols and even words lead to reasoning, and fallacies other than those facts can only be errors in the calculations.
The formation and invention of such a language or mathematical notation is difficult, but reading it without the aid of any dictionary is easy. This was Leibniz's dream of "universal symbols" at the age of 20 - in the 1760s - and its development two centuries later - in Glassman's work in the 1840s. Grassmann's "symbolic logic" of the 1840s.
Leibniz's ideas were ahead of their time!
(ii)
In 1667, at the age of 21, Leibniz joined a group of alchemists in Nuremberg, Germany, as secretary. Through this group, he became acquainted with the political figure Baron of Boyneburg, who recommended him to the Elector of Mainz as an assistant to his legal advisor, and Leibniz later ascended to the political arena when he was quickly promoted to the position of jury judge at the Court of Appeal.
Leibniz attempted to recodify the statutes, hoping to put them in order by using a few basic legal concepts to define all of them; and by deducing all of the specific statutes from a very small set of natural, just, and indisputable principles. He wanted to knit together the natural statutes into one system, and to this end he published his New Method of Teaching Law.
In 1669, through reading the Journal of the Royal Society, Leibniz learned that Huygens, a Dutch physicist, was discussing the problem of "collision" with others, which prompted him to start thinking about natural science issues such as force and energy.
In 1671, Leibniz wrote a book entitled "New Hypotheses in Physics," which included "Principles of Concrete Motion" and "Principles of Abstract Motion" for the Royal Society of England and the Academy of Sciences in Paris.
Beginning in 1671, Leibniz utilized diplomacy to develop extensive contacts with the outside world, and correspondence was his primary means of obtaining information about the outside world and exchanging ideas with others. From that year onward, he corresponded for decades with Ortenberg, the secretary of the Royal Society of England, and with leading scholars of the Paris Academy of Sciences.
In 1671-1672, Leibniz was commissioned by the Elector of Mainz to prepare a plan to stop France's attack on Germany, and in 1672 he traveled to Paris as a diplomat to persuade King Louis XIV of France to give up his attack, but he was never able to meet with the King of France, and the diplomatic campaign ended in failure.
But during his stay in Paris from 1672 to 1676, Leibniz, who was about to enter his "prime", began his academic career. At that time, Paris was the scientific and cultural center of Europe. Leibniz studied French, met many famous people in the scientific and philosophical circles, so that his thoughts and actions began to go beyond Germany to the world.
For example, in January 1673, in order to promote reconciliation between Britain and the Netherlands, he went to London to mediate, but he took the opportunity to establish contact with the British academic community of well-known scholars, met with Ottemberg, who had been in correspondence for three years, and became acquainted with Hooker, Boyle, etc. In March 1673, he returned to Paris, and in April, he was recommended to be a member of the Royal Society of Great Britain. In October 1676, he met Levenhuk in Holland. Levenhuk used a microscope to observe bacteria, protozoa, and sperm for the first time, which had an impact on Leibniz's philosophical thinking. Leibniz became increasingly interested in the natural sciences. Many of his life's scientific achievements and scientific ideas were acquired and developed during this period.
As early as 1671 to 1672, Leibniz set out to design and create a mechanical computer - able to add, subtract, multiply, divide, and square operations. 1673, he traveled to London, carrying a wooden computer with him, which aroused great interest, and he himself was very proud of this invention.
In 1674, Leibniz, with the help of the biologist Mariotte, made a computer, and submitted it to the Paris Academy of Sciences for acceptance, and later he also made a public demonstration. Leibniz designed this new type of computer, its fixed part for addition and subtraction, following the Pascal adder, but the multiplier and divider, especially the two rows of gears (the multiplied number wheel and multiplier wheel) is Leibniz's first. Many of the devices in this computer later became standards of technology, and those gears became known as "Leibniz wheels".
Leibniz fully recognized the importance of the computer, stating, "It is very valuable. Putting the calculations in the hands of machines frees the best minds from the drudgery of calculations." He also predicted, "What I have said about the construction of the machine and its future applications will certainly be better in the future, and, I am sure, will be seen more clearly for those who will be able to see it in the future."
(iii)
At the end of 1676, at the age of 30, Leibniz left Paris, France, where he had already lived for five years, and returned to Hanover, Germany, by way of London, England, to take up his position as legal adviser and librarian to the Dukedom of Brunswick. From then on, he made Hanover his permanent residence for 40 years until his death in 1716 at the age of 70.
After settling in Hanover, Leibniz extensively studied philosophy and various scientific and technical problems. His philosophical thought gradually matured. At the same time, he also engaged in a wide range of academic, cultural and socio-political activities. Soon he became a member of the court, and began to be famous in society, and his life became rich as a result.
In 1682, Leibniz and Menke founded the Latin scientific journal, "Teacher's Journal" (also known as "Academic Chronicle"). Most of his mathematical and philosophical articles appeared in the journal.
On March 15, 1679, Leibniz's paper entitled "Binary Arithmetic" discussed the binary system quite fully and made a full comparison with the decimal system. He not only completely solved the problem of binary representation, but also gave the correct rules for addition and multiplication in the binary system.
Sixteen years later, in May 1695, Archduke Rudolf Auguste, in a conversation with Leibniz, was very interested in his binary system, arguing that the fact that "all numbers can be created from 0 and 1" provided the basis for the Christian Bible's account of Genesis. Leibniz took advantage of the Archduke's idea to draw attention to his binary system, and in 1697, in a letter to the Archduke, he dedicated as a New Year's gift a medallion he had designed to symbolize the binary system. On the obverse of the medallion is an image of the Archduke, on the reverse is a story symbolizing the creation of the world - a darkness shrouding the waters, with the sun shining brightly at the top, and in the center is arranged a table of comparison of the numbers of the binary and decimal systems, flanked by examples of addition and multiplication.
In 1701, Leibniz sent his paper on the binary system to the French Academy of Sciences in Paris, but asked that it not be published for a while. Two years later, he gave his revised and supplemented paper to the Paris Academy of Sciences again and asked that it be published, and so, in 1703, the binary system became public.
Leibniz invented the decimal computer, and binary, but he did not use the binary system for computers, this is because in the conditions of the time, a binary machine will increase the technical difficulties. It was only with the development of modern technology that people were able to combine the two effectively. The notion that Leibniz invented binary for computers is contrary to historical fact.
(iv)
In 1684, at the age of 38, Leibniz first published his treatise on differentiation in the Teachers' Journal, which he founded, three years before Newton's Mathematical Principles of Natural Philosophy (1687), which made it the world's earliest publicly available document on calculus.
The full text of Leibniz's treatise on differentiation is only six pages long, but the title is so long that it is generally abbreviated to "A New Method for Finding the Greatest Extremes and Tangents," which contains a modern notation for differentiation and the fundamental laws of differentiation, and gives important results such as the condition dy = 0 for the extremes and d2y = 0 for the points of inflection.
In 1686, at the age of 40, Leibniz again published for the first time in the same journal his treatise on integrals, "Abstruse Geometry with Indivisible Quantities and the Analysis of the Infinite," which likewise appeared in print for the first time in the integral notation used to this day. In this paper he also expressed examples of transcendental curves in terms of integrals, such as ∫a2±x2dx .
One year later, in 1687, at the age of 44, Newton published a scientific tome, The Mathematical Principles of Natural Philosophy, in which he first announced his method of calculus, the method of the streams, to which he added the following commentary:
"Ten years ago, when I was giving a lecture to the Ten years ago, in a letter to the learned mathematician Leibniz, I pointed out that I had discovered a method for finding great and small values, for making tangents, and for solving other similar problems, and that this method was also applicable to irrational numbers. The celebrity wrote back that he had discovered a similar method and showed me his method. His method is much the same as mine, with no substantial difference except in the terms, symbols, arithmetic, and the manner in which the quantities are produced."
Leibniz also spoke highly of Newton's mathematical accomplishments.
When asked by the Queen of Prussia what she thought of Newton at a banquet at the royal palace in Berlin in 1701, Leibniz said:
"Throughout all the mathematics that has ever been written, Newton has done more than half the work."
But the submission of a paper to the Royal Society in 1699 by the Swiss mathematician Fathiodier, which affirmed that Newton was the first inventor of calculus and that Leibniz may have plagiarized, set off a protracted battle between England and continental Europe over the priority of calculus. Out of narrow national prejudice, English mathematicians were slow to accept Leibniz's excellent system of notation, stuck to Newton's flow counting, and thus lagged relatively behind in subsequent advances in calculus. And mathematicians on the European continent soon accepted Leibniz's superior notation, and the efforts of the Bernoulli family, Euler, D'Alembert, Lagrange, Laplace, and others soon yielded fruitful results that guided the development of modern mathematics.
Before and after 1700, Leibniz was keen to organize the work of scientific groups. From 1695, he has been for the establishment of the Academy of Sciences in Berlin and running around, for which he went to Berlin in 1698; 1700, Leibniz was called to be the tutor of the Prussian Queen of Berlin, when his wish to establish the Academy of Sciences was finally realized, and became the first president of the Berlin Academy of Sciences. Subsequently, more than 10 years, he ran in Austria, Russia, advocating the establishment of the Academy of Sciences, these ideas in his lifetime did not come to fruition, but then the Vienna Academy of Sciences, Petersburg Academy of Sciences has been established. Legend has it that Leibniz also wrote a letter suggesting that Emperor Kangxi establish an Academy of Sciences in Beijing.
However, Leibniz also spent a lot of time and energy for his employer, such as for the Brunswick family tracing and genealogy, in order to prove that the family has a right of succession to the throne of Europe, but the family's history of intermarriage is so chaotic that the almighty Leibniz can not make it "seamless". In the course of his investigations for this work, Leibniz often sat in a bumpy, windy, rattling, worn-out carriage, running here and there on the oxcart paths of 17th-century Europe. However, he was able to think, read, and even write continuously in such an environment. The manuscripts of his scholarly writings, which he left behind, are of different sizes and qualities of paper, but they shine with the light of wisdom.
(v)
Leibniz was truly a "master of all trades". In chemistry, in 1677, he wrote the "history of the discovery of phosphorus"; in physics, in addition to the "new hypothesis of physics" in 1671, his academic achievements include the 1684 paper on the mechanics of materials, "a new analytical proof of the force of solids", in 1686 in the measurement of force, "on the Cartesian and others in the laws of nature of the notable errors in the short proofs of the"; in geology he published, in 1693, a book on the primitive earth, and so on.
During the last 20 years of his life, Leibniz turned his interest to philosophy as his main spiritual support. The Leibniz-Wolf system, which he founded with his disciple Wolf, greatly influenced the development of German philosophy.
Leibniz was on a par with Aristotle in the history of philosophy. His "monadology" is one of the main representatives of idealism, which contains some dialectical elements, such as the monad is the unity of the one and the many, and the monad is an entity with its own dynamism. He divided truth into necessary truth and contingent truth, recognizing both necessity and contingency. His philosophical works, such as Metaphysical Talks, A New Treatise on Human Reason, The Theory of Divine Positivity, The Theory of Monads, and The Principle of Nature and Divine Grace Based on Reason, are important representatives of rationalism in the confrontation between empiricism and rationalism, the two major schools of European philosophy. Feuerbach once said, "The richest philosophy in the field of modern philosophy after Descartes and Spinoza is Leibniz." Leibniz pioneered German natural philosophy, and he influenced Kant, Hegel and even Russell in the 20th century.
Like Newton, Leibniz remained unmarried throughout his life. Unlike Newton, Leibniz never taught at a university, and he never entered a church. He died on November 14, 1716, at the age of 70, of gout and gallstones, which the clergy used as an excuse to ignore, and the court did not ask questions, and no one went to the funeral. In contrast to Newton, who was buried in Westminster Abbey, Leibniz was buried in an unmarked grave, visited only by his private secretary and laborers with shovels. Nevertheless, seventy to eighty years after his death, a monument was erected in his honor in Hanover in 1793; a standing statue of him was erected near a church in Leipzig in 1883; and in 1983, the "Leibniz House", which had been destroyed in the Second World War, was rebuilt in its original state in Hanover for posterity.
To the casual observer, Leibniz's careful consideration of all the issues in his published articles and unpublished manuscripts seems incredible.
It is said that Leibniz's skull, which was exhumed and measured as a subject of interest to osteologists and anatomists, was found to be surprisingly smaller than that of a normal adult. It is not known whether this claim is reliable or not, but it may have some truth to it.
(From Wang Yusheng, Popular Science and Technology Daily)
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