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Ann Varela: Was Gottfried Wilhelm Leibniz a True Renaissance man?

Jul 7, 2017 by

An Interview with Ann Varela: Was Gottfried Wilhelm Leibniz a True Renaissance man?

Michael F. Shaughnessy –

1) Ann, Leibniz seems to have been an extraordinary scholar, philosopher, mathematician, among other things. He lived from 1646-1716. First of all, where was he born and do we know much about his childhood?

Leibniz grew up in a home filled with books.  His father was a professor of moral philosophy and provided young Leibniz with an ample supply of reading material.  Self-taught in Latin and Greek at a young age, Leibniz seized every opportunity to advance his learning.  By the time he was only 15 years old, Leibniz was ready to attend the University of Leipzig, in the town of his birth.  Leibniz was so dedicated and motivated to obtain his advanced degree that he finalized his doctoral dissertation by the age of 20 at Altdorf in Nuremberg, as the University of Leipzig refused to award a degree to someone of Leibniz’s age.  He now had his Doctorate and license to practice Law.

2) Now, could he be considered a true Renaissance man?

The term “Renaissance man” frequently pertained to extraordinarily talented people of the fourteenth to seventeenth centuries who wanted to polish their talents in the areas of intellectual, artistic, social and physical pursuits.  Such a man was multi-talented in a wide range of subjects.  Could Leibniz be such a man?  Well, he studied law, became a secretary to an alchemical society, was an assistant to the minister of the Elector of Mainz where he had a role in political negotiations, developed differential and integral calculus, studied energy and momentum, made discoveries in the life sciences, medicine, game theory, economics, and paleontology, developed a calculating machine, was a member of the Royal Society, met Spinoza, the Dutch philosopher who wrote about intellectual and philosophical movements involving reason and the principal source of power and justice, and adopted some of Spinoza’s ideas, and was promoted to Privy Counselor of Justice to the House of Brunswick (as historian and political adviser).  Since Leibniz contributed to such a diverse collection of fields, one could conclude that he, indeed, is an example of a Renaissance man.

3) His early years- what were they like and what were his initial interests?

Early in his career, Leibniz was an assistant to an alchemist.  Transforming elements to gold seems to have been a popular endeavor of that time period.  Soon after that assistance-ship, Leibniz’s interests were political in nature, as his next position found him redrafting the legal code for the Electorate.  By 1669, he was chosen as the Accessor to the Court of Appeal.  This position did not last long due to the death of Baron Johann Christian von Boineburg in 1672, but he did manage to assume an ambassadorial role.  He was tasked with dissuading King Louis XIV of France from attacking German regions.  Leibniz’s plans were never brought to fruition, but his efforts caught the attention of high-ranking government officials in London.

His vigorous political career did not deter Leibniz from following other pursuits in the area of mathematics.  Leibniz developed the mathematical idea of a function to symbolize geometric concepts derived from a curve.  See Figure 1.

Figure 1


Leibniz also developed a system of infinitesimal calculus, independently from Newton.  The matter of who developed calculus first was up for debate, but after great deliberation, Leibniz was credited with its conception because he, in fact, published his work with unique calculus notations before Newton published his work with differing calculus notations.

Two years after Boineburg died, Leibniz was discharged from his diplomatic position.  Fortunately for him, Leibniz had the opportunity to show the Royal Society his newly developed, though incomplete counting machine which used the binary system.  The binary number system is in base two, which utilizes only the digits 0 and 1.  Leibniz had been working on the machine since 1670, which was prior to his dismissal.  He did not begin using the binary system for the counting machine until 1679.  See Figure 2.  The machine was capable of computing four mathematical operations including addition, subtraction, multiplication, division, and roots.

Figure 2

The Royal Society is an academic society for science and fulfills a number of responsibilities such as advocating science and its benefits, recognizing brilliance in science, supporting exceptional science, providing scientific guidance for policy, encouraging international and worldwide co-operation, and education and public engagement.

4) What were his later forays into? What subjects and contributions did he make?

In 1669, Leibniz was offered a position as Councilor and librarian in Duke Johann Friedrich’s court.  Although he accepted the position, he did not relocate to Hanover until 1676.  Leibniz spent his time in Hanover as a full-time politician and representative.  This position allowed Leibniz to travel extensively, meet scientists, and continue his intellectual research, all the while publishing his discoveries.

Some of the mechanical devices that Leibniz worked on include:  hydraulic presses, windmills, lamps, clocks, water pumps, and submarines.  He is also credited with anticipating contemporary geology based on his primitive fossil research.

Along with the more mechanical type of manuscripts, Leibniz was also devoted to writing about the history of the Guelf family, of which the house of Brunswick was a part.  He gathered information on the family by traveling to Bavaria, Austria, and Italy in the late 1680’s.  Once again, he managed to carve out some time to meet and deliberate with other mathematicians like Viviani (Galileo’s last student), Grandi (worked on geometry and hydraulics), Varignon (worked on graphical statics and mechanics), and Jacob Bernoulli (famous for studying catenary -the curve under a string).  Although Leibniz wrote nine volumes of documentation on the Guelf family, he neglected to publish the work that he was appointed.

5) Is there any one single thing that Leibniz is known for? I have read about his ideas of monads.  But from a mathematical point of view- what were his main ideas?

According to Leibniz, a monad is a complete concept, that is, it contains within itself all the foundations or origins of the subject of which it is part of the concept.  The complete concept then relates all monads in the universe to each other.  Therefore, each monad is self-supporting; hence, one monad does not necessarily have influence over another monad.

Monads relate to math and other disciplines in that there does not necessarily have to be a particular cause and effect relationship.  More importantly, the direction of the relationship does not matter.  For example, Leibniz suggests the example that a ship pushes the water to produce circles in the water, yet one could argue that the water is caused to produce all these circles and that it causes the ship to move.  Leibniz’s reasoning states that the way around the relation has no bearing on how it is understood because the relation itself is not real.  Rather, Leibniz suggests a pre-existing harmonization to understand the interconnected behavior of things.

6) Some of these scholars we have reviewed have had interesting lives, and interesting stories—is there anything you want to add?

Leibniz’s travels afforded him the ability to establish over 600 scholarly correspondents in Europe.  There is no doubt that these acquaintances inspired, instructed, and influenced Leibniz’s creativity, prolific stream of ideas, and ultimate outpouring of documentation, manuscripts, and publications.

7) What was his later life like and what were his later contributions?

Leibniz is thought of as a great polymath who traveled extensively, had intellectual pursuits, and saw no boundaries among disciplines.  He was not deterred from publishing transcripts despite his occasional lack of credentials to write on a certain topic, and he was highly critical of universities as foundations due to the lack of interdisciplinary collaboration.  I think Leibniz would be pleased that universities in the twenty first century encourage collegial activity, such as this series of interviews.

8) What have I neglected to ask?

I think that it was quite forward thinking of Leibniz to suggest the establishment of conservatoires, or schools, to make education more practical and accessible.

Even though such schools did not come into existence during his life time, they did develop after his death, such as St. Petersburg Academy and the Berlin Academy.

Another important contribution of Leibniz’s was his use of the binary system.  Today, the binary system is the foundation for representing the two phases “on” and “off” in almost all modern computer and electronic systems.  Leibniz’s manuscripts were vital in the computer development process.

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