Gottfried Wilhelm von Leibniz ITEC 495-V2WW Assignment 1-4-2 Professor G. Dilts May 16, 2010

Quick Facts Gottfried Wilhelm von Leibniz Birth Well known as a Death July 1, 1646 Well known as a Mathematician Philosopher Death November 14, 1716 Gottfried Wilhelm von Leibniz, born in Leipzig on July 1, 1646, which is a part of the current-day state of Saxony, Germany. His father was a professor of Moral Philosophy at Leipzig University (Ross, 1984, p.3). It is claimed that he was self-taught until the age of seven, at which he entered school and began studying a demanding curriculum including German history, Latin, Greek, theology and [most importantly] logic (Ross). He entered Leipzig University at the age of 14 and graduated two years later. He spent three years working toward advanced levels of a law degree, at which point he attempted to obtain a law tutorship, but was unable to do so due to the high number of candidates and low number of positions (Ross). Instead, in 1666, he entered the university at Altdorf, which at the time, was a major science and technology university (Ross). Image courtesy of Wikipedia: http://en.wikipedia.org/wiki/File:Gottfried_Wilhelm_von_Leibniz.jpg

Varied Areas of Interest Law / History Alchemy Religion Philosophy Library / Encyclopedia Throughout his life, Leibniz had a passion for many subject areas. Learning from an early age the roots of language and history in Latin and Greek, he studied many facets of history that enabled him to become well known. He had a life long fascination with the subject of alchemy, hoping to turn earn a small fortune from it, but unfortunately, it was not to be (Ross). A Lutheran from birth, during the course of his life he had many friends convert to Catholicism. While he was considering following them, he was never comfortable with making a formal conversion. He composed several commentaries that relate to philosophy and religion, some of which were never officially published. Through one such published work, the Discourse on Metaphysics, he hoped it would help to bring together the Protestant religion and the Roman Catholics (Jolley, 2005). During his professional life, he obtained several jobs as a legal advisor, and made many connections across Europe, receiving job offers from many prestigious libraries. A number of the jobs he was offered he declined, due to them being from high ranking officials within the Catholic Church. Having never completed the conversion, he felt uncomfortable in accepting them (Ross). Leibniz had a fascination with information, to the point that one of his ‘cornerstones’ was that of a ‘universal encyclopedia’ containing all current knowledge and information. To create this encyclopedia, he also came up with the idea of an ‘alphabet of human thought,’ which helped him formulate some of his latter ideas.

‘Universal language’ Early attempt toward creating what would be known as a ‘Turing machine’ Term ‘Turing’ not used, due to the machine and test being named for the eventual inventor, Alan Turing The universal language that Leibniz was working on creating intended on providing the ability to break down complex thought into characters that represented simpler thought. Through this language, Leibniz thought it would be possible to break down any problem into one solvable through an equation.

Mathematics & Technology: Pre-IT Binary arithmetic Was not the first to discover Tied more into the ‘universal language’ and metaphysical interests Although Leibniz did very little with the binary arithmetic system that he constructed in terms of developing a fully utilized system or theorems, he considered it to be a very important achievement. The system enabled him to further refine his idea of the universal language on being able to convert, or construct, any thought, or even the universe, into a number (Ross).

Leibniz Calculating Machine First ‘advanced’ ‘calculator’ Could perform the four base arithmetic functions Addition Subtraction Multiplication Division First calculator able to perform multiplication and division. Leibniz also designed a prototype of a calculating machine using his binary arithmetic, but did not proceed to develop it. The combination of the binary system with the calculating machine could potentially have been combined and used to create a ‘computer’, however the technical resources required to do so would have been immense due to the technological development of the time period. Image courtesy of IBM Archives: http://www-03.ibm.com/ibm/history/exhibits/attic3/attic3_037.html

Mathematics & Technology: Pre-IT “I understand. You dispute Newton’s claim that he invented calculus and you want to put Gottfried Leibniz at the top [of the tree].” ~Sheldon Cooper CBS’ The Big Bang Theory “The Maternal Congruence”

Mathematics & Technology: Pre-IT Calculus Developed independently of Newton Aimed to ‘square the circle’ Found out about Newton’s development after reading Newton’s 1689 paper, Principles of Mathematical Philosophy Although Leibniz was not the first to discover an infinitesimal calculus system in 1675, he was the first to publish it in 1684 (Ross). Unlike Newton’s system, Leibniz coined the term ‘function’ to refer to a differential calculus method of “determining the rate of change at any instant of a quantity which is continuously changing in relation to another quantity” (Ross, p. 31). A major difference in the Leibniz system over Newton’s was the way the system was constructed. Leibniz used an algebraic basis, whereas Newton based his system on geometry. It is said that the Leibniz system is superior to Newton’s because of this approach to development (Ross, p. 34).

Mathematics & Technology: Pre-IT Logic Universal language and characteristic Stopped short of developing Boolean algebra and truth-tables that computers are based on Basing some of his later life logic work on his idea of the universal language, Leibniz was able to construct tables that showed relationships between concepts, borrowing ideas from mathematics such as the =, + and -. For example, using A to represent ‘man’, B to represent ‘rational’ and C to represent ‘animal’, “A=B+C meaning that the concept of man is the same as the concept of a rational animal’” and “A-B=C, where negating the rational aspect of man left the concept of animal” (Ross, p. 70). Subtraction and negation would have major differences in concept; such as in this example, Leibniz realized that he could not negate ‘B’ as it would create a contradiction , but would need to subtract the concept. Using logical ‘calculations’ such as this, Leibniz was able to modify his borrowed symbols and form tables in which he could show logical relationships. His research and notations stopped short of representing all possible relationships – this would come later when George Boole would fully develop the idea.

Digital Age without Leibniz Leibniz developed a number of computing technologies on a rudimentary level Would they have been developed otherwise? Calculating machine was the basis of his election into the Royal Society of London for the Improvement of Natural Knowledge It is difficult to say if Leibniz had not created so many works if the ideas he came up with would have been delayed for years, or even come up with at all. Without researching into those that followed, I cannot say if people like George Boole or Alan Turing had based much of their research and discovery on the writings of Leibniz; but it is an assumption that at least some of the work Leibniz came up with had an impact on more modern theorists and technologists.

References Jolley, N. (2005). Leibniz. New York: Routledge. Ross, G. (1984). Leibniz. New York: Oxford University Press. Images http://en.wikipedia.org/wiki/File:Gottfried_Wilhelm_von_Leibniz.jpg http://www-03.ibm.com/ibm/history/exhibits/attic3/attic3_037.html CBS’ The Big Bang Theory