Respect For The Masters: Gottfried Wilhelm Leibniz




"Binary Numeral System"

Gottfried Wilhelm Leibniz (sometimes von Leibniz or Leibnitz) was a German mathematician and philosopher.
Leibniz occupies a prominent place in the history of mathematics and the history of philosophy. He developed the infinitesimal calculus independently of Isaac Newton, and Leibniz's mathematical notation has been widely used ever since it was published. His visionary Law of Continuity and Transcendental Law of Homogeneity only found mathematical implementation in the 20th century. He became one of the most prolific inventors in the field of mechanical calculators. While working on adding automatic multiplication and division to Pascal's calculator, he was the first to describe a pinwheel calculator in 1685 and invented the Leibniz wheel, used in the arithmometer, the first mass-produced mechanical calculator. He also refined the binary number system, which is at the foundation of virtually all digital computers. In philosophy, Leibniz is mostly noted for his optimism, e.g., his conclusion that our Universe is, in a restricted sense, the best possible one that God could have created. Leibniz, along with René Descartes and Baruch Spinoza, was one of the three great 17th century advocates of rationalism. The work of Leibniz anticipated modern logic and analytic philosophy, but his philosophy also looks back to the scholastic tradition, in which conclusions are produced by applying reason to first principles or prior definitions rather than to empirical evidence. Leibniz made major contributions to physics and technology, and anticipated notions that surfaced much later in philosophy, probability theory, biology, medicine, geology, psychology, linguistics, and information science. He wrote works on philosophy, politics, law, ethics, theology, history, and philology. Leibniz's contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters, and in unpublished manuscripts. He wrote in several languages, but primarily in Latin, French, and German. As of 2012, there is no complete gathering of the writings of Leibniz.
Leibniz may have been the first computer scientist and information theorist. Early in life, he documented the binary numeral system (base 2), then revisited that system throughout his career. He anticipated Lagrangian interpolation and algorithmic information theory. His calculus ratiocinator anticipated aspects of the universal Turing machine. In 1934, Norbert Wiener claimed to have found in Leibniz's writings a mention of the concept of feedback, central to Wiener's later cybernetic theory.
In 1671, Leibniz began to invent a machine that could execute all four arithmetical operations, gradually improving it over a number of years. This "Stepped Reckoner" attracted fair attention and was the basis of his election to the Royal Society in 1673. A number of such machines were made during his years in Hanover, by a craftsman working under Leibniz's supervision. It was not an unambiguous success because it did not fully mechanize the operation of carrying. Couturat reported finding an unpublished note by Leibniz, dated 1674, describing a machine capable of performing some algebraic operations.
Leibniz was groping towards hardware and software concepts worked out much later by Charles Babbage and Ada Lovelace. In 1679, while mulling over his binary arithmetic, Leibniz imagined a machine in which binary numbers were represented by marbles, governed by a rudimentary sort of punched cards.  Modern electronic digital computers replace Leibniz's marbles moving by gravity with shift registers, voltage gradients, and pulses of electrons, but otherwise they run roughly as Leibniz envisioned in 1679.

Source:
http://en.wikipedia.org/wiki/Gottfried_Leibniz

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