Editing Gottfried Wilhelm Leibniz (section)

===Technology===
In 1906, Garland published a volume of Leibniz's writings bearing on his many practical inventions and engineering work. To date, few of these writings have been translated into English. Nevertheless, it is well understood that Leibniz was a serious inventor, engineer, and applied scientist, with great respect for practical life. Following the motto ''theoria cum praxi'', he urged that theory be combined with practical application, and thus has been claimed as the father of [[applied science]]. He designed wind-driven propellers and water pumps, mining machines to extract ore, hydraulic presses, lamps, submarines, clocks, etc. With [[Denis Papin]], he created a [[steam engine]]. He even proposed a method for desalinating water. From 1680 to 1685, he struggled to overcome the chronic flooding that afflicted the ducal silver mines in the [[Harz Mountains]], but did not succeed.<ref>Aiton (1985), 107–114, 136</ref>

===={{anchor|Information technology}}Computation====
Leibniz may have been the first computer scientist and information theorist.<ref>Davis (2000) discusses Leibniz's prophetic role in the emergence of calculating machines and of formal languages.</ref> Early in life, he documented the [[binary numeral system]] ([[radix|base]] 2), then revisited that system throughout his career.<ref>See Couturat (1901): 473–478.</ref> While Leibniz was examining other cultures to compare his metaphysical views, he encountered an ancient Chinese book ''[[I Ching]]''. Leibniz interpreted a diagram which showed yin and yang and corresponded it to a zero and one.<ref>{{Cite journal |jstor = 1399337|title = Leibniz' Binary System and Shao Yong's "Yijing"|journal = Philosophy East and West|volume = 46|issue = 1|pages = 59–90|last1 = Ryan|first1 = James A.|year = 1996|doi = 10.2307/1399337}}</ref> More information can be found in the [[#Sinophology|Sinophology]] section. Leibniz had similarities with [[Juan Caramuel y Lobkowitz]] and [[Thomas Harriot]], who independently developed the binary system, as he was familiar with their works on the binary system.<ref>{{Cite journal|last1=Ares|first1=J.|last2=Lara|first2=J.|last3=Lizcano|first3=D.|last4=Martínez|first4=M.|date=2017|title=Who Discovered the Binary System and Arithmetic?|journal=Science and Engineering Ethics|volume=24|issue=1|pages=173–188|pmid=28281152|doi=10.1007/s11948-017-9890-6|s2cid=35486997|hdl=20.500.12226/69|hdl-access=free}}</ref> Juan Caramuel y Lobkowitz worked extensively on logarithms including logarithms with base 2.<ref>{{cite journal|last1=Navarro-Loidi|first1=Juan|title=The Introductions of Logarithms into Spain|journal=Historia Mathematica|date=May 2008|volume=35|issue=2|pages=83–101|doi=10.1016/j.hm.2007.09.002|doi-access=free}}</ref> Thomas Harriot's manuscripts contained a table of binary numbers and their notation, which demonstrated that any number could be written on a base 2 system.<ref>{{cite journal|last1=Booth|first1=Michael|title=Thomas Harriot's Translations|journal=The Yale Journal of Criticism|date=2003|volume=16|issue=2|pages=345–361|issn=0893-5378|doi=10.1353/yale.2003.0013|s2cid=161603159}}</ref> Regardless, Leibniz simplified the binary system and articulated logical properties such as conjunction, disjunction, negation, identity, inclusion, and the empty set.<ref>{{cite journal|last1=Lande|first1=Daniel|title=Development of the Binary Number System and the Foundations of Computer Science|journal=The Mathematics Enthusiast|pages=513–540}}</ref> He anticipated [[Lagrange polynomial|Lagrangian interpolation]] and [[algorithmic information theory]]. His [[calculus ratiocinator]] anticipated aspects of the [[universal Turing machine]]. In 1961, [[Norbert Wiener]] suggested that Leibniz should be considered the patron saint of [[cybernetics]].<ref>Wiener, N., ''Cybernetics'' (2nd edition with revisions and two additional chapters), The MIT Press and Wiley, New York, 1961, p. 12.</ref> Wiener is quoted with "Indeed, the general idea of a computing machine is nothing but a mechanization of Leibniz's Calculus Ratiocinator."<ref>{{cite journal |last1=Wiener |first1=Norbert |title=Time, Communication, and the Nervous System |journal=Annals of the New York Academy of Sciences |date=1948 |volume=50 |issue=4 Teleological |pages=197–220 |doi=10.1111/j.1749-6632.1948.tb39853.x |pmid=18886381 |bibcode=1948NYASA..50..197W |s2cid=28452205 |url=https://nyaspubs.onlinelibrary.wiley.com/doi/abs/10.1111/j.1749-6632.1948.tb39853.x |language=en |access-date=23 July 2021 |archive-date=23 July 2021 |archive-url=https://web.archive.org/web/20210723233238/https://nyaspubs.onlinelibrary.wiley.com/doi/abs/10.1111/j.1749-6632.1948.tb39853.x |url-status=dead }}</ref>

In 1671, Leibniz began to invent a machine that could execute all four arithmetic 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 his supervision. They were not an unambiguous success because they did not fully mechanize the [[Carry (arithmetic)|carry operation]]. Couturat reported finding an unpublished note by Leibniz, dated 1674, describing a machine capable of performing some algebraic operations.<ref>Couturat (1901), 115</ref> Leibniz also devised a (now reproduced) cipher machine, recovered by [[Nicholas Rescher]] in 2010.<ref>See N. Rescher, ''Leibniz and Cryptography'' (Pittsburgh, University Library Systems, University of Pittsburgh, 2012).</ref> In 1693, Leibniz described a design of a machine which could, in theory, integrate differential equations, which he called "integraph".<ref>[http://amatterofmind.org/Pierres_PDFs/TRANSLATIONS/4._GOTTFRIED_LEIBNIZ_SELECTIONS_FROM_ACTA_ERUDITORUM.pdf "The discoveries of principle of the calculus in Acta Eruditorum"] (commentary, pp. 60–61), translated by Pierre Beaudry, amatterofmind.org, Leesburg, Va., September 2000. (pdf)</ref>

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.<ref>{{cite web|url=http://www.edge.org/discourse/schirrmacher_eurotech.html|title=The Reality Club: Wake Up Call for Europe Tech|website=www.edge.org|access-date=11 January 2006|archive-date=28 December 2005|archive-url=https://web.archive.org/web/20051228133959/http://www.edge.org/discourse/schirrmacher_eurotech.html|url-status=dead}}</ref><ref>{{cite book|last1=Agarwal|first1=Ravi P|last2=Sen|first2=Syamal K|title=Creators of Mathematical and Computational Sciences|date=2014|publisher=Springer, Cham|isbn=978-3-319-10870-4|page=28}}</ref> 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.