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NOT LEIBNIZ SANDBOX prior to peer review


Mathematics

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Leibniz also believed that the sum of an infinite number of zeros would equal to one half using the analogy of the creation of the world from nothing. [1] Leibniz was also one the pioneers in actuarial science, calculating the purchase price of life annuities and the liquidation of a state's debt.[2]

Linear systems

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Leibniz laid down the foundations and theory of determinants, although Seki Kowa discovered determinants well before Leibniz.[3][4] His works show calculating the determinants using cofactors.[5] Calculating the determinant using cofactors is named the Leibniz formula. Finding the determinant of a matrix using this method proves impractical with large n, requiring to calculate n! products and the number of n-permutations.[6] He also solved systems of linear equations using determinants, which is now called Cramer's rule. This method for solving systems of linear equations based off of determinants was found in 1684 by Leibniz (Cramer published his findings in 1750).[7] Although Gaussian elimination requires arithmetic operations, linear algebra textbooks still teach cofactor expansion before LU factorization .[8][9]

Computation

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Leibniz may have been the first computer scientist and information theorist.[10] Early in life, he documented the binary numeral system (base 2), then revisited that system throughout his career.[11] 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.[12]More information can be found in the Sinophile section. Leibniz may have plagiarized Juan Caramuel y Lobkowitz and Thomas Harriot, who independently developed the binary system, as he was familiar with their works on the binary system.[13] Juan Caramuel y Lobkowitz worked extensively on logarithms including logarithms with base 2.[14] Thomas Harriot's manuscripts contained a table of binary numbers and their notation, which he realized any number could be written on a base 2 system.[15] Regardless, Leibniz simplified the binary system and articulated logical properties such as conjunction, disjunction, negation, identity, inclusion, and the empty set.[16] Leibniz interpreted binary arithmetic to the image of Creation with one representing God and zero representing the void.[17] He anticipated 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.[18]

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 operation. Couturat reported finding an unpublished note by Leibniz, dated 1674, describing a machine capable of performing some algebraic operations.[19] Leibniz also devised a (now reproduced) cipher machine, recovered by Nicholas Rescher in 2010.[20] In 1693, Leibniz described a design of a machine which could, in theory, integrate differential equations, which he called "integraph".[21]

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.[22][23] 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.

Philologist

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Leibniz the philologist was an avid student of languages, eagerly latching on to any information about vocabulary and grammar that came his way. He refuted the belief, widely held by Christian scholars in his day, that Hebrew was the primeval language of the human race. He also refuted the argument, advanced by Swedish scholars in his day, that a form of proto-Swedish was the ancestor of the Germanic languages. He puzzled over the origins of the Slavic languages and was fascinated by classical Chinese. Leibniz was also an expert in the Sanskrit language.[24]

Sinophile

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He mulled over the possibility that the Chinese characters were an unwitting form of his universal characteristic. He noted with fascination how the I Ching hexagrams correspond to the binary numbers from 000000 to 111111, and concluded that this mapping was evidence of major Chinese accomplishments in the sort of philosophical mathematics he admired.[25] Leibniz communicated his ideas of the binary system representing Christianity to the Emperor of China hoping it would convert him.[26] Leibniz may be the only major Western philosopher who attempted to accommodate Confucian ideas to prevailing European beliefs.[27]

Geometry

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The Leibniz formula for π states that

Leibniz wrote that circles "can most simply be expressed by this series, that is, the aggregate of fractions alternately added and subtracted."[28] However this formula is only accurate with a large number of terms, using 10,000,000 terms to obtain the correct value of to 8 decimal places.[29] Leibniz attempted to create a definition for a straight line while attempting to prove the parallel postulate. [30]

Leibniz Death

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Leibniz died in Hanover in 1716: at the time, he was so out of favor that neither George I (who happened to be near Hanover at that time) nor any fellow courtier other than his personal secretary attended the funeral. Even though Leibniz was a life member of the Royal Society and the Berlin Academy of Sciences, neither organization saw fit to honor his passing. His grave went unmarked for more than 50 years

Topology

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Would like to add more on this section Geometry and Monadology: Leibniz’s Analysis Situs and Philosophy of Space, by Vincenzo De Risi.


Article evaluation

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History of computing

  • Is everything in the article relevant to the article topic? Is there anything that distracted you?

The article explains early tools for computing such as the abacus. It wasn't distracting to me as it was organized.

  • Is the article neutral? Are there any claims, or frames, that appear heavily biased toward a particular position?

The article seems neutral to me, adding early computing tools from different regions of the world.

  • Are there viewpoints that are overrepresented, or underrepresented?

Computing after 1990s seems to be missing from this article, although there is a main article for that subject matter.

  • Check a few citations. Do the links work? Does the source support the claims in the article?

Citation 16 seems to work, but nowhere does the source specify it had 1 MB of RAM.

  • Is each fact referenced with an appropriate, reliable reference? Where does the information come from? Are these neutral sources? If biased, is that bias noted?

The sources come from academic jounrnals or scholarly research

  • Is any information out of date? Is anything missing that could be added?

The wasn't anything about calculating with an electronic computer, such as Boolean algebra, Taylor series, or binary numbers.

  • Check out the Talk page of the article. What kinds of conversations, if any, are going on behind the scenes about how to represent this topic?

. The conversations range from the title of the article to the involvement of people.

  • How is the article rated? Is it a part of any WikiProjects?

Start class, history of science wiki project

  • How does the way Wikipedia discusses this topic differ from the way we've talked about it in class?

We haven't talked about this in class

Computation

Leibniz may have been the first computer scientist and information theorist.[31] Early in life, he documented the binary numeral system (base 2), then revisited that system throughout his career.[32] He anticipated 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.[33]

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. Leibniz may have plagiarized Juan Caramuel y Lobkowitz as he was familiar with his works on the binary system.[34] He anticipated 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.

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 operation. Couturat reported finding an unpublished note by Leibniz, dated 1674, describing a machine capable of performing some algebraic operations. Leibniz also devised a (now reproduced) cipher machine, recovered by Nicholas Rescher in 2010. In 1693, Leibniz described a design of a machine which could, in theory, integrate differential equations, which he called "integraph".

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.

Peer Review byNjanrd (talk) 20:07, 18 March 2018 (UTC)

[edit]

So far, I think you have great information about Gottfried Wilhelm Leibniz. I could not track down your first reference to check if it was valid or not. I am not sure if it was intentional, or by accident, but your first and second paragraph include the same information. I think it would be interesting if you could find more information on whether or not Gottfried was in fact the first computer scientist and information theorist and if there is any other proof pointing to him plagiarizing someone elses work. Overall, What you have is good and you have a good amount of references for the amount of writing you have done. Maybe just work on the links to the articles.Njanrd (talk) 20:20, 18 March 2018 (UTC)

Things in the peer review were not mine except the plagiarism part. They were the original Wikipedia text. Also, I did not work in this sandbox before 18 March 2018. Rtthb (talk) 01:15, 27 April 2018 (UTC)

Added Thomas Harriot (plagiarism part) Rtthb (talk) 01:17, 27 April 2018 (UTC)

  1. ^ Agarwal, Ravi P; Sen, Syamal K (2014). Creators of Mathematical and Computational Sciences. Springer, Cham. p. 186. ISBN 978-3-319-10870-4. {{cite book}}: Cite has empty unknown parameter: |1= (help)
  2. ^ Leader, editor, Timothy Gowers ; associate editors, June Barrow-Green, Imre (2008). The Princeton Companion to Mathematics. Princeton: Princeton University Press. p. 745. ISBN 978-0691118802. {{cite book}}: |first1= has generic name (help)CS1 maint: multiple names: authors list (link)
  3. ^ Agarwal, Ravi P; Sen, Syamal K (2014). Creators of Mathematical and Computational Sciences. Springer, Cham. p. 180. ISBN 978-3-319-10870-4. {{cite book}}: Cite has empty unknown parameter: |1= (help)
  4. ^ Leader, editor, Timothy Gowers ; associate editors, June Barrow-Green, Imre (2008). The Princeton Companion to Mathematics. Princeton: Princeton University Press. p. 744. ISBN 978-0691118802. {{cite book}}: |first1= has generic name (help)CS1 maint: multiple names: authors list (link)
  5. ^ Knobloch, Eberhard (13 March 2013). Leibniz’s Theory of Elimination and Determinants. Springer. pp. 230–237. ISBN 978-4-431-54272-8.
  6. ^ Concise Dictionary of Mathematics. V&S Publishers. pp. 113–114. ISBN 978-9381588833.
  7. ^ Leader, editor, Timothy Gowers ; associate editors, June Barrow-Green, Imre (2008). The Princeton Companion to Mathematics. Princeton: Princeton University Press. p. 744. ISBN 978-0691118802. {{cite book}}: |first1= has generic name (help)CS1 maint: multiple names: authors list (link)
  8. ^ Lay, David C. (2012). Linear algebra and its applications (4th ed. ed.). Boston: Addison-Wesley. ISBN 978-0321385178. {{cite book}}: |edition= has extra text (help)
  9. ^ (ed.), Takeshi Tokuyama (2007). Algorithms and Computation: 18th International Symposium, ISAAC 2007, Sendai, Japan, December 17-19, 2007 : proceedings. Berlin [etc.]: Springer. p. 599. ISBN 9783540771203. {{cite book}}: |last1= has generic name (help)
  10. ^ Davis (2000) discusses Leibniz's prophetic role in the emergence of calculating machines and of formal languages.
  11. ^ See Couturat (1901): 473–78.
  12. ^ Ryan, James. "Leibniz' Binary System and Shao Yong's "Yijing"". University of Hawaii Press: 59–90.
  13. ^ Ares, J.; Lara, J.; Lizcano, D.; Martínez, M. (2017). "Who Discovered the Binary System and Arithmetic? Did Leibniz Plagiarize Caramuel?". Science and Engineering Ethics. 24: 173–188. eISSN 1471-5546 – via Springer.
  14. ^ Navarro-Loidi, Juan (May 2008). "The Introductions of Logarithms into Spain". Historia Mathematica. 35 (2): 83–101.
  15. ^ Booth, Michael (2003). "Thomas Harriot's Translations". The Yale Journal of Criticism. 16 (2): 345. ISSN 0893-5378.
  16. ^ Lande, Daniel. "Development of the Binary Number System and the Foundations of Computer Science". The Mathematics Enthusiast: 513-540.
  17. ^ Agarwal, Ravi P; Sen, Syamal K (2014). Creators of Mathematical and Computational Sciences. Springer, Cham. p. 186. ISBN 978-3-319-10870-4. {{cite book}}: Cite has empty unknown parameter: |1= (help)
  18. ^ Wiener, N., Cybernetics (2nd edition with revisions and two additional chapters), The MIT Press and Wiley, New York, 1961, p. 12.
  19. ^ Couturat (1901), 115
  20. ^ See N. Rescher, Leibniz and Cryptography (Pittsburgh, University Library Systems, University of Pittsburgh, 2012).
  21. ^ "The discoveries of principle of the calculus in Acta Eruditorum" (commentary, p. 60-61), translated by Pierre Beaudry, amatterofmind.org, Leesburg, Va., September 2000. (pdf)
  22. ^ The Reality Club: Wake Up Call for Europe Tech
  23. ^ Agarwal, Ravi P; Sen, Syamal K (2014). Creators of Mathematical and Computational Sciences. Springer, Cham. p. 28. ISBN 978-3-319-10870-4. {{cite book}}: Cite has empty unknown parameter: |1= (help)
  24. ^ Agarwal, Ravi P; Sen, Syamal K (2014). Creators of Mathematical and Computational Sciences. Springer, Cham. p. 186. ISBN 978-3-319-10870-4. {{cite book}}: Cite has empty unknown parameter: |1= (help)
  25. ^ On Leibniz, the I Ching, and binary numbers, see Aiton (1985: 245–48). Leibniz's writings on Chinese civilization are collected and translated in Cook and Rosemont (1994), and discussed in Perkins (2004).
  26. ^ Agarwal, Ravi P; Sen, Syamal K (2014). Creators of Mathematical and Computational Sciences. Springer, Cham. p. 186. ISBN 978-3-319-10870-4. {{cite book}}: Cite has empty unknown parameter: |1= (help)
  27. ^ Cook, Daniel. "Leibniz, China, and the Problem of Pagan Wisdom". Project Muse. Project Muse. Retrieved 12 April 2018.
  28. ^ Jones, Matthew L. (2006). The Good Life in the Scientific Revolution : Descartes, Pascal, Leibniz, and the Cultivation of Virtue ([Online-Ausg.]. ed.). Chicago [u.a.]: Univ. of Chicago Press. p. 169. ISBN 9780226409542.
  29. ^ Davis, Martin (2018-02-28). The Universal Computer : The Road from Leibniz to Turing, Third Edition. CRC Press. p. 7. ISBN 9781138502086.
  30. ^ Risi, Vincenzo De (2016). Leibniz on the Parallel Postulate and the Foundations of Geometry. p. 31. ISBN 978-3-319-19863-7.
  31. ^ Davis (2000) discusses Leibniz's prophetic role in the emergence of calculating machines and of formal languages.
  32. ^ See Couturat (1901): 473–78.
  33. ^ Wiener, N., Cybernetics (2nd edition with revisions and two additional chapters), The MIT Press and Wiley, New York, 1961, p. 12.
  34. ^ Ares, J.; Lara, J.; Lizcano, D.; Martínez, M. (2017). "Who Discovered the Binary System and Arithmetic? Did Leibniz Plagiarize Caramuel?". Science and Engineering Ethics. 24: 173–188. eISSN 1471-5546 – via Springer.
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