User:Rtthb/sandbox

NOT LEIBNIZ SANDBOX prior to peer review

Mathematics
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. Leibniz was also one the pioneers in actuarial science, calculating the purchase price of life annuities and the liquidation of a state's debt.

Linear systems
Leibniz laid down the foundations and theory of determinants, although Seki Kowa discovered determinants well before Leibniz. His works show calculating the determinants using cofactors. 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. 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). Although Gaussian elimination requires $$O(n^3)$$ arithmetic operations, linear algebra textbooks still teach cofactor expansion before LU factorization.

Computation
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. 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. 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. Juan Caramuel y Lobkowitz worked extensively on logarithms including logarithms with base 2. 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. Regardless, Leibniz simplified the binary system and articulated logical properties such as conjunction, disjunction, negation, identity, inclusion, and the empty set. Leibniz interpreted binary arithmetic to the image of Creation with one representing God and zero representing the void. 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.

Philologist
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.

Sinophile
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. Leibniz communicated his ideas of the binary system representing Christianity to the Emperor of China hoping it would convert him. Leibniz may be the only major Western philosopher who attempted to accommodate Confucian ideas to prevailing European beliefs.

Geometry
The Leibniz formula for $\pi$ states that
 * $$1 \,-\, \frac{1}{3} \,+\, \frac{1}{5} \,-\, \frac{1}{7} \,+\, \cdots \,=\, \frac{\pi}{4}.$$

Leibniz wrote that circles "can most simply be expressed by this series, that is, the aggregate of fractions alternately added and subtracted." However this formula is only accurate with a large number of terms, using 10,000,000 terms to obtain the correct value of $$\frac{\pi}{4}$$ to 8 decimal places. Leibniz attempted to create a definition for a straight line while attempting to prove the parallel postulate.

Leibniz Death
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
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
History of computing The article explains early tools for computing such as the abacus. It wasn't distracting to me as it was organized. The article seems neutral to me, adding early computing tools from different regions of the world. Computing after 1990s seems to be missing from this article, although there is a main article for that subject matter. Citation 16 seems to work, but nowhere does the source specify it had 1 MB of RAM. The sources come from academic jounrnals or scholarly research The wasn't anything about calculating with an electronic computer, such as Boolean algebra, Taylor series, or binary numbers. .      The conversations range from the title of the article to the involvement of people. Start class, history of science wiki project We haven't talked about this in class
 * Is everything in the article relevant to the article topic? Is there anything that distracted you?
 * Is the article neutral? Are there any claims, or frames, that appear heavily biased toward a particular position?
 * Are there viewpoints that are overrepresented, or underrepresented?
 * Check a few citations. Do the links work? Does the source support the claims in the article?
 * 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?
 * Is any information out of date? Is anything missing that could be added?
 * 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?
 * How is the article rated? Is it a part of any WikiProjects?
 * How does the way Wikipedia discusses this topic differ from the way we've talked about it in class?

Computation

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 1961, Norbert Wiener suggested that Leibniz should be considered the patron saint of cybernetics.

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. 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)
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)