User:Rtvw9/sandbox

Geometry
The Leibniz formula for π states that

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 $\pi⁄4$ to 8 decimal places. Leibniz attempted to create a definition for a straight line while attempting to prove the parallel postulate. While most mathematicians defined a straight line as the shortest line between two points, Leibniz believed that this was a merely property of a straight line rather than the definition.

House of Hanover
Duke Johann Friedrich of Hanover offered Leibniz a position since the duke was interested intellectual matters and gave promise of financial security. Leibniz accepted the offer but asked for the "freedom to pursue his own studies for the benefit of mankind".

... Leibniz managed to delay his arrival in Hanover until the end of 1676 after making one more short journey to London, where Newton accused him of having seen Newton's unpublished work on calculus in advance.[37] This was alleged to be evidence supporting the accusation, made decades later, that he had stolen calculus from Newton. On the journey from London to Hanover, Leibniz stopped in The Hague where he met van Leeuwenhoek, the discoverer of microorganisms. He also spent several days in intense discussion with Spinoza, who had just completed his masterwork, the Ethics.[38]

section above not needed anymore

In 1677, he was promoted, at his request, to Privy Counselor of Justice, a post he held for the rest of his life. Leibniz served three consecutive rulers of the House of Brunswick as historian, political adviser, and most consequentially, as librarian of the ducal library. He thenceforth employed his pen on all the various political, historical, and theological matters involving the House of Brunswick; the resulting documents form a valuable part of the historical record for the period.

....

Leibniz began promoting a project to use windmills to improve the mining operations in the Harz Mountains. This project did little to improve mining operations and was shut down by Duke Ernst August in 1685.

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Among the few people in north Germany to accept Leibniz were the Electress Sophia of Hanover (1630–1714), her daughter Sophia Charlotte of Hanover (1668–1705), the Queen of Prussia and his avowed disciple, and Caroline of Ansbach, the consort of her grandson, the future George II. To each of these women he was correspondent, adviser, and friend. In turn, they all approved of Leibniz more than did their spouses and the future king George I of Great Britain.

china
of major Chinese accomplishments in the sort of philosophical mathematics he admired. Leibniz may be the only major Western philosopher who attempted to accommodate Confucian ideas to prevailing European beliefs.

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. 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.

Original 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. 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.

Would like to add more to this section such as Chinese/Confucian influence, European contemporaries, etc. Rtthb (talk) 01:36, 23 March 2018 (UTC)

Linear systems (new section)
Leibniz arranged the coefficients of a system of linear equations into an array, now called a matrix, in order to find a solution to the system if it existed. This method was later called Gaussian elimination.

Leibniz contributed to linear systems with his works on determinants in attempt to find solutions to higher degree polynomials. Finding the solutions of using a matrix is now called Gaussian elimination. His works show calculating the determinants using cofactors, which eventually led to the Leibniz formula for determinants.

Original linear systems
Leibniz was the first to see that the coefficients of a system of linear equations could be arranged into an array, now called a matrix, which can be manipulated to find the solution of the system, if any. This method was later called Gaussian elimination.

Linear system notes

Would like to add more about Leibniz using matrices or proof he was using it. Done

Notes: There really isn't much about Leibniz and his contributions to this section. Rtthb (talk) 01:34, 23 March 2018 (UTC)

Monads
Leibniz's best known contribution to metaphysics is his theory of monads, as exposited in Monadologie. He proposes his theory that the universe is made of an infinite number of simple substances. These simple substances or monads are the "ultimate units of existence in nature". Monads have no parts but still exist by the qualities that they have. These qualities are continuously changing over time, and each monad is unique. They lack divisibility and are the "true atoms of nature". They are also not affected by time and are subject to only creation and annihilation. All monads have perception and appetition (the inner drive of change), but some monads have consciousness and memory are to known as souls. Monads are centers of force; substance is force, while space, matter, and motion are merely phenomenal.

Leibniz's proof of God can be summarized in the Théodicée. Reason is governed by the principle of contradiction and the principle of sufficient reason. Using the principle of reasoning, Leibniz concluded that the first reason of all things is God. All that we see and experience are subject to change, and the fact that this world is contingent can be explained by the possibility of the world being arranged differently in space and time. The contingent world must have some necessary reason for its existence. Leibniz uses a geometry book as an example to explain his reasoning. If this book was copied from an infinite chain of copies, there must be a some reason for the content of the book. Leibniz concluded that there must be the "monas monadum" or God.

Original Monads
Leibniz's best known contribution to metaphysics is his theory of monads, as exposited in Monadologie. According to Leibniz, monads are elementary particles with blurred perceptions of one another. Monads can also be compared to the corpuscles of the Mechanical Philosophy of René Descartes and others. Monads are the ultimate elements of the universe. The monads are "substantial forms of being" with the following properties: they are eternal, indecomposable, individual, subject to their own laws, un-interacting, and each reflecting the entire universe in a pre-established harmony (a historically important example of panpsychism). Monads are centers of force; substance is force, while space, matter, and motion are merely phenomenal.

The ontological essence of a monad is its irreducible simplicity. Unlike atoms, monads possess no material or spatial character. They also differ from atoms by their complete mutual independence, so that interactions among monads are only apparent. Instead, by virtue of the principle of pre-established harmony, each monad follows a preprogrammed set of "instructions" peculiar to itself, so that a monad "knows" what to do at each moment. By virtue of these intrinsic instructions, each monad is like a little mirror of the universe. Monads need not be "small"; e.g., each human being constitutes a monad, in which case free will is problematic.

Monads are purported to have gotten rid of the problematic:

interaction between mind and matter arising in the system of Descartes; lack of individuation inherent to the system of Spinoza, which represents individual creatures as merely accidental.

To-do list
- check citations; most are broken

- check which sections are plag.

- find sources for plagiarized sections

List of plag.:

Leibniz, G. W. (1714/1720). The Principles of Philosophy known as Monadology (transl. by Jonathan Bennett, 2007) Rtthb (talk) 02:38, 9 March 2018 (UTC)

Bad citations

112 - non-peer reviewed blog

- write section w/o plagiarizing Rtvw9 (talk) 02:32, 9 March 2018 (UTC)

Peer Review by Jnhkb4 (talk) 21:00, 18 March 2018 (UTC)
What you have so far seems to be pretty good. It's great that you know what you want to do and noted how you want to add to each section. Fixing sections without citations and plagiarism and rewording them to be better understood is pretty important for this article. Things that could be needing some touch up would be forming a connection about monads to reasoning and god in the second paragraph. Jnhkb4 (talk) 21:00, 18 March 2018 (UTC)

Thanks for the peer review. I wanted to link monads to God but I currently do not have enough information to do so. I'm still working on rewording the section and I also need to add more citations in this section. Rtvw9 (talk) 16:31, 23 March 2018 (UTC)

Response by Rtthb (talk) 16:20, 23 March 2018 (UTC)
I haven't removed the plagiarism in he article, because I haven't found any other sources to help reword it. I continued to add more content, specifically he computation heading. The monads and reasoning with God is very lengthy. It is hard to break it down to main points. I found sources such as Leibniz researching Chinese Confucianism and his monadology views. I'm still working on what Leibniz thought about God (I read something about binary and existence of God). I'll try to added citations to the rough draft

tl;dr We're working on changes on monads and God. Added computation contributions

Peer ReviewNjanrd (talk) 21:46, 18 March 2018 (UTC)
So far, I think you have great information about Gottfried Wilhelm Leibniz. I think the outline that you have is very helpful for the future of you edits. I think that it would be beneficial for you to include references even in the rough draft so it is easier to move it to the actually wiki page and so that others could better peer review you draft. Something I think would be interesting to see is if you could find information on how Leibniz can to postulate his idea about monads Njanrd (talk) 21:46, 18 March 2018 (UTC)

I've added a references section to make things easier. I can try to find out how Leibniz postulate his ideas but it will take time and would likely not be a priority. Rtvw9 (talk) 16:34, 23 March 2018 (UTC)

Article Evaluation
Byzantine science

Articles in Byzantine science are relevant, but some have little to say about certain topics. The mathematics section is only a small paragraph that mentions three mathematicians and how math contributed to the building of the Hagia Sophia. Surely there are other mathematicians and improvements made in field of math. It looks like this article can potentially have more sections.

The article as a whole assumes the reader knows what the Byzantine Empire was and leaves out background information about its formation. This may or may not have an effect on the development of science in the empire.

There is also a section about Greek fire which goes into detail on how it was effective in naval battles. I would have tried to create a section of something like "Warfare" which includes some science and technology that contributes to Byzantine military.

Some citations are broken. The second reference to Byzantine medicine has a broken URL. Also, there are very few people on the talk page.