Talk:History of logarithms

Is the passage re Varasena reliable?

The passage in this article strongly suggests that "ardhacheda" or "ardhaccheda" is a term that can be applied only to powers of two, and is defined in a way that means essentially the binary logarithm. However, in The Crest of the Peacock [1] Joseph gives a very different interpretation of this term: that it can be applied to any number (not only a power of two) and gives the number of factors of two by which it can be divided without leaving a remainder. Joseph's interpretation is not a logarithm (even though Joseph himself says it is), and should not be described as if it were a logarithm; it is instead much more like a p-adic order. But besides Gupta here and Joseph (both more popular than scholarly) I am having difficulty resolving this question, and I am aware that the subject of Indian discoveries in mathematics is filled both with parallel or earlier discoveries of Western mathematics and pitfalls involving nationalist claims for far more than can be justified by the original sources. Are there other search terms I should be searching for to find more-scholarly sources for this material? —David Eppstein (talk) 07:53, 25 November 2015 (UTC)

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The natural logarithm was first described by Nicholas Mercator in his work Logarithmotechnia published in 1668,<ref {{Citation|author1=J. J. O'Connor|author2=E. F. Robertson |url=http://www-history.mcs.st-and.ac.uk/HistTopics/e.html |title=The number e |publisher=The MacTutor History of Mathematics archive |date=September 2001 |accessdate=2009-02-02}} /ref> although the mathematics teacher John Speidell had already in 1619 compiled a table of what were effectively natural logarithms, based on Napier's work.<ref {{Citation|last=Cajori |first=Florian |authorlink=Florian Cajori |title=A History of Mathematics|edition=5th|location=Providence, RI|publisher=AMS Bookstore |year=1991 |isbn=978-0-8218-2102-2|url=https://books.google.com/books?id=mGJRjIC9fZgC&printsec=frontcover#v=onepage}}, p. 152 /ref>

Euclid Speidell published, his father John is more obscure. Mercator's contribution has been otherwise profiled. — Rgdboer (talk) 02:29, 3 November 2020 (UTC)

Your change obscures the distinction between logarithms as a general topic (including other basis and Napier's offset logarithms) and the natural logarithm more specifically, and removes the explicit credit to Mercator for inventing the natural logarithm. After your change, the section titled "Natural logarithm" now has five paragraphs of text about what appears to be other stuff before offhandedly mentioning the natural log at the end of a block quote and then appearing to give credit to Euler for inventing it. And the history section of our natural logarithm article waffles by saying that the solution to the hyperbolic quadrature by Saint-Vincent and Sarasa "had the properties now associated with the natural logarithm" without saying that it IS the natural logarithm function, or even that it was recognized to be a logarithm. This history does indeed need clarification, but I think your change may have done the opposite. —David Eppstein (talk) 06:53, 3 November 2020 (UTC)

Thank you for your observations. At 1615 Napier should be higher than natural logarithm. The decimal shift with 10⁷ is curious since it is claimed that Napier used decimals, promulgated in Europe by Stevin in De Thiende (1585). Napier worked close to but not exactly with natural logarithm. Efforts to find logarithmus naturalis in Mercator have come up empty, perhaps an editor can supply a page number. The five authors cited worked geometrically before Euler introduced exponential functions to provide a fascile approach. Corrections by a fellow editor are expected. — Rgdboer (talk) 18:51, 3 November 2020 (UTC)

Ok, but you're still not explaining why you are pushing all this other stuff, which is not actually the natural logarithm, into the section specifically titled to be about natural logarithms. If I want to read about the early history of logarithms, before natural logarithms were introduced, I will go elsewhere in the article. If I want to read about the history of the natural logarithm, specifically and explicitly, then I don't want to have to go searching for it among a haystack of not-very-relevant material. And your "efforts to find..." are problematic, because that's not how Wikipedia content should work. We should work on the basis of what reliable sources on the history of mathematics say (such as the MacTutor and Cajori sources, which you removed) not on our own original research into the history of these topics. —David Eppstein (talk) 22:54, 3 November 2020 (UTC)

The name Logarithm - from where arises?!

Please, include references. Alicupe (talk) 12:56, 8 March 2022 (UTC)

Form this article under Napier: 'Napier first called L an "artificial number", but later introduced the word "logarithm" to mean a number that indicates a ratio: λόγος (logos) meaning proportion, and ἀριθμός (arithmos) meaning number.' Perhaps this fact should be easier to find.--agr (talk) 13:23, 8 March 2022 (UTC)