2020-06-22, 19:49   #8
ewmayer
2ω=0

Sep 2002
República de California

100110001111112 Posts

Quote:
 Originally Posted by xilman Yeah, I spotted that passage. Seems to me that it is a gross underestimate. From what little I have already learned the estimate is at least a factor of ten too low.
a factor of 10 - Additive, multiplicative, logarithmic, what? And which factor of 10, 2 or 5?

Quote:
 Originally Posted by xilman It may be premature to suggest that all this material be moved to a sub-forum of Hobbies and threads devoted to Latin, Middle Egyptian, Sumerian and Akkadian be created within it. (Sadly, my knowledge of Ancient Greek, Hittite and Sanskrit is non-existent. Perhaps in a year or two ...) If created, we could not only encourage others to learn to read the languages we could discuss mathematics as well. The basics of number theory and geometry were established by people who wrote in those languages. Special cases of theorems of Πυθαγόρας and Εὐκλείδης were well known to Egyptians and Babylonians. Babylonian tablets from 2000 BCE give an algorithm for solving quadratic equations.
My webpage on the history and various useful applications of what is these days commonly known as the Newton-Raphson iterative-approximation method notes this re. the ancient Babylonians:
Quote:
 The iterative scheme [Sqrt2] whereby one takes an initial guess at the square root of c, divides c by the guess and then takes the arithmetic average of the current guess x and c/x to obtain an improved approximation is also interesting due to its long historical pedigree. Amazingly, this very same method for successively approximating square roots was known to and used by the ancient Babylonians, who themselves did not possess an algorithm for long division (much like the lack of a direct division capability by early compute hardware of that other ancient period, the 1940s through 1980s), again necessitating use of approximation algorithms to compute the needed inverse 1/x. In the case of the Babylonians, they used − ta da! − lookup tables for the needed reciprocals. Thus, this particular implementation of a quadratically convergent square-root-finding method likely predates the more general Newton-Raphson method by over 3000 years.
Getting back to the Latin, I came across a useful phrase recently in the context of one of the Sopabox threads: "Quod licet Iovi, non licet bovi." I believe Orwell's version of the concept was "some animals are more equal than others." Paul, help me out - is the c in 'licet' pronounced like the one in 'license' or like the ch in linchpin'? And the pronunciation is the same as in 'vici'? (E.g. J. Caeser's famous 'veni, vidi, vici'.)