
Re: RMP # 48
Posted:
Oct 7, 2007 11:52 AM


Lee, Franz:
It is important to note the difference between proposition and supposition. A proposition offers a hypothesis, and an open method of proof, before accepting its outcome as fact. Supposition, on the other hand, as used in false supposition, only offers an outcome without an open 'proof' process being offered.
That is, false position, or false supposition, a term that RobinsShute used in 1897, and its related algorithm of finding roots may date to an Indian 300 BC text, as reviewed by:
http://en.wikipedia.org/wiki/False_position
related to the well documented arrival of the Chinese Remainder Theorem from China, as Needham and others have discussed, rather than an 800 AD in an Arab text.
As I noted yesterday:
My view is that false position was an Arab innovation developed around 800 AD, (or a 300 BC Indian text) 2,400 (or 1,1300 years) too late to have been known by Ahmes and Egyptian scribes.
My proof is documented by Ahmes' algebra problems, RMP 2438, 47, 8081. Each of Ahmes' algebra problems (that did not rely on any form of algorithm, the intellectual method that documents 'false position' as connected to the Chinese Remainder Theorem and the Liber Abaci's false position method) had been solved by Ahmes, documented in his shorthand, by a small number of steps, compared to the relatively awkward, and historically unproven Arab 'false position' method.
RobinsShute's review of the RMP suggests that partial products and remainders were used (so RobinsShute nearly grasped Ahmes' remainder arithmetic's quotients and remainders) to solve multiplication and division problems (page 18), a point missed by Peet and his group. RobinsShute's title for 'false position' is 'false supposition' (page 37), a term that discloses the revisionist nature of the 'false position' method.
For example, RMP 33, asks Ahmes to solve
x + (2/3 + 1/2 + 1/7)x = 37
(a problem that I have solved and posted to HM several times, as noted by collecting x's such that
x(1 + (28 + 21 + 6)/42) = 37
97/42 x = 37
x = (37*42)/97
and solved in two subtraction steps to find)
and lists a quotient = 14, and remainder answer:
14 + 1/4 + 1/56 + 1/97 + 1/94 + 1/338 + 1/679 + 1/776
an answer than can not be directly found by 'false supposition'. Only the use of vulgar fractions (using ancient and modern rational numbers) as intermediate steps directly, and easily, solves this problem, a point that has been noted by several scholars.
Best Regards,
Milo Gardner

