The British Museum unrolled a 26 problem hieratic text in 1927, and missed the abstract arithmetic used therein, such as 1/8 = 1/25 + 1/15 + 1/75 + 1/200 that scaled 1/8(25/25) = (8 + 17)/200 = 1/25 + (17/200)(5/5) = 102/1200 = 1/25 + (80 + 16 + 6)/1200 = 1/25 + 1/15 + 1/75 + 1/200. A set of closely related 2/n table and hekat facts were not reported well by Chace in 1927, Gillings in 1972, nor by Claggett in 1999. The 2/n table used one LCM to scale 2/5, 2/7, 2/9, ..., 2/101. The two LCM scaling method was used over 80 times in the RMP, and five times in the Akhmim Wooden Tablet that exactly scaled the hekat by (64/64) and (5/5).
http://planetmath.org/mathematicsinegyptmathematicalleatherroll2014update
Sorry-- mathematics is one area where I might describe myself as "discalculic."
innumerate is a word I understand ... discalculic is a word that has not come my way before ...is it a mental word, or a paper and pencil word?
Scribes 4,000 years ago were mentally numerate computing rational number arithmetic, much as we use today. But final scribal pencil and papyrus numbers and shorthand 'show your work" calculations were required to be written as exact unit fraction series
https://www.academia.edu/5825764/Mathematics_in_Egypt_2014_Update_
It might be useful
http://dial.uclouvain.be/vital/access/manager/Repository/boreal:75526?site_name=UCL
Thanks for the reminder. In have been reading French authors since 1906. Daresay in 1906 tried to scale five hekat problems by a cubit rather than the correct hekat unity (64/64) decoded by Hana Vynazolova in 2002.
Michael is a serous writer that does great work to a point. I can not read her hekat weights and measure papers that follow Vymazolova or generally adds back all hieratic arithmetic statement to an initio points. Michael leaves hieratic arithmetic in shorthand forms and thereby does not correctly translate hieratic arithmetic operations
For example, dvision reported as false position ihas been a major scholarly error since the time of Peer and Chace. Hieratic multiplication and division were inverse operation in hekat partitions ..akhmim wooden tablet and RMP 38.
"Ab initio" is the term Peet suggested ... one that I have have taken seriously ...by adding back missing shorthand arithmetic statements so that precise longhand translations can be written into modern base 10 decimals. Michel locks her hieratic texts into hieroglyphic multiplication that oddly assumes 'false position' as its paired division operation ... which it surely was not in Ahmes 87 probems ... Ahmes only used duplation proofs for multiplication, no hieroglyhohic divison opetation was discussed... Ahmes arithemtic used in hieratiu algebra and geometry problems used scaled rational numbers by LCM so that n/p x m/m = mn/mp with the best divisorrs of mp summed mn in red auxiliary numbers ... facts used in the RMP table shorthand ... to decode Ahmes' longhand required 'ab initio' adding back of missing data ...
Thanks for the links. I will download them and use google translate to read most of her well intentioned details.
Best Regards,
Milo Gardner
Paired multiplication and division operations were recorded in hieratic hekat partitions by. (64/64) x 1/3 = 21/64 + 1/192(5/5) = (16 + 4 + 1)/64 + 5/3 (1/320) = (1/4 + 1/16 + 1/64)hekat + (1+ 2/2) to, since to = 1/320 of a hekat. A 1900 BCE scribe proved his answer correct BT multiplying the teopart quotient and remained answer by 3 obtaining (64/64). As Hana Vymazalova ppublished in 2002, thereby directing the cubit scaling attempt of Daresay in 1906. Note that multiplication and vision were inverse operations to each other, the same algebraic relationship that exists in base 10 decimal arithneetc.
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