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Akhmim Wooden Tablet

• Message 1.Β 

  Posted by Milo Gardner (U14346264) on Wednesday, 24th February 2010

  Not only did this month's Βι¶ΉΤΌΕΔ Rhind Mathematical Papyrus broadcase omit mentioning the EMLR, as an introduction of the RMP 2/n table, scholars also skipped over the very signigicant Akhmim Wooden Tablet (AWT):
  
  
  
  an 1800 BCE weights and measures text, that gathered dust in the Cairo Museum until 2002. The AWT showed that a hekat unity, written as (64/64), was divided by 3, 7, 10, 11 and 13 in a scaled remainder manner that the RMP used over 40 times, 29 times in RMP 82.
  
  The AWT limited divisors n to the range:
  
  1/64 < n < 64, such that:
  
  (64/64)/n = (Q/64)hekat + (5R/n)1/320
  
  with Q as quotient and R a remainder with the scaled by (5/5) 1/320 remainder replaced by the word ro.
  
  For example, the two most difficult AWT divisors, n = 11 and 13, were muddled by Georges Daressy in 1906.
  
  In 2002 Hana Vymazalova showed that all five division answers were returned to 64/64, unity.
  
  What Vymazalova did not show was the scribal calculation of each answer. Two calculations are shown by:
  
  1. (64/64)/11 = (5/64)hekat + (45/11)ro =
  
  (1/4 1/64)hekat + (4 1/4 1/11 + 1/44)ro
  
  since (4/11)(4/4) = 16/44 = (11 + 4 + 1)/44
  
  and,
  
  2. (64/64)/13 = (4/64)hekat + (60/13)ro =
  
  (1/4)hekat + (4 + 1/2 + 1/13 + 1/26)ro
  
  since 8/13(2/2) = 16/26 = (13 + 2 + 1)/26
  
  The five binary quotient and scaled remainder answers were returned to (64/64) by multiplying each answer by their initial divisors,i.e. 11 and 13, respectively, a set of facts reported by Hana Vymazalova in 2002, summarized by the (64/64)/13 answer:
  
  [(1/4)hekat + (4 + 1/2 + 1/13 + 1/26)ro]x 13 =
  
  (52/64) hekat + (52 + 13/2 + 13/13 + 13/26)1/320
  
  returned the scaled remainder to a 1/64 unit
  
  (52/64 + 12/64)hekat = (64/64)hekat = 1 hekat
  
  In conclusion, it should be noted that Ahmes did not scale remainders when divisors n were outside the range:
  
  1/64 < n < 64
  
  Unscaled units,
  
  1. 1/10 of a hekat: hin,
  
  2. 1/64 of a hekat: dja
  
  (proven by Tanja Pemmerening in 2002 and 2005),
  and
  
  3. 1/320 of hekat: ro
  
  were written as:
  
  1. 10/n hin
  
  2. 64/n dja
  
  3. 320/n ro
  
  and so forth ...
  
  
  Best Regards,
  
  Milo Gardner
  adding military crytanalytics as a required Egyptian math decoding disciple.

  Link to this forum: Akhmim Wooden Tablet

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• Message 2

  , in reply to message 1.

  Posted by Milo Gardner (U14346264) on Wednesday, 24th February 2010

  The calculation side of the AWT was decoded in 2005 per this analysis:
  
  
  
  A formal paper on the topic was published 2006, not in Europe, but in India, where ancient texts are allowed to be reported as the ancient scribes intended.
  
  Best Regards to all,
  
  Milo Gardner
  

  Link to this forum: Akhmim Wooden Tablet

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• Message 3

  , in reply to message 1.

  Posted by Milo Gardner (U14346264) on Wednesday, 24th February 2010

  Blogs have been created to better discuss the AWT. One is my own per:
  
  
  
  One day the Βι¶ΉΤΌΕΔ may consider to broadcast two introductions to an updated 1650 BCE Rhind Mathematical Papyrus program. The first program can report the contents and implications of the 1850 BCE Egyptian Mathematical Leather Roll. The second program can report the contents and implications of the 1800 BCE Akhmim Wooden Tablet.
  
  Best Regards to everyone,
  
  Milo Gardner
  
  

  Link to this forum: Akhmim Wooden Tablet

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• Message 4

  , in reply to message 3.

  Posted by Andrew Host (U1683626) on Thursday, 25th February 2010

  Hi Milo,
  
  You've got three threads open on pretty much the same subject. Really it'd be best to stick to just one thread as otherwise it becomes a blog rather than a discussion. If you're finding members aren't really engaging with what you want to talk about try entering some other threads that take your interest and join in the discussion on the topic in-hand - get to know a few people and then perhaps you'll find people take more of an interest.
  
  
  Cheers
  
  
  
  Andrew

  Link to this forum: Akhmim Wooden Tablet

• Message 5

  , in reply to message 4.

  Posted by Milo Gardner (U14346264) on Thursday, 25th February 2010

  Andrew,
  
  Thank you for the comment. The three open threads discuss three different topics, as reviewed by:
  
  The first thread discusses the RMP as the Βι¶ΉΤΌΕΔ and British Museum staff and other scholars did not, containing ancient number theory as it unifying mathematical context.
  
  The second thread detailed the EMLR, the sibling document to the RMP, a vital topic that Βι¶ΉΤΌΕΔ did not report. The EMLR is a required introduction to the RMP 2/n table, a point that will be clear if you actually read and understand the scribal introduction to 2/n tables, a topic reported on Wikipedia by:
  
  
  
  The third thread details the Akhmim Wooden Tablet (AWT), a text that drew dust in the Cairo Museum from 1906 to 2002. Its importance in explaining one of two weights and measures unit, a hekat unity written as 64/64, can be directly understood by dividing 64/64 by 3, 7, 10, 11 and 13 as the scribe detailed, and as Peet in 1923 only reported the 1/320 = ro aspect. Daressy in 1906 offered a clearer understanding of the AWT, grasping the exact aspects of the divisor n 3, 7, and 10 cases, not decoding the n = 11 and 13 cases in exact ways.
  
  Hana Vymazalova in 2002 removed most of the dust concerning the proof side of the returning each binary quotient and scaled remainder answer, oddly implying that Peet understood the calculation side of the topic (when Peet did not). Vymazalove showed that unity, 64/64, was calculated in all five problems by multiplying each answer by the initial divisor. The remaining dust, the calculation of
  
  (64/64)/n
  
  into
  
  (Q/64) hekat + (5R/n)ro
  
  statements, a method that the RMP used over 40 times, 29 times in RMP 82, was not removed until 2005, and published in 2006.
  
  Best Regards,
  
  Milo Gardner
  
  

  Link to this forum: Akhmim Wooden Tablet

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• Message 6

  , in reply to message 5.

  Posted by Milo Gardner (U14346264) on Thursday, 25th February 2010

  Andrew,
  
  A few comments, marked by ***comment*** may be pertinent to fully respond to your paragraph:
  
  "You've got three threads open on pretty much the same subject.
  
  ***The Βι¶ΉΤΌΕΔ RMP program oddly condensed, or totally omitted, these three topics in a manner that needs to be corrected, a major point that members of this discussion group have not commented on.
  
  Are you an apologist for the Βι¶ΉΤΌΕΔ and its recent RMP program?***
  
  Really it'd be best to stick to just one thread as otherwise it becomes a blog rather than a discussion.
  
  *** I'd be happy to return to the Βι¶ΉΤΌΕΔ distorted version of the RMP, as the central theme of my posts. Since no one on this discussion group explicitly disagrees with the Βι¶ΉΤΌΕΔ and its recent Euro-centric review of the RMP, I will continue with at least one more example, the Kahun Papyrus and its 2/n table, in a future thread.***
  
  If you're finding members aren't really engaging with what you want to talk about try entering some other threads that take your interest and join in the discussion on the topic in-hand - get to know a few people and then perhaps you'll find people take more of an interest."
  
  ***Coffee shop conversations do lower the content and scope of ancient math topics in the manner that you have summarized. If I was interested in finding friends, by ignoring the advise of the ancient scribes, your suggestion would be taken.***
  
  Thanks again for this opportunity to stand up for Ahmes to report the attested meta contents of Middle Kingdom mathematics in a manner that the Βι¶ΉΤΌΕΔ, the British Museum, and others that were featured on this month's Βι¶ΉΤΌΕΔ broadcast were unwilling or unable to do.
  
  Best Regards to all,
  
  Milo Gardner
  

  Link to this forum: Akhmim Wooden Tablet

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