Talk:Ancient Egyptian units of measurement

Untitled

Please see ancient weights and measures for previous edit history and discussions wrt this article.

khet

The khet, as far as I can tell from other sources, was a unit of length (v., e.g., Gillings, Mathematics in the Time of the Pharoahs, p. 137). The phrase "Ro or parts of areas are found as strips such as the khet which is 100 cubits long by 1 cubit wide" seems to say that it is an area. —Preceding unsigned comment added by Scorwin (talk • contribs) 14:51, 22 January 2009 (UTC)

Sources [1] [2]. I see mention of a square khet. Dougweller (talk) 10:32, 8 August 2009 (UTC)

I have included a short discussion of the square khet (setjat) in the article. And the strips mentioned above are also discussed now. --AnnekeBart (talk) 13:59, 12 August 2010 (UTC)

photographs

Can we get a photograph of an Egyptian ruler? RJFJR (talk) 18:12, 21 June 2009 (UTC)

I have some pictures of the cubit rod of Maya and a picture of the ropes used for measuring length on my own website. But I need further permission from friends to include them here on wikipedia. --AnnekeBart (talk) 14:00, 12 August 2010 (UTC)

Spell it

"h3yt"? Is that transliterated correctly? Or do I need browser support? TREKphiler ^{hit me ♠} 07:22, 29 July 2009 (UTC)

Egyptian Ramen, Cubit and Royal Cubit, digit and Roman cubit

Flinders Petrie, sometimes called the father of Egyptology claimed that the theoretical length of the royal cubit was not exactly 7 palms, but rather the diagonal of a square of 1 ramen on a side. A ramen is 5x4=20 digits, therefore a royal cubit is 20x square root of 2 ~28.28+ digits.

The digit, which he derived in various ways including regularly spaced checkerboards of lines one digit apart is 0.727 inches http://www.touregypt.net/petrie/c20.htm ~1.85 cm and the regular cubit of 6 palms = 24 digits = 44.4 cm = Roman cubit.

This same cubit is found in the tunnel connecting the Shiloach Spring to the Gihon Spring in Jerusalem. The digging of this tunnel is described in the Bible. An inscription in the wall (cut out and brought to Turkey, now on display there) says that the tunnel was 1200 cubits long. The tunnel is 533 meters long, which gives an cubit of 44.4 cm. http://en.wikipedia.org/wiki/Siloam_inscription —Preceding unsigned comment added by Emeslyaakov (talk • contribs) 08:16, 31 May 2010 (UTC) Emeslyaakov (talk) 08:18, 31 May 2010 (UTC)

This must be the "short cubit" or "standard cubit". There were apparently two units referred to as the cubit and did differ in size. --AnnekeBart (talk) 14:02, 12 August 2010 (UTC)

Scaling khar and 'quadruple hekats' to hekats in RMP 42 and RMP 43

RMP 42 calculated a cubit^3 by 3/2 to calculate khar units, meaning that a cubit^3 = 2/3 khar.

RMP 43 began on line 2, diameter 8, height 6, applying a Kahun Papyrus volume formula V = (2/3)(H)[4/3)D]^2 khar, Ahmes input V = (2/3)(6) and wrote 4. Ahmes input [4/3(8)] and wrote 32/3 times 32/3 = 1024/9 times 4 = 4096/6 concluding with 455 1/9 khar. On lines 3 and 4 Ahmes multiplied 455 1/9 khar by 1/20 = 4096/18, writing (22 + 1/2 + 1/4 + 1/180) quadruple hekat ( many read 1/180 as 1/45 (Ahmes poor hand writing)). Clearly on line 5 Ahmes converted 1/180 'quadruple hekat' by 100/180 = 5/9 hekat, recording (1/2 + 1/32 + 1/64)hekat + (2 + 1/2 + 1/4 + 1/36)ro exactly following the Akhmim Wooden Tablet binary quotient and ro scaled remainder. From the above a khar contained 5 hekat, based on Ahmes writing 2200 hekat + 1/2 (100 hekat) + 1/32 (100 hekat) + 1/64 (100 hekat) + 1/180 (100 hekat) = 2275 7/9 hekat. Given that Ahmes noted (22 1/2 1/4 1/180)quadruple hekat, each quadruple hekat contained 100 hekats. Q.E.D. (line 1 of RMP 43 repeated RMP 42 info to show that a 3/2 conversion of cubit^3 to khar were not needed. Milogardner (talk) 02:48, 10 September 2010 (UTC)

1 khar = 2/3 of a cubic cubit (see Clagett)

1 khar = 20 heqat in the Middle Kingdom.

The computations in RPM 41 and 42 shows that they compute the number of heqats from khar by dividing by 20. So 1 khar = 20 heqat.

Your "computations" contradict what all others that I have read write. That means it's original research. Find any writer other than yourself who claims 1 khar = 5 heqat. Then we can use that as a reference. Consistently citing you own work is in violation of wikipedia rules (WP:OR, WP:COI). This has now been pointed out ad nauseum. Read the editing conventions. It still seems to be a continuing problem.--AnnekeBart (talk) 03:19, 10 September 2010 (UTC)

Response

":: 1 khar = 2/3 of a cubic cubit (see Clagett)" (correct, period!) my apologies to Anneka Milogardner (talk) 20:19, 14 September 2010 (UTC)

RMP 42 reported V = (H)[(8/9)(D)]^2 (cubit^3) and took 3/2 of the cubit^3 (64000/81) to compute 96000/81 khar, meant

a formula V = (3/2)(H)[(8/9)(D)]^2 (khar) was used to find (96000/81 khar). Hence a Khar was one and one-half times larger than a cubit^3, and conversely, to convert a khar into a cubit^3 multiply (96000/81) khar by 2/3 to obtain 64000/81 cubit^3 (a point that you or Clagett seem to have muddled), calculation also found in RMP 41 with 640 cubit^3 and 960 khar.

":: 1 khar = 20 heqat in the Middle Kingdom." (not true). Your conclusion assumes that the numerator divided by 20 was scaled to 1 hekat. But Ahmes' numerator was a khar scaled to 5 hekat. Dividing one khar (5 hekat) by 20 meant that a new unit 5 x 20 = 100-hekat was created (that oddly was named a quadruple-hekat by linguists), the exact 100-hekat scaling unit used by Ahmes in RMP 43, LINE 5. as noted above to convert 1/180 (100-hekat) to 5/9 hekat recorded as a unit fraction series:

(1/2 + 1/32 + 1/64)hekat + (2 + 1/2 + 1/4 + 1/36)ro

":: The computations in RPM 41 and 42 shows that they compute the number of heqats from khar by dividing by 20". (yes, input the actual numbers and you'll see that the answer created a 100-hekat unit -- since the numerator was a khar = 5 hekat unit.)

True concerning RMP 41, RMP 42 and RMP 43. RMP 41 increased 640 cubit^3 to 960 khar, by D = 9 and H =10

line 1: (9 - 9/9) = 8 x 8 = 64 x 10 = 640 cubit^3

followed by taking 1/2 of 640 = 320, and adding obtaining

khar = 960 khar, as mentioned above.

"So 1 khar = 20 heqat". Not true ... this is the problem that I muddled for one week.

Your "computations" contradict what all others that I have read write. That means it's original research. Find any writer other than yourself who claims 1 khar = 5 heqat.

I'll forward Bruce Friedman's email of yesterday, and see for yourself ... not in my words ... but his words. Thank you for the humble request ...

Then we can use that as a reference. Consistently citing you own work is in violation of wikipedia rules (WP:OR, WP:COI).

The 100-hekat value was also reported by Peet, 80 years ago ... how about that source? Gee, am I really in violation of Wikipedia rules when Peet is cited? Peet was not always wrong, nor am I, or yourself. We all make subtle and not so subtle mistakes.

This has now been pointed out ad nauseum. Read the editing conventions. It still seems to be a continuing problem.

Best Regards, and updated on 9/14/10 to agree with Anneka Bart related to CC and khar scaling. Milogardner (talk) 20:19, 14 September 2010 (UTC)

The responses should leave a record of the original comments by other posters. Editing my posts is not appropriate. Using my comments in a response should be done in quoting it in a separate text below. You seem to be deliberately misinterpreting my comments about WP:OR and WP:COI. And ignoring the fact that by the time you were done the table contents were no longer in line with the column headings.

The text I have added is given a reputable inline reference. --AnnekeBart (talk) 18:46, 10 September 2010 (UTC)

the 100 heqat refers to what is usually translated as the 4-heqat, so Peet doesn't support your khar to heqat conversion. --AnnekeBart (talk) 18:49, 10 September 2010 (UTC)

Regarding this quote:

a formula V = (3/2)(H)[(8/9)(D)]^2 (khar) was used to find (96000/81 khar). Hence a Khar was one and one-half times larger than a cubit^3, and conversely, to convert a khar into a cubit^3 multiply (96000/81) khar by 2/3 to obtain 64000/81 cubit^3 (a point that NEITHER you or Clagett muddled), calculation also found in RMP 41 with 640 cubit^3 and 960 khar.

That is one of the basic mathematical mistakes I'm talking about. There is no muddling here. You just don't seem to understand what is being said. 1 khar = 2/3 cubic cubit (write as CC). So to convert from say X cubic cubits to khar, you use the standard change of unit approach: X CC * 1 khar/ (2/3) CC = 3/2 X khar. I mean, do you really think all the experts are going to get this wrong for more than a century? The smart thing to do when your work disagrees with all the experts is to check your own work. --AnnekeBart (talk) 19:08, 10 September 2010 (UTC)

Please accept this humble apology for writing over your post, rather than citing it in a proper manner. I will not do that again. as well as not properly citing Clagett with respect to CC and khar scaling. Milogardner (talk) 20:19, 14 September 2010 (UTC)

Returning to the serious discussion at hand. Your incorrect conclusion that 1 khar is 2/3 a cubit-cubit was muddled. One khar was clearly 3/2 a cubit-cubit in RMP 41, 42 and 43. Bruce Friedman copied an unknown for an identical false conclusion. To place a khar in the context of a cubit-cubit (actually a cubit^3), considering:

A cubit-cubit was 3/2 of a khar, in your view, as documented by Ahmes. Ahmes in RMP 41 a volume of 640 cubit-cubit was increased by 1/2 to 640, 320, to report 960 khar. Wow, I had misread this fact for one week. Inputting raw data from RMP 43, 455 1/9 KHAR was found. Inputting the same RMP 43 dimensions, H = 6, D = 8 in the RMP 41 formula == 303 33/81 CC ... wow, was I surprised .... and therefore placed in an apology mode. Milogardner (talk) 20:19, 14 September 2010 (UTC)

The same procedure was used in RMP 42 and RMP 43, take 1/2 a cubit-cubit and add the original cubit-cubit to find khar.

You suggested the inverse, 3/2 per

1 cubic cubit = 3/2 khar = 7 and 1/2 single hekats = 3/40ths of a "quadruple hekat"

I agree that 3/40 of a 'quadruple hekat', but where did your 3/2 khar come from? I now see ... wow, was I surprised today! Milogardner (talk) 20:19, 14 September 2010 (UTC)

The following is background information.

V = (2/3)(H)[(4/3)D]^2 khar

But as we know in RMP 41 and 42 Ahmes reported

V = (H)[(8/9)]^2 cubit^3

RMP 41 raw data: D = 9, H = 10

V = (10)[(8/9)(9)]^2 =

640 cubit^3 + 320 = 960 khar

RMP 42 raw data: D = 10, H = 10

V = (10)([(8/9)(10)] = 64000/81 cubit^3

since (10 - 10/9) = 80/9 X 80/9 = 6400/81 (were Ahmes' calculations)

with Ahmes taking 1/2 of 64000/81, 32000/81 and added 64000/81 = 96000/81 khar

and the KP scribe earlier reported the use of

V = (2/3)(H)[(4/3)D]^2 khar (KP and RMP 43 khar formula)

Added discussion (the correction steps) ... begin with

V = (H)[(8/9)]^2 cubit^3

and RMP 42 shows

V = (3/2)V (H)[(8/9)]^2 khar

scaling both sides by 3/2

(3/2)V = (3/2)(3/2)(H)(8/9)(8/9)(D)(D) = (H)[(4/3)(D)]^2 khar

multiplying both sides by 2/3 completes the formula

V = (2/3)(H)[(4/3)(D)]^2 khar

Hence, a khar from Bruce Friedman's previous analysis Anneka Bart's scaling of a CC to a khar was correct ... and I humbly apologize. Milogardner (talk) 20:19, 14 September 2010 (UTC)

meant that a cubit-cubit was valued at (3/2)(5) = 15/2 hekat, a controversial point that Dr. Bart or others can take up at another time. Milogardner (talk) 20:19, 14 September 2010 (UTC)

Hence, a cubit-cubit, was scaled by Ahmes from a khar by 3/2 (a calculation I accepted today Milogardner (talk) 20:19, 14 September 2010 (UTC). Ahmes calculated in that direction to obtain a khar from a cubit-cubit, he increased a cubit-cubit by 3/2.

Best Regards to all, Milogardner (talk) 20:19, 14 September 2010 (UTC)

The fact that you do not seem to understand that the 1 khar = 2/3 cubic cubits relation gives the exact results found in the problems proves my point. You seem to be very confused about some basic facts. And btw quoting your co-author as a source is not really what is meant when asking for an appropriate reference. --AnnekeBart (talk) 14:21, 11 September 2010 (UTC)

I agree with Anneka's repeated and correct valuations that 1 khar was 2/3 a cubit-cubit within one of nine (9) scribal scaling relationships. A complete list is submitted for Anneka Bart's review and comment:

a. 1 cubit^3 = (3/2) khar = 15/2 hekat b. (2/3) cubit^3 = 1 khar = 5 hekat c. (2/15)cubit^3 = (1/5)khar = 1 hekat

issues that can be deferred as controversial and placed in another category, to be discussed later.

All nine scaled units need to be placed on a Wikipedia documentation list, each double checking the other, issues that can be discussed later. Ahmes listed his scaling steps in RMP 41, 42 and 43, facts that speak for themselves. I'll be searching for appropriate Wikipedia references (including Clagett's corrrect raw data) to detail all nine relationships. Clagett was an editor, and not a mathematician. I thank him for his hard work, but scaling discussion errors are easilY corrected by Clagett's own raw datas. In RMP 43, Clagett cited Gillings, a correct 455 1/9 khar, related to lines 2, 3 and 4, oddly omitting line 5. Clagett, stressed Peet's incorrect use of line 1, a fragment from RMP 42 that in total reported "take (10 - 10/9) = 80/9 times 80/9 = 6400/81 times 10 = 64000/81 cubit^3, and adding 32000/81 cubit^3 = 96000/81 khar, 4800/81 (100-hekat) and finally 480000/81 hekat". Annette Imhausen's use of algorithms, that you advocate may attempts to merge lines 1, 2, 3, 4 and 5 into one calculation. No algorithm exists (that I know of that merge slines 1, 2, 3, 4, 5. Line 1 must be thrown out (again in my humble view, a view that Gillings correctly reported, citing cubit^3, khar and hekat scaling facts from RMP 41, 42 and 43 in one table (the one revised listed above corrteced on 9/14/10). The table, once verified by all parties, does close an important chapter. The time is not at hand to do that. Line 1 fragments of RMP 42 were included in RMP 43 by Ahmes to show that a direct calculation of a khar can be made, without calculating a cubit^3, facts that the Lahun Mathematical Papyrus aptly reports per John Legon and others. Best Regards to all. Milogardner (talk) 20:19, 14 September 2010 (UTC)

Are there any published sources for this reasoning? At the moment this is all looking a lot like WP:SYNTHESIS with material from a lot of different sources being combined in a complex argument. That does seem to be against wikipedia policy. So what published source claims 1 khar = 5 heket?--Salix (talk): 07:26, 14 September 2010 (UTC)

Clagett in RMP 41 began by writing 4800 hekat was contained in 640 CC. Ahmes calculated 4800 hekat by dividing 960 khar by 20 and multiplying by 100, as well as showing a volume calculation from a formula V = (H)[(8/9)(D)}^2 with H = 10 and D =9. Ahmes increased 640 CC by 320 CC and obtained 960 khar. Does not 4800/960 = 5 hekat per khar? Anneka has been shown this 5 hekat = 1 khar scaled data in RMP 42 AND 43, and offers no comment. Does not Clagett's raw data mean anything until a scholar reports the raw data conversion? Suggesting that a 'letter of the law' rule is being applied on Wikipedia, Schack-Schnackenberg and other scholars that worked closely with RMP 41-43 will be consulted. Gillings mentioned that a smaller cubit (f) was used elsewhere. Was a 1/4 smaller hekat in use? As importantly, what has been the history of 'quadruple hekat' a term that has been associated with the 100-hekat unit mentioned by Peet and Clagett whenever a khar was multiplied by 1/20? If a 1/4 hekat size was actually reported in RMP 41, 42 and 43 the scaling problem under discussion would be resolved. Once detailed scholarly RMP 41,42, and 43 CC and khar discussions and conversions to a hekat are located, I'll return, to complete an important scribal story line ... thereby possibly documenting another controversy. Only interdisciplinary teams such as the 2009 group established by Annette Imhausen and Tanja Pemmerening can formally resolve any controversy. That is, my purpose to post to Wikipedia has never been to resolve any of the Egyptian math controversies. I document suggested approaches for interdisciplinary teams to consider. Once the appropriate schools of thought are brought into the same room, and feel energized to resolve a particular controversy, Wikipedia can report formal results. Best Regards, Milogardner (talk) 13:49, 15 September 2010 (UTC)

Fully agree with Salix. Wikipedia is not the place to present WP:original research. We are not qualified to judge its merits. The figure in the literature is the one that is WP:Verifiable. If you think you have good grounds for your figures present a short paper to a journal on it and if it is peer reviewed and accepted then the result can be pur in here, and it wouldn't require any of the above computation to put it here - just a citation. Dmcq (talk) 11:08, 14 September 2010 (UTC)

As other editors have said, Wikipedia is not the place for original research, nor for "documenting suggested approaches for interdisciplinary teams to consider", nor for "bringing appropriate schools of thought into the same room", nor for "reporting formal results". Wikipedia is for repeating results that have already been published in peer-reviewed literature. -- Radagast3 (talk) 12:01, 16 September 2010 (UTC)

I agree with Dmcg and Radagast, pseudonyms for a reason I suspect. "Cherry picking" one aspect of Egyptian math published in the last 20 years, omitting papers that conflict with their positions, as well as omitting older papers dating back 100 years or more, is not the type of scholarship that Wikipedia advocates and supports. There are Egyptian math topics that are controversial. The first one is attested scribal method(s) for writing rational numbers into scaling factors, red auxiliary numbers, 2/n tables, and concise unit fraction series (the central topic of the 2/n table and RMP 1 - 20, and secondary topics in RMP 21-87, and all other hieratic math texts). Does a longer list of controversial issues need to be submitted? Omitting documented scholarly aspects of any on-going controversy reduces the reliability of any group or individual that posts to Wikipedia. Best Regards, Milogardner (talk) 16:48, 16 September 2010 (UTC)

Hand vs Span of Hand

Half of a cubit is called a "hand" in the Units of Length table, but other sources I have seen call half a cubit a "span of the hand" or "span." I also see reference to other sources say that a hand is 5 fingers. History of measurement calls it "span of the hand" and http://www.britannica.com/EBchecked/topic/933255/large-span refers to half a cubit as a "span" and defines a "hand" as 5 digits. Can someone help clear this up? --Onmywaybackhome (talk) 16:47, 21 September 2010 (UTC)

The Turin cubit-rod clearly shows the hand (with thumb) above the fifth digit, immediately after the palm (without thumb), as do I believe other extant cubit-rods. I'm a total layman here, but every other source I've looked at today gives a hand as five digits, a value not far different from its present value. Is it possible that there is some mistake here? Justlettersandnumbers (talk) 18:00, 3 July 2011 (UTC)

henu or hinu

The section Ancient Egyptian units of measurement#Volume, Capacity and Weight mentions a unit "henu" in the text and "hinu" in the table. Are these the same unit? Is there a preferred spelling?--Salix (talk): 19:34, 24 September 2010 (UTC)