Posted on 11/27/2010 12:09:10 PM PST by pillut48
If the cost of digging a trench is 9 gin, and the trench has a length of 5 ninda and is one-half ninda deep, and if a worker’s daily load of earth costs 10 gin to move, and his daily wages are 6 se of silver, then how wide is the canal?
Or, a better question: if you were a tutor of Babylonian scribes some 4,000 years ago, holding a clay tablet on which this problem was incised with cuneiform indentations — the very tablet that can now be seen with 12 others from that Middle Eastern civilization at the Institute for the Study of the Ancient World — what could you take for granted, and what would you need to explain to your students? In what way did you think about measures of time and space? How did you calculate? Did you believe numbers had an abstract existence, each with its own properties?
And how would you have figured out the width of that canal (which, the tablet tells us, is one-and-a-half ninda)?
(Excerpt) Read more at nytimes.com ...
They earned more than we do.
It's all fine and dandy, but such a problem quickly becomes a nightmare when values greater than single digits need to be considered, and multiplied (eg., hand multiply XVIII times XXIV. Gave up?). That's when the genius of the modern base 10, place-value system with the zero and decimal place-holders, a.k.a. the "Arabic" system, comes in.
P.S: The Arabs had nothing to do with the development of this system. They stole it from the Hindus to pass off as their own.
“If the cost of digging a trench is 9 gin, and the trench has a length of 5 ninda and is one-half ninda deep, and if a worker’s daily load of earth costs 10 gin to move, and his daily wages are 6 se of silver, then how wide is the canal? “
3 widths of a boat.
Not too many nindas gonna be dug after 9 gin.
"Farmer Brown had 31.2 acres planted in potatoes.
Farmer Smith had a yield of 42 bushels of oats from his proppity.
What color was the new dress Farmer Grey bought for his wife?"
Answer: "Any damn culla she wanted after she caught him with Farmer Smith's wife."
I usually drink gin only in the summer — with tonic. Don’t like to dig too many ditches then.
The length is 5 ninda (feet?). The depth is 0.5 ninda. That product is 2.5 ninda^2 (feet^2?), not 30.
Maybe the Babylonians had a unit equal to a foot-inch. 2.5 ninda^2 = 30 foot-inches. However the article should have mentioned such a unit.
(A reciprocal in Babylonian arithmetic is in relation to 60, so the reciprocal of 10 is 6.)
But 6 * 30 does not equal 3. No, I think the Babylonians took reciprocals the way we do. 0.1 day/gin * 30 foot-inches = 3 ft-inch-day/gin.
However instead of using foot-inches we should use square nindas. 0.1 day/gin* 2.5x cubic nindas = 0.25x ninda^3-day/gin.
The next part is a bit confusing for me also.
Multiply the wages by 3, and you will get 6. Take the reciprocal of 6, and multiply it by 9, the total cost in silver, and you will get its width. One and a half ninda is the width. Such is the procedure.
I'm thinking there's a relationship between the ninda and the se that Babylonians were aware of but the author isn't telling us. It looks as though 1 se = 1 gin/ninda but I'm not sure. 0.25x ninda^3-day/gin * 6 se/day = 1.5 ninda^3-se/gin.
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Decimal (base 10) of course is a better way to manipulate numbers, but didn’t the Babylonians use the sexigesimal (base 60) system? How easily do the operations flow in that numeric system?
The same way I figured out math problems in high school. I guessed.
Go on-line and get Netflix today!!!!!!
Yeah......
Length
Smallest unit of length is the she (barleycorn), of about 1/360 meter.
6 she = 1 shu-si (finger)
30 shu-si = 1 kush (cubit - about 1/2 m.)
6 kush = 1 gi / qanu (reed)
12 kush = 1 nindan/ GAR (rod - 6 m.)
10 nindan = 1 eshe (rope)
60 nindan = 1 USH (360 m.)
30 USH = 1 beru (10.8 km.)
length conversion calculator
Area
The basic area unit is the sar, an area of 1 sq. nindan, or about 36 sq. m. The area she and gin are used as generalized fractions of this basic unit.
180 she = 1 gin
60 gin = 1 sar (garden plot 1 sq. nindan - 36 sq. m.)
50 sar = 1 ubu
100 sar = 1 iku (1 sq. eshe - 0.9 acre, 0.36 ha.)
6 iku = 1 eshe
18 iku = 1 bur
1 bur is an area 1 beru long by 1 nindan wide. area conversion calculator
Volume
Volume units are the same as the area units and follows the relationship that
1 volume-unit = 1 area-unit x 1 kush.
For example, a volume-sar is the volume of the solid with base 1 area-sar and height 1 kush (cubit).
Bricks are considered to be rectangular solids such that 720 bricks make one brick-sar. There are numerous (fairly standard) sizes of bricks in use in Old Babylonian mathematics texts.
Capacity: used for measuring volumes of grain, oil, beer, etc. The basic unit is the sila, about 1 liter. The semi-standard Old Babylonian system used in mathematical texts is derived from the ferociously complex mensuration systems used in the Sumerian period.
180 she = 1 gin
60 gin = 1 sila - 1 liter
10 sila = 1 ban
6 ban = 1 bariga
5 bariga = 1 gur
volume conversion calculator
Weight
The basic unit of weight is the mana, about 1/2 kilogram.
180 she = 1 gin/ shiqlu (shekel)
60 gin = 1 mana (mina - 500 gm.)
60 mana = 1 gu/ biltu (talent, load - 30 kg.)
http://it.stlawu.edu/~dmelvill/mesomath/obmetrology.html
:’) Thanks, I needed something like that for my computer wallpaper, for when I program in B. ;’)
whats missing is the relationship of 6 se silver , a workers daily wage to a gin(total cost of the trench). Given that relationshp its simple math. Kind of weird otherwise.
That gave me that old queasy feeling (same as looking at the formulas [formuli?] in those managerial finance texts.) Let’s all give thanks for the Creator giving us Texas Instruments!
That really cleared the whole thing up for me. Thank you, bhf!
Hmm. It still doesn’t seem to follow.
The only thing I can figure is that there was an expectation that such a worker would dig 2.5 cubic ninda-se per gin-day, something unknown to us moderns.
Note to self: return DVDs to Netflix.
My understanding is very easily. I also think that their base 60 system gave us our time measurements, IIRC.
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