Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Babylonian mile
Replies: 1   Last Post: Apr 27, 1996 6:29 AM

 Messages: [ Previous | Next ]
 Eleanor Robson Posts: 34 Registered: 12/3/04
Re: Babylonian mile
Posted: Apr 27, 1996 6:29 AM

Dear Walter,

There is no Mesopotamian length unit which approximates a mile. In
the standard system introduced by Sargon of Akkad (c. 2350 BC) and in use
to the end of the Old Babylonian period (when the vast majority of
'Babylonian' maths comes from), the length units are (in Sumerian,

1 she 1 uttetum 1 barleycorn c. 3 mm
1 shu-si 1 ubanum 1 finger = 6 barleycorns c. 17 mm
1 kush 1 ammatum 1 cubit = 30 fingers c. 0.5 m
1 gi 1 qanum 1 reed = 6 cubits c. 3 m
1 nindan 1 nindanum 1 rod = 12 cubits c. 6 m
1 USH 1 ... 1 ?? = 60 rods c. 360 m
1 danna 1 beru 1 stage = 30 ??s c. 10.8 km

There are other units too, but these are the main ones. Even in Akkadian
texts (such as OB maths) metrological units are usually written in
Sumerian because it is quicker. In general you need just one cuneiform
sign to write a Sumerian word with no grammatical indicators, but several
to write its Akkadian equivalent, because it has to be split into
syllables. So the length '60 rods' is always written with the sign USH
(which might be read in several different ways, as most cuneiform signs
are polyvalent), so that we've no idea what its Akkadian equivalent is,
and therefore how to translate it.

After c. 1600 BC there are several different competing systems, some
having impractical divisions such as 14 cubits to a rod. (Because 14
irregular, one can't divide nicely with it in sexagesimal.) For more
details, the definitive survey on all Mesopotamian metrology is:

M A Powell, "Masse und Gewichte" in _Reallexikon der Assyriologie_ 7
(1987-1990), 457-517.

Don't be fooled by the title - it's in English.

I'm not quite sure what you mean by the question "how is it tied to OB
geometry?". The basic unit of measurement in OB maths is the rod (just as
we use the metre) and although lengths are usually given in the mixture
of units I listed above, for calculation purposes they are converted into
nindan. For instance, a student's exercise on finding the area of a square:

The length of a square is 1 rod, 4 cubits. What is its area?

The student writes this as 1;20 rods (perhaps using a metrological
conversion table to help), and calculates the square of 1;20 = 1;46 40.
This is converted back to area units: 1 2/3 plots, 6 2/3 shekels.

(NBC 8082, from Neugebauer and Sachs, _Mathematical Cuneiform Texts_ (New
Haven 1945), p 10. For more examples, see Neugebauer and Sachs,
"mathematical and metrological texts", _Journal of Cuneiform Studies_ 36
(1984), 243-251.

With best wishes,

Eleanor.

Dr. E. Robson
The Oriental Institute
University of Oxford
eleanor.robson@wolfson.ox.ac.uk

Date Subject Author
4/27/96 Walter Mallory
4/27/96 Eleanor Robson