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Analysis of Empty Spaces on Plimpton 322

Sources are Neugebauer's Photograph and Robson's Drawing.

For a larger drawing click on picture.

 

Line
Number
Column One Column Two Column Three
1 Tablet broken but very wide blank space
discernible for (59) 00 15.
   
2 Tablet broken but 50 06 conflated to 56.
Numbers tightly fit with no blank space.
Small blank space between 56 and 07. Medium blank space between erroneous (3 12 and 01).
3 Tablet broken. 07 missing. Small blank space between leading 1 and 16 on 1 16 41 Medium blank space between 1 50 and 49.
4 Tablet broken. 10 missing.   Small blank space between 5 and 09;
medium blank space between 09 and 01.
5 Very wide blank space between 54 and 01. Wide blank space between 1 and 05. Discernible blank space between leading 1 and 37.
6 Very wide blank space between
47 and 06.
  Tablet broken but small
blank space between (9) and 01
7 Sexagesimal string with all spaces tightly fit.   Small blank space between 59 and 01.
8 Wide blank space between conflated 59 and 03.   Medium blank space between 20 and 49.
9 Tightly fit sexagesimal string. Small blank space between (9) and 01. Small blank space between leading 12 and 49.
10 Medium blank space between 10 and 02. Small blank space between leading 1 and 22. Small blank space between 16 and 01.
11 Tightly fit sexagesimal string.   Possible blank space between leading 1 and 15.
12 Medium blank space between 54 and 02.    
13 Very wide blank space between 27 and 00 03. Small blank space (7 12 and 01).  
14 Medium blank space between 35 and 06.    
15 Tightly fit sexagesimal string.    

 

Comments:

In all cases blank spaces are provided where "zero" digits occur in sexagesimal notation. Clearly they had a conceptual need to express an "empty space."  But these empty spaces are not marked in any way, no tick marks, or other indication of their purpose. One must assume that either one "zero" occurs, or two "zeros" occur. In line 10 the double zero from 10 and 02 has a medium wide space. In lines 1 and 13 the double-zeros have a very wide space, but the distance between 54 and 02 in line 12 is not significantly different from 00 and 03 in line 13.

Leading numbers sometimes contain spacing to separate them from following numbers, but not always. There is no positional importance for very large numbers, as in line 4. All numbers are left-justified in all columns regardless of positional importance. One must deduce where to begin calculation of number.

If an OB scribe came across this list without prior knowledge, how would he know where to begin calculation of any of the numbers? How do we in the modern world know except by trial and error? In line 4 we can find 3 X 3600 = 10,800 + 31 X 60 = 1,860, + 49 to equal 12,709, but in the following line do we multiply 1 X 3600 + 5 X 60 to get 3900 and assume blank spaces in the single digits position, or do we start with 1 X 60 + 5 to get 65, which is what we are really after?

 

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