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Visualizing Babylonian numbers
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Posted by: Philip Ronald Dutton
If one considers the babylonian number system transformed to use digits 0-9 and to use pairs of such digits (to represent the pairing notion of their 2 symbols) then one might express such Babylonian numbers as follows (informally):
Notes: the least significant pair would be at the right; I am using a psuedo perl-like regular expression code:
(([0-5],[1-9]))*
The digit 0 represents that nothing was written down in that "spot."
If one enumerated the first 20,000 sets of pairs and converted the sets of pairs to binary number strings, and finally concatenated all these strings, and then moving on to the next number on the number line, then it would be interesting to compare to the visualization in the NKS book on page 117.
http://www.wolframscience.com/nksonline/page-117
Philip Ronald Dutton
Posted by: Philip Ronald Dutton
I should note that, in my post above, I am talking about the Babylonian numbers before they adopted the "double-wedge" (used for the zero place holder).
I casually submit that I could change the pair notation to something like :
(([0-5],[1-9])/([0]))*
Where the "/" symbol means "or". I do not think it would make much of a difference in terms of visualization purposes (since any "0" place holder would not produce more than 1 digit after doing the conversion I talked about).
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