Re: [asa] Number systems in the OT

Hi, Phil,

I'm not aware of any ancient civilization using base-7 arithmetic & indeed
can't really see the motivation for using it. The ancient Babylonians used
base 60, certainly as early as 1900 BC and probably before. 60 was chosen
because it has many divisors (and of course we see remnants of it in the 360
degrees in a circle, 60 minutes in an hour 60 seconds in a minute.

I think it was Michael Roberts that expressed the opinion that 7 was
considered a sacred number because it is the first number that does NOT
divide into 60; hence 1/7 could not be expressed in a finite expansion in
Babylonian sexagesimal notation ( 1/60, 1/3600 etc).

To use base-7 would seem counterintuitive, as it has no divisors.

When you say 1,8 and 9 are used less frequently, what about 7? Numbers in
base 7 would not contain the digit 7.

There is a simple but initially puzzling law (Benford's law) that states
that the numeral 1 occurs more frequently as the most significant digit than
all the others in naturally occurring numbers. Apparently it can be used to
detect fraudulent bank accounts where the numbers were generated by a random
number generator.

Read it up at http://math.suite101.com/article.cfm/benfords_law

Iain

On Fri, Aug 22, 2008 at 5:37 AM, <philtill@aol.com> wrote:

> Does anybody on this list have expertise or any good resources on the
> ancient number systems, in particular the Sumerian, Akkadian, Babylonian,
> Egyptian, Canaanite, and/or Hittite systems from the time of Abraham (21st
> century BCE) up to the time of the Exodus (15th through 13th centuries BCE)?
>
> The reason I ask is because I have been analyzing the numerals contained in
> the two censuses in the book of Numbers and I'm convinced that these were
> originally written in a base-7 system. Only 7 different digits are used
> with very few exceptions (omitting 1, 8, and 9 for the most part in the
> numbering of each tribe) in both censuses. The odds of such low usage of
> any three numerals occurring by chance** are about 1 in a half million. If
> you convert them to base-7 (with a particular twist in the conversion, to be
> explained in the paper) then it becomes obvious how the numbers were
> mistranslated and then edited a bit to make the sums work out for each
> groupin of three tribes and for the overall nation in each census. I want
> to write this up and submit to a journal. But I need more background on the
> other number systems that existed at the time and before that time before I
> can write a really good paper.
>
> The upshot of this base-7 analysis is that the Pentateuch must have been
> composed at a sufficiently early date that base-10 had not become
> universally accepted, yet, and at a sufficiently early date that the Jewish
> scholars who edited the Pentateuch (during the Captivity) no longer
> remembered that the numbers were originally base-7. That forgetfulness led
> to the mistranslation of the numerals and editing to make the text
> consistent. Fortunately for us, this provided numerical artefacts in the
> text so that we can constrain the dating of its original composition. The
> use of base-7 pushes the composition of the Pentateuch back to a very early
> date, I believe. It's interesting to note that the census at the time of
> David bears none of the artefacts of an underlying base-7 system, being
> fully base-10.
>
> In particular, I want to know if the Mesopotamian civilization(s) used a
> 6-day work week (or what kind of week?); if the Mesopotamians began adopting
> base-10 from the Egyptians, Greeks, Persians or others, and by what date;
> What the Egyptians used prior to their base-10 heiratic system; what number
> systems the other peoples in the Levant (such as the Hittites or Canaanites)
> used; if anybody knows about the Hyksos's number system? And similar
> questions.
>
> Thanks for any help you can provide.
> Phil
>
> (** to be more precise: the odds were calculated for the occurrence of the
> 6 non-zero numerals being in a contiguous block such as 2-7, as they are
> found in the text. This is a little less likely than any 7 numerals being
> used regardless of their contiguity. There is a particular reason why the
> block would be contiguous and not include the numeral 1, as I'll explain in
> the paper that I plan to write.)
>
>
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