Re: [asa] Number systems in the OT

Hi Iain,

I'd rather not discuss the specifics of the usage of the 7 numerals until it has been submitted to the journal.? But the main point of the paper is to explain exactly that -- why the numbers in the census for each of the 12 tribes use the seven digits 0 and 2-7, skipping 1 and not using 8 or 9.? (There are some exceptions, but not enough to explain the odd statistical features.? The total theory also explains the exceptions -- provides a motivation for the editing and also explains why there was no such editing in the 2nd census.)? The numbers don't appear to be base-7 at first blush due to the usage of 7, but there is a really interesting explanation and the motive to do this becomes apparent (I think) when it is all laid out.

I agree base-7 has no numerical benefits, but base-10 is only marginally better since it only factors into 2 and 5.? The Babylonians didn't really use a "base-60" in the modern sense.? Each?numerical place had a different base.? So the units were in base-6, the?next higher position?was base-10, and then it alternated to 6 again and then 10 again.? So the third place would be units of 60, but they didn't have 60 different numerals.? And that was just the system that become dominant.? Earlier, every city state had different systems, and often they used different systems for counting different things.? They might use one system for counting goats and another system for counting bushels of grain.? I suppose they hadn't yet idealized the concept of numbers as something existing independently of the concrete objects being counted.

I can imagine only only two motivations for using base-7.? One is?because of the length of the Jewish week, and because it divides into the 28 day lunar cycle.? The other?is to make a religious statement about being different than the culture from which they came.? If the Mesopotamian culture was using base-6 (for its units-place), and their work week was 6 days long, then the Semitic people leaving that culture may have adopted base-7 at the same time that they added?the 7th day to the week.? ("Sabbath" is philologically equivalent to "Seventh" although I've never seen it connected as such despite the obviousness of it.)? Their Seventh-day was?something they saw as making them unique from the other peoples, because they gave everyone including slaves a day of rest from the otherwise incessant labor in the agricultural fields.? The significance of their 7 replacing 6 might be a motivation to start counting with base-7.? That's what I'm hoping to investigate if I can find out
 where to begin looking.

The Jews obviously didn't keep base-7 for long, if they did use it.? Evidence for it drops away quickly after the Pentateuch and doesn't exist (IMO) by the time of the kingdom.

There was an old?book called "The Bible Dates Itself," which argues that the Jews used base-7.? The author's argument was strongest when he laid out the timeline of Joseph.? The years just don't add up in base-10, but become very naturally concordant in base-7.? He had lots of anciliary arguments related to Joseph, as well.? However, I think he carried it too? far when he argued that the Jews kept base-7 all through the kingdom years.? His arguments became ad hoc and didn't persuade me much beyond the Exodus.? I haven't found anything else saying the Jews used base-7, and the author of that book did not notice the pattern in the two censuses.? I think the two censuses plus the argument from Joseph make a decent case that the Jews at one time in their history used the base-7 system.

Any ideas where I should look?

thanks,

Phil

-----Original Message-----
From: Iain Strachan <igd.strachan@gmail.com>
To: philtill@aol.com
Cc: asa@calvin.edu
Sent: Fri, 22 Aug 2008 3:17 am
Subject: 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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