Gordon,
?
Below is a link to an excerpt from a book on the Indo-European bases for our language, and it explains that most languages base their number-words on counting fingers (which explains the inherent base-10).? Surprisingly, the Sumerians had their number-words based on the 5 fingers of one hand, such that six was verbalized as 5+1 and seven was verbalized as 5+2, even though (as we know) their system of counting was base-6 in the units place (and base-60 when you go up to the third place).? So the sumerian's number-words were base-5 and yet the sumerian "numerals" were base-6. ? In general, it seems, the words representing numbers and the numerals representing numbers do not necessarily derive from the same base.? How strange!
Phil
-----Original Message-----
From: philtill@aol.com
To: Gordon.Brown@Colorado.EDU; asa@calvin.edu
Sent: Sat, 23 Aug 2008 9:45 pm
Subject: Re: [asa] Number systems in the OT
Hi Gordon,
Good question.? Thanks for pointing that out.
From the little reading I've done, it's generally believed that the OT was written with numerals of some type but then at a late date -- sometime in the Captivity or afterwards -- the Jews decided to spell-out all the numbers with Hebrew words rather than using numerals.? This is believed because there are numerical copying errors in the text we have today and they are the sort of errors that would occur in copying numerals but not in copying spelled-out words.? I can't point to any examples (except maybe the king who is listed as 8 years old and again as 18 yeas old in Kings and in Chronicles alternately), but that is what I have read.
I've also read that there is a common Indo-European vocabulary that seems to bely a base-10 system (you are referring to a similar thing in the family of languages that includes Hebrew and Arabic).? Base-10 existed very early-on among the Egyptians, for example, but it was a heiratic system, not a place-holder system.? So it's not too surprising to find base-10 language very early, even though the base-10 _placeholder_ system was not developed until the 400's to 700's AD.? In contrast to a base-10 placeholder system, A base-10 heiratic system uses 9 distinct symbols in the units that are different than the 9 distinct symbols used in the tens-place, etc.? That sort of base-10 system may be what underlies the common Indo-European language as well as the common Hebrew/Arab family of languages.? It may be that very early-on there were people using heiratic systems that were base-10, and that's where the common roots in the languages come from.
But I wouldn't think the Semitic people would always automatically be using a base-10 system just because the roots of their language came originally from some kind of base-10 system.? Note that even in our language today we still
have remnants of non-base-10 systems.? We use "dozen" and "gross", which are the second and
third places in a base-12 system.? (Where did that come from?!!)? Also, in telling time we use a "minute" as a
sixtieth part of an "hour" because the Babylonians used base-60 (sort
of), and a "second" as a sixtieth part of a minute.? "Minute" is the actual name for an amount in a base-60 system.? Note in the early Babylonian systems they used different methods of couting different quantities -- sheep and acres would not be counted with the same system of numerals.? Likewsie "time" today is still counted in a non-decimal system going all the way back to the Babylonians.? But we have updated our numeral system to express those amounts of time -- our language and the underlying math are no longer connected when it comes to time.
When Abraham was in Mesopotamia, though he was Semitic (presumably with the same base-10 system we see in Hebrew today???), he undoubtedly used their sexigesimal system, or whatever local variant Ur was using at that time.? He woudln't have been using base-10 to do commerce or record birthdays when he was a part of that culture.? When the Hebrews were in Egypt they may have been fluent in the Egyptian heiratic system to communicate with the Egyptians but they may have kept their own system for commerce among themselves, depending how thoroughly they were acclimated to the Egyptian culture.? When they moved to Canaan they probably moved toward using the Canaanite system (after all, they were even adopting the Canaanite Baals!).? I believe the Jews were using base-10 by the time of David's census since there are no numerical oddities in the numbers.? But the Patriarch's ages certainly have statistical oddities perhaps belying a Mesopotamian system, and the census at the time of
th Exodus has oddities of a different type, so there may have been more than one system in use at different points in their history.
Phil
-----Original Message-----
From: gordon brown <Gordon.Brown@Colorado.EDU>
To: philtill@aol.com
Cc: asa@calvin.edu
Sent: Sat, 23 Aug 2008 11:21 am
Subject: Re: [asa] Number systems in the OT
Phil,?
?
The Hebrew system for naming the numbers reflects a base-ten system. I
have a small dictionary that gives the translations of 1000 words in 26
different languages. I looked up the translations of the numbers one
through twenty as well as thirty, forty, etc. and hundred and thousand,
and I found that the Hebrew and Arabic names are obvious cognates in all
cases. This suggests to me that base ten was used in the common ancestral
language of Hebrew and Arabic and hasn't been tinkered with since. Do you
have another explanation for this??
?
Gordon Brown (ASA member)?
?
On Fri, 22 Aug 2008, 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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Received on Sun, 24 Aug 2008 22:47:25 -0400
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