From: <philtill@aol.com>

Date: Sat Oct 13 2007 - 09:21:51 EDT

Date: Sat Oct 13 2007 - 09:21:51 EDT

Hi Iain,

I was on travel last week and just catching up on e-mails, so I am sorry for the delay.

Yes, there is no 1 symbol used, but almost exclusively 0 and 2-7.? An older numerical system would have no zero symbol, so the symbols were in a contiguous block of 6 numerals.?

The exception in which a 9 is used on?time is understandable.???The problem that the ancients would have faced, after adopting a base-10 system and having lost memory of an earlier base-7, is that the addition recorded in the census would no longer?work.? They would have struggled to understand the meaning of the symbols to make the arithmetic correct.? (We see evidence of this in the Patriarch ages, too, where 100 is added to many of the dates in the Septuagint versus the other two versions, or in the Septuagint and Masoretic together versus the Samaritan alone.)? Remarkably, it turns out that if they interpreted the 6 symbols as 2-7 instead of 1-6 then the additions become much closer to the recorded values in most cases.? Final editing would then be required to remove the remaining "errors", and the exceptional use of a few digits like 1, 8 and 9 would have occurred at that time.? This is the problem you must face in doing forensices on ancient?base systems.??The texts hav

e been edited and so?you can?use only statistics to?discern the earlier use of?a?different base.? Here, the statistics are overwhelming that?a?different base had been used.? This is excactly the kind of evidence that would appear, and you cannot expect any better evidence than this if in fact a?different base had been used.? So I am claiming that the evidence is 100% consistent with the earlier use of base-7, and it is not good science to presume that base-10 had been used at that time contrary to the strong statistical evidence.? The exceptions in the statistics were considered in the odds?that?I had calculated.? There was about 1 in a half million chance in using only?that number of contiguous digits with no more than that many exceptions occurring.

I did a lot of reading on the Mesopotamian systems and one of the interesting ideas was that they were based (in part) on the smallest number (60) that can be factored by the number of years it takes Jupiter and Saturn each to complete their cycles.? So I agree that factoring was used.? But I think those systems were evolved over a vast number of different systems, whereas a Hebrew use of base-7 would have been by choice and not evolved.? So it would not necessarily have the use of factoring that made sense in other systems.

I plan to write a paper on the census statistics, but I have so many irons in the fire and this is not my top priority.

Phil

-----Original Message-----

From: Iain Strachan <igd.strachan@gmail.com>

To: philtill@aol.com <philtill@aol.com>

Cc: asa@lists.calvin.edu; gbrown@colorado.edu

Sent: Tue, 9 Oct 2007 4:02 pm

Subject: Re: [asa] New Evidence for Two Human Origins

Hi, Phil,

Concerning base-7 in the Numbers census figures.? I do not see this.? There seem to be several instances of the numeral 7 & if it were genuinely base-7 arithmetic, it would only be 0-6.? Also the first census has a 9 digit..(Simeon 59,300).? So I don't understand this ( did you mean that the second census contains 2-7 and no 1? even so, it doesn't seem to make what I'd understand as a base-7 number system).

Concerning the base-10 system.? A history of Maths professor I know has a theory that 10 was selected as the base because of the belief in the sacredness of the number 10, being a "Triangular number"? (1+2+3+4), and because of the "Tetratkys".? He thinks this is more plausible than the number of fingers.

It would appear that the ancient Babylonians (who were very strong on algebra) did care about factors, and hence chose base 60.? Even that system was part-base 10 - the 59 cuneiform "digits" comprised different numbers of two different wedge-like symbols, one of which counted as 10 (up to five of these) and one of which counted as as a one.

Cheers,

Iain

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Received on Sat Oct 13 09:24:14 2007

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