From: Merv <mrb22667@kansas.net>

Date: Tue Oct 09 2007 - 19:33:35 EDT

Date: Tue Oct 09 2007 - 19:33:35 EDT

In base seven shouldn't Moses have originally enumerated "13"

commandments? Obviously what we have now is the decimal 10 applying to

the actual countable ten. So did later scribes just ignore the base 7

rendering (if base 7 was the case) and, unlike the non-verifiable large

quantities from elsewhere, just count it for themselves and discard

previously used number systems? You would think the checkable items

like this ought to make a good base-line for any scribe at any later

time who wonders what number system is employed by earlier scribes. Of

course base 60 wouldn't be checkable this way.

--Merv

Iain Strachan wrote:

*> 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
*

*>
*

*> On 10/9/07, *philtill@aol.com <mailto:philtill@aol.com>*
*

*> <philtill@aol.com <mailto:philtill@aol.com>> wrote:
*

*>
*

*>
*

*> Phil,
*

*>
*

*> All these speculations about base-7 arithmetic are
*

*> fascinating, but is there really any evidence that any past
*

*> civilisations used base-7 (apart from it making the
*

*> patriarchal ages work). A quick perusal of Wikipedia (not the
*

*> found of all knowledge, I admit) shows that the commonly used
*

*> bases are 2,5,8,10,12,16, 20 and 60. There is an entry on
*

*> "septenary" arithmetic that gives no historical connections
*

*> (apart from use in a computer game!). The big problem with it
*

*> is that few fractions in "decimal" ("septimal") notation can
*

*> be expressed other than by infinitely recurring digits ( e.g.
*

*> 1/2 has a problem). Only when the demoninator is a power of
*

*> seven is this possible.
*

*>
*

*> Generally, number bases with lots of factors are preferable
*

*> (which is why 60 was used by the ancient Babylonians).
*

*>
*

*> Best wishes,
*

*> Iain
*

*>
*

*>
*

*>
*

*> The strongest evidence for base-7, IMO, is census data in
*

*> Numbers. It is a 1 out of about 500,000 probability that only 7
*

*> contiguous numerals would be used in that many digits if it were
*

*> by chance.
*

*>
*

*> The factoring issue is a good observation but were the Hebrews or
*

*> other ancients really that logical about it? The most common
*

*> Mesopotamian system was evolved and selected out from many
*

*> divergent systems that existed in the various city-states, and so
*

*> it was probably not so intentionally designed as much as evolved.
*

*> If the Hebrews did design to use a base-7 (to set themselves apart
*

*> from other nations), then it may have inherently been less useful
*

*> than a designed system, since they were not so adept at arithmetic
*

*> as we are and would not have foreseen the possible problems. If
*

*> they discovered that it didn't work very usefully in subsequent
*

*> years, then that could explain why it was dropped before the
*

*> census of David occurred. They may have eventually adopted the
*

*> base-10 we see in the Davidic census because that was the Egyptian
*

*> system and they had close contact with Egypt.
*

*>
*

*> Even our (and Egypt's) base-10 fails the factoring test. It only
*

*> factors by 2 and 5, so it is marginally better than a base-5
*

*> system which is no better than base-7. 10 and 5 feel like
*

*> important numbers to us only because we are used to them in our
*

*> number system. They have no real advantages. Why did the
*

*> Egyptians pick 10? Maybe from the number of fingers, but that
*

*> neglects the zero numeral. Our hands are actually a base-11
*

*> system if you include zero, since zero = "no-fingers" plus the 10
*

*> fingers you can put up makes a total of 11 numerals and that is
*

*> base-11, not base-10.
*

*>
*

*> One hand alone represents base-6, not base-5, for the same
*

*> reason. If your second hand represents the next higher digit,
*

*> then you can count up to 35 (6^2-1) with two hands. You can use
*

*> tokens to represent the next higher digit (units of 36), and Earle
*

*> in his book speculated that this is how the Mesopotamian system
*

*> with its use of 6's evolved. It is a more natural finger-counting
*

*> base than 5 or 10.
*

*>
*

*> Phil
*

*>
*

*>
*

*>
*

*> ------------------------------------------------------------------------
*

*>
*

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Received on Tue Oct 9 19:22:49 2007

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