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

Date: Tue Oct 09 2007 - 16:02:38 EDT

Date: Tue Oct 09 2007 - 16:02:38 EDT

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 <philtill@aol.com> wrote:

*>
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*>
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*> Phil,
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*>
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*> All these speculations about base-7 arithmetic are fascinating, but is
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*> there really any evidence that any past civilisations used base-7 (apart
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*> from it making the patriarchal ages work). A quick perusal of Wikipedia
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*> (not the found of all knowledge, I admit) shows that the commonly used bases
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*> are 2,5,8,10,12,16, 20 and 60. There is an entry on "septenary" arithmetic
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*> that gives no historical connections (apart from use in a computer game!).
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*> The big problem with it is that few fractions in "decimal" ("septimal")
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*> notation can be expressed other than by infinitely recurring digits ( e.g.
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*> 1/2 has a problem). Only when the demoninator is a power of seven is this
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*> possible.
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*>
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*> Generally, number bases with lots of factors are preferable (which is why
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*> 60 was used by the ancient Babylonians).
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*>
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*> Best wishes,
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*> Iain
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*>
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*>
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*>
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*> The strongest evidence for base-7, IMO, is census data in Numbers. It is
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*> a 1 out of about 500,000 probability that only 7 contiguous numerals would
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*> be used in that many digits if it were by chance.
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*>
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*> The factoring issue is a good observation but were the Hebrews or other
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*> ancients really that logical about it? The most common Mesopotamian system
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*> was evolved and selected out from many divergent systems that existed in the
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*> various city-states, and so it was probably not so intentionally designed as
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*> much as evolved. If the Hebrews did design to use a base-7 (to set
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*> themselves apart from other nations), then it may have inherently been less
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*> useful than a designed system, since they were not so adept at arithmetic as
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*> we are and would not have foreseen the possible problems. If they
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*> discovered that it didn't work very usefully in subsequent years, then that
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*> could explain why it was dropped before the census of David occurred. They
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*> may have eventually adopted the base-10 we see in the Davidic census because
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*> that was the Egyptian system and they had close contact with Egypt.
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*>
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*> Even our (and Egypt's) base-10 fails the factoring test. It only factors
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*> by 2 and 5, so it is marginally better than a base-5 system which is no
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*> better than base-7. 10 and 5 feel like important numbers to us only because
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*> we are used to them in our number system. They have no real advantages.
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*> Why did the Egyptians pick 10? Maybe from the number of fingers, but that
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*> neglects the zero numeral. Our hands are actually a base-11 system if you
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*> include zero, since zero = "no-fingers" plus the 10 fingers you can put up
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*> makes a total of 11 numerals and that is base-11, not base-10.
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*>
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*> One hand alone represents base-6, not base-5, for the same reason. If
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*> your second hand represents the next higher digit, then you can count up to
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*> 35 (6^2-1) with two hands. You can use tokens to represent the next higher
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*> digit (units of 36), and Earle in his book speculated that this is how the
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*> Mesopotamian system with its use of 6's evolved. It is a more natural
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*> finger-counting base than 5 or 10.
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*>
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*> Phil
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*>
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*>
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*> ------------------------------
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*> Email and AIM finally together. You've gotta check out free AOL Mail<http://o.aolcdn.com/cdn.webmail.aol.com/mailtour/aol/en-us/index.htm?ncid=AOLAOF00020000000970>
*

*> !
*

*>
*

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