Whorl arithmetic -- Fibonacci sequence

Paul Zinn-Justin · 04 Jul 2008, 04:12 · from 2008-July.txt.gz

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From: pzinn at lpthe.jussieu.fr (Paul Zinn-Justin)
Date: Fri, 04 Jul 2008 06:12:06 +0200
Subject: (urth) Whorl arithmetic -- Fibonacci sequence
In-Reply-To: <1bf4dd40807031343s37b07578w6b671774db006c0c at mail.gmail.com>
References: <1bf4dd40807031343s37b07578w6b671774db006c0c at mail.gmail.com>
Message-ID: <486DA316.8040402 at lpthe.jussieu.fr>

Hi,
First post here, as a mathematician I felt compelled to respond...
Unfortunately your base 9 theory does not work.
The reason is, note that in your quote it is never mentioned that one
should consider only the *first* terms of the Fibonacci series.
In fact, the correct property is
"the 7th term in any sequence of 10 successive numbers from the
Fibonacci series is the eleventh of the sum of the sequence"
however, if you replace 10 with 9 and 7 with 6, the property is no more
true. (in other words, the equality you mention with 88 is a coincidence).

Paul

Dave Tallman wrote:
> In CotLS chapter 5, Maytera Marble/Rose thinks "... as predictably as 
> the sixth term in a Fibonacci series of ten was an eleventh of the whole."
>
> This is peculiar, because the Fibonacci series is:
> 1. 1
> 2. 1
> 3. 2
> 4. 3
> 5. 5
> 6. 8
> 7. 13
> 8. 21
> 9. 34
> 10. 55
>
> The sum of the first ten terms is 143 = 11*13, so it's the seventh 
> term that is the eleventh of the whole, not the sixth.
> The sum of the first nine terms is 88 = 11*8, which means the sixth 
> term is the eleventh of the whole, as stated.
>
> In base 9, our nine is represented as 10. To make the statement 
> correct, we have to translate the "series of ten" in base-9 arithmetic 
> and the "eleventh" in the decimal system.
>
> Did the Maytera make a mistake, or did Wolfe, or should we revive the 
> old base-9 controversy about Whorl arithmetic? There's another passage 
> where the children seemingly make trvial arithmetic mistakes, as 
> pointed out by Borski.
>
>     In _Nightside the Long Sun_, on p. 29, Wolfe has Maytera Marble presiding
>     over a mathematics lesson, "watching the children take nineteen from
>
>     twenty-nine and get nine, add seven and seventeen and get twenty-three."
>     This, however, is only possible in a base 9 numbering system, and a strange
>     one at that, since a conventional base 9 system would only include the
>
>     digits 0 to 8 (there should thus no 9, 19, or 29).
>
>
>  Both statements could be correct if done in base 9, provided we 
> solved the "9" representation problem and allow mixed translations:
>   (28+1)(base 9) - (18+1)(base 9) = 9 (decimal)
>   7(base 9) + 17(base 9) = 23 (decimal)
>
> There might be some more clues involving costs with cards and bits, if 
> we look for them.
>
>
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