Whorl arithmetic -- Fibonacci sequence

Dave Tallman · 03 Jul 2008, 20:43 · from 2008-July.txt.gz

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From: davetallman at msn.com (Dave Tallman)
Date: Thu, 3 Jul 2008 14:43:31 -0600
Subject: (urth) Whorl arithmetic -- Fibonacci sequence
Message-ID: <1bf4dd40807031343s37b07578w6b671774db006c0c at mail.gmail.com>

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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