Whorl arithmetic -- Fibonacci sequence

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).

--- Dave Tallman <davetallman at msn.com> 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.

_______________________________________________

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. ------------------------------------------------------------------------ _______________________________________________

Paul Zinn-Justin wrote: 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).