Whorl arithmetic -- Fibonacci sequence

Dave Tallman · 04 Jul 2008, 13:20 · from 2008-July.txt.gz

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From: davetallman at msn.com (Dave Tallman)
Date: Fri, 04 Jul 2008 07:20:39 -0600
Subject: (urth) Whorl arithmetic -- Fibonacci sequence
In-Reply-To: <486DA316.8040402 at lpthe.jussieu.fr>
References: <486DA316.8040402 at lpthe.jussieu.fr>
Message-ID: <486E23A7.3020608 at gmail.com>

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).
>   

Hi Paul, thanks for posting. I can see how it works when I write it out 
symbolically (a, b, a+b, a+2b,...).

It looks like Maytera Marble's mistake -- possibly from her aging memory 
or from confusion after her merge with Rose.

It's still an open question if another base might be used. I think not. 
There's a place where Marble compares her strength to another chem and 
says it is 4.25 times stronger than she is. That's a nice fraction in 
base 10, but not in base 9.

The number of bits to a card might be 9, though. They are "small squares 
sheared from so many cards" (Lake 2). If cards themselves are square 
then the number of bits per card should be a square number too. They 
wouldn't want to waste the precious card material, and they can't make 
too many cuts per card.

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