ONT Re: Rote Ariffmetic
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[Archive Copy]
Subj: Re: Integer Sequence Finder
Date: Thu, 13 Jun 2002 11:36:32 -0400
From: Jon Awbrey <jawbrey<at>oakland.edu>
To: Ben Udell <budell<at>hdgonline.net>
Benjamin Udell wrote:
>
> Jon,
>
> This is not meant to start an off-list conversation,
> I just wanted to thank you for the URLs, but I can’t
> Peirce-ify most of this stuff.
i just threw in those bits about riffs and rotes
out of some resonance with the musical motives.
i used to draw these structures in a way that
resembled musical phrases:
2 = p, 3 = p_p, 4 = p^p, 5 = p_p_p, 6 = p p_p, 7 = p_p^p, 8 = p^p_p, ...
where you will have to imagine how they look with
the higher echelons of subscripts & superscripts,
sort of like this, the riffs on 4 nodes or notes:
o===========================================================o
| |
| p |
| p< p p_p p |
| p< p<_p p< p_p< p p_p p_p_p |
| p< p< p< p< p< p< |
| |
| 2^16 2^9 2^8 2^7 2^6 2^5 |
| 65536 512 256 128 64 32 |
| |
o-----------------------------------------------------------o
| |
| p |
| p< p p_p p |
| p_p< p_p<_p p_p< p_p_p< p< p_p_p_p |
| p p_p |
| |
| p_16 p_9 p_8 p_7 p_6 p_5 |
| 53 23 19 17 13 11 |
| |
o-----------------------------------------------------------o
| |
| p^p p_p p p |
| p< p< p< p< |
| p p p^p p_p |
| |
| 3^4 3^3 7^2 5^2 |
| 81 27 49 25 |
| |
o-----------------------------------------------------------o
| |
| p |
| p p< p p< p^p p_p p p_p_p |
| p p^p |
| |
| 18 14 12 10 |
| |
o===========================================================o
i once explored various relationships of these forms to
some recursive generalizations of fourier analysis, and
used to speculate about all sorts of pythagorean ideas.
> I’ve visited those sites. That’s the first time I’ve actually
> seen recursive functions. I’ve heard about them only: that
> Gödel used them in his incompleteness proof so that he wouldn’t
> need to use set theory when he talked about set theory; & that
> some logicians are interested in them as representing the future
> of mathematical logic (that’s what I hoyd, I dunno from Adam).
> Anyway, I hope you don’t think I’ve been representing myself as
> a logician; I mentioned my non-logicianhood in Peirce-l posts
> some time back, probably before you appeared on the list.
> I can’t think of permanent solution except to sign off
> as "B. Udell, layperson" or some such.
"theory of recursive functions" is just another name for computability theory.
and "computable function" is just a synonym for "recursive partial function".
gödel's use of "general recursive finctions" (same thing again) was just one
of many, as it turned out, equivalent ways of bringing computability intuit.
> The integer sequence search is cool. I was playing with
> a combinatorial thing some months ago, & got a sequence
> with which I just stumped the integer sequence finder,
> but when I shortened the sequence, I discovered that
> I was doing an infinitary-alphabet version of:
>
> Name: Word structures of length n using a 6-ary alphabet.
> Comments: Permuting the alphabet will not change a word structure.
> Thus aabc and bbca have the same structure.
>
> Now I know what to call it! It stumped me to find a formula for it (like
> stumping me means anything). Each prospective formula turned into a version
> of the sequence (if that makes sense to you), & shots at relationships to
> other sequences showed tantalizing patterns, then never panned out.
>
> Anyway, thanks for the fun.
yes, the wrong sort of person can lose years of their life in that funhouse.
jon awbrey
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