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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