Message-Id: <199906012002.QAA14564@mail2.lig.bellsouth.net>
From: "Joe E. Dees" <joedees@bellsouth.net>
To: memetics@mmu.ac.uk
Date: Tue, 1 Jun 1999 15:03:56 -0500
Subject: Re: Personal Constructs and Memes
From: "William Chambers" <williamc@roman.net>
To: <memetics@mmu.ac.uk>
Subject: Re: Personal Constructs and Memes
Date sent: Tue, 1 Jun 1999 15:15:38 -0500
Send reply to: memetics@mmu.ac.uk
> Joe wrote:
>
> There are 24 possible distinct juxtapositions of four numbers, and
> six possible of three (and 120 possible of five, 720 possible of six,
> etc. n! (n factorial)(1 x 2 x ...x (n - 1) x n) determines the number
> of possible combinations for any quantity n of distinct numbers).
> Just keeping the math straight so that your proposed grid will
> circumscribe all possibilities.
>
>
> Joe,
>
> I like your math. There are, however, constrictions on the coordinate grid that these equations do not take into account.
>
> 1. The diagonal will contain "1" ranks, indicating that each figure is most like itself.
> 2. Each row will contain all ranks 1-k.
> 3. There will be no repetitions of ranks in any row (unless we allow tied ranks, as in Platonic solids).
> 4. For perfect integrative complexity, each row will equal its corresponding column.
>
> These conditions dramatically reduce the number of possibilities. To my knowledge, the mandala pattern is one of only two patterns that satisfies all four conditions (disallowing tied ranks).
> The other pattern is logically inconsistent and I have never seen it in real data.
>
> I suppose the matrix would be more formally called an ordinal self-conjugate latin square, following the descriptions of Winer and (I think Kirk) in their texts on analysis of variance etc.
>
> With regard to integrative complexity, the mandala grid expresses a completely non redundant pattern of elaboration, in the sense that no rank occurs more than once is any row or column. The analysis follows the logic of Tversky's feature analysis in reverse, If person (figure) A is rnaked
2nd like person B while person B is ranked 4th like person A, then person A contains more information than does person B. Think of two circles, as in a Venn diagram. Person A is a larger circle. Person B is a smaller circle, Their overlap covers 75% of B but only 25% if A. There is nothing
illogical about this pattern. It just means that person A includes more information than person B, With perfect integrative complexity, each person contributes an equal amount of information defining "genearl similarity." If stereotypes are used, some figures will be less information rich.
Others will b
>
> Bill Chambers
>
OK, so you know about
1234
1243
1324
1342
1423
1432
2134
2143
2314
2341
2413
2431
3124
3142
3214
3241
3412
3421
4123
4132
4213
4231
4312
4321
but have no need to use them all.
On an interesting little tangent, there are only two ways to arrange
the first five positive numbers so that none of them represent their
position in line (1 is not first, 2 is not 2nd, etc). They are:
24153
31524
strangely enough, they blend to form the seven member reiterative
patterns
24153152415315...or
31524153152415...depending on with which of the two you
begin.
The common structure is easily represented:
24 3 24 3 or 3 24 3 24
15 15 15 15... 15 15 15 15...
Useless, but cute.
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