From:             BillJanie@aol.com
Date sent:        Thu, 15 Feb 1996 09:25:58 -0500
To:               pcp@mailbase.ac.uk
Subject:          elaboration and mandala grid
Send reply to:    pcp@mailbase.ac.uk

Elaboration concerns the extension and definition of constructs.
Extension is the comprehensive expansion of ranges of convenience.
Definition concerns the
 clarity and explicitness of constructs. The following coordinate grid
portrays an ideal form of elaboration.
                a  b  c  d  e  f   g  h
          a.   1  2  3  4  5  6  7  8
          b.   2  1  4  3  6  5  8  7
          c.   3  4  1  2  7  8  5  6
          d.   4  3  2  1  8  7  6  5
          e.   5  6  7  8  1  2  3  4
           f.   6  5  8  7  2  1  4  3
           g.  7  8  5  6  3  4  1  2
           h.  8  7  6  5  4  3  2  1

The row and columns represent the same figures/constructs.  The matrix
is integratively complex (it is equal to its transpose). It is also
perfectly logical (the above explicit ranks equal the implicit ranks-
those derived by ranking the correlations across the inter row
correlations. The size of the matrix can be extended to infinity,
retaining integrative complexity and logical consistency. The matrix
also replicates itself in the manner that fractal theorists describe as
self-similar. 

The matrix is an example of what statisticians call as self-conjugate
Latin Square. Scientists use such matrices to develop elaborate
experimental designs. Color the cells by their numbers and you will see
why I call this a mandala grid.

William Chambers