To: alt.magick
From: baldwin@cogsci.ucsd.edu (Ken Baldwin)
Subj: Magick Square 3 - Saturn (0000.msqstrn.kb)
Date: unknown


Recently, I've become interested in the following figure:

                        4 9 2
                        3 5 7
                        8 1 6

This is the "magic square" of order 3, so-called because it sums to 15
along all the rows, columns, and principal diagonals. (Similar squares
of higher order can also be constructed.)

Among the ancient Chinese, this was known as the *Lo shu* (Lo River
Map). According to Joseph in the THE CREST OF THE PEACOCK: NON-EUROPEAN 
ROOTS OF MATHEMATICS (1991) it was seen as a symbol of "the universe itself,"
because of the remarkable balance between the odd [considered yin] and 
even [considered yang] numbers:
        
> ...gradually an extensive folklore grew up around the magical properties 
> of the *Lo shu*...it came to be described as the nine rooms or halls of the
> cosmic temple, the Ming Tang, and later writers would refer to the 
> construction of this square as the 'nine halls calculation' (chui
> kung suan). The belief in the magical powers of this square spread into
> the neighboring areas, among the Tibetans, Koreans and Mongolians...
>       
> West of China, the subject of magic squares was first discussed by the
> Arabs, towards the end of the ninth century AD...possible links from
> China through trade links cannot be ruled out...one finds more or less
> the same ingredients of occult, numerology and combinatorial analysis
> as in the Chinese sources...

The symbol was in use among the Sufis according Idries Shah, though the only
example he gives is as a key for deciphering the meaning of other symbols.
I've also been reading a bio of Sir Richard Burton. The symbol appears
among the illustrations (with no discussion in the text), along with a 
statement that Burton was taught by the Sufis how to use it for medical 
diagnosis.

A book I consulted on the mathematics of magic squares mentioned that this
symbol also appears in many alchemical writings from the middle ages (e.g., 
Agrippa, De Occulta Philosphia, II, 42).

So...I'm really curious what this thing is all about! I have philosophic
reasons for being interested in any ternary decomposition of Reality...
as opposed to the much more common binary systems. None of the sources
I've been able to locate give any real information about what sort of
philosophic/mystical significance was attached to the square, or how it
might have been used. Pointers to *any* related references would be
greatly appreciated. Thanks,

Ken Baldwin
(baldwin@cogsci.ucsd.edu)