Cleaning out the outbox - Magic squares

[Guest guest]

Well, this post has been sitting in my Outgoing box for almost a year now, so

maybe its time to send it.

I promised some time back that I would try to summarize Marie-Louise

Von Franz's (MVF) writings on m-squares (which he has a particular interest

in), and there were several other Circle members interesting in Number (at

least at that time...), so for what it's worth here goes...

MVF published 4 works that touch on the archetype of Order: " Number and Time "

(N & T), " Psyche and Matter " (P & M), " On Divination and Synchronicity " (D & S),

and " Time, Rhythm and repose " (TRR). I will draw from all of these, but

principally N & T. The preface of this book begins:

" After CGJ had completed his work on synchronicity in " Synchronicity: an

Acausal Connecting Principle " he hazarded the conjecture, already briefly

stated in his paper, that it might be possible to take a further step into

the realization of the unity of psyche and matter through research into the

archetypes of the natural numbers. He even began to note down some of the

mathematical characteristics of the first five integers on a slip of paper.

But, about two years before his death, he handed this slip over to me with

the words " I am too old to be able to write this now, so I hand it over to

you " .

Clearly, for him to burden MVF in such a fashion, Jung must have thought this

was a subject worthy of pursuit. MVF tells us a little bit more about this

slip of paper in P & M: " He made a note 3 inches square, on which he wrote:

one, the all; two, the only even prime number; three, the first uneven prime

number, the sum of one and two, the first triangular number; four, the first

quadrangular number, the first *square* number " . As an aside, I asked Sonu

Shamdasani the Jung historian who spoke here in St. last summer what had

become of this slip of paper and he wasn't aware of its existence!!

From TRR: " Number, according to Jung, is the most basic and primitive of the

archetypes, which are the 'arrangers' of our conscious ratiocinations " .

MVF mentions magic squares directly only in passing, observing that the

Chinese Lo-shu model is a 3x3 m-square. However, she states that the Lo-shu

and its parallel the Ho-t'ou are the basis of the I Ching, and goes on to

base much of her discussion on these two structures. She notes that these

are matrices, mathematical concepts that underlie much of modern science.

The key idea is discussed in Chapter 8 of N & T, which perhaps as an

interesting synchronicity I just noticed has its page number printed

upside-down in the table of contents! It is entitled " Archetypes and Numbers

as " Fields " of Unfolding Rhythmical Sequences " . She states that historical

attempts at hierarchical numerical constructs such as the lambdoma, the

kaballah, etc. were " attempts to outline the total order of the collective

unconscious " . She states " number appears to pertain essentially to the

behavior of archetypal dynamics -- the archetypes are given to manifesting

themselves in an ordered sequence " . " The idea of a fieldlike arrangement of

the archetypes...derives from the fact that the archetypes exist in a state

of mutual contamination " and draws a picture of a web of archetypes, with

their " contaminations " as the links that bind them (Edinger draws another

such web of the Apocalypse archetype on pg. 4 of his book).

In D & S, MVF shows how the Ho-t'ou was the basis of Jung's pyramidal model of

the Self. The m-square is also a mandala, an expression of the Self.

So, what I make of all this is that m-squares are a constellation of the Self

archetype. The fact that they have " grabbed " people of diverse cultures for

millenia illustrates its numinousity. As each natural number is an

archetype, an m-square is an expression of the relationship between

archetypes, an attribute not surprising for the archetype of Wholeness.

Sorry I took so long to post this , and in truth, the little drivel I

have written here does little justice to the topic, which is probably why it

sat in my Outbox so long. But we're getting to the end of the Millenium, a

very good time to complete unfinished business, n'est-ce pas?

FWIW,

--Kurt