Don to Jerry : Math
Jan 27, 1994 09:59 AM
by Donald DeGracia
Thanks for the nice letter and adding to the discussion. I think you
raised a very good point about the aspect of math that *is* culturally
independant and that being that we cannot imagine existence without some
concept of number. For afterall, concepts of numbers and their
interrelationships are actually an expression of the reality of
differentiation, or variety, or seperateness, that is inherent in
physical existence. From this angle, all languages and cultural
symbol sytems will find some means of expressing this fundamental fact
of physical reality.
Now, when you start from this point of departure, you have a basis to
compare how different cultures symbolize the fact of "different-ness".
Raising the point of the old Hebrew thought where numbers and letters
were associated, as in the Quabalah is a good point for illustrating
just how variegated can be different cultures appraoch to the fact of
different-ness. This ancient hebrew thinking is very far divorced from
how we percieve math today. Likewise with astrology. In the Middle ages,
the term "mathematician" meant an astrologer. Again, we don't think
like this today, at least academic mathematicians don't. We here on
the list do though<g>!
So, I think its good to broaden the discussion out and realize that
what we call mathematics is actually our particular society's way of
dealing with the fact of seperateness in our physical expereince. What
you can then observe is how the particular sysmbol system we have
evolved has gone off on its own line of evolution. We have moved from
numbers as simple devices for counting - used mainly in an economic
context to more abstract generalizations. Building on the ancient
Greek mentality, we have taken the idea of abstract math way beyond
what the Greeks could have envisioned. Asking the question of why this
is the case is illuminating and also is an example of something
sociologists (European sociologists, not American sociologists who are
quite dim in comparrison) have discovered:
The reason the Greeks only went so far with their ideas is basically,
because of their religious beliefs. Or to say it as I already have,
because of their metaphysical beliefs. The European culture that created
modern abstract math had a much different metaphysics - a mechanistic
metaphysical outlook - that the Greeks did not have. The ancient
Greeks had a much more "mystical" metaphysical underpinning than
Reniasance European mathematicians.
What is ironic though is that the "mystical" beliefs of the ancient
Greeks served to stifle the evolution of abstract thought. This is what
sociologist have discovered. That, when you compare mystical
other-wordly views to pragmatic, sensory oriented views, that the
sensory oriented views tend to develop, in the long run, much more
abstract lines of thought. You see the same pattern in the evolution of
science amongst various cultures. Why, for example, did not ancient
Hindus, who were very abstract thinkers - develop abstract theories of
the physical world like we have in modern times? Again, its the same
answer. The aof the Hindus, which were very "other-worldly" prevented
them from developing or spending a lot of time concentration on the
world of the senses.
This all raises interesting questions about the relationship between
"mystical" and "sensory oriented" metaphysics: Is there a happy medium?
Can you have the best of both world-views? In otehr words, what is the
metaphysics that can allow one to do astrology and topology at the
same time? Do astral project and do physics at the same time?
And, as is probably apparent, I'm funneling this discussion in the
direction where Gerald and I like to hang out: the relation between
science, occultism and mysticism. And the idea that John raised about
the metaphysical status of mathematics actually plays a fundamental
role in the synthesis of these 3 world-views.
Persoanlly, I think that math does exist indepentant of the human mind.
In effect, the world of mathematics are regions of the mental plane. It
is a human potential to access this region as the human mind can access
any region of the mental plane. Plato's "world of pure ideation" is much
more literal a reality, when seen from the occult viewpoint of the
planes, than most academic types would admit to today. So in this
sense, math is a very real and object thing: is is a region on the
mental plane. However, as such, it is still just another element in
the Maya so to expect nirvana from math is something akin to jnana
yoga. It probably can be done, that is, find God through math. Yet, in
our particula society we associate extremely secular and aspirtual
overtones with math, so you'd better be the kind of nut who would find
this list interesting, to go seeking God in math <g>!
Regarding the relationship between math and physical nature. This
relationship gets illuminated when seen in terms of the planes, and in
particular in terms of the Hermitic axion. The latter states "As
above, so below", and the relationship between math and physical
nature is probably just another example of the hermitic axiom in
action. "As above so below" can mean that higher planes are
*self-similar* to lower planes. Thus, as one finds the mandelbrot set
within itself, one finds the patterns of the higher planes inside the
lower planes. Therefore, patterns we discover in the mental plane
(math) map to patterns we discover in the physical plane (science).
And of course, the human brain/mind combination, being a part of this
system, maps equally well to both the physical and mental worlds Thus,
when seen from an occult viewpoint, the fact that there is
correspondance between our abstract thought (math) and physicl nature
is no suprise whatsoever.
Then we get the issue of the "messy" and imperfect physical world, and
the perfect world of math ideas. Here I think we are dealing more with
cultural attitudes than anything else. For what we have done in
presenting this attitude is, in our ignorance of all possible
mathematics, we have taken the little bit we do know and said "well,
nature does not fit this bit math that we know, so nature must be
imperfeect because math is holy and therefore perfect" (or something
like this). But this attitude is the folly of the half-knowledge of a
pretentious intellect, and a secular, aspiritual one at that! For
example, look at how fractals and chaos math have changed everything.
Or just as good an example, look at the development and subseqent
application of nonEuclidean geometry. Both of these examples
illustrate that math can very effectively represent nature. However,
prior to the development of these branches of meth, we thought that
nature was imperfect because it wasn't made of euclidean circles and
spheres. Now we know that nature has perfect mathematical regularity
as fractals and chaotic dynamic plots.
So, my feeling is that saying that nature is imperfect and math is
perfect is putting the cart before the horse. For in all likelyhood,
if there is some part of nature that doens't gel well with whatever
math we presently know, its not that nature is imperfect, its that our
knowledge of math is imperfect. Both nature and math are perfect. What
needs work is human understanding of both.
Nuff for now!
Best to All of you!!!
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