Roger, Ken, Rob, Horse, Fintan and all interested Pirsigers:
Roger, the post that synthesizes autopoiesis with Nishida was obviously
well thought out and I sensed a genuine passion for the ideas on your
part. Thank you !
I feel like you've provided a valuable service. Roger's Synthesizer
Services could make real money in a just world!
Do I dare try to summarize all your work? I want to be sure I really get
it.
"The apparent materiality of the world is really just the outward
structure of experience"?
I know its a little too pithy and simplictic, but isn't the main idea
expressed? Have I misunderstood? Matter and mind are not seperate at
all, but are two aspects of one reality, like the wave and particle.
The structure of Intellectual patterns isn't fundamentally different
than any other level of reality. Does the brain structure the mind, or
does the mind structure the brain? The only answer in YES!
I want to shift gears here, but should say a few introductory words so
nobody's clutch gets burned. The following is about the structure under
the structure, the ultimate pattern, if you will. I hope it provides new
ideas, but also supports Rogers fabulous post, if I understand it
properly. My thoughts are based on the riddle of the golden mean, as it
was explained to me by a mystic art professor back in college, and on a
movie called pi, which I saw just yesterday. (The movie is out on video
and I urge you to see it. The title on the box is actually the Greek
symbol, which I can't make with this keyboard, but you know what it
looks like.) I believe this is all relevant to the MOQ.
I forget who introduced "the golden mean" in a recent post. My
understanding of "the golden mean" is totally unrelated to the idea of
Aristotelain moderation described in said posting. I only mention it to
prevent confusion.
The Academy founded by Plato asked just one question as an entrance
exam. To be admitted into Plato's Academy one had to solve the riddle of
the golden mean. The riddle was permanently presented to everyone,
aspiring student or not, at the stone gates of the first university.
There, carved into stone, were two basic geometic shapes; a circle and a
square. These two ideal forms were positioned in a particular way with
respect to each other, and solving the riddle requires an understanding
of that positional relationship and it's meaning. BTW, this is
supposedly real history.
It'll be very difficult to describe this geometic riddle in words. I
know this sounds wierd, but it will help if you get yourself a pencil
and a sheet of paper to help work it out and visualize it better.
Draw, or imagine, a geometrically perfect circle. Size doesn't matter.
:-) Make a line across the circle, from side to side, that disects it
into perfectly equal parts. On top of the line, but just inside the
cirlce, draw a geometrically perfect square. The square also has to be
resting and centered on the disecting line. Because the verticle lines
of the square have to be the same length as the base, by definition,
there is only one square that will fit in any given circle. The verticle
lines of the square move up from the disecting line base to reach the
edge of the circle. Naturally, the top of the square is parallel to the
base and the disecting line it rests upon. So, we have a disected circle
with a sqaure on top of the line, but within the circle.(There could be
a square UNDER the line too, but it would otherwise be exactly the same
and so it would be pointless repetition.) That's what was carved into
stone at the entrance of Plato's academy. If and when you could explain
the meaning of this geometric diagram, you'd be admitted as a student.
(sorry if that was tedious)
I'll tell you what it means, just in case you ever go back in time.
Size really doesn't matter, the solution to the riddle is in the
relationship of these geometric forms. Since there is always just one
square that fits in any given circle their relationship is mathematical.
The circle and the tightly fitted square represent a ratio. You could
express it in terms of the total area of each form or the length of
their boundries. But the solution to the riddle of the golden mean was
actually found in the disecting line. Their idea of a trick question?
Still have your paper and pencil?
The disecting line intersects the left and right edges of the circle.
Two more points are created as the "correct" square's verticle segments
touch the disecting line. That gives us four points. (That have been
derived by the relationship between three geometric shapes, a line, a
circle and a square.) Going from left to right on the disecting line,
point A is at the left edge of the circle. Points B and C are where the
square's two verticle segments meet the disectling line and point D is
at the right edge of the circle. Just to be crystal clear, all four
points are on the disecting line and read ABCD from left to right.
The line has been divided into three segments, AB, BC and CD. Segment AB
is the distance between the left edge of the circle and the left edge of
the square. Segment BC is simply the length of the square's base. (And
the length of all its sides, by definition.) Segment CD is exactly the
same length as segment AB and is the distance between the right edge of
the square and the right edge of the circle. The total segment, from A
to D is simply the diameter of the circle.
We don't even need segment CD to solve the riddle, it would just be a
pointless repetition like another square under the line instead of on
top of it. Just throw segment CD out the window and forget about it.
Sorrythe length of this explaination. Its so hard with words. Wish I
could draw a picture. It would be so much easier. But please indulge me,
we're very close to the riddle's solution now.
The length of our two remaining segments, AB and BC, is the key that
unlocks the whole riddle. More precisely, the ratio of the two lengths
is the key. The ancient Greeks didn't have a zero in their numbering
system, but today we can express the ratio as 1 to 1.6180. If segment
AB were 1 meter long, segment BC would be 1.6180 meters long. (You've
probably noticed that this is alot like pi, and this info will help in
appreciating the movie by that name.)
Plato described the ratio with words instead of numbers, saying
enigmatically, "the lesser is to the greater as the greater is to the
whole". He somehow saw that without zeros or decimals. The lesser is
segment AB, which is 1 meter long in our example. The greater segment is
BC and is 1.6180 meters long. The whole is segment AC and simply the sum
of AB and BC. Segment AC is 2.6180 meters long. You can check this with
a calculator. The ratio between the length of segments AB and BC is the
same as the ratio between segments BC and AC.
"The lesser is to the greater, as the greater is to the whole."
The riddle's solution is in the recognition that this relationship, this
ratio derived from ideal geometiric forms that don't really exist
anywhere except the human intellect, is found througout nature! The
ratio is exhibited in the shape of galaxies, the structure of human
bodies, fingerprints, DNA, sun flowers and most conspicuously in the
structure of the chambered nautilus. It is a pattern that seems to
underly all other patterns.
I'll have to finish this later. All out of time.
David
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