August 19, 2016. 6 a.m.
Found amongst the shards of the Lost Library of Marpa, in one of my folders. I wrote this, or channeled it from some corner of the Greater Self. I remember it now as I read it, but I couldn't write this today, so it raises the Quest-ion again: WHO AM I? This little self seems to be an outpost on the frontier, connected in MEM-ory to a Lost Civilization that sank beneath the Etheric Waves.
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The Pythagoreans of fifth century b.c.e. Greece made an
important distinction between counting and geometry. Counting was associated
with commerce, imported to Greece from the Middle East by the Phoenicians. It
was obviously limited to integers (1, 2, 3, ...). So the early Greek
philosophers disdained counting both because of its limitations and because of
its commercial associations.
In contrast was the mathematics of geometry whose very name
-- "measuring the world" -- implied a more global and even
cosmological conception of the role of numbers. The world was made up of
objects that were not all matched perfectly by integers of counting. In order to
measure distances accurately, you necessarily had to understand numbers that
fell between integers-that is, fractions: 1/2, 1/3, 7/5, called the rational
numbers because they were made by ratios of integers. Nonetheless, Pythagorean
mathematics was still anchored to real and tangible manifestations in the
world, however idealized the concept of Line and Point were for the purposes of
their logical manipulation. Geometry measured the dimensions of the earth and
the objects on them. Numbers used in counting, the integers, measured things,
discrete objects that could be held and owned.
For them, manipulating numbers via proving statements about
regular geometric forms was a means of communion with God's mind. "They
proclaimed that true understanding of the world came through numbers, because
all things in the world possess numbers." So when one of the Pythagoreans,
Hyppasos the Akousmatic, stumbled upon the idea of Ã2 and the geometric proof
that it was incommensurate to any integer or ratio between integers, the
Pythagoreans suppressed it. In Book X of Euclid's Elements, a nearly
contemporary commentator recounts the tale, which he received from Iamblichus
of Hippus, that Hyppasos was enticed onto a chartered cruise by his fellow
Pythagoreans, but never arrived at his destination!
The whole incident speaks to their commitment to the sort of
Idealism which later emerges in Platonic philosophy. Numbers were the idealized
root of reality, just as geometry was the idealized shape hidden behind all the
worldly forms. For there to be a number to which no corresponding reality could
be found was intolerable, blasphemous, heretical. It simply did not compute in
their metaphysics, and thus was excluded from their rational system. And so was
Hyppasos, for opening this can of worms!
Finally, a fellow named Eudoxos found a way of expressing
this that seemed to solve this dilemma. First, he drew a line to show the
continuum of ALL “things.”
Suppose that all the integers were mapped onto a line at
equal spaces:
. . . . . . . . . .
0 1 2 3 4 5 6 7 8 9 ...
Now map all the rational fractions which fall between them:
. . . . . . . . . . ... .
0 ...1/16 ...1/15/... 1/14 .... 1/2 ... 2/3 ...3/4 ...
4/5...18/20... 78/99...475/511 ...1
Eudoxos' stroke of genius lay in asking a simple question:
What numbers describe the points which lie between the
rational numbers?
This visual image got it across that there was much more to
Reality than that which you can name and count.
As it turns out, a few centuries later the great
mathematician Gregor Cantor showed that not only was Eudoxos correct, but that the set of irrational
numbers forms an infinity larger than that of the rational numbers. (An
“infinity larger” must be one helluva lot more!
I’m no mathematician, so please forgive my poetic paraphrasings as we
carry on)
Most of our culture thinks of the Irrational as meaning
madness, senseless, meaningless. Well it IS senseless, in that it is beyond the
reach of the little sensory tweezers we use; but think of the Irrational as the
Unspeakable, the Ungraspable, the Tao, the Continuum that can't be packaged up
and bottled.
So now mathematics tells us that the irrationals
"outnumber" the rationals. Those manageable, logical bits and pieces
we like to juggle around in our craniums are dwarfed by what we can’t juggle,
the inexpressible, extensionable, always trailing off flows of reality that
can't be held in the grasp of the rational mind. Our nervous system is like a
shutterbug fire brigade of busy beavers bucketing up bits and bytes, little
grabs of reality, passing them along synapse to synapse, where they're dumped
on the brainial librarian's table, that Wizard of Odd we call "I."
We'll never encompass the Ocean of the Unmeasureable with those puny little buckets.
The point is that Realism is not the same as science and
rationalism. Realism means acknowledging the unknowable complexity of natural
phenomena - its "irrationality" including its unmeasurable
properties-unmediated by instrumentalities or theories or models. And of all
the slippery irrational phenomena out there in reality which we have attempted
to define and replicate rationally, the slipperiest and most elusive is the
brain/mind. The persistent delusion that we can define the brain mechanically
and merely rationally, when what it does best is quite irrational and
irreducible, is the defining delusion of postmodern science, and has become the
central debate of postmodernism generally.
Think about what the
brain does. In simplest terms, it takes physical impressions from an
irrational, non-fragmented reality and transmutes it into thoughts, sensations,
and the will to action. That is, it takes information from out there and
translates it into meaning in here, in a thoroughly different realm requiring a
thoroughly different medium. At the risk of belaboring the obvious, the brain
(not the mind, but the physical organ the brain) is a metaphor machine,
operating continuously to carry meaning between realms that are in the larger
sense thoroughly incommensurable (the map will not adequately lay over the
territory).
In that great phrase of J.B.S. Haldane, "Not only is
the Universe stranger than we imagine, it is stranger than we CAN
imagine."
So the great Ocean of Reality is beyond our logical reach.
To live solely in the world of the bits and pieces is to live in the Maya
(="measurement", the parts you can grab). Vitvan advises us to
develop our native ability to "feel-know," to consciously live in the
world of flowing energy, the Seamless Garment of the Bride (Light Mother
substance).
When Vitvan reminds us "along with your getting, get
understanding," he doesn't mean get
a degree, get an outline, get a Cliff Notes summary of Reality, but jump into
the water and shut down that chattermonkey between your ears. You don’t have to
be able to describe water to KNOW what it is![1]
So don’t be afraid to let go of that mental handrail. Don’t
worry. Mother will catch you.
For now, just remember the
sage words of those Fab Four Philosophers, the Beatles: "Turn off
your mind, relax, and float downstream....it is not dying."
[1]
Although the pasting of labels onto objective reality is what sets humankind
apart from the animals. It was the defining moment in Helen Keller’s education
when she realized in a bolt of illumination that words can have a separate
meaning from the objects. At that moment she was bootstrapped up from the
animal mind into the human. (but leave us save that topic for another day!)
