Friday, August 19, 2016

The Great Irrationality

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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We all think of ourselves as “rational” folks, able to sift truth from fiction. But the mental software we use is still having the bugs worked out. We take it for granted that earlier peoples think the way we do. It might be instructive to look back at Greece, where a lot of our current modes of abstracting the world got off the ground.

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 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!)


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