Saturday, November 19, 2005

all that geometry....

About five years ago, my daughter and I took the Tube to Paris from London. The anticipation of the day was a Total Solar Eclipse, so while we were traveling on the train many of the passengers were looking through special glasses or in our case we had poked a hole through a piece of paper to view the event. It was only later that I learned how unique this experience was; there will only be 18 solar eclipses from 1996-2020 for which the eclipse will be total on some part of the Earth's surface.

“The common perception that eclipses are infrequent is because the observation of a total eclipse from a given point on the surface of the Earth is not a common occurrence. For example, it will be two decades before the next total solar eclipse visible in North America occurs.”

In spite of the excitement, I found myself grateful for the harvest. Looking out the train window we past numerous fields with round hay bales by the hundreds geometrically spaced. All those curves but I just saw rows and right angles. Peaceful proportion and a much-needed equilibrium, all that geometry had a calming effect.

A friend of mine said, “Geometry does comfort, as you suggest, even as a lack of order frightens…. There's an optimal way to harvest, which results in curled up stacks of hay equally dispersed over a large field. All of that wild Life neatly brought to heel. We're under no threat, and consider the wonder of it beautiful.”

A while back I was wading through Albert Einstein’s, Relativity: The Special and General Theory and had found it to be surprisingly readable…

“Geometry sets out from certain conceptions such as ‘plane,’ ‘point,’ and ‘straight line,’ with which we are able to associate more or less definite ideas, and from certain simple propositions (axioms) which, in virtue of these ideas, we are inclined to accept as "true." Then, on the basis of a logical process, the justification of which we feel ourselves compelled to admit, all remaining propositions are shown to follow from those axioms, i.e. they are proven. A proposition is then correct (‘true’) when it has been derived in the recognized manner from the axioms. The question of ‘truth’ of the individual geometrical propositions is thus reduced to one of the "truth" of the axioms.”

“The concept "true" does not tally with the assertions of pure geometry, because by the word "true" we are eventually in the habit of designating always the correspondence with a ‘real’ object; geometry, however, is not concerned with the relation of the ideas involved in it to objects of experience, but only with the logical connection of these ideas among themselves.”

Einstein later illustrates this by description, “I stand at the window of a railway carriage which is traveling uniformly, and drop a stone on the embankment, without throwing it. Then, disregarding the influence of the air resistance, I see the stone descend in a straight line. A pedestrian who observes the misdeed from the footpath notices that the stone falls to earth in a parabolic curve. I now ask: Do the ‘positions’ traversed by the stone lie ‘in reality’ on a straight line or on a parabola?”

Similar to the consideration of the importance of position when viewing a solar eclipse, and like the illustration of the straight line or the parabolic curve, we tend to see what we look for, we reduce truth so it is manageable and our understanding is constrained to those axioms we believe. People often fail to grasp the influence or resistance of speed and motion inherent to living. Most of us don’t like change and we tend to resist “life’s wiggles” for the calming safety of order and predictability.

Einstein’s definition of geometry and his illustration seem to connect with my friend’s reference to Alan Watts. In the book Tao: The Watercourse Way, he says, “Geometrization always reduces natural form to something less than itself, oversimplification and rigidity which screens out the dancing curvaceousness of nature. It seems that rigid people feel some basic disgust with wiggles; they cannot dance without seeing a diagram of steps, and feel that swinging the hips is obscene. They want to ‘get things straight,’ that is, in linear order…”

Wendell Berry says, “For quite a while it has been possible for a free and thoughtful person to see that to treat life as mechanical or predictable or understandable is to reduce it. Now, almost suddenly, it is becoming clear that to reduce life to the scope of our understanding (whatever ‘model’ we use) is inevitably to enslave it, make property of it, and put it up for sale. This is to give up on life, to carry it beyond change and redemption, and to increase the proximity of despair…. One of our problems is that we humans cannot live without acting; we have to act. Moreover, we have to act on the basis of what we know is incomplete. What we have come to know so far is demonstrably incomplete, since we keep on learning more, and there seems little reason to think that our knowledge will become significantly more complete. The mystery surrounding our life probably is not significantly reducible. And so the question of how to act in ignorance is paramount.”

In short Berry says, “To treat life as less than a miracle is to give up on it.”

Annie Dillard expresses a similar outlook in her observations of creation in the book Pilgrim at Tinker Creek. “Our life is a faint tracing of leaf miners on the face of a leaf. We must somehow take a wider view, look at the whole landscape, really see it, and describe what’s going on here. Then we can at least wail the right question into the swaddling band of darkness, or if it comes to that, choir the proper praise.”

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