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The Crossing of the River Styx

©2001 Lewis Bruser

 

There have been many epochal water crossings: Washington crossing the Delaware, Columbus crossing the Atlantic, Caesar crossing the Rubicon, Moses crossing the Red Sea, and of course the epic pissing match between Hector and Agamemnon.

None of these had posed so complex or bewildering a challenge as the crossing of the river Styx. To start with, it consisted not of one but of fifteen crossings. The river circled what was believed to be the "lower world" seven times; the distance between each circle was unknown and the span across the lower world itself could not even be guessed at.

The greatest minds of antiquity applied themselves to this problem. Eratosthenes, who had already calculated the diameter of the Earth, threw up his hands in despair after two fruitless years of drawing triangles in the sand. Archimedes reportedly made some progress but abandoned the project to pursue some lucrative spin-offs.

The quest inspired Sappho to compose a love sonnet, which began:

Euclid, thou shouldst be living at this hour!
Athens hath need of thee!
How wouldst thou scale a fen of Stygian waters?
Let me count the ways . . . .

The sonnet closes with a couplet that Joseph Brodsky has called "the most beautiful ever written by a dead white female." It is also, arguably, at once the most subtle and most succinct ever written by anyone. It expresses the confounding by the gods of man's puny intellect, and the rejection of his corporeal essence by the vestal virgins—and the severe consequences they are willing to bear—all in one sweeping metaphor:

As from Olympus thrown a mighty curve,
They also wait who only stand to serve.

It was a later poet, an obscure troubadour of wave-particle duality, who, in a startling adumbration of the well-known galactic red-shift theory, pointed out that with each spiral of the torrent of water the rotational velocity changes, resulting in a shift in the frequency of light reflected from the surface of the water, and that by measuring the initial velocity of the water in the outer spiral, and the frequency of light reflected from each successive spiral, one could determine the changes in velocity, hence the changes in the diameters of the spirals, hence the total distance across the diameter of the seven spirals and whatever lay between them in the center. The underlying mathematics, known as the Fundamental Theorem of Inferential Calculus, is still regarded by poets and women as the first principle of decision analysis.

Nowadays as we zoom across on a ten-lane elevated freeway, unaware of what lies below, smoothly propelled by our automatic transmission, we forget that it all began with the Styx shift.

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