The Geometric Proof of the Existence of God
from The Prelude Book VI
More frequently from the same source I drew
A pleasure quiet and profound, a sense
Of permanent and universal sway,
And paramount belief; there, recognised
A type, for finite natures, of the one
Supreme Existence, the surpassing life
Which—to the boundaries of space and time,
Of melancholy space and doleful time,
Superior, and incapable of change,
Nor touched by welterings of passion—is,
And hath the name of, God. Transcendent peace
And silence did await upon these thoughts
That were a frequent comfort to my youth.
Ah, but Wordsworth did love his geometry, no matter how poorly mastered. He saw in its beauty, simplicity and rounds the variety of existence. He saw in it the permanence that would one infer from its survival from the time of Euclid to today. What he did not yet know was its "ineluctable modality" and its gorgeous mutability as exhibited by the soaring expressions of Reimann and Lobachevsky (Nikolai Ivanovich--to be precise). And I think had he known of these transformations, he would have been every bit as entranced, seeing in them the beauty of how a few simple rules creates a new universe. We derive both geometries from a simple denial of one of Euclid's postulates--"Through every point outside of a given line there is one and only one line that can be constructed that is parallel to the given line." Reimann changes the postulate to say that there are none, Lobachevsky changes it to say that there are an infinite number. From Reimann, we have the geometry on the surface of a sphere, from Lobachevsky, the geometric of Einsteinian space/time. And how Wordsworth would have delighted in both of these--or so I suppose because I really am with him on this point. The beauty of mathematics points to an infinite beauty that is beyond ready and easy grasp.
And, if one then wants to consider the simplicity of God as a series of plays on Euclid's postulates, the analogic becomes clearer--more profound. Or perhaps only to those of us who play around the periphery of mathematics the way some skirt the sea looking for the profound mystery--but not its resolution.