Monday, March 7, 2011
Circular Motion and Directionality
As part of his effort to distinguish infinite circular motion from finite rectilinear motion, Aristotle argues that unlike the latter, the former has no contrary. Among several counter-arguments that he entertains, one is that circular motion is always either clockwise or counter-clockwise, so it does admit of a contrary. His response--that since the co-existence of both directions is impossible, circular motion does not admit of a contrary--seems, in the context, designed only to defend the uni-directionality of the infinite rotation of the heavens, not to explain how both do actually exist, even if not simultaneously at the same locus. Furthermore, the premise framing his argument, i. e. that infinitude excludes contrariety, is questionable, as the examples of odd numbers and even numbers demonstrate. But his perhaps insuperable problem on the topic is that even infinite circular motion is directional, and directionality, as an ordered two-place relation, entails, at least in principle, a contrary.
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No comments on Emerson's "Circles"?
ReplyDeleteI guess similutudes would constitute a digression... ;)
What is the relevance of what Emerson has to say to the themes that I am currently developing? Does it either significantly reinforce them? Does it cast doubt on them? In either case: if so, how?
ReplyDeleteIf any 19th-Century theory of 'Circularity' is relevant here, it is Nietzsche's concept of Eternal Recurrence. Of particular interest to me right now is his notion 'willing backwards', introduced in the section of Thus spoke Zarathustra titled 'Redemption'.
ReplyDeleteWhat about "radial" motion? Wheels may go round and round, but waves...
ReplyDeleteThe key to every man is his thought. Sturdy and defying though he look, he has a helm which he obeys, which is the idea after which all his facts are classified. He can only be reformed by showing him a new idea which commands his own. The life of man is a self-evolving circle, which, from a ring imperceptibly small, rushes on all sides outwards to new and larger circles, and that without end. The extent to which this generation of circles, wheel without wheel, will go, depends on the force or truth of the individual soul. For it is the inert effort of each thought, having formed itself into a circular wave of circumstance, -- as, for instance, an empire, rules of an art, a local usage, a religious rite, -- to heap itself on that ridge, and to solidify and hem in the life. But if the soul is quick and strong, it bursts over that boundary on all sides, and expands another orbit on the great deep, which also runs up into a high wave, with attempt again to stop and to bind. But the heart refuses to be imprisoned; in its first and narrowest pulses, it already tends outward with a vast force, and to immense and innumerable expansions.
Every ultimate fact is only the first of a new series. Every general law only a particular fact of some more general law presently to disclose itself. There is no outside, no inclosing wall, no circumference to us. The man finishes his story, -- how good! how final! how it puts a new face on all things! He fills the sky. Lo! on the other side rises also a man, and draws a circle around the circle we had just pronounced the outline of the sphere. Then already is our first speaker not man, but only a first speaker. His only redress is forthwith to draw a circle outside of his antagonist. And so men do by themselves. The result of to-day, which haunts the mind and cannot be escaped, will presently be abridged into a word, and the principle that seemed to explain nature will itself be included as one example of a bolder generalization. In the thought of to-morrow there is a power to upheave all thy creed, all the creeds, all the literatures, of the nations, and marshal thee to a heaven which no epic dream has yet depicted. Every man is not so much a workman in the world, as he is a suggestion of that he should be. Men walk as prophecies of the next age.
Nietzsche was a huge Emerson fan.
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