[UA] The End of the World, and so on.

[Nick Wedig]

>> One thing that's always bothered me is that Xeno's paradox (the one most commonly presented, anyway, involving an infinity of halfway points) is based on a mathematical mistake (not dividing both sides of an equation by the same amount) and Aristotle pointed this out millenia ago, but people still keep bringing it up.
>
>Huh... this must be a different version from the one I've heard. Isn't
>Xeno's paradox the same as an asymptotic increasing value? You know, it
>keeps moving forward but never passes value X because the rate of change
>is decreasing exponentially, or however that math works out?
>
>Or did Xeno leave out the change in the rate of change altogether, and
>that's why his paradox isn't a paradox?

The most commonly presented of Zeno's paradoxes involves attempting to cross from point A to point B.  To do so, you must cross point C, the halfway point.  But to make it to point C you must cross point D, halfway between A and C.  To get to point D requires passing point E, etc, etc ad infinitum.  Zeno claims that moving any distance requires crossing an infinite number of points, which would take an infinite amount of time.

But Aristotle pointed out that moving an infinitely small distance takes an infinitely small amount of time.  That is, motion is a ratio between distance and time and what Zeno did was divide one side (distance) by infinity while not dividing the other by the same, a mathematical fallacy.  The two infinities cancel out, leaving the ratio the same.  

ObUA: a- logical paradoxes make for the grounding of magickal schools.  b-the quarrels of philosophers seem like a good place for UA occulty bits.  Especially something along the lines of some artifact constructed by two adepts, who then disagreed on the fine points of magickal/philosophical/metaphysical theory, and fell into fighting over said artifact, and on until PCs become involved. 

Mr. teapot
the weeping philosopher

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