youtube : numberphile : Zeno's Paradox
http://www.youtube.com/watch?v=u7Z9UnWOJNY
[Hans-Georg Lundahl:]
You can actually solve both problems in diagrams, without "limits".
Horizontal=distance, vertical=time.
In Achilles and tortoise you get two lines differently slanted, in hand clap (if hands meet) you can actually use "negative distance" for distance covered the other direction, so slant will be same but crossing like a St Andrew's cross, and in arrow paradox the target will be a verticla line.
Then you analyse the paradox part of it: in tortoise example you need to draw lines horizontally and vertically between the two slants, and they will be smaller and smaller and divide it less and less, in arrow example you subdivide the arrow's slant into one half, into a quarter and so on.
But they will not be infinite equal parts added together making a rally infinite process, they will only be shamming an infinite subdivision of a movement.
Which is where St Thomas' Prima Via on impossibility of infinite regress differs from the Zeno paradox.
Bergson thought he had refuted Prima Via thereby, but he was wrong to reduce it to a Zeno paradox. He started out as a fan of infinitesimal calculus before he became concerned with philosophy.
You see, divisibility of a continuum and addibility of separate steps are two different things.
Commented on in Friday 7-VI-2013,
Feast of the Most Sacred Heart of Jesus,
from Library Georges Pompidou/HGL
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