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Achilles and the Tortoise
Posted 05 June 2012 - 01:54 AM
Posted 22 December 2012 - 10:28 AM
Motion itself is a truthful resolution of an underlying paradox to our perspective. Motion is made up of time and distance. Truth may be communicated instantly between objects but to a particular perspective it must communicate the order and structure of the objects it is communicating and this communication has a revealed order which we call time. Distance is simply the degree of truthful separation. Distance or space has a time element to it as further objects must be communicated after near objects but time is much more than distance or space because it involves "other" events where A has to happen before B which has to happen before C in a linear vector sort of manner. This being said truth itself is discrete and Achilles smallest halfway point will reach it and cross it in a flash.
Posted 16 February 2013 - 03:16 AM
Zeno simply describes Achilles' approach to the tortoise in vanishingly small increments of distance.
It does not describe what happens after that. In fact, the tortoise does not even have to be present.
We could examine his separation from a fixed wall at geometrically decreasing intervals of time.
The fact that an infinite number of snapshots can be taken before the time of intercept does not prove
the wall will not be reached or the tortoise overtaken. It's a pseudo paradox.
Any supposed difficulty here belies lack of familiarity with the nature of real numbers.
- Bertrand Russell
Posted 22 March 2013 - 02:27 AM
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