According to both ancient and present day physics, objects in motion have determined relative positions. Indeed, the physics of motion from Zeno to Newton and through to today take this assumption as given. Lynds says that the paradoxes arose because people assumed wrongly that objects in motion had determined positions at any instant in time, thus freezing the bodies motion static at that instant and enabling the impossible situation of the paradoxes to be derived. "Theres no such thing as an instant in time or present moment in nature. Its something entirely subjective that we project onto the world around us. That is, its the outcome of brain function and consciousness."
http://www.eurekalert.org/pub_releases/2003-07/icc-gwi072703.php
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