Thanks for that link, I hadn't heard of Lynd before but I agree that it's possible to "redefine" time which in turn could provide new insights. Case in point, the imaginary time you referenced.<br /><br />I think the Achilles paradox is a math paradox not a time paradox. <br /><br />For example, instead of Achilles vs the Tortoise in a race we can think of the paradox in terms of a basketball game where each basket counts 1 point.<br /><br />Assume Achilles gives the tortoise a 10 point lead but that Achilles can score 10 points for every point the tortoise scores. After Achilles scores 10 points the score will be Tortoise 11, Achilles 10. (Notice that time does not play a role.) Next Achilles scores 1 point, then a second. Achilles has 12 points but the tortoise is still at 10 because you can't score 1/10th of a point. The tortoise remains stuck on 10 until Achille's score reaches 20. <br /><br />I am not saying that this resolves the paradox. But, I think it points out that the crux of the Achilles paradox is not time, rather it is the assumption of continuity.<br /><br />We could restore the paradox to the basketball game if we allow the score to increase continuously from 11 to 12. In this case after Achilles scores his 11th point the tortoise will have 11.1 pts. After Achilles scores .1 pts the score will be 11.11 to 11.1 and so on. Again, notice that it does not matter how much time it takes Achilles to score, only that we impose the restriction that the scoring is continous and we force the tortoise's score to increase in fixed proportion to Achilles. <br /><br />So in my view, time is an innocent bystander in the Achilles paradox. Time is just the human construct that allows us to measure the progress of Achilles in his impossible task of overcoming the tortoise given the assumptions of contintuity and fixed proportional progress.