ladkin@kestrel.ARPA (Peter Ladkin) (07/30/87)
In article <5845@princeton.Princeton.EDU>, ahw@notecnirp.Princeton.EDU (Arthur Watson) writes: > [..] (though it solves Zeno's: > the Zeno time sequence converges to the time when the hare overtakes > the tortoise -- the rest of the race precedes from there; what could > be more unparadoxical?) Just in case anyone believes that Zeno's questions have been `solved', I should mention that you need to make explicit assumptions to say that the above piece of reasoning is a solution to the best known of Zeno's paradoxes. Among these assumptions are that time intervals are infinitely divisible, and that they may have durations measurable with arbitrarily small real or rational numbers. Because of the relative success of Newtonian physics for a couple of centuries, people tend to believe that these assumptions are `confirmed', and the paradox `solved'. If we consider that the notion of time quanta is not inherently contradictory, we can resurrect some of the more entertaining of Zeno's questions, such as the stadium paradox. There's a good book on the subject, edited by Wesley Salmon. peter ladkin ladkin@kestrel.arpa