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Am I wrong in my understanding of his solution?Gene Callahanhttp://www.blogger.com/profile/10065877215969589482noreply@blogger.comtag:blogger.com,1999:blog-7225373.post-79234714893345969322008-01-28T19:24:00.000-05:002008-01-28T19:24:00.000-05:00Thank goodness Aristotle solved this problem.Thank goodness Aristotle solved this problem.Roderick T. Longhttp://praxeology.net/longnoreply@blogger.comtag:blogger.com,1999:blog-7225373.post-1197652303847736722008-01-27T16:16:00.000-05:002008-01-27T16:16:00.000-05:00Point taken, Gene. Cantor's classification of dif...Point taken, Gene. Cantor's classification of different types of infinity may be of some help, though I am still trying to tease out how.John Goeshttp://www.blogger.com/profile/00206464455510064541noreply@blogger.comtag:blogger.com,1999:blog-7225373.post-6426846122252315852008-01-25T18:08:00.000-05:002008-01-25T18:08:00.000-05:00I don't think infinitesimals, even if properly for...I don't think infinitesimals, even if properly formalized, really handle the problem. It is one thing to devise a coherent, formal handling of some mathematical entity, but another to say it applies to real space/time. In terms of real space/time, either an infinitesimal occupies some amount of space, or it doesn't. If it does, it can be sub-divided per Zeno. If it doesn't, then no number of those fellows can add up to any finite amount of space.Gene Callahanhttp://www.blogger.com/profile/10065877215969589482noreply@blogger.comtag:blogger.com,1999:blog-7225373.post-90788832767896369942008-01-24T20:37:00.000-05:002008-01-24T20:37:00.000-05:00I think if they make contact before the snap the w...I think if they make contact before the snap the whistle is always blown, but I'm not sure.Gene Callahanhttp://www.blogger.com/profile/10065877215969589482noreply@blogger.comtag:blogger.com,1999:blog-7225373.post-81196685279029953112008-01-24T15:40:00.000-05:002008-01-24T15:40:00.000-05:00Isn't it up to the referees as to when they blow a...Isn't it up to the referees as to when they blow a play over? I believe if a defensive player steps offside, the refs have the option of allowing the play to continue. This would then turn into an advantage for the offense, since if the play has a desirable outcome for the offense the penalty can be declined. If the play is unfavorable to the offense, the penalty can be accepted and the down replayed. <BR/><BR/>My guess is that the writers of NFL rules anticipated the possibility of a Zeno strategy, without ever having heard of Zeno of Elea.Robert Wallachhttp://www.blogger.com/profile/14504118813220894825noreply@blogger.comtag:blogger.com,1999:blog-7225373.post-20363771769521731592008-01-24T15:29:00.000-05:002008-01-24T15:29:00.000-05:00Quana are rigid nondeformable coextensive immensit...Quana are rigid nondeformable coextensive immensities, each occupying the entire universe. Their reciprocals are quanta.<BR/><BR/>There is a "nonstandard" version of the calculus in which infinitesimals and their infinitely large reciprocals are as real as integers. It's better than the version they taught you.Wabulonhttp://www.blogger.com/profile/16838347174718251102noreply@blogger.comtag:blogger.com,1999:blog-7225373.post-8194113325564316942008-01-23T16:44:00.000-05:002008-01-23T16:44:00.000-05:00That's 'quanta', not 'quana'.That's 'quanta', not 'quana'.John Goeshttp://www.blogger.com/profile/00206464455510064541noreply@blogger.comtag:blogger.com,1999:blog-7225373.post-13716459033778437672008-01-23T16:13:00.000-05:002008-01-23T16:13:00.000-05:00This is why the infinitesimal approach to calculus...This is why the infinitesimal approach to calculus is more beautiful than the somewhat deceptive limit approach. The notion of an infinitely small quantity is needed to make some sense of Zeno's paradox, something like the notion of quana, except infinitely more plastic.<BR/><BR/>In regard to the football rules, I've thought about that. I think the refs do have the power to charge unsportsmanlike conduct for something like that, and/or the league may levy fines on a discretionary basis. There is probably some general rule by which the ref may be allowed to make executive decisions in times where people are trying to exploit loopholes at the expense of the spirit of the game.John Goeshttp://www.blogger.com/profile/00206464455510064541noreply@blogger.com