{"id":976,"date":"2003-03-04T03:04:24","date_gmt":"2003-03-04T19:04:24","guid":{"rendered":"http:\/\/michaelhans.com\/eclecticism\/2003\/03\/04\/zenos-paradox\/"},"modified":"2019-12-06T08:56:26","modified_gmt":"2019-12-06T16:56:26","slug":"zenos-paradox","status":"publish","type":"post","link":"https:\/\/michaelhans.com\/eclecticism\/2003\/03\/04\/zenos-paradox\/","title":{"rendered":"Zeno&#039;s Paradox"},"content":{"rendered":"<p>Ever since I read Douglas Hofstadter&#8217;s <a href=\"http:\/\/www.amazon.com\/exec\/obidos\/ASIN\/0465026567\/djwudicom-20\" title=\"Godel, Escher, Bach: An Eternal Golden Braid\">G\u00f6del, Escher, Bach: An Eternal Golden Braid<\/a>, I&#8217;ve had the paradox postulated by Zeno of Elea (c.\u00a0450 B.C.) bouncing around in my head. To summarize the paradox:<\/p>\n<blockquote><p>\n  Zeno&#8217;s Paradox may be rephrased as follows. Suppose I wish to cross the room. First, of course, I must cover half the distance. Then, I must cover half the remaining distance. Then, I must cover half the remaining distance. Then I must cover half the remaining distance&#8230;and so on forever. The consequence is that I can never get to the other side of the room.<\/p>\n<p>  What this actually does is to make all motion impossible, for before I can cover half the distance I must cover half of half the distance, and before I can do that I must cover half of half of half of the distance, and so on, so that in reality I can never move any distance at all, because doing so involves moving an infinite number of small intermediate distances first.\n<\/p><\/blockquote>\n<p>I knew there must be a solution, as we all do manage to move around quite handily, I just never knew what it was. Luckily enough, I managed to stumble across an explanation of the paradox <a href=\"http:\/\/www.mathacademy.com\/pr\/prime\/articles\/zeno_tort\/\" title=\"Zeno's Paradox of the Tortoise and Achilles\">and its solution<\/a> today. Nifty!<\/p>\n<p>(Via <a href=\"http:\/\/www.kottke.org\/03\/03\/030304natures_klei.html\" title=\"Kottke.org: Nature's Klein Bottle\">Jason Kottke<\/a>)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Zeno&#8217;s Paradox may be rephrased as follows. Suppose I wish to cross the room. First, of course, I must cover half the distance. Then, I must cover half the remaining distance. Then, I must cover half the remaining distance. Then I must cover half the remaining distance&#8230;and so on forever. The consequence is that I can never get to the other side of the room.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[2036],"tags":[2200,39],"_links":{"self":[{"href":"https:\/\/michaelhans.com\/eclecticism\/wp-json\/wp\/v2\/posts\/976"}],"collection":[{"href":"https:\/\/michaelhans.com\/eclecticism\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/michaelhans.com\/eclecticism\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/michaelhans.com\/eclecticism\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/michaelhans.com\/eclecticism\/wp-json\/wp\/v2\/comments?post=976"}],"version-history":[{"count":0,"href":"https:\/\/michaelhans.com\/eclecticism\/wp-json\/wp\/v2\/posts\/976\/revisions"}],"wp:attachment":[{"href":"https:\/\/michaelhans.com\/eclecticism\/wp-json\/wp\/v2\/media?parent=976"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/michaelhans.com\/eclecticism\/wp-json\/wp\/v2\/categories?post=976"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/michaelhans.com\/eclecticism\/wp-json\/wp\/v2\/tags?post=976"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}