{"id":285,"date":"2007-11-01T14:59:17","date_gmt":"2007-11-01T18:59:17","guid":{"rendered":"https:\/\/scottaaronson.blog\/?p=285"},"modified":"2007-11-01T14:59:17","modified_gmt":"2007-11-01T18:59:17","slug":"unparadox-contest","status":"publish","type":"post","link":"https:\/\/scottaaronson.blog\/?p=285","title":{"rendered":"Unparadox Contest"},"content":{"rendered":"<p>In a recent talk at MIT, Umesh Vazirani appealed to the famous <a href=\"http:\/\/en.wikipedia.org\/wiki\/Birthday_paradox\">Birthday Paradox<\/a> to say that two random subsets of {1,&#8230;,N}, each of size o(\u221aN), probably wouldn&#8217;t intersect each other.  Of course we all understood what he meant, but it occurred to me that Umesh was actually appealing to the Birthday <em>Unparadox<\/em>: &#8220;If you put three people in a room, chances are no two of them will have the same birthday.&#8221;<\/p>\n<p>Once I realized that, I started seeing unparadoxes everywhere I looked:<\/p>\n<p><strong>The Banach-Tarski Unparadox:<\/strong> If you cut an orange into five pieces using a standard knife, then put them back together, the result will have exactly the same volume as the original orange.<\/p>\n<p><strong>Braess&#8217; Unparadox:<\/strong> If you add an extra lane to a highway, one possible result will be to decrease congestion.<\/p>\n<p><strong>Hempel&#8217;s Unparadox:<\/strong> If you observe a bunch of ravens and find that all of them are black, this might increase your likelihood for the statement &#8220;All ravens are black.&#8221;<\/p>\n<p><strong>Russell&#8217;s Unparadox:<\/strong> The set of all sets that contain themselves as a member, might or might not contain itself as a member (either way is fine).<\/p>\n<p>In the spirit of my highly-successful <a href=\"https:\/\/scottaaronson.blog\/?p=40\">Best Umeshism<\/a> and <a href=\"https:\/\/scottaaronson.blog\/?p=101\">Best Anthropicism<\/a> contests (remember those?), I now open the floor to you: come up with the best unparadox!  The winner will receive absolutely nothing.  (If you have to ask what the point is, this contest isn&#8217;t for you.)<\/p>\n<p><input id=\"gwProxy\" type=\"hidden\" \/><!--Session data--><input onclick=\"jsCall();\" id=\"jsProxy\" type=\"hidden\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In a recent talk at MIT, Umesh Vazirani appealed to the famous Birthday Paradox to say that two random subsets of {1,&#8230;,N}, each of size o(\u221aN), probably wouldn&#8217;t intersect each other. Of course we all understood what he meant, but it occurred to me that Umesh was actually appealing to the Birthday Unparadox: &#8220;If you [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"_wpas_customize_per_network":false},"categories":[14,30],"tags":[],"class_list":["post-285","post","type-post","status-publish","format-standard","hentry","category-contests","category-mirrored-on-csail-blog"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/285","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=285"}],"version-history":[{"count":0,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/285\/revisions"}],"wp:attachment":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=285"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=285"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=285"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}