{"id":103,"date":"2006-07-23T14:03:00","date_gmt":"2006-07-23T14:03:00","guid":{"rendered":"https:\/\/scottaaronson.blog\/?p=103"},"modified":"2006-07-23T14:03:00","modified_gmt":"2006-07-23T14:03:00","slug":"and-they-say-complexity-has-no-philosophical-implications","status":"publish","type":"post","link":"https:\/\/scottaaronson.blog\/?p=103","title":{"rendered":"And they say complexity has no philosophical implications"},"content":{"rendered":"<p>From <a href=\"http:\/\/www.math.ohio-state.edu\/%7Efriedman\/pdf\/Princeton532.pdf\">these lecture notes<\/a> by Harvey Friedman comes one of the best metamathematical anecdotes I&#8217;ve ever heard (and yes, I&#8217;ve heard my share).  Apparently Friedman was attending a talk by the &#8220;ultra-finitist&#8221; Alexander Yessenin-Volpin, who challenged the &#8220;Platonic existence&#8221; not only of infinity, but even of large integers like 2<sup>100<\/sup>.  So Friedman raised the obvious &#8220;draw the line&#8221; objection: in the sequence 2<sup>1<\/sup>,2<sup>2<\/sup>,&#8230;,2<sup>100<\/sup>, which is the first integer that Yessenin-Volpin would say doesn&#8217;t exist?<\/p>\n<p>Yessenin-Volpin asked Friedman to be more specific.<\/p>\n<p>&#8220;Okay, then.  Does 2<sup>1<\/sup> exist?&#8221;<\/p>\n<p>Yessenin-Volpin quickly answered &#8220;yes.&#8221;<\/p>\n<p>&#8220;What about 2<sup>2<\/sup>?&#8221;<\/p>\n<p>After a noticeable delay: &#8220;yes.&#8221;<\/p>\n<p>&#8220;2<sup>3<\/sup>?&#8221;<\/p>\n<p>After a longer delay: &#8220;yes.&#8221;<\/p>\n<p>It soon became clear that Yessenin-Volpin would answer &#8220;yes&#8221; to every question, but would take twice as long for each one as for the one before it.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>From these lecture notes by Harvey Friedman comes one of the best metamathematical anecdotes I&#8217;ve ever heard (and yes, I&#8217;ve heard my share). Apparently Friedman was attending a talk by the &#8220;ultra-finitist&#8221; Alexander Yessenin-Volpin, who challenged the &#8220;Platonic existence&#8221; not only of infinity, but even of large integers like 2100. So Friedman raised the obvious [&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_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"{title}\n\n{excerpt}\n\n{url}","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,"jetpack_post_was_ever_published":false},"categories":[3],"tags":[],"class_list":["post-103","post","type-post","status-publish","format-standard","hentry","category-procrastination"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/103","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=103"}],"version-history":[{"count":0,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/103\/revisions"}],"wp:attachment":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=103"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=103"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=103"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}