{"id":234,"date":"2007-05-02T05:32:25","date_gmt":"2007-05-02T13:32:25","guid":{"rendered":"https:\/\/scottaaronson.blog\/?p=234"},"modified":"2007-05-02T05:32:25","modified_gmt":"2007-05-02T13:32:25","slug":"refilling-your-rss-glass-before-the-entree-arrives","status":"publish","type":"post","link":"https:\/\/scottaaronson.blog\/?p=234","title":{"rendered":"Refilling your RSS glass before the entr\u00e9e arrives"},"content":{"rendered":"<p>A reader points me to <a href=\"http:\/\/www.math.toronto.edu\/alex\/bettitopology.ps\">this<\/a> recent <em>Topology<\/em> paper by Nabutovsky and Weinberger, which probably contains the biggest numbers to have ever arisen naturally in mathematics.  Specifically, the authors show that, if we maximize the k<sup>th<\/sup> Betti number (for k\u22653) over all groups whose presentation has size N (while keeping the number finite), then it grows like the <a href=\"http:\/\/www.scottaaronson.com\/writings\/bignumbers.html\">&#8220;super-duper Busy Beaver function&#8221;<\/a> (that is, Busy Beaver with an oracle for the halting problem with an oracle for the halting problem).<\/p>\n<p>The <em>spiked<\/em> magazine survey I blogged about <a href=\"https:\/\/scottaaronson.blog\/?p=212\">earlier<\/a> has <a href=\"http:\/\/www.spiked-online.com\/index.php?\/innovationsurvey\/listing\/C87\/\">finally been published<\/a>.  (<strong><font color=\"red\">Warning:<\/font><\/strong> Spouters ahead.)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A reader points me to this recent Topology paper by Nabutovsky and Weinberger, which probably contains the biggest numbers to have ever arisen naturally in mathematics. Specifically, the authors show that, if we maximize the kth Betti number (for k\u22653) over all groups whose presentation has size N (while keeping the number finite), then it [&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":[11,3],"tags":[],"class_list":["post-234","post","type-post","status-publish","format-standard","hentry","category-nerd-interest","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\/234","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=234"}],"version-history":[{"count":0,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/234\/revisions"}],"wp:attachment":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=234"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=234"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=234"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}