{"id":100,"date":"2006-07-11T16:19:00","date_gmt":"2006-07-11T16:19:00","guid":{"rendered":"https:\/\/scottaaronson.blog\/?p=100"},"modified":"2021-10-12T21:02:48","modified_gmt":"2021-10-13T02:02:48","slug":"something-to-munch-on-while-i-take-a-long-succulent-post-out-of-the-procrastination-oven","status":"publish","type":"post","link":"https:\/\/scottaaronson.blog\/?p=100","title":{"rendered":"Something to munch on while I take a long, succulent post out of the procrastination oven"},"content":{"rendered":"<p>I&#8217;m convinced that the following diagram means something precise:<\/p>\n<p><a href=\"http:\/\/www.scottaaronson.com\/blog2\/uploaded_images\/prog-772148.jpg\"><img decoding=\"async\" border=\"0\" src=\"http:\/\/www.scottaaronson.com\/blog2\/uploaded_images\/prog-763977.jpg\"><\/a>My question is, what does it mean?<\/p>\n<p>Intuitively, it means that if your software package can solve SDP&#8217;s, then you can easily use it to solve LP&#8217;s; if it can solve LP&#8217;s, you can easily use it to invert matrices, and so on, but not vice versa.  But it can&#8217;t mean (for example) that SDP&#8217;s are harder than LP&#8217;s in the usual complexity theory sense, since both problems are P-complete!<\/p>\n<p>Maybe it means that, if your axiom system is strong enough to prove SDP is in P, then it&#8217;s also strong enough to prove LP is in P, and so on &#8212; but not necessarily vice versa.  But how would we show such a separation?<\/p>\n<p>(Sorry, no money this time.  We&#8217;ll see if it makes any difference &#8212; I&#8217;m guessing that it doesn&#8217;t.)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I&#8217;m convinced that the following diagram means something precise: My question is, what does it mean? Intuitively, it means that if your software package can solve SDP&#8217;s, then you can easily use it to solve LP&#8217;s; if it can solve LP&#8217;s, you can easily use it to invert matrices, and so on, but not vice [&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_seo_schema_type":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_hide_featured_image":false,"_jetpack_featured_image_duplicate_dismissed":0,"_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":[5],"tags":[],"class_list":["post-100","post","type-post","status-publish","format-standard","hentry","category-complexity"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/100","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=100"}],"version-history":[{"count":1,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/100\/revisions"}],"predecessor-version":[{"id":6004,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/100\/revisions\/6004"}],"wp:attachment":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=100"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=100"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=100"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}