{"id":7050,"date":"2013-04-26T18:21:49","date_gmt":"2013-04-27T01:21:49","guid":{"rendered":"http:\/\/dabacon.org\/pontiff\/?p=7050"},"modified":"2013-04-26T18:21:49","modified_gmt":"2013-04-27T01:21:49","slug":"non-chaotic-irregularity","status":"publish","type":"post","link":"https:\/\/dabacon.org\/pontiff\/2013\/04\/26\/non-chaotic-irregularity\/","title":{"rendered":"Non-chaotic irregularity"},"content":{"rendered":"<p>In principle, barring the intervention of chance, identical causes lead to identical effects.\u00a0 And except in chaotic systems, similar causes lead to similar effects.\u00a0 Borges&#8217; story &#8220;<a href=\"http:\/\/www.coldbacon.com\/writing\/borges-quixote.html\" target=\"_blank\" rel=\"noopener noreferrer\">Pierre Menard<\/a>&#8221; exemplifies an extreme version of this idea: an early 20&#8217;th century writer studies Cervantes&#8217; life and times so thoroughly that he is able to recreate several chapters of &#8220;Don Quixote&#8221; without mistakes and without consulting the original.<br \/>\nMeanwhile, back at the ShopRite parking lot in Croton on Hudson, NY,\u00a0 they&#8217;d installed half a dozen identical red and white parking signs, presumably all from the same print run, and all posted in similar environments, except for two in a sunnier location.<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/i0.wp.com\/dabacon.org\/pontiff\/wp-content\/uploads\/2013\/04\/Similar-Parking-Sign-Cracks.jpg?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" class=\"size-large wp-image-7061 aligncenter\" title=\"Similar Parking Sign Cracks\" alt=\"\" src=\"https:\/\/i0.wp.com\/dabacon.org\/pontiff\/wp-content\/uploads\/2013\/04\/Similar-Parking-Sign-Cracks-1024x861.jpg?resize=525%2C441&#038;ssl=1\" width=\"525\" height=\"441\" \/><\/a><\/p>\n<p><span><span>The irregular patterns of cracks that formed as the signs weathered were so similar that at first I thought the cracks had also been printed, but then I noticed small differences. The sharp corners on letters like S and E,\u00a0 apparently points of high stress, usually triggered near-identical cracks in each sign, but not always, and in the sunnier signs many additional fine cracks formed.\u00a0 <\/span><\/span><br \/>\n<span><span>Another example of reproducibly irregular dynamics was provided over 30 years ago by Ahlers and Walden&#8217;s <a href=\"http:\/\/journals.aps.org\/prl\/abstract\/10.1103\/PhysRevLett.44.445\">experiments <\/a>on convective turbulence, where a container of normal liquid helium, heated from below, exhibited nearly the same sequence of temperature fluctuations in several runs of the experiment. <\/span><\/span><br \/>\n<img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" alt=\"\" src=\"https:\/\/i0.wp.com\/dabacon.org\/pontiff\/wp-content\/uploads\/2013\/08\/959.png?resize=525%2C387&#038;ssl=1\" width=\"525\" height=\"387\" \/><br \/>\n<span><span>\u00a0<\/span><\/span><br \/>\n&nbsp;<br \/>\n&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In principle, barring the intervention of chance, identical causes lead to identical effects.\u00a0 And except in chaotic systems, similar causes lead to similar effects.\u00a0 Borges&#8217; story &#8220;Pierre Menard&#8221; exemplifies an extreme version of this idea: an early 20&#8217;th century writer studies Cervantes&#8217; life and times so thoroughly that he is able to recreate several chapters &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/dabacon.org\/pontiff\/2013\/04\/26\/non-chaotic-irregularity\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Non-chaotic irregularity&#8221;<\/span><\/a><\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":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}},"categories":[41,53],"tags":[],"class_list":["post-7050","post","type-post","status-publish","format-standard","hentry","category-mathematics","category-physics"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/dabacon.org\/pontiff\/wp-json\/wp\/v2\/posts\/7050","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dabacon.org\/pontiff\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/dabacon.org\/pontiff\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/dabacon.org\/pontiff\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/dabacon.org\/pontiff\/wp-json\/wp\/v2\/comments?post=7050"}],"version-history":[{"count":0,"href":"https:\/\/dabacon.org\/pontiff\/wp-json\/wp\/v2\/posts\/7050\/revisions"}],"wp:attachment":[{"href":"https:\/\/dabacon.org\/pontiff\/wp-json\/wp\/v2\/media?parent=7050"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dabacon.org\/pontiff\/wp-json\/wp\/v2\/categories?post=7050"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dabacon.org\/pontiff\/wp-json\/wp\/v2\/tags?post=7050"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}