{"id":66,"date":"2005-08-16T20:00:33","date_gmt":"2005-08-16T10:00:33","guid":{"rendered":"http:\/\/www.somethinkodd.com\/oddthinking\/?p=66"},"modified":"2007-10-07T21:36:03","modified_gmt":"2007-10-07T11:36:03","slug":"colouring-history","status":"publish","type":"post","link":"https:\/\/www.somethinkodd.com\/oddthinking\/2005\/08\/16\/colouring-history\/","title":{"rendered":"Colouring History"},"content":{"rendered":"<p><!-- UnMarkedDown_2_01132526334--><\/p>\n<p>Every now and again, when I think I am working on something terribly esoteric and pointless, I am heartened by considering the lifetime work of <a href=\"http:\/\/www-groups.dcs.st-and.ac.uk\/~history\/Mathematicians\/Jordan.html\">Camille Jordan<\/a>. (Actually his name was Marie, but he called himself by one of his middle names &#8211; Camille. Perhaps the fact that his wife&#8217;s name was Marie-Isabelle had something to do with that.)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/oddthinking.somethinkodd.com\/images\/CamilleJordan.jpg\" alt=\"Portrait of Camille Jordan\" width=\"259\" height=\"326\" align=\"center\"\/><\/p>\n<p>To understand the genius of this well-regarded French mathematician, we need to do a little experiment together.<\/p>\n<p>Posit a simple closed curve, <i>C<\/i>,  in the plane <b>R<\/b><sup>2<\/sup>&#8230; oh err&#8230; sorry. Please permit me to start again.<\/p>\n<p>Take out a pencil and a sheet of paper. Start drawing a swirly line, around the page and, without lifting the pencil and without letting the line cross, make sure you finish up at the same point you started, to form a curvy loop.  With me so far? What you just drew is called a <em>Jordan Curve<\/em> after our hero Monsieur Jordan.<\/p>\n<p>The next step is to take out a felt-tipped pen and colour in the inside of the loop. Still with me?<\/p>\n<p>If you are, you clearly do not have the genius of Jordan, because he was the first person to say &#8220;Whoa!  Wait a moment!  You can&#8217;t just <em>assume<\/em> that such a loop has an inside and an outside!  That&#8217;s something you need to <em>prove<\/em> first!&#8221; (Of course, he probably said it in French, which probably made it sound more geniusy.)<\/p>\n<p>Legend has it, he then spent much of the rest of his life trying to prove that you could colour the inside of a Jordan Curve. He thought he had succeeded at one stage, but his proof turned out to be incorrect. It wasn&#8217;t until after Jordan&#8217;s death that <a href=\"http:\/\/en.wikipedia.org\/wiki\/Oswald_Veblen\" title=\"Wikipedia definition of Oswald_Veblen\" class=\"wikipedia\">Oswald Veblen<\/a> managed to finally prove the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Jordan_curve_theorem\" title=\"Wikipedia definition of Jordan_curve_theorem\" class=\"wikipedia\">Jordan curve theorem<\/a>, and colourers-in around the world could finally nod in relief, and break out the <a href=\"http:\/\/www.pencils.co.uk\/products\/\">Derwents<\/a>.<\/p>\n<p>So, if what you are working on seems rather pointless, remember Jordan. Remember his esoteric, pointless and ultimately futile goal in life made him famous enough to have a curve, an <a href=\"http:\/\/hamilton.dm.unipi.it\/cgi-bin\/astdys\/astibo?objects:Camillejordan;main\">asteroid<\/a> and an <a href=\"http:\/\/math.univ-lyon1.fr\/\">institute<\/a> named after him.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>To understand the genius of Camille Jordan, we need to do a little experiment together.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_s2mail":"","footnotes":""},"categories":[23,31,35,41],"tags":[70],"class_list":["post-66","post","type-post","status-publish","format-standard","hentry","category-based-on-a-true-story","category-geek","category-heroic-failures","category-story-telling","tag-mathematics"],"_links":{"self":[{"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/posts\/66","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/comments?post=66"}],"version-history":[{"count":0,"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/posts\/66\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/media?parent=66"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/categories?post=66"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.somethinkodd.com\/oddthinking\/wp-json\/wp\/v2\/tags?post=66"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}