{"id":2377,"date":"2016-10-25T03:54:40","date_gmt":"2016-10-25T08:54:40","guid":{"rendered":"http:\/\/blogs.ams.org\/blogonmathblogs\/?p=2377"},"modified":"2016-10-26T10:42:51","modified_gmt":"2016-10-26T15:42:51","slug":"topology-in-the-limelight","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/blogonmathblogs\/2016\/10\/25\/topology-in-the-limelight\/","title":{"rendered":"Topology in the Limelight"},"content":{"rendered":"<p class=\"p1\"><span class=\"s1\">Topology is having a moment. Maybe not as much as this\u00a0<a href=\"https:\/\/twitter.com\/NateSilver538\/status\/790026426653282308\"><span class=\"s2\">never-ending<\/span><\/a> <a href=\"http:\/\/blogs.ams.org\/blogonmathblogs\/2016\/10\/13\/how-polling-works-or-doesnt-work\/\"><span class=\"s2\">election season<\/span><\/a> or <span class=\"s2\"><a href=\"https:\/\/twitter.com\/JaneEspenson\/status\/790579416594132992\">this Pringles &#8220;ringle&#8221;<\/a><\/span>\u00a0with 40,000 retweets and counting (seriously, you should go look\u2014it\u2019s a self-supporting ring of potato\u00a0chips, need I say more?), but it\u2019s been getting more recognition than usual for a field of theoretical math. Somewhat ironically, it\u2019s all because of the Nobel prize, and there\u2019s not even a Nobel for math. (And no, it\u2019s <a href=\"https:\/\/blogs.scientificamerican.com\/roots-of-unity\/how-to-talk-about-the-fields-medal-at-your-next-cocktail-party\/\"><span class=\"s2\">not because a mathematician had an affair with Nobel\u2019s wife<\/span><\/a>; he was a bachelor.) Earlier this month, the Nobel prize in physics went to <a href=\"https:\/\/www.nobelprize.org\/nobel_prizes\/physics\/laureates\/2016\/press.html\"><span class=\"s2\">three physicists for their work on topological phase transitions and topological phases of matter<\/span><\/a>.<\/span><\/p>\n<div id=\"attachment_2378\" style=\"width: 650px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.flickr.com\/photos\/wikidave\/4793247844\/in\/photolist-8iyDAd-5d1zf-8QfyW9-7MJEBJ-q5tC7x-7BCJZ9-8J94Nj-acgRQz-61tcLS-9Lmteh-6Hfoaq-4EhWdG-cSvLCq-7Qu74r-9LiERP-618PGc-8yGu9x-bpkoFZ-7nCPqS-4CCc4c-3474eX-9nCgxH-7sBhkX-qTSoN-8WZbq-5W8bcD-bFtGRt-8VJQZD-p9ystw-4nKQzq-6mBaqM-7Sv9k1-7QmLER-goLr1-4ydbnG-5j1f5X-uycao-8VJQWc-uycc7-uycha-hYCZM-4UkVAw-5TqyNQ-83zKkn-2TWqoy-FnbYe-uyce9-7frEaf-mg5aA9-mg5hLS\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-2378\" class=\"size-full wp-image-2378\" src=\"https:\/\/i0.wp.com\/blogs.ams.org\/blogonmathblogs\/files\/2016\/10\/4793247844_6ed87f4da7_z.jpg?resize=640%2C427\" alt=\"Delicious topology. Image: Dave Crosby, via Flickr. CC BY-SA 2.0\" width=\"640\" height=\"427\" srcset=\"https:\/\/i0.wp.com\/blogs.ams.org\/blogonmathblogs\/files\/2016\/10\/4793247844_6ed87f4da7_z.jpg?w=640&amp;ssl=1 640w, https:\/\/i0.wp.com\/blogs.ams.org\/blogonmathblogs\/files\/2016\/10\/4793247844_6ed87f4da7_z.jpg?resize=300%2C200&amp;ssl=1 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/a><p id=\"caption-attachment-2378\" class=\"wp-caption-text\">Delicious topology. Image: Dave Crosby, via Flickr. CC BY-SA 2.0<\/p><\/div>\n<p class=\"p1\"><span class=\"s1\">As science news editors across the globe sighed and shelved their pre-written explainers about <a href=\"http:\/\/phys.org\/news\/2016-10-gravitational-dark-eyed-nobel-physics.html\"><span class=\"s2\">LIGO and gravitational waves<\/span><\/a>, they got to work figuring out how to talk about the work that actually won the prize this year. The easiest part of the prize to explain ends up being the most off-putting word, topology, so the <a href=\"https:\/\/en.wikipedia.org\/wiki\/File:Mug_and_Torus_morph.gif\"><span class=\"s2\">bagels and coffee cups<\/span><\/a> were at the ready. <\/span><\/p>\n<span class=\"embed-youtube\" style=\"text-align:center; display: block;\"><iframe loading=\"lazy\" class=\"youtube-player\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/zO8esJuQIMs?version=3&#038;rel=1&#038;showsearch=0&#038;showinfo=1&#038;iv_load_policy=1&#038;fs=1&#038;hl=en-US&#038;autohide=2&#038;wmode=transparent\" allowfullscreen=\"true\" style=\"border:0;\" sandbox=\"allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox\"><\/iframe><\/span>\n<p class=\"p1\"><span class=\"s1\">Nobel Committee member Thor Hans Hansson had an adorable illustration of the basic idea of a topological property, in this case genus. But his explanation and some of the other ones I saw\u00a0sometimes gave people the impression that the physicists were studying literal, if miniature, bagel- and pretzel-shaped objects floating around in superconducting materials. That\u2019s not quite right. I tried to make it a bit\u00a0clearer in an <a href=\"https:\/\/www.scientificamerican.com\/article\/bagels-pretzels-and-the-nobel-prize-in-physics\/\"><span class=\"s2\">article I wrote for Scientific American<\/span><\/a>. I can also recommend <a href=\"https:\/\/theconversation.com\/the-nobel-prize-for-physics-goes-to-topology-and-mathematicians-applaud-66532\"><span class=\"s2\">Kevin Knudson\u2019s article about it for The Conversation<\/span><\/a> and <a href=\"http:\/\/www.smithsonianmag.com\/smart-news\/nobel-physics-prize-awarded-exploration-exotic-matter-explained-bagels-180960681\/\"><span class=\"s2\">Brian Handwerk\u2019s piece for Smithsonian<\/span><\/a>. <a href=\"http:\/\/thewire.in\/74307\/topological-metamaterials-metaphors\/\"><span class=\"s2\">Vasudevan Mukunth also has a nice article on The Wire<\/span><\/a> reminding us that the value of these physics discoveries is not necessarily in their utility or applications.<\/span><\/p>\n<p class=\"p1\"><span class=\"s1\">For me, one of the most fun things to come out of the Nobel\u2019s mathematical connection is a <a href=\"https:\/\/picturethismaths.wordpress.com\/2016\/10\/10\/defining-topology-through-interviews\/\"><span class=\"s2\">series of interviews<\/span><\/a> Rachael Boyd did on the blog <a href=\"https:\/\/picturethismaths.wordpress.com\/\"><span class=\"s2\">Picture This Maths<\/span><\/a>. (<a href=\"http:\/\/blogs.ams.org\/blogonmathblogs\/2016\/07\/06\/picture-this\/\"><span class=\"s2\">I wrote about Picture This Maths this past July<\/span><\/a>.) One of the interviewees, <a href=\"https:\/\/picturethismaths.wordpress.com\/2016\/10\/16\/defining-topology-through-interviews-interview-three-with-ruben-verresen\/\"><span class=\"s2\">Ruben Verresen<\/span><\/a>, complains about the usual description of topology so many of us give of topology, which tends to be of the donut-coffee mug variety. \u201cThe issue is that they seem very arbitrary: what\u2019s so special about holes?\u201d Even if a reader or listener understands what you\u2019re describing, he thinks it\u2019s not all that interesting. He writes, \u201cif I explain topology by comparing a donut to a coffee mug, I can just see my listener slowly turning off.\u201d Instead, he thinks we should emphasize the difference between properties that are local and those that aren\u2019t. Local properties even include things like height, anything that can be assessed by looking at the property in a small region and then combining those observations over the entire object. He says that emphasizing this distinction can make it more clear why someone should care about topology in the first place.<\/span><\/p>\n<p class=\"p1\"><span class=\"s1\">Boyd\u2019s interviews also made me aware that someone\u2019s been writing a comic strip about topology and nobody told me! The strip, by <a href=\"http:\/\/chalkdustmagazine.com\/category\/regulars\/comic\/\"><span class=\"s2\">Tom Hockenhull, is in Chalkdust Magazine<\/span><\/a>. <\/span><\/p>\n<p class=\"p1\"><span class=\"s1\">I\u2019ve seen topology around a few other places recently, so this post comes with a dessert course. Mathematician <a href=\"https:\/\/arxiv.org\/abs\/1608.00152\"><span class=\"s2\">Jean-Luc Thiffeault used ideas from topology<\/span><\/a> to analyze taffy-pullers, both modern and old-timey, and I was ON IT for <a href=\"http:\/\/www.smithsonianmag.com\/science-nature\/using-math-build-ultimate-taffy-machine-180960849\/\"><span class=\"s2\">Smithsonian<\/span><\/a>. Candy and math? Yes, please. Then there\u2019s this <a href=\"http:\/\/www.nature.com\/news\/inside-microsoft-s-quest-for-a-topological-quantum-computer-1.20774\"><span class=\"s2\">Nature News Q&amp;A with Microsoft researcher Alex Bocharov<\/span><\/a> about why Microsoft is investing to heavily in building a topological quantum computer. One of the most interesting things I learned when I was writing about the physics Nobel prize was that physicists are trying to figure out how to use topology to build a quantum computer. Once you\u2019ve heard it, it makes sense: topological properties are more robust to small perturbations than other properties, so in theory, information would be less prone to degradation from outside noise. <\/span><\/p>\n<p class=\"p1\"><span class=\"s1\">Finally, behold the <a href=\"http:\/\/www.pnas.org\/content\/113\/40\/11094.abstract.html?etoc\"><span class=\"s2\">ultradonut topology of the nuclear envelope<\/span><\/a>, a <a href=\"https:\/\/twitter.com\/neuraltheory\/status\/783420582641532928\"><span class=\"s2\">real paper title<\/span><\/a> from the Proceedings of the National Academy of Sciences. Mmm, ultradonut.<\/span><\/p>\n<div style=\"margin-top: 0px; margin-bottom: 0px;\" class=\"sharethis-inline-share-buttons\" ><\/div>","protected":false},"excerpt":{"rendered":"<p>Topology is having a moment. Maybe not as much as this\u00a0never-ending election season or this Pringles &#8220;ringle&#8221;\u00a0with 40,000 retweets and counting (seriously, you should go look\u2014it\u2019s a self-supporting ring of potato\u00a0chips, need I say more?), but it\u2019s been getting more &hellip; <a href=\"https:\/\/blogs.ams.org\/blogonmathblogs\/2016\/10\/25\/topology-in-the-limelight\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n<div style=\"margin-top: 0px; margin-bottom: 0px;\" class=\"sharethis-inline-share-buttons\" data-url=https:\/\/blogs.ams.org\/blogonmathblogs\/2016\/10\/25\/topology-in-the-limelight\/><\/div>\n","protected":false},"author":61,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[2,23],"tags":[631,214,60],"class_list":["post-2377","post","type-post","status-publish","format-standard","hentry","category-applied-math","category-theoretical-mathematics","tag-nobel-prize","tag-physics","tag-topology"],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p3tW3N-Cl","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/posts\/2377","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/users\/61"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/comments?post=2377"}],"version-history":[{"count":4,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/posts\/2377\/revisions"}],"predecessor-version":[{"id":2382,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/posts\/2377\/revisions\/2382"}],"wp:attachment":[{"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/media?parent=2377"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/categories?post=2377"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/tags?post=2377"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}