{"id":37212,"date":"2024-06-26T02:50:00","date_gmt":"2024-06-26T06:50:00","guid":{"rendered":"https:\/\/alumni.cornell.edu\/cornellians\/?p=37212"},"modified":"2024-07-03T10:02:49","modified_gmt":"2024-07-03T14:02:49","slug":"math-juggling","status":"publish","type":"post","link":"https:\/\/alumni.cornell.edu\/cornellians\/math-juggling\/","title":{"rendered":"Doctoral Student Juggles Math and \u2026 Juggling!"},"content":{"rendered":"\n<p class=\"has-large-font-size\">Working to make his passion an Olympic sport, Jonah Botvinick-Greenhouse knows how to keep many balls in the air (literally)<\/p>\n\n\n\n<p><em>This story was condensed from <\/em><a href=\"https:\/\/news.cornell.edu\/stories\/2024\/06\/going-paris-gold-math-scholar-aids-jugglings-olympic-bid\" target=\"_blank\" rel=\"noopener noreferrer\"><em>a feature<\/em><\/a><em> in the<\/em> Cornell Chronicle.<\/p>\n\n\n\n<p>By <strong>James Dean<\/strong><\/p>\n\n\n\n<p class=\"has-drop-cap\">Outside Gates Hall as spring classes ended, Jonah Botvinick-Greenhouse juggled a flurry of white balls\u2014five, if you could keep track\u2014hands occasionally crisscrossing, at times juggling entirely behind his back or above his head.<\/p>\n\n\n\n<p>Suddenly launching several balls skyward, the doctoral student in applied math pirouetted twice before calmly receiving the plummeting projectiles and lofting them back to lower altitudes.<\/p>\n\n\n\n<p>\u201cWow,\u201d says a passing student, taking out a phone to record the scene. \u201cCool,\u201d remarks another. \u201cThat\u2019s dope,\u201d agrees a third, pausing mid-jog. Others wander by, too distracted to notice one of the world\u2019s best jugglers at work.<\/p>\n\n\n\n<figure class=\"wp-block-embed alignwide is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Video: Math scholar aids juggling\u2019s Olympic bid\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/zc1ub9FYRJk?start=2&#038;feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>In late June, Botvinick-Greenhouse\u2014a two-time winner of the <a href=\"https:\/\/www.thewjf.com\/\" target=\"_blank\" rel=\"noopener noreferrer\">World Juggling Federation<\/a>\u2019s Advanced Overall Championship\u2014competed in Paris for the WJF\u2019s first Ultimate Overall Championship. He finished a very close second, only about a 10th of a point behind the winner.<\/p>\n\n\n\n<p>The Paris Olympic Committee had invited the WJF to host the competition and an annual convention as part of pre-Summer Games festivities\u2014a platform the WJF is using to build a case for juggling as an Olympic sport.<\/p>\n\n\n\n<p>ESPN will broadcast the event\u2014which featured routines with balls, rings, and club\u2014on August 2.<\/p>\n\n\n\n<p>\u201cHis patterns, his control, his symmetry, and his accuracy I think are unparalleled,\u201d federation president Jason Garfield says of Botvinick-Greenhouse. <\/p>\n\n\n\n<p>\u201cJonah\u2019s juggling is very aesthetically pleasing. It\u2019s rare, and I would say comforting, but also inspiring\u2014and almost not believable, because it looks like it was programmed, like it\u2019s a simulation.\u201d<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>His patterns, his control, his symmetry, and his accuracy I think are unparalleled.<\/p>\n<cite><strong>Jason Garfield<\/strong>, president, World Juggling Federation<\/cite><\/blockquote>\n\n\n\n<p>Perhaps that\u2019s appropriate for someone whose research in the <a href=\"https:\/\/www.cam.cornell.edu\/cam\" target=\"_blank\" rel=\"noopener noreferrer\">Center for Applied Mathematics<\/a> focuses on dynamical systems, and who as an undergraduate co-authored an article called \u201c<a href=\"https:\/\/pubs.aip.org\/physicstoday\/article\/73\/2\/62\/914452\/Juggling-dynamicsWith-complex-throwing-patterns-of\" target=\"_blank\" rel=\"noopener noreferrer\">Juggling Dynamics<\/a>\u201d in <em>Physics Today<\/em>.<\/p>\n\n\n\n<p>Botvinick-Greenhouse, who earned math and physics degrees at Amherst, not only takes pleasure in the act of juggling, but in the math underlying its patterns and the numerical notation system used to describe them, called \u201csiteswap.\u201d<\/p>\n\n\n\n<p>\u201cIt turns out there are a lot of exciting connections between mathematics and juggling, so many people who happen to like math will take to juggling pretty easily,\u201d he says. \u201cIt\u2019s kind of the go-to language for how jugglers talk to each other and communicate about the tricks that they\u2019re doing.\u201d<\/p>\n\n\n\n<p><\/p>\n\n\n\n<div class=\"wp-block-media-text alignwide is-stacked-on-mobile\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"884\" height=\"720\" src=\"https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_019.jpeg\" alt=\"Jonah Botvinick-Greenhouse, math PhD student, writes out &quot;siteswap&quot; notation in Malott Hall.\" class=\"wp-image-37233 size-full\" srcset=\"https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_019.jpeg 884w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_019-300x244.jpeg 300w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_019-768x626.jpeg 768w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_019-632x515.jpeg 632w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_019-316x257.jpeg 316w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_019-400x326.jpeg 400w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_019-200x163.jpeg 200w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_019-100x81.jpeg 100w\" sizes=\"auto, (max-width: 884px) 100vw, 884px\" \/><figcaption>Writing out \u201csiteswap\u201d notation in Malott Hall.<\/figcaption><\/figure><div class=\"wp-block-media-text__content\">\n<p>&#8220;Siteswap&#8221; is a mathematical abstraction developed in the mid-1980s that counts the number of beats until an object is manipulated again\u2014a number roughly corresponding to its throw height\u2014and the order in which objects are swapped between hands.<\/p>\n\n\n\n<p>Jugglers can analyze siteswaps to determine if a pattern can be juggled. <\/p>\n\n\n\n<p><\/p>\n<\/div><\/div>\n\n\n\n<p>For example, since averaging a siteswap\u2019s digits reveals the number of objects being juggled, the average cannot be a fraction.<\/p>\n\n\n\n<p><a href=\"https:\/\/math.cornell.edu\/allen-knutson\" target=\"_blank\" rel=\"noopener noreferrer\">Allen Knutson<\/a>, a math professor who once held a world record\u201468 catches of 12 balls with a partner\u2014says jugglers can read siteswaps to confirm two essential conditions: that no two objects will land at the same time, and that an object will always be available to throw. Validate one condition and the other follows\u2014a mathematical statement, says Knutson.<\/p>\n\n\n\n<p>\u201cIf you boil something down sufficiently, then it will become mathematics,\u201d he says. \u201cThings sufficiently well understood can\u2019t help but become mathematics.\u201d<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>If you boil something down sufficiently, then it will become mathematics.<\/p>\n<cite>Professor <strong>Allen Knutson<\/strong><\/cite><\/blockquote>\n\n\n\n<p>Bennett Santora \u201926, an information science major and former <a href=\"https:\/\/www.juggle.org\/\" target=\"_blank\" rel=\"noopener noreferrer\">International Jugglers\u2019 Association<\/a> junior gold medalist, wrote a college admissions essay about siteswap.<\/p>\n\n\n\n<p>\u201cIt made this technical progression of juggling possible,\u201d says Santora, who can juggle seven balls consistently and has juggled as many as nine. \u201cWhen everything was just kind of vaudeville tricks, it wasn\u2019t obvious what the next hardest thing in the progression was. Now it\u2019s just a question of, can you do it?\u201d<\/p>\n\n\n\n<p>For Botvinick-Greenhouse, more than most, the answer is yes.<\/p>\n\n\n\n<p>Introduced to juggling by a friend when he was 10, he adopted YouTube as his mentor. <\/p>\n\n\n\n<figure class=\"wp-block-image alignwide size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_022-1024x576.jpg\" alt=\"Jonah Botvinick Greenhouse, math PhD student, juggles with the Cornell Juggling Club in the Physical Science Building..\" class=\"wp-image-37228\" srcset=\"https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_022-1024x576.jpg 1024w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_022-300x169.jpg 300w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_022-768x432.jpg 768w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_022-800x450.jpg 800w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_022-608x342.jpg 608w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_022-304x171.jpg 304w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_022-152x85.jpg 152w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_022-1184x666.jpg 1184w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_022-592x333.jpg 592w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_022-296x166.jpg 296w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_022-1264x711.jpg 1264w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_022-632x356.jpg 632w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_022-316x178.jpg 316w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_022-400x225.jpg 400w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_022-200x113.jpg 200w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_022-100x56.jpg 100w, https:\/\/alumni.cornell.edu\/cornellians\/wp-content\/uploads\/sites\/2\/2024\/06\/2024_1174_022.jpg 1280w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Practicing with the Cornell Juggling Club in the Physical Sciences Building.<\/figcaption><\/figure>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>Hours of daily practice ensued, and he won a WJF junior title at age 12, just two years before claiming his first advanced overall championship\u2014the youngest to do so. His progression is documented on <a href=\"https:\/\/www.youtube.com\/user\/Xjuggler23X\" target=\"_blank\" rel=\"noopener noreferrer\">YouTube<\/a> and <a href=\"https:\/\/www.instagram.com\/jbotvinick\/\" target=\"_blank\" rel=\"noopener noreferrer\">Instagram<\/a>.<\/p>\n\n\n\n<p>\u201cI\u2019m not surprised that I\u2019m the kind of person who enjoyed learning to juggle four or five balls when I was 10 and 11, and now I\u2019m doing math research,\u201d says Botvinick-Greenhouse, also an advanced cellist who plays in a campus quartet.<\/p>\n\n\n\n<p>\u201cIt seems like a similar thing going on in the brain that enjoys that type of progression. You\u2019re not going to find the solution to a research question right away, and it\u2019s going to take a lot of persistence and failing over and over again, but you enjoy the process of trying to work up to it.\u201d<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>I\u2019m not surprised that I\u2019m the kind of person who enjoyed learning to juggle four or five balls when I was 10 and 11, and now I\u2019m doing math research.<\/p>\n<\/blockquote>\n\n\n\n<p>As in figure skating or gymnastics, whose scoring systems the WJF\u2019s mimics, sport jugglers must balance ambitions to perform very difficult, high-scoring moves with the risk of errors that would earn deductions\u2014ranging from collisions and drops to asymmetrical patterns, moving one\u2019s feet too much, bad posture, or other poor form.<\/p>\n\n\n\n<p>\u201cThere\u2019s less crossover than you would hope between the theory and practice of it,\u201d he says. <\/p>\n\n\n\n<p>\u201cIt\u2019s fun to think about mathematically and physically, but at the end of the day, the only thing that can help me improve and do good routines is practice. Just look up, and juggle.\u201d<\/p>\n\n\n\n<p><em>Top: Botvinick-Greenhouse juggles outside Milstein Hall. (All photos and video by Jason Koski \/ Cornell University.)<\/em><\/p>\n\n\n\n<p class=\"has-small-font-size\">Published June 26, 2024; updated July 3, 2024<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n","protected":false},"excerpt":{"rendered":"<p>Working to make his passion an Olympic sport, Jonah Botvinick-Greenhouse knows how to keep many balls in the air (literally)<\/p>\n","protected":false},"author":68,"featured_media":37216,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"alumni_hub_syml_posts":[32080,31997,36953],"footnotes":""},"categories":[223],"tags":[],"cornell_year_post":[],"post_folder":[],"class_list":["post-37212","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-students"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Doctoral Student Juggles Math and \u2026 Juggling! 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