{"id":845,"date":"2008-12-27T23:46:25","date_gmt":"2008-12-28T06:46:25","guid":{"rendered":"https:\/\/staging.opexlearning.com\/resources\/?p=845"},"modified":"2019-11-22T00:49:46","modified_gmt":"2019-11-22T05:49:46","slug":"twitter-as-combinatorics","status":"publish","type":"post","link":"https:\/\/staging.opexlearning.com\/resources\/twitter-as-combinatorics\/845\/","title":{"rendered":"Factorial Equations of a Tweet"},"content":{"rendered":"<div class=\"a296a24fa2fc69ef5487857f02f111e8\" data-index=\"9\" style=\"float: none; margin:10px 0 10px 0; text-align:center;\">\n<script async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script>\r\n<!-- Single Post readerboard -->\r\n<ins class=\"adsbygoogle\"\r\n     style=\"display:inline-block;width:728px;height:90px\"\r\n     data-ad-client=\"ca-pub-8207522353004717\"\r\n     data-ad-slot=\"1144967431\"><\/ins>\r\n<script>\r\n(adsbygoogle = window.adsbygoogle || []).push({});\r\n<\/script>\n<\/div>\n<p>Ever since I discovered Twitter, I&#8217;ve been amazed at <a href=\"http:\/\/twitter.com\/ev\" class=\"broken_link\">@ev<\/a>, @biz, and @jack&#8217;s idea of simplicity and usefulness.\u00a0 Lately, @windley (Phil Windley&#8217;s <a href=\"http:\/\/www.windley.com\/archives\/2008\/12\/asymmetric_follow_a_core_web_20_pattern.shtml\">article<\/a>), @monkchips, and JP have approached Twitter from a more theoretical perspective.\u00a0 This article is my contribution to that healthy conversation (this blog post will be followed by a short tweet, of course).<\/p>\n<h2 style=\"text-align: left;\">Twitter as Asymmetric Follow<\/h2>\n<p>James Governor attempts to define a pattern found in Twitter and other social media and calls it &#8220;Asymmetric Follow&#8221;.\u00a0 He defines <a href=\"http:\/\/www.redmonk.com\/jgovernor\/2008\/12\/05\/assymetrical-follow-a-core-web-20-pattern\/\" class=\"broken_link\">Asymmetric Follow<\/a> as the following:<\/p>\n<blockquote><p>Asymmetric Follow is a core pattern for Web 2.0, in which a social network user can have many people following them without a need for reciprocity.\u00a0 Asymmetric Follow is unlike email for example, which tends to be within small groups, with all users knowing each other (newsletters are a clear exception here). If you see a social network where someone has 5000 followers and only follows 150 back &#8211; that&#8217;s Asymmetric Follow.<\/p><\/blockquote>\n<p>So, if I were to explain James&#8217; definition to a teenager <sup class='footnote'><a href='#fn-845-1' id='fnref-845-1' onclick='return fdfootnote_show(845)'>1<\/a><\/sup> , I might say something like:<\/p>\n<blockquote><p>&#8220;Asymmetric Follow is when the popular kid in school is admired by a bunch of less popular kids and when the popular kid speaks, everyone usually listens and when the less-popular kids speak, the popular kid can choose to listen or respond or do nothing&#8221;.<\/p><\/blockquote>\n<p>If I&#8217;ve been charitable in my understanding and summary of James&#8217; definition of Asymmetric Follow, then his explanation and definition makes sense to me.\u00a0 From my experience as a former High School student of the less-popular type, that&#8217;s how life was.<\/p>\n<p>I have to note, however, that James&#8217; definition confounds the behavioral economics definition of Information Asymmetry &#8212; but he means something different.\u00a0 The <a href=\"https:\/\/staging.opexlearning.com\/resources\/how-twitter-solves-voter-and-other-types-of-information-asymetry\/618\/\">historical definition<\/a> has more to do with the direction of communication and the &#8220;stickiness&#8221; of that information and how that &#8220;stickiness&#8221; can impact decisions and rational choice.\u00a0 James Governor doesn&#8217;t address the definition in behavioral economics but does use a similar term.<\/p>\n<p><strong>Twitter as Combinatorics<\/strong><\/p>\n<p>But, let&#8217;s quantify what James is talking about.\u00a0 In fact, when we do, we&#8217;ll find out that it&#8217;s actually basic combinatorics.<\/p>\n<p>Suppose there are persons A and B, who follow each other.\u00a0 In this scenario there are 2 communication links (AB, BA).\u00a0 Add person C who follows and is followed-by persons A and B, now we have 6 communication links, (ABC, ACB, BCA, BAC, CAB, CBA).\u00a0 So, inductively, as inter-followership <sup class='footnote'><a href='#fn-845-2' id='fnref-845-2' onclick='return fdfootnote_show(845)'>2<\/a><\/sup> permutation grows, the raw combinatorial communication link counts grows quadratically, not linearly.<\/p>\n<p>To demonstrate this, we use basic statistics of the form n-choose-r, where !, such as n!, is equivalent to n factorial, to arrive at the formula for how many pairs or permutations we can choose from n items:<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-4553 aligncenter\" title=\"combinatorics-twitter\" alt=\"twitter combinations\" src=\"https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2008\/12\/combinatorics-twitter.jpg\" width=\"107\" height=\"49\" \/><\/p>\n<p>For the number of pairs, we can reduce the above formula to the following:<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-4554 aligncenter\" title=\"twitter-as-combinatorics\" alt=\"tweet as often as you like\" src=\"https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2008\/12\/twitter-as-combinatorics-1024x545.jpg\" width=\"717\" height=\"382\" srcset=\"https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2008\/12\/twitter-as-combinatorics-1024x545.jpg 1024w, https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2008\/12\/twitter-as-combinatorics-600x320.jpg 600w, https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2008\/12\/twitter-as-combinatorics-300x159.jpg 300w, https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2008\/12\/twitter-as-combinatorics.jpg 1087w\" sizes=\"(max-width: 717px) 100vw, 717px\" \/><\/p>\n<p>Visually, as inter-followership grows, the communication links grows non-linearly, but quadratically (n! grows exponentially) &#8212; in either case, the function is clearly not linear:<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-4555 aligncenter\" title=\"twitter-follower-factorial\" alt=\"factorial equation for tweets\" src=\"https:\/\/staging.opexlearning.com\/resources\/wp-content\/uploads\/2008\/12\/twitter-follower-factorial.jpg\" width=\"57\" height=\"44\" \/><\/p>\n<p><strong>Mutually Exclusive, Comprehensively Exhaustive (MECE)<br \/>\n<\/strong><\/p>\n<p>JP runs a really fun experiment that validates his hypothesis that tweets in the universe of Twitter are comprehensively exhaustive <sup class='footnote'><a href='#fn-845-3' id='fnref-845-3' onclick='return fdfootnote_show(845)'>3<\/a><\/sup>.\u00a0 What his experiment does not show is the exclusiveness of the tweets &#8212; that is, their uniqueness from each other.\u00a0 On its face, this is not a big deal, but in scientific inquiry, being able to compartmentalize objects in unique buckets is helpful.<\/p>\n<p>One reason it is difficult to classify tweets as mutually exclusive in content is because there are Replies and Retweets.\u00a0 There is probably an innovative way to find the unique and mutually exclusive clusters in the corpus that is Twitter &#8212; that would be fun work for a computational linguist.<\/p>\n<p>For this post, this is not a big deal, but I just make this point for clarity &#8212; really great experiment, JP.<\/p>\n<p><strong>A Conclusion<\/strong><\/p>\n<p>Ummm, I don&#8217;t really have a conclusion or a point, except for that I think Twitter is pretty amazing and that Twitter can and should encourage computer scientists, computational linguists, behavioral economists, combinatorial mathematicians, set theory geekzoids, <a href=\"https:\/\/staging.opexlearning.com\/resources\/digg-as-a-game\/197\/\">game theory freakonomica<\/a>, cultural anthropologists, and others to participate in and learn from this massively human experiment.<\/p>\n<p>I really like Twitter &#8212; oh, by the way &#8212; retweet this post&#8230;<\/p>\n<div class='footnotes' id='footnotes-845'>\n<div class='footnotedivider'><\/div>\n<ol>\n<li id='fn-845-1'> my personal criteria for an atomic and pragmatic definition of a concept is if it can be explained to normally-functioning-and-average human that is 15 human years or younger <span class='footnotereverse'><a href='#fnref-845-1'>&#8617;<\/a><\/span><\/li>\n<li id='fn-845-2'> I make a distinction between inter-followership and intra-followership where the former is a set where each member follows each other and the latter is a set where the followership is disjointed.\u00a0 However, for the purposes of Twitter, inter-followership and intra-followership doesn&#8217;t matter so much since a follower has the same rank as the non-follower to the one being followed &#8212; their voices are not weighted differently <span class='footnotereverse'><a href='#fnref-845-2'>&#8617;<\/a><\/span><\/li>\n<li id='fn-845-3'> This is my term that I use to explain his point, but he does not use the terms Mutually Exclusive or Comprehensively Exhaustive in his writings. <span class='footnotereverse'><a href='#fnref-845-3'>&#8617;<\/a><\/span><\/li>\n<\/ol>\n<\/div>\n<!--CusAds0-->\n<div style=\"font-size: 0px; height: 0px; line-height: 0px; margin: 0; padding: 0; clear: both;\"><\/div>","protected":false},"excerpt":{"rendered":"<p>Ever since I discovered Twitter, I&#8217;ve been amazed at @ev, @biz, and @jack&#8217;s idea of simplicity and usefulness.\u00a0 Lately, @windley (Phil Windley&#8217;s article), @monkchips, and JP have approached Twitter from a more theoretical perspective.\u00a0 This article is my contribution to that healthy conversation (this blog post will be followed by a short tweet, of course). [&hellip;]<\/p>\n","protected":false},"author":12327,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[190],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v23.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Factorial Equations of a Tweet<\/title>\n<meta name=\"description\" content=\"this article shows how twitter as an information medium is really combinatorics in action -- social media, word of mouth marketing, net promoter score (NPS)\" \/>\n<meta name=\"robots\" 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