{"id":837,"date":"2010-01-04T11:34:30","date_gmt":"2010-01-04T11:34:30","guid":{"rendered":"http:\/\/scientopia.org\/blogs\/goodmath\/2010\/01\/04\/big-numbers-and-air-travel\/"},"modified":"2010-01-04T11:34:30","modified_gmt":"2010-01-04T11:34:30","slug":"big-numbers-and-air-travel","status":"publish","type":"post","link":"http:\/\/www.goodmath.org\/blog\/2010\/01\/04\/big-numbers-and-air-travel\/","title":{"rendered":"Big Numbers and Air Travel"},"content":{"rendered":"<p> As you&#8217;ve surely heard by now, on christmas day, some idiot attempted to<br \/>\nblow up an airplane by stuffing his underwear full of explosives and then<br \/>\nlighting his crotch on fire. There&#8217;s been a ton of coverage of this &#8211; most of<br \/>\nwhich takes the form of people running around wetting their pants in terror.<\/p>\n<p> One thing which I&#8217;ve noticed, though, is that one aspect of this whole mess<br \/>\nties in to one of my personal obsessions: scale. We humans are really,<br \/>\n<em>really<\/em> lousy at dealing with big numbers. We just absolutely<br \/>\nhave a piss-poor ability to really comprehend numbers, or to take what we<br \/>\nknow, and put it together in a quantitative way.<\/p>\n<p><!--more--><\/p>\n<p> The context in which this comes up is in many articles written by<br \/>\npeople criticizing the pants-wetters. The point that they&#8217;re trying to<br \/>\nmake is that airport security is actually pretty damned good. When<br \/>\nyou consider the number of flights, and the number of people on each flight,<br \/>\nand then put the number of terrorists who&#8217;ve managed to get onto a plane<br \/>\nand try something &#8211; successful or not &#8211; the number who get through are<br \/>\namazingly small. For example, here&#8217;s one of my favorite ranters,<br \/>\nfrom <a href=\"http:\/\/www.youaredumb.net\/node\/1457\">youaredumb.net<\/a>:<\/p>\n<blockquote><p>\nAnd the second part of the deal is that there aren&#8217;t that many<br \/>\npeople trying. Even if you assume that for every one attempt that makes the<br \/>\nnews, there are ten attempts kept secret, which is a wildly unlikely ratio in<br \/>\na world where everyone&#8217;s carrying six cameras and wants to be on teevee?<br \/>\nThat&#8217;s still less that 50 attempts on tens of thousands of flights over nearly<br \/>\na decade. There simply aren&#8217;t that many people trying to blow up planes.\n<\/p><\/blockquote>\n<p> His argument is perfectly good. He&#8217;s right that the new airport security<br \/>\nmeasures are aimed at making you <em>think<\/em> that they&#8217;re doing more to<br \/>\nprotect you than they used to, rather than actually <em>doing<\/em> more. But<br \/>\n<em>ten of thousands<\/em> of flights over the last decade? Ummm&#8230;. No.<\/p>\n<p> Tens of thousands <em>seems<\/em> like a lot. But it&#8217;s so far off<br \/>\nthat it&#8217;s laughable. It&#8217;s off by more than 4 <em>orders of magnitude<\/em>. It&#8217;s<br \/>\nsmaller than the <em>square root<\/em> of the actual number of flights.<\/p>\n<p> Let&#8217;s take one busy airport: Newark Airport in NJ. Newark is in full operation<br \/>\nfor about 14 hours per day. Based on my time watching planes take off and<br \/>\nland there, I&#8217;d guess that they average at least one takeoff every three<br \/>\nminutes. But let&#8217;s guess that I&#8217;m wrong, and double the time between<br \/>\ntakeoffs, assuming one every 6 minutes.  That&#8217;s 10 flights per hour,<br \/>\nwhich adds up to about 140 flights per day. That&#8217;s definitely <em>way<\/em><br \/>\nto small &#8211; but it adds up to well over 50,000 flights per day. <\/p>\n<p> And that estimate turns out to be rank garbage. Looking up official<br \/>\ninformation, there were over 225,000 takeoffs at Newark in 2007 &#8211; which is a<br \/>\nsignificant <em>reduction<\/em> over previous years. So even biasing towards<br \/>\nthe low side, Newark airport alone had well over 2 <em>million<\/em> flights<br \/>\ntake off in the last decade.<\/p>\n<p> According to the FAA, there were about 37,000 commercial flights per day<br \/>\nin 2008 &#8211; for a total of over 13 <em>million<\/em> commercial flights per year.<br \/>\nAnd that&#8217;s a dramatic <em>decrease<\/em> compared to a few years earlier, before<br \/>\nhigh fuel prices drove many airlines out of business, and forced others to reduce<br \/>\ntheir schedules.<\/p>\n<p> All of us who live in metropolitan areas see ton of airplanes taking off and<br \/>\nlanding every day. But we&#8217;ve got absolutely no intuitive understanding of just<br \/>\nwhat that actually means. I constantly rant about how piss-poor we are at<br \/>\nunderstanding scale, but I was seriously surprised by the number of flights per day<br \/>\naround NYC. Once we get beyond numbers that we can easily count to, our<br \/>\nintuitions about numbers are just a total disaster. We just don&#8217;t really<br \/>\nunderstand scale; we don&#8217;t understand how big numbers add up.<\/p>\n<p> And on the topic of airport security: put the numbers into context, and you&#8217;ll realize<br \/>\nthat all of the panic over terrorism on airplanes is really amazingly overblown. The chances of being hurt by someone who got past airport security, even without things<br \/>\nlike the full-body scanners being deployed after this latest panic, are smaller than dying<br \/>\nin your dentist&#8217;s office from an anaesthesia error. And how often does anyone worry about that?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>As you&#8217;ve surely heard by now, on christmas day, some idiot attempted to blow up an airplane by stuffing his underwear full of explosives and then lighting his crotch on fire. There&#8217;s been a ton of coverage of this &#8211; most of which takes the form of people running around wetting their pants in terror. [&hellip;]<\/p>\n","protected":false},"author":1,"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":[6,9],"tags":[],"class_list":["post-837","post","type-post","status-publish","format-standard","hentry","category-bad-probability","category-big-numbers"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p4lzZS-dv","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/837","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/comments?post=837"}],"version-history":[{"count":0,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/837\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/media?parent=837"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/categories?post=837"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/tags?post=837"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}