{"id":102,"date":"2005-12-01T19:11:42","date_gmt":"2005-12-01T19:11:42","guid":{"rendered":"http:\/\/www.sixthform.info\/maths\/?p=102"},"modified":"2005-12-01T19:11:42","modified_gmt":"2005-12-01T19:11:42","slug":"gratuitous-mathematics","status":"publish","type":"post","link":"https:\/\/www.sixthform.info\/maths\/?p=102","title":{"rendered":"Gratuitous Mathematics"},"content":{"rendered":"<ul><img src='\/maths\/latexrender\/pictures\/d9b4725a6683bcbd6ff6fa075a519b56.gif' title='\\displaymath q_x=1-e^{-\\int^1_0\\mu_{x+t}}\\:dt' alt='\\displaymath q_x=1-e^{-\\int^1_0\\mu_{x+t}}\\:dt' align=absmiddle><br \/>\n<i>The meaning of life? (Not quite but this formula will tell you much of it you have left*)<\/i><\/ul>\n<p>That&#8217;s how the Guardian today publicised its article on life expectancy. It then attempted to &#8216;explain&#8217; the formula with a tiny note saying <i>*Details overleaf<\/i>. These &#8216;details&#8217; were: <\/p>\n<ul><i>The force of mortality at age <img src='\/maths\/latexrender\/pictures\/9dd4e461268c8034f5c8564e155c67a6.gif' title='x' alt='x' align=absmiddle> is defined as: <img src='\/maths\/latexrender\/pictures\/6eacd47f0cacd64b3dea04cf4875e872.gif' title='\\mu=GM(r,s)' alt='\\mu=GM(r,s)' align=absmiddle>, with parameters <img src='\/maths\/latexrender\/pictures\/476edf069027dbfd9a94863cb808d205.gif' title='a_1,\\dots,a_r' alt='a_1,\\dots,a_r' align=absmiddle> and <img src='\/maths\/latexrender\/pictures\/79a204b6973fbf43aa6af596dc9a86c2.gif' title='b_1,\\dots,b_r' alt='b_1,\\dots,b_r' align=absmiddle> fitted by maximum likelihood. For example, <img src='\/maths\/latexrender\/pictures\/690efac8773f553b7685ba75b3abc0b4.gif' title='GM(2,3)=a_1+a_2 t+e^{b_1+b_2 t+ b_3 (t^2-1)}' alt='GM(2,3)=a_1+a_2 t+e^{b_1+b_2 t+ b_3 (t^2-1)}' align=absmiddle> where <img src='\/maths\/latexrender\/pictures\/01c1a1da2860a557dff568188f7e561e.gif' title='t=\\frac{(x-70)}{50}' alt='t=\\frac{(x-70)}{50}' align=absmiddle>. The the equation above shows the probability that someone aged <img src='\/maths\/latexrender\/pictures\/9dd4e461268c8034f5c8564e155c67a6.gif' title='x' alt='x' align=absmiddle> will die within one year. Still puzzled? See page 8.<\/i><\/ul>\n<p>On page 8 is the article <a href=\"http:\/\/www.guardian.co.uk\/g2\/story\/0,3604,1654529,00.html\" target=\"_blank\">So, how long have we got?<\/a> which sheds no light on the formula; it doesn&#8217;t even mention it.<\/p>\n<p>So why was this formula there? To make the journalist or the paper look clever? Who knows. But it certainly is completely useless even to mathematicians. The example just makes the whole thing even more obscure. Wouldn&#8217;t it be nice to have more mathematically trained journalists who wouldn&#8217;t just show off but instead make things clearer?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The meaning of life? (Not quite but this formula will tell you much of it you have left*) That&#8217;s how the Guardian today publicised its article on life expectancy. It then attempted to &#8216;explain&#8217; the formula with a tiny note saying *Details overleaf. These &#8216;details&#8217; were: The force of mortality at age is defined as: [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-102","post","type-post","status-publish","format-standard","hentry","category-articles"],"_links":{"self":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/102","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=102"}],"version-history":[{"count":0,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/102\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=102"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=102"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=102"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}