CINXE.COM

Wolfram|Alpha Comes Alive with CDF—Stephen Wolfram Writings

<!DOCTYPE html> <html lang="en" prefix="fb: http://www.facebook.com/2008/fbml, og: http://ogp.me/ns#"> <head> <!-- begin framework head en --> <meta http-equiv="x-ua-compatible" content="ie=edge"> <meta name="viewport" content="width=device-width, initial-scale=1"> <meta charset="utf-8"> <title>Wolfram|Alpha Comes Alive with CDF&mdash;Stephen Wolfram Writings</title> <meta name="description" content="Combine computational knowledge with the interactivity of Computable Document Format (CDF) technology with the new Wolfram|Alpha with CDF."> <meta property="og:title" content="Wolfram|Alpha Comes Alive with CDF&mdash;Stephen Wolfram Writings"> <meta property="og:description" content="Combine computational knowledge with the interactivity of Computable Document Format (CDF) technology with the new Wolfram|Alpha with CDF."> <meta name="twitter:title" content="Wolfram|Alpha Comes Alive with CDF&mdash;Stephen Wolfram Writings"> <meta name="twitter:description" content="Combine computational knowledge with the interactivity of Computable Document Format (CDF) technology with the new Wolfram|Alpha with CDF."> <link rel="stylesheet" href="/common/framework/css/framework.en.css"> <script src="//www.wolframcdn.com/consent/cookie-consent.js"></script> <script src="/common/javascript/wal/latest/walLoad.js"></script> <script defer src="/common/js/announcements/script.js"></script> <script src="/common/framework/js/head.en.js"></script> <script src="/common/js/jquery/3.7.1/jquery.min.js"></script> <script src="/common/js/jquery/plugins/migrate/3.5.2/jquery.migrate.min.js"></script> <script src="/common/javascript/analytics.js"></script> <!-- end framework head en --> <script src="https://writings.stephenwolfram.com/wp-content/themes/sw-writings/jquery.lazy.min.js"></script> <script> $(function() { $('.lazy').Lazy({ effect: 'fadeIn', effectTime: 250, threshold:200 }); }); </script> <script type="text/javascript" src="https://writings.stephenwolfram.com/wp-content/themes/sw-writings/sw.js"></script> <link rel="stylesheet" href="//www.wolframcdn.com/fonts/source-sans-pro/1.0/global.css"> <link rel="stylesheet" href="//www.wolframcdn.com/fonts/hack/3.003/global.css"> <link rel="stylesheet" href="//www.wolframcdn.com/fonts/mathematica/1.0/all.css"> <link rel="stylesheet" href="https://writings.stephenwolfram.com/wp-content/themes/sw-writings/clipboard.css" type="text/css" media="all" /> <link rel="stylesheet" href="https://writings.stephenwolfram.com/wp-content/themes/sw-writings/python-pygments.css" type="text/css" media="all" /> <link rel="stylesheet" href="/common/js/clipboard/2.0/clipboard.css"> <link rel="stylesheet" href="/common/templates/www.stephenwolfram.com/css/responsive-header.css" /> <link rel="stylesheet" href="https://writings.stephenwolfram.com/wp-content/themes/sw-writings/style.css" type="text/css" media="all" /> <link rel="alternate" type="application/rss+xml" title="Stephen Wolfram Writings RSS Feed" href="https://writings.stephenwolfram.com/feed/" /> <link rel="alternate" type="application/atom+xml" title="Stephen Wolfram Writings Atom Feed" href="https://writings.stephenwolfram.com/feed/atom/" /> <script type="text/javascript" src="https://files.wolframcdn.com/pub/writings.stephenwolfram.com/js/menu.js?5db8f077951d5e4ef6fbad86daf24214146552f3ae141ac21f7cf2aef767799678b244ec4070f219c19860ab58d8271a"></script> <link rel="stylesheet" href="/common/javascript/jquery/ui/1.10.2/themes/base/jquery.ui.all.css"> <link rel="stylesheet" href="/common/javascript/jquery/plugins/colorbox/colorbox.css"> <script src="/common/javascript/jquery/ui/1.10.2/ui/jquery.ui.core.js"></script> <script src="/common/javascript/jquery/ui/1.10.2/ui/jquery.ui.widget.js"></script> <script src="/common/javascript/jquery/ui/1.10.2/ui/jquery.ui.mouse.js"></script> <script src="/common/javascript/jquery/ui/1.10.2/ui/jquery.ui.slider.js"></script> <script src="/common/javascript/jquery/plugins/colorbox/jquery.colorbox.js"></script> <link rel="stylesheet" href="/common/javascript/jquery/plugins/magnific/magnific.css"> <link rel="stylesheet" href="/common/javascript/jquery/plugins/magnific/magnific-types.css"> <script src="/common/javascript/jquery/plugins/magnific/magnific.min.js"></script> <script src="/common/javascript/jquery/plugins/magnific/magnific-types.js"></script> <link rel='dns-prefetch' href='//s.w.org' /> <link rel="alternate" type="application/rss+xml" title="Stephen Wolfram Writings &raquo; Wolfram|Alpha Comes Alive with CDF Comments Feed" href="https://writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf/feed/" /> <script type="text/javascript"> window._wpemojiSettings = {"baseUrl":"https:\/\/s.w.org\/images\/core\/emoji\/2.2.1\/72x72\/","ext":".png","svgUrl":"https:\/\/s.w.org\/images\/core\/emoji\/2.2.1\/svg\/","svgExt":".svg","source":{"concatemoji":"https:\/\/writings.stephenwolfram.com\/wp-includes\/js\/wp-emoji-release.min.js?ver=4.7.2"}}; !function(a,b,c){function d(a){var b,c,d,e,f=String.fromCharCode;if(!k||!k.fillText)return!1;switch(k.clearRect(0,0,j.width,j.height),k.textBaseline="top",k.font="600 32px Arial",a){case"flag":return k.fillText(f(55356,56826,55356,56819),0,0),!(j.toDataURL().length<3e3)&&(k.clearRect(0,0,j.width,j.height),k.fillText(f(55356,57331,65039,8205,55356,57096),0,0),b=j.toDataURL(),k.clearRect(0,0,j.width,j.height),k.fillText(f(55356,57331,55356,57096),0,0),c=j.toDataURL(),b!==c);case"emoji4":return k.fillText(f(55357,56425,55356,57341,8205,55357,56507),0,0),d=j.toDataURL(),k.clearRect(0,0,j.width,j.height),k.fillText(f(55357,56425,55356,57341,55357,56507),0,0),e=j.toDataURL(),d!==e}return!1}function e(a){var c=b.createElement("script");c.src=a,c.defer=c.type="text/javascript",b.getElementsByTagName("head")[0].appendChild(c)}var f,g,h,i,j=b.createElement("canvas"),k=j.getContext&&j.getContext("2d");for(i=Array("flag","emoji4"),c.supports={everything:!0,everythingExceptFlag:!0},h=0;h<i.length;h++)c.supports[i[h]]=d(i[h]),c.supports.everything=c.supports.everything&&c.supports[i[h]],"flag"!==i[h]&&(c.supports.everythingExceptFlag=c.supports.everythingExceptFlag&&c.supports[i[h]]);c.supports.everythingExceptFlag=c.supports.everythingExceptFlag&&!c.supports.flag,c.DOMReady=!1,c.readyCallback=function(){c.DOMReady=!0},c.supports.everything||(g=function(){c.readyCallback()},b.addEventListener?(b.addEventListener("DOMContentLoaded",g,!1),a.addEventListener("load",g,!1)):(a.attachEvent("onload",g),b.attachEvent("onreadystatechange",function(){"complete"===b.readyState&&c.readyCallback()})),f=c.source||{},f.concatemoji?e(f.concatemoji):f.wpemoji&&f.twemoji&&(e(f.twemoji),e(f.wpemoji)))}(window,document,window._wpemojiSettings); </script> <style type="text/css"> img.wp-smiley, img.emoji { display: inline !important; border: none !important; box-shadow: none !important; height: 1em !important; width: 1em !important; margin: 0 .07em !important; vertical-align: -0.1em !important; background: none !important; padding: 0 !important; } </style> <link rel='stylesheet' id='howToCiteCss-css' href='https://writings.stephenwolfram.com/wp-content/themes/sw-writings/HowToCite/style.css?ver=4.7.2' type='text/css' media='all' /> <script type='text/javascript' src='https://writings.stephenwolfram.com/wp-content/themes/sw-writings/HowToCite/HowToCite.js?ver=4.7.2'></script> <link rel='https://api.w.org/' href='https://writings.stephenwolfram.com/wp-json/' /> <link rel="wlwmanifest" type="application/wlwmanifest+xml" href="https://writings.stephenwolfram.com/wp-includes/wlwmanifest.xml" /> <link rel='prev' title='Music, Mathematica, and the Computational Universe' href='https://writings.stephenwolfram.com/2011/06/music-mathematica-and-the-computational-universe/' /> <link rel='next' title='Advance of the Data Civilization: A Timeline' href='https://writings.stephenwolfram.com/2011/08/advance-of-the-data-civilization-a-timeline/' /> <link rel='shortlink' href='https://writings.stephenwolfram.com/?p=1515' /> <link rel="alternate" type="application/json+oembed" href="https://writings.stephenwolfram.com/wp-json/oembed/1.0/embed?url=https%3A%2F%2Fwritings.stephenwolfram.com%2F2011%2F08%2Fwolframalpha-comes-alive-with-cdf%2F" /> <link rel="alternate" type="text/xml+oembed" href="https://writings.stephenwolfram.com/wp-json/oembed/1.0/embed?url=https%3A%2F%2Fwritings.stephenwolfram.com%2F2011%2F08%2Fwolframalpha-comes-alive-with-cdf%2F&#038;format=xml" /> <link rel='canonical' href='https://writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf/'/> <style type="text/css">.recentcomments a{display:inline !important;padding:0 !important;margin:0 !important;}</style> </head> <body id="blog" class="post-template-default single single-post postid-1515 single-format-standard"> <a name="top"></a> <div id="wrapper"> <header id="header"> <div class="inner"> <button class="hamburger">&equiv;</button> <h1 id="logo"> <a href="https://www.stephenwolfram.com">Stephen Wolfram <svg viewBox="6.252 51.944 1031.673 96.468"> <g id="logoSVG"> <path d="M643.657,60.162c1.429-0.357,2.501-0.714,3.572-0.714h0.536V53.91h-34.121v5.538h0.536 c4.287,0.357,7.503,1.072,9.468,1.965c1.787,0.894,2.68,1.965,2.68,3.216c0,1.072-0.179,2.322-0.357,3.751 s-0.893,4.288-1.965,8.218c-1.429,5.716-3.395,12.505-5.538,20.544c-2.144,7.682-4.645,16.436-7.503,26.439L588.456,55.16h-6.968 l-22.33,66.812c-4.823-16.971-8.218-29.297-10.719-37.693c-2.501-8.575-4.287-15.006-5.181-18.758c0-0.357-0.179-1.072-0.357-1.786 c-0.179-0.715-0.179-1.251-0.179-1.608c0-1.072,1.607-1.608,3.037-1.965c2.322-0.536,5.002-0.714,8.218-0.893h0.536V53.91h-38.23 v5.538h0.536c1.071,0,2.322,0.357,3.751,0.714c1.43,0.357,2.502,0.894,3.573,1.608c1.251,0.893,2.144,1.787,2.858,2.68 s1.251,2.144,1.607,3.394c1.608,5.538,4.646,16.257,9.111,32.514c4.466,16.078,8.933,31.799,13.22,46.805l0.179,0.357h6.432 l23.581-69.314l22.509,68.957l0.179,0.357h6.61l0.178-0.357c4.646-14.827,9.111-29.119,13.041-42.339 c4.109-13.22,7.504-24.832,10.54-34.657c0.715-2.144,1.43-3.751,2.323-5.002c0.893-1.25,2.144-2.144,3.572-3.215 C640.978,61.234,642.406,60.698,643.657,60.162z" /> <path d="M693.856,87.673c-2.858-3.037-6.253-5.359-10.183-6.967c-3.931-1.608-8.039-2.501-12.506-2.501 c-4.287,0-8.396,0.893-12.147,2.501c-3.931,1.607-7.324,3.93-10.183,6.967c-2.858,3.037-5.359,6.789-6.968,11.076 c-1.607,4.288-2.501,9.111-2.501,14.47c0,4.823,0.894,9.647,2.322,13.935c1.608,4.287,3.752,8.039,6.61,11.076 s6.253,5.537,10.004,7.324c3.931,1.786,8.218,2.68,12.862,2.68c4.288,0,8.396-0.894,12.327-2.502 c3.751-1.607,7.146-3.93,10.183-6.967s5.359-6.788,6.967-11.076c1.608-4.287,2.501-9.11,2.501-14.291s-0.893-10.004-2.501-14.292 C699.037,94.462,696.715,90.71,693.856,87.673z M690.998,113.041c0,4.287-0.357,8.218-1.251,11.791 c-0.714,3.395-1.965,6.609-3.751,9.289l0,0c-1.608,2.68-3.752,4.823-6.253,6.252c-2.501,1.43-5.538,2.323-8.575,2.323 c-3.394,0-6.431-0.715-8.753-2.144c-2.501-1.43-4.467-3.573-6.074-6.253s-2.858-5.896-3.752-9.29 c-0.714-3.572-1.25-7.502-1.25-11.969c0-3.93,0.357-7.86,1.071-11.434c0.715-3.572,1.787-6.788,3.395-9.289 c1.608-2.68,3.573-5.002,6.074-6.61s5.538-2.501,9.11-2.501c3.216,0,6.074,0.714,8.575,2.144s4.466,3.395,6.253,5.896 c1.607,2.68,2.858,5.716,3.751,9.468C690.641,104.467,690.998,108.754,690.998,113.041z" /> <path d="M760.49,126.082c-0.714,1.787-1.786,4.109-3.394,6.967c-1.608,2.859-3.037,5.002-4.288,6.432 c-0.356,0.357-0.893,0.715-1.786,1.072s-1.786,0.535-2.858,0.715c-1.071,0.178-2.322,0.356-3.395,0.356 c-1.25,0-2.322,0.179-3.572,0.179c-2.501,0-4.466,0-5.896-0.179c-1.25-0.179-2.322-0.536-2.858-0.894 c-0.715-0.535-1.071-1.25-1.25-2.322c-0.179-1.071-0.357-2.68-0.357-4.645V89.46c0-0.893,0.179-1.787,0.535-2.68 c0.357-0.714,0.894-1.25,1.787-1.608c0.536-0.179,1.607-0.536,2.858-0.714c1.25-0.357,2.501-0.357,3.216-0.536h0.535v-4.287 h-28.583v4.287h0.536c0.715,0,1.786,0.179,3.037,0.536c1.25,0.357,2.144,0.714,2.858,1.072c0.893,0.357,1.607,1.072,1.786,1.608 c0.357,0.714,0.536,1.608,0.536,2.501v46.983c0,1.071-0.179,1.966-0.536,2.68c-0.357,0.715-0.894,1.251-1.786,1.608 c-0.536,0.178-1.43,0.357-2.858,0.535c-1.43,0.179-2.501,0.179-3.216,0.357h-0.536v4.287h51.986l1.429-20.543h-4.108 L760.49,126.082z" /> <path d="M768.708,83.922h0.536c0.715,0,1.965,0.179,3.216,0.536c1.429,0.357,2.501,0.714,3.216,1.072 c0.893,0.357,1.607,1.072,1.786,1.608c0.357,0.714,0.536,1.608,0.536,2.501v47.341c0,1.071-0.179,1.965-0.536,2.68 c-0.357,0.714-0.894,1.251-1.786,1.608c-0.357,0.178-1.072,0.356-2.858,0.535c-1.608,0.179-2.68,0.179-3.752,0.357h-0.536v4.287 h29.298v-4.287h-0.536c-0.714,0-1.965-0.179-3.394-0.536c-1.787-0.356-2.68-0.536-2.858-0.714 c-0.894-0.357-1.608-1.072-1.965-1.787c-0.357-0.715-0.536-1.607-0.536-2.501v-22.151h6.967c1.965,0,3.573,0.178,5.002,0.535 c1.251,0.357,2.322,1.072,3.216,2.145c0.536,0.714,1.072,1.965,1.607,3.572c0.536,1.607,0.894,3.216,0.894,4.467v0.535h4.466 V98.928h-4.466v0.357c-0.179,1.607-0.536,3.037-0.894,4.466c-0.535,1.429-1.071,2.322-1.607,3.037 c-0.894,0.893-1.786,1.607-3.037,2.143c-1.25,0.537-2.858,0.715-5.181,0.715h-6.967V84.458h10.54c1.607,0,3.037,0,4.466,0.179 c1.251,0,2.501,0.179,3.395,0.357c1.786,0.179,3.572,1.787,5.538,4.466c1.965,2.68,3.394,5.359,3.93,7.682l0.179,0.357h4.288V80.17 h-52.165V83.922L768.708,83.922z" /> <path d="M952.534,141.624c-1.072-0.356-1.966-0.536-2.68-1.071c-1.072-0.715-1.787-1.43-2.323-2.145 c-0.535-0.715-1.071-1.607-1.429-2.857l-21.795-56.452l-0.179-0.357h-4.287l-0.179,0.357c-3.037,8.039-6.609,17.15-10.54,27.333 c-3.93,10.182-7.503,19.472-10.897,27.689c-0.714,1.607-1.25,2.858-1.965,3.572c-0.715,0.895-1.607,1.787-2.68,2.502 c-0.715,0.535-1.607,0.893-2.858,1.072c-0.536,0.178-1.071,0.178-1.607,0.356c-0.357,0-0.715-0.179-1.251-0.179 c-1.071-0.178-2.144-0.535-2.858-0.893c-1.071-0.536-2.144-1.251-3.215-2.145c-1.072-0.893-2.323-2.144-3.573-3.93 c-3.037-4.109-5.717-7.682-7.86-10.719c-1.965-2.858-4.645-6.252-7.682-10.183c2.144-0.715,4.108-1.429,5.896-2.322 c1.965-1.072,3.751-2.144,5.002-3.573c1.607-1.43,2.68-3.215,3.572-5.181c0.715-1.965,1.251-4.288,1.251-6.789 c0-2.858-0.536-5.359-1.787-7.503c-1.25-1.965-2.68-3.751-4.645-5.002s-4.287-2.144-6.788-2.858 c-2.501-0.536-5.181-0.893-7.86-0.893H826.59v4.287h0.535c0.894,0,1.965,0.179,3.037,0.357c1.251,0.179,2.144,0.536,2.858,0.715 c1.072,0.357,1.607,0.893,1.965,1.607c0.357,0.715,0.357,1.608,0.357,2.68v47.341c0,1.072-0.179,1.965-0.536,2.68 c-0.356,0.715-0.893,1.25-1.786,1.607c-0.536,0.18-1.429,0.357-2.858,0.537c-1.429,0.178-2.501,0.178-3.216,0.356h-0.535v4.288 h28.583v-4.288h-0.536c-0.894,0-2.144-0.179-3.395-0.356c-1.25-0.18-2.322-0.357-2.858-0.537c-0.893-0.357-1.607-0.893-1.965-1.607 s-0.536-1.607-0.536-2.68v-19.83h5.896c3.573,4.646,6.967,9.29,10.004,13.578c3.037,4.466,6.61,9.825,10.54,15.898l0.179,0.18 h14.471h3.93h21.616v-4.288h-0.536c-2.322-0.179-4.466-0.536-6.431-1.251c-1.786-0.535-2.501-1.429-2.501-2.322 c0-0.535,0-1.071,0.179-1.965c0.179-0.893,0.356-1.965,0.893-3.215c0.357-1.43,0.894-2.859,1.43-4.467 c0.536-1.43,1.25-3.215,1.965-5.359h22.331l5.359,14.291c0.178,0.357,0.178,0.537,0.178,0.895c0,0.356,0,0.714,0,0.893 c0,0.357-0.714,0.893-1.965,1.25c-1.607,0.537-3.572,0.715-5.895,0.894h-0.536v4.288h28.94v-4.288h-0.536 C954.499,141.981,953.605,141.803,952.534,141.624z M928.238,118.579h-18.222l9.11-23.581L928.238,118.579z M866.069,96.963 c0,4.467-1.429,8.039-4.108,10.719s-6.253,3.93-10.183,3.93h-5.538V84.637h7.324c3.931,0,7.146,1.072,9.29,3.394 C864.998,90.175,866.069,93.211,866.069,96.963z" /> <path d="M1037.211,141.981c-0.714,0-1.965-0.179-3.215-0.357c-1.43-0.179-2.322-0.536-2.858-0.894 c-0.894-0.535-1.608-1.071-1.965-1.786c-0.357-0.714-0.536-1.429-0.536-2.501V89.281c0-0.893,0.179-1.786,0.536-2.68 c0.356-0.714,0.893-1.25,1.786-1.608c0.536-0.178,1.607-0.357,2.858-0.714c1.25-0.179,2.322-0.357,3.216-0.357h0.535v-4.287h-22.33 v0.536c0,0.357-0.179,1.25-0.715,3.216c-0.357,1.607-0.894,3.215-1.429,4.645l-15.542,40.016L979.33,79.992l-0.178-0.357h-23.046 v4.287h0.536c1.25,0,2.68,0.357,3.93,0.715c1.251,0.357,2.502,0.893,3.395,1.786c0.715,0.715,1.43,1.608,1.787,2.858 s0.714,2.68,0.714,4.645v33.585c0,4.108-0.179,7.146-0.536,8.932c-0.356,1.607-1.071,2.858-1.965,3.752 c-0.715,0.715-1.965,1.072-3.394,1.429c-1.43,0.357-2.858,0.536-4.288,0.715h-0.357v4.288h27.333v-4.288h-0.536 c-0.357,0-1.429-0.179-4.108-0.894c-1.966-0.535-3.395-1.072-3.931-1.786c-0.893-0.715-1.607-2.144-1.965-3.931 c-0.536-1.965-0.715-4.822-0.715-8.574v-38.23l21.08,56.452h3.037l22.152-55.559v46.805c0,1.071-0.179,1.966-0.536,2.68 c-0.357,0.715-1.072,1.251-1.965,1.786c-0.536,0.357-1.608,0.536-3.216,0.715s-3.037,0.357-3.93,0.357h-0.536v4.287h29.833v-4.287 L1037.211,141.981z" /> <path d="M64.133,103.572L64.133,103.572c-1.786-1.965-3.93-3.572-6.252-5.001s-4.823-2.68-7.503-3.751 c-2.858-1.25-5.717-2.501-8.754-3.573c-3.037-1.072-6.074-2.323-9.111-3.93c-3.394-1.608-6.074-3.752-7.86-6.253 c-1.786-2.501-2.68-5.716-2.68-9.468c0-3.573,1.429-6.789,4.109-9.29c2.68-2.501,6.074-3.751,10.004-3.751 c3.751,0,6.967,0.714,9.468,2.144c2.501,1.429,4.824,3.394,6.61,5.895c1.787,2.501,3.395,5.359,4.466,8.575 c1.25,3.215,2.144,6.431,3.216,10.004l0.178,0.357h6.074l-0.536-31.62h-5.895l-2.501,4.288c-2.68-1.608-5.538-3.037-8.754-4.288 c-3.394-1.25-7.146-1.965-11.433-1.965c-3.751,0-7.324,0.715-10.719,1.965c-3.394,1.25-6.431,3.037-8.932,5.359 c-2.68,2.322-4.824,5.002-6.252,8.039c-1.429,3.037-2.144,6.431-2.144,10.004c0,6.074,1.429,11.255,4.288,15.006 s6.967,6.967,12.148,9.289c2.68,1.251,5.716,2.502,9.29,3.752c3.573,1.25,6.789,2.501,9.646,3.752 c3.93,1.607,6.967,3.93,8.933,6.967c1.965,3.037,3.037,6.432,3.037,10.004c0,2.501-0.357,4.645-0.893,6.432 c-0.714,1.786-1.608,3.395-2.858,4.823s-3.037,2.501-5.181,3.216s-4.645,1.071-7.503,1.071c-3.93,0-7.325-0.714-10.183-2.144 c-2.858-1.43-5.538-3.395-7.682-5.896c-2.322-2.679-4.287-5.538-5.538-8.575c-1.608-3.215-2.858-6.788-3.931-10.539l-0.178-0.357 H6.252l0.894,32.334h5.895l2.68-4.466c2.858,1.786,6.252,3.216,10.183,4.466c4.109,1.251,8.218,1.965,12.327,1.965 c8.932,0,16.435-2.68,22.509-8.039c6.074-5.358,9.111-12.146,9.111-20.365c0-3.395-0.536-6.431-1.429-9.11 S66.099,105.717,64.133,103.572z" /> <path d="M81.462,96.784h4.288l0.179-0.357c0.357-1.072,0.714-2.323,1.429-3.93c0.714-1.608,1.607-3.037,2.501-4.466 c0.893-1.429,1.965-2.68,3.037-3.751c1.072-1.072,1.965-1.608,3.037-1.787c1.25-0.179,2.68-0.179,4.109-0.357 c1.429,0,2.68,0,3.751,0h2.323v54.308c0,1.25-0.179,2.145-0.715,2.858c-0.357,0.715-1.072,1.251-2.144,1.608 c-0.715,0.357-1.965,0.535-3.752,0.714c-1.786,0.179-3.215,0.357-4.108,0.357H94.86v4.288h33.049v-4.288h-0.536 c-0.893,0-2.322-0.179-4.109-0.536c-1.786-0.357-3.037-0.715-3.573-0.893c-1.072-0.357-1.787-1.072-2.144-1.787 c-0.357-0.715-0.536-1.786-0.536-2.68v-53.95h2.322c1.25,0,2.68,0,4.109,0.178c1.429,0,2.68,0.179,3.752,0.357 c0.893,0.179,1.965,0.715,3.037,1.787s2.144,2.322,3.037,3.751s1.787,2.858,2.501,4.466c0.714,1.607,1.25,2.858,1.608,3.93 l0.179,0.357h4.108V77.312H81.462V96.784z" /> <path d="M200.439,125.725c-0.357,1.43-1.429,3.752-3.037,6.789s-3.037,5.359-4.466,6.788 c-0.536,0.536-1.25,0.894-2.501,1.251c-1.251,0.357-2.501,0.535-3.752,0.715c-1.072,0.178-2.68,0.178-4.287,0.178h-4.109 c-2.68,0-4.645,0-6.074-0.178c-1.429-0.18-2.322-0.537-3.215-1.072c-0.715-0.536-1.25-1.251-1.429-2.322 c-0.357-1.072-0.357-2.68-0.357-4.645v-20.188h7.146c1.965,0,3.573,0.179,4.823,0.536c1.072,0.356,2.144,1.071,3.216,2.322 c0.536,0.714,1.072,1.965,1.607,3.573c0.536,1.607,0.894,3.215,1.072,4.823v0.536h4.466V96.963h-4.466v0.357 c-0.179,1.25-0.536,2.858-0.894,4.287c-0.536,1.43-1.072,2.68-1.786,3.573c-0.715,1.071-1.787,1.786-2.858,2.144 s-2.858,0.715-5.181,0.715h-7.146V82.136h10.183c1.787,0,3.216,0,4.645,0.178c1.429,0,2.501,0.179,3.573,0.357 c1.787,0.179,3.751,1.608,5.717,4.288c2.144,2.68,3.394,5.181,4.109,7.503l0.179,0.357h4.466V77.491H146.31v4.288h0.536 c0.893,0,1.965,0.179,3.394,0.536c1.429,0.357,2.501,0.715,3.395,1.072c1.072,0.536,1.607,1.072,1.965,1.786 c0.357,0.715,0.536,1.608,0.536,2.68v48.949c0,1.072-0.179,1.965-0.536,2.68s-1.072,1.25-1.965,1.607 c-0.357,0.18-1.072,0.357-3.037,0.536c-1.608,0.179-2.858,0.357-3.751,0.357h-0.536v4.288h57.167l1.429-21.08h-4.288 L200.439,125.725z" /> <path d="M258.499,81.957c-3.93-3.037-9.29-4.645-15.721-4.645h-31.441V81.6h0.536c0.894,0,1.787,0.179,3.037,0.357 c1.072,0.179,2.322,0.536,3.573,0.893c1.072,0.357,1.608,0.893,1.965,1.787c0.357,0.893,0.536,1.786,0.536,2.858v49.127 c0,1.071-0.179,2.144-0.536,2.858c-0.357,0.715-0.894,1.25-1.787,1.607c-0.536,0.18-1.429,0.357-2.858,0.536 s-2.501,0.357-3.394,0.357h-0.536v4.288h30.012v-4.288h-0.536c-1.25,0-2.501-0.179-3.93-0.357s-2.322-0.356-2.858-0.536 c-1.072-0.357-1.608-0.893-1.965-1.607c-0.357-0.715-0.536-1.787-0.536-2.68v-20.365h7.146c3.216,0,6.432-0.357,9.29-1.251 c2.858-0.894,5.717-2.144,8.218-3.93s4.466-4.108,5.896-6.968c1.429-2.857,2.144-6.074,2.144-9.646 C264.573,89.46,262.608,85.172,258.499,81.957z M251.353,101.25c-0.357,1.608-1.072,3.037-2.144,4.646l0,0 c-1.072,1.429-2.68,2.858-4.645,3.751c-2.144,1.072-4.823,1.608-8.217,1.608h-4.466V82.314h6.252c2.68,0,4.824,0.357,6.61,1.25 c1.787,0.715,3.216,1.965,4.288,3.395s1.787,2.858,2.144,4.823c0.357,1.787,0.715,3.751,0.715,5.359 C251.71,98.213,251.532,99.821,251.353,101.25z" /> <path d="M314.415,81.778h0.536c0.893,0,1.965,0.179,3.037,0.536c1.25,0.357,2.144,0.715,3.037,1.072 c0.894,0.357,1.608,1.072,1.965,1.786c0.357,0.715,0.536,1.608,0.536,2.501v20.187H292.62V87.316c0-1.072,0.179-1.965,0.536-2.68 c0.357-0.715,0.893-1.25,1.965-1.608c0.536-0.179,1.608-0.536,2.858-0.715c1.25-0.178,2.322-0.357,3.216-0.357h0.536v-4.288 h-29.119v4.288h0.536c0.893,0,1.965,0.179,3.037,0.536c1.251,0.357,2.144,0.715,3.037,1.072c0.894,0.357,1.608,1.072,1.965,1.787 c0.357,0.715,0.536,1.608,0.536,2.501v49.127c0,1.071-0.179,2.144-0.536,2.858c-0.357,0.715-1.072,1.25-1.965,1.607 c-0.357,0.179-1.072,0.357-2.858,0.536c-1.429,0.179-2.501,0.179-3.394,0.357h-0.536v4.288h29.119v-4.288h-0.536 c-0.715,0-1.787-0.179-3.216-0.536c-1.25-0.357-2.322-0.535-2.68-0.893c-1.072-0.537-1.608-1.072-1.965-1.787 c-0.357-0.715-0.536-1.607-0.536-2.68V113.22h30.906v23.76c0,1.071-0.179,2.144-0.536,2.858s-1.072,1.25-1.965,1.607 c-0.357,0.179-1.072,0.357-2.858,0.536c-1.429,0.179-2.501,0.179-3.395,0.357h-0.536v4.288h29.119v-4.288h-0.536 c-0.715,0-1.787-0.179-3.216-0.536c-1.25-0.357-2.322-0.535-2.68-0.893c-1.072-0.537-1.607-1.072-1.965-1.787 s-0.536-1.607-0.536-2.68V87.316c0-1.072,0.179-1.965,0.536-2.68c0.357-0.715,0.893-1.25,1.965-1.608 c0.536-0.179,1.608-0.536,2.858-0.715c1.25-0.178,2.322-0.357,3.216-0.357h0.536v-4.288h-29.119V81.778z" /> <path d="M406.596,125.725c-0.357,1.43-1.43,3.752-3.037,6.789s-3.037,5.359-4.466,6.788 c-0.536,0.536-1.251,0.894-2.501,1.251c-1.251,0.357-2.501,0.535-3.752,0.715c-1.072,0.178-2.68,0.178-4.288,0.178h-4.109 c-2.68,0-4.645,0-6.074-0.178c-1.429-0.18-2.322-0.537-3.216-1.072c-0.714-0.536-1.25-1.251-1.429-2.322 c-0.357-1.072-0.357-2.68-0.357-4.645v-20.188h7.146c1.965,0,3.573,0.179,4.824,0.536c1.072,0.356,2.144,1.071,3.037,2.322 c0.536,0.714,1.072,1.965,1.608,3.573c0.536,1.607,0.894,3.215,1.072,4.823v0.536h4.466V96.963h-4.288v0.357 c-0.179,1.25-0.536,2.858-0.893,4.287c-0.536,1.43-1.072,2.68-1.787,3.573c-0.714,1.071-1.787,1.786-2.858,2.144 s-2.858,0.715-5.181,0.715h-7.146V82.136h10.183c1.787,0,3.215,0,4.645,0.178c1.429,0,2.501,0.179,3.573,0.357 c1.786,0.179,3.751,1.608,5.716,4.288c2.144,2.68,3.395,5.181,4.109,7.503l0.179,0.357h4.466V77.491h-53.415v4.288h0.536 c0.893,0,1.965,0.179,3.394,0.536c1.429,0.357,2.501,0.715,3.395,1.072c1.072,0.536,1.608,1.072,1.965,1.786 c0.357,0.715,0.536,1.608,0.536,2.68v48.949c0,1.072-0.179,1.965-0.536,2.68c-0.357,0.715-1.072,1.25-1.965,1.607 c-0.357,0.18-1.072,0.357-3.037,0.536c-1.608,0.179-2.858,0.357-3.751,0.357h-0.536v4.288h57.167l1.429-21.08h-4.287 L406.596,125.725z" /> <path d="M460.01,81.778h0.536c1.072,0,2.501,0.357,4.467,0.893c1.965,0.536,3.394,1.072,4.287,1.608 c0.894,0.714,1.607,1.965,1.965,3.93c0.536,2.144,0.715,5.181,0.715,8.932v30.905l-37.337-50.735h-20.187V81.6h0.536 c1.071,0,2.68,0.536,4.645,1.25s3.395,1.608,4.466,2.68c0.715,0.714,1.43,1.787,1.965,3.216c0.536,1.429,0.715,2.858,0.715,4.287 v33.407c0,4.467-0.179,7.503-0.536,9.289c-0.357,1.787-1.071,3.037-2.144,3.752c-0.357,0.357-1.25,0.715-3.573,1.43 c-1.965,0.535-3.394,0.893-4.287,0.893h-0.536v4.287h28.762v-4.287h-0.535c-0.715,0-2.145-0.357-4.467-0.893 c-2.144-0.537-3.572-1.251-4.287-1.787c-0.894-0.893-1.607-2.322-2.144-4.287c-0.536-2.145-0.715-5.002-0.715-8.933V92.318 l40.374,54.665h4.823V96.784c0-3.394,0.179-6.252,0.536-8.575c0.357-2.144,1.071-3.573,2.144-4.288 c0.715-0.536,1.965-0.893,3.752-1.429c1.786-0.536,3.215-0.714,3.93-0.714h0.536v-4.288h-28.583v4.288H460.01z" /> </g> </svg> </a> </h1> <span class="pipe"></span><a href="https://writings.stephenwolfram.com" class="writings">Writings <svg viewBox="312.131 0 419.71 200"> <g id="writingsSVG"> <path d="M420.941,131.488L420.941,131.488c-2.154-0.07-4.128-1.223-5.248-3.064c-1.103-1.731-2.139-3.562-3.054-5.183 c-6.891-12.237-15.998-23.771-29.493-37.375c-4.692-4.847-10.108-8.938-16.053-12.128l-0.562-0.331 c-0.253-0.143-0.518-0.287-0.793-0.419c-1.489-0.672-1.886-0.551-1.93-0.54c-0.044,0.011-0.32,0.143-0.794,1.279 c-1.599,3.751-2.9,7.622-3.892,11.577c-0.97,3.969-1.797,8.06-2.591,12.029c-0.496,2.502-0.992,5.006-1.543,7.497l-0.066,0.353 c-0.452,2.105-1.202,5.635-5.447,5.998s-5.777-3.054-6.681-5.104c-0.612-1.382-1.128-2.804-1.543-4.256l-12.734-44.102 l-9.515-32.822c-0.188-0.662-0.419-1.312-0.662-2.007c-1.612,0.425-3.331,0.079-4.652-0.937c-1.169-1.037-1.676-2.569-1.533-4.774 c0.099-1.72,0.265-3.451,0.43-5.116c0.077-0.915,0.165-1.841,0.243-2.756c0.077-0.916,0.154-1.775,0.154-2.58 c0-1.577,0-5.767,4.575-6.538c4.829-0.816,6.362,2.205,7.167,4.961c2.602,8.923,5.175,17.85,7.718,26.781 c2.94,10.327,5.902,20.658,8.887,30.992l7.21,25.126c0-0.187,0.077-0.386,0.121-0.573c0.287-1.213,0.551-2.425,0.827-3.638 c0.893-3.947,1.819-8.038,2.855-12.04c0.585-1.913,1.412-3.743,2.458-5.447c2.205-3.958,4.686-5.16,9.118-4.41 c2.019,0.292,3.979,0.898,5.81,1.797c7.361,3.686,14.045,8.592,19.769,14.509c6.957,7.365,13.099,14.146,18.743,20.739 c2.205,2.602,4.267,5.424,6.219,8.147c0.353,0.508,0.717,1.004,1.103,1.512c-0.254-3.782-0.496-7.564-0.75-11.346 c-0.397-5.961-0.786-11.922-1.169-17.883l-0.221-3.374c-0.297-4.311-0.595-8.82-0.694-13.23c-0.209-9.173-1.742-18.401-3.22-27.332 l-0.396-2.403c-0.441-2.668-1.103-5.38-1.72-8.004c-0.475-1.985-0.971-4.035-1.378-6.086c-0.855-4.224-0.504-8.603,1.014-12.635 c0.419-1.103,1.521-4.102,4.686-4.102h0.133c2.315,0.066,3.858,1.566,4.575,4.41c0.188,0.717,0.375,1.444,0.552,2.205 c0.752,2.622,1.323,5.293,1.709,7.994l0.661,5.314c1.301,10.408,2.646,21.18,3.518,31.831c1.014,12.381,1.764,24.983,2.48,37.167 c0.279,4.483,0.551,8.975,0.815,13.473c0.375,5.942,0.75,12.261,0.948,18.512c0.09,1.93-0.381,3.845-1.355,5.513 C424.734,130.367,422.921,131.432,420.941,131.488z" /> <path d="M560.82,121.918c-3.308,0-4.686-2.635-5.248-3.704c-3.562-6.747-7.111-14.102-9.03-22.249l-0.396-1.665 c-0.771-3.241-1.576-6.615-2.117-9.923c0.013-1.077-0.841-1.965-1.918-1.996H542c-2.724-0.529-5.513-1.103-8.302-1.51 c-3.849-0.596-8.313-1.279-12.757-1.808c-1.102-0.077-2.206-0.077-3.308,0c0.177,1.323,0.342,2.547,0.519,3.782 c0.777,6.479,2.329,12.842,4.619,18.952c1.5,3.826,3.308,5.977,6.229,7.178s5.513,2.437,7.597,3.406 c0.761,0.359,1.498,0.768,2.205,1.225l1.025,0.617l1.995,1.169l-1.488,1.786c-1.442,1.78-3.745,2.627-5.998,2.205 c-3.095-0.257-6.168-0.736-9.194-1.434c-2.815-0.649-5.268-2.369-6.836-4.796c-0.562-0.86-1.169-1.698-1.819-2.569 c-0.97-1.266-1.864-2.587-2.679-3.957c-2.28-4.252-3.774-8.879-4.41-13.661c-0.552-3.473-1.103-6.946-1.731-10.496l-0.54-3.197 c-4.367-0.299-8.754-0.181-13.099,0.353l0.529,2.867c0.673,3.627,1.312,7.056,2.205,10.441c0.894,3.385,1.886,6.615,2.889,9.923 c0.849,2.768,1.731,5.635,2.514,8.49c0.348,1.506,0.507,3.051,0.475,4.598c0,0.572,0,1.102,0.065,1.676l0.1,1.367l-1.257,0.562 c-2.58,1.169-4.829,0.64-6.317-1.499l-0.529-0.75c-0.899-1.121-1.642-2.36-2.205-3.683l-0.231-0.64 c-1.687-4.531-3.429-9.229-4.752-13.991c-1.103-3.903-1.963-7.895-2.812-11.764c-0.396-1.83-0.805-3.668-1.224-5.513 c-0.133-0.551-0.287-1.103-0.463-1.687c-0.773,0.015-1.542-0.109-2.271-0.364c-1.563-0.438-2.897-1.46-3.727-2.855 c-0.364-0.772-1.301-3.473,2.304-5.722l0.1-0.066c0.385-0.28,0.824-0.475,1.29-0.573c0.849-0.143,0.959-0.166,0.706-1.852 c-0.298-1.734,0.214-3.509,1.389-4.818c1.165-1.224,2.827-1.845,4.51-1.687c3.1,0.222,5.565,2.688,5.788,5.788 c0.012,0.17,0.033,0.34,0.066,0.507c0.146,0.207,0.312,0.399,0.496,0.573c3.638,0,7.343-0.066,10.937-0.166h1.103l-0.231-2.37 c-0.253-2.79-0.529-5.678-0.849-8.49c-1.235-10.768-2.492-21.536-3.771-32.304l-0.65-5.513c-0.316-2.69-0.644-5.38-0.981-8.071 l-0.529-4.333c-0.463-3.892,1.389-6.615,4.851-7.111c1.54-0.276,3.123,0.126,4.345,1.103c1.509,1.381,2.349,3.346,2.304,5.392 c0,1.18,0,2.359,0,3.506c0,1.621,0,3.143,0.133,4.653c0.419,4.608,0.926,9.283,1.411,13.815c0.242,2.282,0.496,4.575,0.728,6.869 c0.254,2.458,0.496,4.928,0.75,7.387c0.33,3.396,0.672,6.802,1.036,10.198c0.408,3.859,0.849,7.718,1.279,11.533l0.396,3.506 l27.045,3.793c0.122-0.32,0.254-0.629,0.375-0.948c1.103-2.624,3.308-3.848,5.513-3.032c1.719,0.695,3.066,2.079,3.716,3.815 c0.425,1.399,0.695,2.841,0.805,4.3c0.066,0.606,0.133,1.213,0.231,1.808c1.673,11.613,4.4,23.049,8.148,34.168 c0.198,0.562,0.451,1.102,0.716,1.72c0.265,0.617,0.662,1.499,0.938,2.326c0.211,0.739,0.318,1.503,0.319,2.271 c0,0.286,0,0.573,0.056,0.87l0.177,1.765l-1.742,0.353C561.76,121.861,561.291,121.912,560.82,121.918z" /> <path d="M713.775,141.665h-0.783c-4.397-0.225-8.778-0.703-13.12-1.434l-1.676-0.243c-1.169-0.164-4.719-0.672-4.41-4.498 c0.045-1.053,0.538-2.036,1.356-2.701c1.103-0.882,2.745-1.102,4.994-0.771c1.314,0.244,2.645,0.391,3.98,0.441 c3.958,0,8.181,0,12.426-0.133c1.009-0.105,1.985-0.422,2.866-0.926c1.323-0.684,2.139-1.5,2.304-2.293 c0.023-1.015-0.376-1.993-1.102-2.701c-2.385-2.823-4.964-5.476-7.719-7.939c-4.686-4.266-8.621-7.64-12.392-10.617 c-9.328-7.364-16.538-14.575-21.875-22.05c-6.482-8.986-4.498-17.222,4.719-24.509c7.718-6.119,16.473-7.607,28.666-4.686 c2.836,0.819,5.523,2.084,7.961,3.749c1.499,0.737,2.562,2.139,2.866,3.782c0.231,1.995-1.103,3.594-2.139,4.619 c-1.506,1.441-3.162,2.716-4.939,3.804c-1.394,0.779-3.111,0.685-4.41-0.243c-0.896-1.023-1.271-2.402-1.015-3.738 c0.054-0.484,0.161-0.961,0.32-1.422c-0.759-0.597-1.703-0.909-2.669-0.882c-0.874-0.022-1.744-0.122-2.602-0.298l-0.794-0.132 c-5.887-0.94-11.882,0.845-16.295,4.852c-1.657,1.266-2.753,3.13-3.055,5.193c-0.005,2.044,0.827,4,2.305,5.413 c6.737,7.715,14.114,14.848,22.051,21.323c4.663,3.704,9.019,7.872,13.23,11.919c1.422,1.355,2.845,2.723,4.289,4.079 c1.154,1.159,2.128,2.486,2.888,3.937c2.01,3.247,2.394,7.245,1.037,10.815c-1.52,3.435-4.545,5.971-8.192,6.868 C719.905,141.135,716.852,141.613,713.775,141.665z" /> <path d="M449.178,120.717h-0.54c-2.794-0.27-5.002-2.486-5.26-5.281c-0.396-2.459-0.782-4.906-1.103-7.365 c-0.871-5.578-1.764-11.367-2.866-16.979c-0.882-4.476-2.205-8.997-3.451-13.374c-0.298-1.103-0.606-2.084-0.904-3.131 c-0.272-0.779-0.643-1.52-1.103-2.205c-0.242-0.43-0.484-0.871-0.705-1.301c-1.643-3.308-0.904-6.527,1.83-8.125 c1.455-0.852,3.194-1.075,4.818-0.618c1.691,0.449,3.133,1.557,4.002,3.076c0.425,0.733,0.74,1.524,0.938,2.348 c0.97,4.179,1.94,8.357,2.921,12.624c0.364-2.205,0.761-4.41,1.246-6.692c0.802-3.429,1.985-6.757,3.528-9.923 c3.528-7.442,11.963-11.235,21.488-9.658c0.86,0.137,1.691,0.416,2.459,0.827c2.078,1.004,3.285,3.222,2.999,5.513 c-0.408,3.109-3.374,3.572-4.631,3.76c-0.782,0.118-1.577,0.118-2.359,0c-0.254,0-0.519-0.066-0.783-0.077 c-6.615-0.375-8.82,1.94-10.573,6.361c-3.01,7.497-4.035,15.149-5.05,24.377c-0.342,3.175-0.375,6.482-0.407,9.691 c0,1.93,0,3.914-0.133,5.888c-0.088,1.962-0.38,3.909-0.871,5.81C454.156,118.88,451.844,120.756,449.178,120.717z" /> <path d="M546.135,59.25c-0.18,0.011-0.36,0.011-0.541,0c-1.195-0.199-2.178-1.051-2.547-2.205 c-1.289-4.091-2.514-8.093-3.506-12.128c-0.684-2.823,1.103-5.513,4.212-6.406c2.506-0.891,5.259,0.417,6.152,2.921 c0.49,1.245,0.888,2.523,1.19,3.826c0.133,0.507,0.265,1.025,0.408,1.532l0.54,1.896l-1.015,0.287c0,0.221-0.055,0.452-0.077,0.673 c-0.198,1.665-0.396,3.385-0.661,5.083c-0.184,1.078-0.618,2.097-1.268,2.977C548.365,58.657,547.29,59.231,546.135,59.25z" /> <path d="M482.981,53.561l-1.709-1.103c-4.697-2.844-5.612-7.155-6.108-10.959c-0.375-2.933,1.688-5.436,4.918-5.954 c3.23-0.519,5.512,1.025,6.174,3.859c0.904,4.013,0.177,8.048-2.205,12.348L482.981,53.561z" /> <path d="M677.094,55.876c-0.234-2.991-1.067-5.903-2.447-8.567c-1.051-2.274-3.35-3.711-5.854-3.66 c-4.201,0.022-7.277,0.97-9.714,2.988c-6.683,5.544-11.577,12.939-14.068,21.257c-3.003,9.579-4.396,19.59-4.123,29.625v1.488 c0.079,1.039,0.079,2.082,0,3.12c-0.664,0.172-1.338,0.304-2.018,0.397c-0.761,0.132-1.676,0.286-2.778,0.507 c-7.332,1.488-13.804,0.187-19.317-3.87c-5.034-3.883-9.357-8.609-12.777-13.969c-1.104-1.665-2.205-3.308-3.309-4.972 c-2.381-3.672-4.84-7.464-7.562-11.025c-2.459-3.22-5.546-5.017-8.678-5.017c-2.23,0.031-4.364,0.915-5.965,2.47 c-0.705-1.478-1.443-2.966-2.281-4.41c-1.057-1.778-2.251-3.47-3.572-5.061c-1.531-1.875-4.287-2.165-6.175-0.651 c-1.95,1.261-2.644,3.786-1.609,5.866c0.156,0.351,0.345,0.687,0.562,1.003c0.083,0.115,0.157,0.236,0.22,0.364 c0.606,1.478,1.257,2.944,1.919,4.41c1.519,3.218,2.822,6.533,3.903,9.923c3.045,10.105,4.471,20.628,4.223,31.18 c0.006,2.899,0.347,5.789,1.014,8.61c0.257,1.77,1.383,3.293,2.999,4.058c1.786,0.659,3.784,0.373,5.314-0.761 c2.012-1.247,3.07-3.586,2.679-5.92l-0.595-5.679c-0.529-5.304-1.136-10.783-1.632-16.163l-0.056-0.65 c-0.496-5.259-0.948-10.221,0.231-15.127c0.091-0.323,0.221-0.634,0.387-0.926c1.428,1.102,2.626,2.473,3.527,4.036 c4.058,7.012,9.129,15.148,16.075,22.348c7.276,7.553,16.703,10.86,27.993,9.835l7.409-0.673c0,0.1,0,0.21,0,0.309 c0.231,1.456,0.452,2.823,0.629,4.19c0.221,1.741,0.407,3.483,0.595,5.226c0.375,3.43,0.75,6.979,1.4,10.452 c1.136,6.13,2.371,12.337,3.562,18.335c1.521,7.476,3.054,15.215,4.41,22.834c0.698,4.063,0.831,8.204,0.396,12.305 c-0.118,1.707-1.104,3.235-2.612,4.046c-1.84,0.905-4.008,0.839-5.789-0.177c-1.195-0.703-2.506-1.191-3.869-1.444 c-1.101-0.138-2.206,0.21-3.029,0.952c-1.564,1.41-1.689,3.822-0.278,5.388c2.844,3.539,6.218,5.325,10.055,5.325 c0.231,0,0.452,0,0.661-0.021c2.165-0.037,4.312-0.409,6.362-1.104c3.429-1.312,7.497-3.451,8.5-8.512 c0.565-2.493,0.763-5.057,0.585-7.607c-0.529-5.469-1.225-11.874-2.404-18.423c-1.18-6.55-2.458-13.175-3.682-19.593 c-1.511-7.717-3.043-15.699-4.41-23.561l-0.122-0.694c-0.672-3.749-1.334-7.618-0.672-11.29l1.422-0.85 c1.715-0.924,3.322-2.033,4.796-3.307c3.513-3.107,6.731-6.533,9.614-10.232c1.267-1.897,2.209-3.991,2.79-6.196 c0.297-0.893,0.562-1.731,0.882-2.547C674.238,77.376,677.832,67.145,677.094,55.876z M665.771,69.735l-1.411,3.914 c-1.532,4.245-3.109,8.644-4.752,12.922c-1.693,4.485-4.831,8.278-8.92,10.783c-0.011-0.118-0.011-0.235,0-0.353 c0.232-11.874,1.896-21.125,5.271-29.107c2.58-6.031,6.186-10.287,11.025-12.977c0.471,0.565,0.693,1.297,0.617,2.028 C667.788,61.286,667.168,65.623,665.771,69.735z" /> </g> </svg> </a> <nav id="nav"> <ul> <li> <ul class="links"> <li class="about"><a href="//www.stephenwolfram.com/about/">ABOUT</a></li> <li class="blog"><a href="//writings.stephenwolfram.com">WRITINGS</a></li> <li class="publications"><a href="//www.stephenwolfram.com/publications/">PUBLICATIONS</a></li> <li class="media"><a href="//www.stephenwolfram.com/media/">MEDIA</a></li> <li class="scrapbook"><a href="//www.stephenwolfram.com/scrapbook/">SCRAPBOOK</a></li> <li class="contact"><a href="//www.stephenwolfram.com/contact/">CONTACT</a></li> </ul> </li> <li> <ul class="social"> <li><a class="twitter" href="//x.com/stephen_wolfram" class="big-social-icon twitter" title="X" target="_blank"></a></li> <li><a class="facebook" href="//www.facebook.com/Stephen-Wolfram-188916357807416/" class="big-social-icon facebook" title="Facebook" target="_blank"></a></li> <li><a class="linkedin" href="//www.linkedin.com/in/stephenwolfram" class="big-social-icon linkedin" title="LinkedIn" target="_blank"></a></li> <li><a class="soundcloud" href="https://soundcloud.com/stephenwolfram/" class="big-social-icon soundcloud" title="SoundCloud" target="_blank"></a></li> <li><a class="twitch" href="https://www.twitch.tv/stephen_wolfram" class="big-social-icon twitch" title="Twitch" target="_blank"></a></li> </ul> </li> </ul> </nav> </div> <div class="stripe"></div> </header> <script> $('.hamburger').click(function(e){ e.stopPropagation(); $('.links').toggleClass('show'); $('#header > .inner').toggleClass('open'); if($('.overlay').length < 1 && !$('.links').hasClass('hide')) { $('#header').append('<div class="overlay">'); } else { $('.overlay').remove(); } }); $('body').click(function(){ $('.links').removeClass('show'); $('.overlay').remove(); $('#header > .inner').removeClass('open'); }); </script> <div class="writings-sidebar-additions"> <div class="inner"> <div class="sidebar-additions"> <div class="recent-categories"><a href="https://writings.stephenwolfram.com">Recent</a> | <div class="categories-list-wrapper"> <button class="categories">Categories</button> <div class="categories-list-menu hide"> <ul class="categories-list"> <li><a href="/category/artificial-intelligence">Artificial Intelligence</a></li><li><a href="/category/big-picture">Big Picture</a></li><li><a href="/category/companies-and-business">Companies &amp; Business</a></li><li><a href="/category/computational-science">Computational Science</a></li><li><a href="/category/computational-thinking">Computational Thinking</a></li><li><a href="/category/data-science">Data Science</a></li><li><a href="/category/education">Education</a></li><li><a href="/category/future-perspectives">Future Perspectives</a></li><li><a href="/category/historical-perspectives">Historical Perspectives</a></li><li><a href="/category/language-and-communication">Language &amp; Communication</a></li><li><a href="/category/life-and-times">Life &amp; Times</a></li><li><a href="/category/life-science">Life Science</a></li><li><a href="/category/mathematica">Mathematica</a></li><li><a href="/category/mathematics">Mathematics</a></li><li><a href="/category/new-kind-of-science">New Kind of Science</a></li><li><a href="/category/new-technology">New Technology</a></li><li><a href="/category/personal-analytics">Personal Analytics</a></li><li><a href="/category/philosophy">Philosophy</a></li><li><a href="/category/physics">Physics</a></li><li><a href="/category/ruliology">Ruliology</a></li><li><a href="/category/software-design">Software Design</a></li><li><a href="/category/wolfram-alpha">Wolfram|Alpha</a></li><li><a href="/category/wolfram-language">Wolfram Language</a></li><li><a href="/category/other">Other</a></li> </ul> </div> </div> </div> <span class="pipe">|</span> <form class="search-link" method="get" action="https://writings.stephenwolfram.com/"> <svg version="1.0" class="search-button" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px" viewBox="0 0 18.2 18.5" enable-background="new 0 0 18.2 18.5" xml:space="preserve"> <g> <path class="circle" fill="#c42c1f" d="M7.7,14.2H7.6c-3.6,0-6.5-2.9-6.5-6.4V7.7c0-3.5,2.9-6.4,6.5-6.4h0.1 c3.6,0,6.5,2.9,6.5,6.4v0.1C14.2,11.3,11.3,14.2,7.7,14.2z M7.6,2.5c-2.9,0-5.2,2.3-5.2,5.1v0.1c0,2.8,2.3,5.1,5.2,5.1h0.1 c2.9,0,5.2-2.3,5.2-5.1V7.7C12.9,4.8,10.6,2.5,7.6,2.5L7.6,2.5z" /> <g> <path class="handle" fill="#c42c1f" d="M16.8,15.4l-4.4-4.4l-1.5,1.6l4.4,4.5c0.2,0.2,0.5,0.3,0.7,0.3s0.5-0.1,0.7-0.3 C17.2,16.5,17.2,15.8,16.8,15.4z" /> </g> </g> </svg> <input class="search-field hide" type="text" value="" name="s" placeholder="Search Writings" /> <span class="close hide">&times;</span> </form> </div> </div> </div> <div class="inner"> <div id="content"><script type="text/javascript"> $(document).ready(function() { $("#join-small").addClass('join-small-js'); $("#exit-button").addClass('exit-button-js'); $("#respond").addClass('respond-js'); }); </script> <article id="postid-1515" > <h1 class="blog-post-title">Wolfram|Alpha Comes Alive with CDF</h1> <time class="date" datetime="2011-08-11">August 11, 2011</time> <div class="post_content" > <p>Two weeks ago we made a major announcement: building on technology that we&#8217;ve been developing for more than 20 years, we released <a href="http://www.wolfram.com/cdf" target="_self">Computable Document Format (CDF)</a>. I think CDF is going to have a big effect on the way all sorts of things can be  communicated. Because for the first time it makes it practical to include live computation as a routine part of a document.</p> <p>There are many important applications of CDF that we’ll no doubt be seeing over the months and years to come. But today I&#8217;m pleased to announce an experimental one from us: <a href="http://www.wolframalpha.com/cdf-experiment/" target="_self">Wolfram|Alpha with CDF</a>.</p> <p><a href="http://www.wolframalpha.com/input/?i=sin%28|x|%29^|x|" class="cdf-example-link"><img src="https://content.wolfram.com/sites/43/2011/08/image-11.jpg" alt="sin(|x|)^|x|" title="sin(|x|)^|x|" width="500" height="530" style="border:0px" class="aligncenter size-full wp-image-1604" srcset="https://content.wolfram.com/sites/43/2011/08/image-11.jpg 500w, https://content.wolfram.com/sites/43/2011/08/image-11-283x300.jpg 283w" sizes="(max-width: 500px) 100vw, 500px" /></a></p> <p>Starting today, as soon as you have the free <a href="http://www.wolfram.com/cdf-player/" target="_self">CDF plugin</a> installed (or if you have <a href="http://www.wolfram.com/mathematica/" target="_self"><em>Mathematica</em> 8</a> on your system) you can go to the top right-hand corner of the Wolfram|Alpha website, and set CDF on, with the result that Wolfram|Alpha will generate not just a static web page, but instead full CDF output&#8212;that you can directly interact and compute with.<span id="more-1515"></span></p> <p>There are some immediate consequences—like rotating 3D graphics, interactively reading off values in plots, and resizing graphics inline.</p> <p>But where Wolfram|Alpha with CDF really starts to get exciting is in letting you interactively manipulate parameters—and actually do computations right inside your browser. Wolfram|Alpha without CDF might just give you one particular plot. Wolfram|Alpha with CDF will automatically  sprout sliders or other controls that let you immediately change parameters, and continuously update the plot.</p> <p><a href="http://www.wolframalpha.com/input/?i=y%27%27+-+cosx+y+%3D+x" class="cdf-example-link"><img class="aligncenter size-full wp-image-1561" style="border:0px" title="y'' - cosx y = x" src="https://content.wolfram.com/sites/43/2011/08/image-2.jpg" alt="y'' - cosx y = x" width="500" height="418" /></a></p> <p>Sometimes being able to change parameters dynamically just enriches what is already rather complete output. But often, it&#8217;s what really makes the output meaningful. Like when Wolfram|Alpha with CDF gives you controls for image processing, that let you interactively pick different features in an image.</p> <p><a href="http://www.wolframalpha.com/input/?i=edge+detect+Abraham+Lincoln+image+with+radius+x" class="cdf-example-link"><img class="aligncenter size-full wp-image-1563" style="border:0px" title="Edge detect Abraham Lincoln image with radius x" src="https://content.wolfram.com/sites/43/2011/08/image-3.jpg" alt="Edge detect Abraham Lincoln image with radius x" width="500" height="375" srcset="https://content.wolfram.com/sites/43/2011/08/image-3.jpg 500w, https://content.wolfram.com/sites/43/2011/08/image-3-300x225.jpg 300w" sizes="(max-width: 500px) 100vw, 500px" /></a></p> <p>Or when Wolfram|Alpha with CDF dynamically shows you the behavior of some simulated system.</p> <p><a href="http://www.wolframalpha.com/input/?i=Double+pendulum" class="cdf-example-link"><img class="aligncenter size-full wp-image-1567" style="border:0px" title="Double pendulum" src="https://content.wolfram.com/sites/43/2011/08/image-4.jpg" alt="Double pendulum" width="500" height="354" srcset="https://content.wolfram.com/sites/43/2011/08/image-4.jpg 500w, https://content.wolfram.com/sites/43/2011/08/image-4-300x212.jpg 300w" sizes="(max-width: 500px) 100vw, 500px" /></a></p> <p>Usually Wolfram|Alpha with CDF will start off by showing you a fairly simple set of controls. But often there&#8217;s a + you can press to open up a much more sophisticated &#8220;control panel&#8221; that allows you to change all sorts of features and parameters in a computation.</p> <p><a href="http://www.wolframalpha.com/input/?i=sinz+%2B+1%2F2+sin2z" class="cdf-example-link"><img class="aligncenter size-full wp-image-1569" style="border:0px" title="sin(z) + 1/2 sin(2z)" src="https://content.wolfram.com/sites/43/2011/08/image-5.jpg" alt="sin(z) + 1/2 sin(2z)" width="500" height="390" /></a></p> <p>Some of what Wolfram|Alpha with CDF does is to give enhanced interactive versions of results you&#8217;d already see some version of even without CDF. But we&#8217;re experimenting with all sorts of completely new kinds of results that only exist in interactive CDF form.</p> <p><a href="http://www.wolframalpha.com/input/?i=sin%28z%29" class="cdf-example-link"><img class="aligncenter size-full wp-image-1570" style="border:0px" title="sin(z)" src="https://content.wolfram.com/sites/43/2011/08/image-6.jpg" alt="sin(z)" width="500" height="373" srcset="https://content.wolfram.com/sites/43/2011/08/image-6.jpg 500w, https://content.wolfram.com/sites/43/2011/08/image-6-300x223.jpg 300w" sizes="(max-width: 500px) 100vw, 500px" /></a></p> <p>So how does Wolfram|Alpha with CDF work? What&#8217;s happening is that instead of the Wolfram|Alpha servers sending you HTML to be rendered by your web browser, they&#8217;re sending CDF, which in effect contains dynamically generated programs to be executed by your CDF plugin.</p> <p>It&#8217;s an interesting and powerful technology stack—all ultimately based on the <a href="http://www.wolfram.com/mathematica/" target="_self"><em>Mathematica</em></a> language. Your query comes in to the Wolfram|Alpha servers, where it&#8217;s processed using lots of <em>Mathematica</em> code—that ultimately generates a result consisting of a chunk of CDF. Then that CDF is sent to your computer, where it runs using the <em>Mathematica</em> kernel—but now under your control, locally inside your CDF plugin.</p> <p>The result of this is that you get the best of both worlds. You have access to both large-scale computational power and stored knowledge in the main Wolfram|Alpha servers, and you get highly responsive interaction from local computations on your computer.</p> <p><a href="http://www.wolframalpha.com/input/?i=All+visible+satellites" class="cdf-example-link"><img class="aligncenter size-full wp-image-1573" title="All visible satellites" src="https://content.wolfram.com/sites/43/2011/08/image-7.jpg" alt="All visible satellites" width="500" height="426" style="border:0px" srcset="https://content.wolfram.com/sites/43/2011/08/image-7.jpg 500w, https://content.wolfram.com/sites/43/2011/08/image-7-300x255.jpg 300w" sizes="(max-width: 500px) 100vw, 500px" /></a></p> <p>And what makes this possible is that by being based on the <em>Mathematica</em> language, CDF is able to describe high-level algorithmic processes in a standard way that can readily be delivered to your computer.</p> <p>If one looks at different applications of CDF, some typically involve human authoring of CDF—say to create interactive Demonstrations of the kind in the <a href="http://demonstrations.wolfram.com/" target="_self">Wolfram Demonstrations Project</a>. But other applications involve automatic generation of CDF—say in producing interactive reports.</p> <p>And in a sense, Wolfram|Alpha with CDF is the beginning of the ultimate kind of automatic CDF generation. You start from simple free-form linguistics, and Wolfram|Alpha automatically generates CDF for whatever you describe.</p> <p>We&#8217;re only at the early stages of this right now. But already what we have is very useful—if nothing else in producing the core of what&#8217;s needed for a particular interactive CDF document.</p> <p>I don&#8217;t want to confuse the technology stack even further—but there&#8217;s a case of Wolfram|Alpha with CDF that is in some ways even more powerful: Wolfram|Alpha with CDF not in a web browser, but inside <em>Mathematica</em>.</p> <p>In a sense, this is an extension of the <a href="http://www.wolfram.com/mathematica/new-in-8/free-form-linguistic-input/" target="_self">free-form linguistic programming</a> that we introduced last year with <a href="http://www.wolfram.com/mathematica/" target="_self"><em>Mathematica</em> 8</a>. But what&#8217;s new is that one&#8217;s now starting to be able to go directly from free-form linguistics to complete interactive <em>Mathematica</em> programs that involve constructs like <a href="http://reference.wolfram.com/mathematica/ref/Manipulate.html" target="_self"><tt>Manipulate</tt></a>.</p> <p><a href="http://www.wolframalpha.com/input/?i=vary+c+in+cos%28cx%29%3Dx" class="cdf-example-link"><img src="https://content.wolfram.com/sites/43/2011/08/image-8-1.jpg" alt="vary c in cos(cx)=x" title="vary c in cos(cx)=x" width="500" height="415" style="border:0px" class="aligncenter size-full wp-image-1607" srcset="https://content.wolfram.com/sites/43/2011/08/image-8-1.jpg 500w, https://content.wolfram.com/sites/43/2011/08/image-8-1-300x249.jpg 300w" sizes="(max-width: 500px) 100vw, 500px" /></a></p> <p>For me, it&#8217;s fascinating and exciting to see these kinds of unifications in these different forms of technology that we&#8217;ve been developing for so long. And every time we do such a unification, it opens up all sorts of new possibilities that we could barely imagine before. But today&#8217;s Wolfram|Alpha with CDF is just the beginning. Over the next several months, we&#8217;ll be introducing all sorts of enhancements.</p> <p>For example, as of now you have to choose to get either all-HTML output from Wolfram|Alpha or all CDF. If you choose HTML, you get to make use of the full range of optimizations in your web browser. If you choose CDF, you get to have computable CDF output that you can interact with.  In the future, CDF will automatically be interspersed with HTML, so you can get the best of both worlds.</p> <p>And right now, there are only particular kinds of Wolfram|Alpha output that use dynamic interactivity with CDF. In the future, there&#8217;ll be broader coverage—so that absolutely anything that could reasonably be interactive will automatically be so.</p> <p>But already today it&#8217;s exciting to see Wolfram|Alpha begin to come alive with interactive CDF output. Let us know what you think of it!</p> </div> <div class="post_foot single"> <div class="category"> <div class="citingsOuterWrapper"> <div class="citingsInnerWrapper"> <button type="button" class="citingsOpenButton"> <span class="citingsOpenButtonText">Cite this as</span> </button> <button type="button" class="citingsCloseButton"> <div class="citingsCloseButtonIcon"></div> </button><span class="citingClosedPlainText citingText wolfram-c2c-wrapper" data-C2C-Inline="Stephen Wolfram (2011), &quot;Wolfram|Alpha Comes Alive with CDF,&quot; Stephen Wolfram Writings. writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf." data-C2C-type="text/plain">Stephen Wolfram (2011), &quot;Wolfram|Alpha Comes Alive with CDF,&quot; Stephen Wolfram Writings. writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf.</span><div class="citing"><div class="citingType">Text</div><div class="citingText wolfram-c2c-wrapper" data-C2C-Inline="Stephen Wolfram (2011), &quot;Wolfram|Alpha Comes Alive with CDF,&quot; Stephen Wolfram Writings. writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf." data-C2C-type="text/plain">Stephen Wolfram (2011), &quot;Wolfram|Alpha Comes Alive with CDF,&quot; Stephen Wolfram Writings. writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf.</div></div><div class="citing"><div class="citingType">CMS</div><div class="citingText wolfram-c2c-wrapper" data-C2C-Inline="Wolfram, Stephen. &quot;Wolfram|Alpha Comes Alive with CDF.&quot; Stephen Wolfram Writings. August 11, 2011. writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf." data-C2C-type="text/plain">Wolfram, Stephen. &quot;Wolfram|Alpha Comes Alive with CDF.&quot; Stephen Wolfram Writings. August 11, 2011. writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf.</div></div><div class="citing"><div class="citingType">APA</div><div class="citingText wolfram-c2c-wrapper" data-C2C-Inline="Wolfram, S. (2011, August 11). Wolfram|Alpha comes alive with CDF. Stephen Wolfram Writings. writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf." data-C2C-type="text/plain">Wolfram, S. (2011, August 11). Wolfram|Alpha comes alive with CDF. Stephen Wolfram Writings. writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf.</div></div> </div> <div class="citingsShowSpacer"></div></div> <p>Posted in: <a href="https://writings.stephenwolfram.com/category/new-technology/" rel="category tag">New Technology</a>, <a href="https://writings.stephenwolfram.com/category/wolfram-alpha/" rel="category tag">Wolfram|Alpha</a></p> </div> </div> <div id="comments_wrapper"> <span id="comments"></span> <div id="respond"> <!-- <h3 class="comments-heading"><div class="cancel-comment-reply"><a rel="nofollow" id="cancel-comment-reply-link" href="/2011/08/wolframalpha-comes-alive-with-cdf/#respond" style="display:none;">cancel [x]</a></div></h3> --> <div id="join-small"> <input type="text" id="fakeComment" placeholder="Join the discussion"> </div> <form action="https://writings.stephenwolfram.com/wp-comments-post.php" method="post" id="commentform"> <div id="join-big"> <div id="exit-button"><div id="exit-image"></div><div style="clear: both;"></div></div> <div id="comment-area"> <textarea name="comment" id="comment" tabindex="1"></textarea> <p><span id="commentError" style="display:none">Please enter your comment (at least 5 characters).</span></p> </div> <div class="level"> <div class="half-length"><label for="author">Name (required)</label></div> <div class="half-length "><div class="pad-left"><label for="email">Email (will not be published; required)</label></div></div> <div style="clear:both;"></div> </div> <div> <div class="half-length"><input type="text" name="author" id="author" value="" size="22" tabindex="2" aria-required='true' /><p><span id="nameError" style="display:none">Please enter your name.</span></p></div> <div class="half-length "><div class="pad-left"><input type="text" name="email" id="email" value="" size="22" tabindex="3" aria-required='true' /></div> <p><span id="emailError" style="margin-left: 10px; display:none">Please&nbsp;enter&nbsp;a&nbsp;valid&nbsp;email&nbsp;address.</span></p></div> <div style="clear:both;"></div> </div> <div class="level"> <div class="half-length"><label for="url">Website</label></div> <div style="clear:both;"></div> <div class="half-length"><input type="text" name="url" id="url" value="" size="22" tabindex="4" /></div> <div style="clear:both;"></div> <p><input name="submit" type="submit" id="submit" class="button" tabindex="5" value="Submit comment &raquo;" onclick="return checkCommentFields()" /></p> <div style="clear:both;"></div> </div> <div class="post_separator_no_margin"></div> </div> <h3 id="comments-heading"> <span class="expand-collapse expand"></span> 14 comments </h3> <div id="comment-section"> <div class="comment-nav"> <div class="nav-left"></div> <div class="nav-right"></div> </div> <ol class="commentlist"> <li class="comment even thread-even depth-1" id="li-comment-1041"> <div id="comment-1041" class="comment-content"> <div class="comment-content-body"> <p>This is amazing, thank you for making the internet and me smarter 🙂<br /> I love Wolfram Alpha!</p> </div> <div class="comment-meta comment-byline">Mat</div> <div class="comment-meta comment-date"><a class="comment-permlink" href="https://writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf/#comment-1041">August 11, 2011 at 5:47 pm</a></div> </div> </li><!-- #comment-## --> <li class="comment odd alt thread-odd thread-alt depth-1" id="li-comment-1042"> <div id="comment-1042" class="comment-content"> <div class="comment-content-body"> <p>This is amazing! Great work, this is really exciting. I think this has so much potential to help students intuitively understand certain mathematical operations and functions, in a way that was previously very difficult. Applying it that way reminds me a bit of the Kill Math project (<a href="http://worrydream.com/KillMath/" rel="nofollow">http://worrydream.com/KillMath/</a>) (no affiliation). Anyway, thanks for the great work &#8211; I&#8217;ll be sure to play around with this.</p> </div> <div class="comment-meta comment-byline">Justin Mares</div> <div class="comment-meta comment-date"><a class="comment-permlink" href="https://writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf/#comment-1042">August 11, 2011 at 10:43 pm</a></div> </div> </li><!-- #comment-## --> <li class="comment even thread-even depth-1" id="li-comment-1045"> <div id="comment-1045" class="comment-content"> <div class="comment-content-body"> <p>Wow!!! This is just what was needed!<br /> I&#8217;ll start using this today.</p> </div> <div class="comment-meta comment-byline"><a href='http://RiversideComputer.COM' rel='external nofollow' class='url'>Dave Scharffenberg</a></div> <div class="comment-meta comment-date"><a class="comment-permlink" href="https://writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf/#comment-1045">August 12, 2011 at 8:58 am</a></div> </div> </li><!-- #comment-## --> <li class="comment odd alt thread-odd thread-alt depth-1" id="li-comment-1046"> <div id="comment-1046" class="comment-content"> <div class="comment-content-body"> <p>As Stephen notes above, Mathematica 8 makes free-form linguistics an integral part of longer computations inside Mathematica notebooks, see also <a href="http://blog.stephenwolfram.com/2010/11/the-free-form-linguistics-revolution-in-mathematica/" rel="nofollow">http://blog.stephenwolfram.com/2010/11/the-free-form-linguistics-revolution-in-mathematica/</a> . The Wolfram|Alpha-CDF unification may effectively permit free-form linguistic input to CDF documents outside of Mathematica. As a rather contrived though perhaps instructive example, a text editor could be created by inputing text into Wolfram|Alpha, which outputs a CDF, manipulating CDF locators to move words around, and feeding the CDF back into Wolfram|Alpha along with text additions, which outputs an updated CDF, and so forth cycling through Wolfram|Alpha input, CDF output, CDF manipulation, and re-input to Wolfram|Alpha. Even without this fancy stuff, free access to the unified Wolfram|Alpha input and CDF output adds the enormous appeal of free-form linguistics to CDF document applications. This new unified Wolfram|Alpha-CDF interface will surely help popularize CDF and build business for free-form linguistic input in Mathematica notebooks, which underlie CDF technology.</p> </div> <div class="comment-meta comment-byline"><a href='http://www.appliednewscience.com' rel='external nofollow' class='url'>Christopher Haydock</a></div> <div class="comment-meta comment-date"><a class="comment-permlink" href="https://writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf/#comment-1046">August 12, 2011 at 3:17 pm</a></div> </div> </li><!-- #comment-## --> <li class="comment even thread-even depth-1" id="li-comment-1067"> <div id="comment-1067" class="comment-content"> <div class="comment-content-body"> <p>Single execuable(.exe) &#8211; All Languages Support for Content<br /> &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;</p> <p>In a single Mathematica ver 8.0 Software Application (.exe) giving a choice of selecting Languages in drop down list.</p> <p>Drop down list i mean is a combo box giving choice of selecting Languages which is the first form &#8211; Startup (Similar to a Home Page in Web site) while running the executable (.exe).<br /> The default content for selecting a choice of language will be English.</p> <p>For example if the end user selects English from drop down list, the user will be redirected to English version and the subsequent forms will be English content</p> <p>For example if the end user selects French from drop down list, the user will be redirected to French version and the subsequent forms will be French content</p> <p>For example if the end user selects German from drop down list, the user will be redirected to German version and the subsequent forms will be German content</p> <p>and so on for different languages …..</p> <p>Thanks &amp; Regards,<br /> Prashant S Akerkar.</p> </div> <div class="comment-meta comment-byline"><a href='http://www.linkedin.com/in/prashantakerkar' rel='external nofollow' class='url'>Prashant S Akerkar</a></div> <div class="comment-meta comment-date"><a class="comment-permlink" href="https://writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf/#comment-1067">August 21, 2011 at 3:12 pm</a></div> </div> </li><!-- #comment-## --> <li class="comment odd alt thread-odd thread-alt depth-1" id="li-comment-1431"> <div id="comment-1431" class="comment-content"> <div class="comment-content-body"> <p>How did we live in the past?</p> </div> <div class="comment-meta comment-byline">Ken McDougall</div> <div class="comment-meta comment-date"><a class="comment-permlink" href="https://writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf/#comment-1431">October 16, 2011 at 10:48 am</a></div> </div> </li><!-- #comment-## --> <li class="comment even thread-even depth-1" id="li-comment-1447"> <div id="comment-1447" class="comment-content"> <div class="comment-content-body"> <p>Mathematica blows my mind. There should be a Nobel Prize for the whole company. This is the future of textbooks.</p> </div> <div class="comment-meta comment-byline">Stephen</div> <div class="comment-meta comment-date"><a class="comment-permlink" href="https://writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf/#comment-1447">October 18, 2011 at 12:36 pm</a></div> </div> </li><!-- #comment-## --> <li class="comment odd alt thread-odd thread-alt depth-1" id="li-comment-1486"> <div id="comment-1486" class="comment-content"> <div class="comment-content-body"> <p>OMG. You guys are so awesome. You guys made a guys dream come to life.</p> </div> <div class="comment-meta comment-byline"><a href='http://popgigs.com' rel='external nofollow' class='url'>McH</a></div> <div class="comment-meta comment-date"><a class="comment-permlink" href="https://writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf/#comment-1486">November 1, 2011 at 12:34 am</a></div> </div> </li><!-- #comment-## --> <li class="comment even thread-even depth-1" id="li-comment-1507"> <div id="comment-1507" class="comment-content"> <div class="comment-content-body"> <p>Wow, i officially fell in love. Thank you!</p> </div> <div class="comment-meta comment-byline">Daniella Scheers</div> <div class="comment-meta comment-date"><a class="comment-permlink" href="https://writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf/#comment-1507">November 10, 2011 at 5:31 pm</a></div> </div> </li><!-- #comment-## --> <li class="comment odd alt thread-odd thread-alt depth-1" id="li-comment-1519"> <div id="comment-1519" class="comment-content"> <div class="comment-content-body"> <p>Thank you so much, you&#8217;re helping bring us closer to the eschaton. I&#8217;m very excited to see what breath-taking revelations the future holds.</p> </div> <div class="comment-meta comment-byline"><a href='http://www.my-big-toe.com' rel='external nofollow' class='url'>Scott Douglas</a></div> <div class="comment-meta comment-date"><a class="comment-permlink" href="https://writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf/#comment-1519">November 17, 2011 at 2:35 am</a></div> </div> </li><!-- #comment-## --> <li class="comment even thread-even depth-1" id="li-comment-1531"> <div id="comment-1531" class="comment-content"> <div class="comment-content-body"> <p>wooooo! amazing!!!! Guys! you&#8217;re crazy!!! I love your cool stuff! and the CDF plugin idea rocks! 🙂 </p> <p>Good luck Wolfram team and keep up the good work!!!! 😛</p> </div> <div class="comment-meta comment-byline">Daniel Flores</div> <div class="comment-meta comment-date"><a class="comment-permlink" href="https://writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf/#comment-1531">November 22, 2011 at 1:38 am</a></div> </div> </li><!-- #comment-## --> <li class="comment odd alt thread-odd thread-alt depth-1" id="li-comment-1556"> <div id="comment-1556" class="comment-content"> <div class="comment-content-body"> <p>Thank you very, very, very much for developing this milestone in human evolution.</p> </div> <div class="comment-meta comment-byline"><a href='http://www.azuredraco.com' rel='external nofollow' class='url'>Azure</a></div> <div class="comment-meta comment-date"><a class="comment-permlink" href="https://writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf/#comment-1556">December 2, 2011 at 3:18 pm</a></div> </div> </li><!-- #comment-## --> <li class="comment even thread-even depth-1" id="li-comment-2248"> <div id="comment-2248" class="comment-content"> <div class="comment-content-body"> <p>hello</p> <p>i know how much I sleeb and how healthy I am. Do I really need a graphic who tells me how fit I am?</p> <p>but interesting anyway 🙂</p> </div> <div class="comment-meta comment-byline">stingelin</div> <div class="comment-meta comment-date"><a class="comment-permlink" href="https://writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf/#comment-2248">March 12, 2012 at 3:11 am</a></div> </div> </li><!-- #comment-## --> <li class="comment odd alt thread-odd thread-alt depth-1" id="li-comment-5535"> <div id="comment-5535" class="comment-content"> <div class="comment-content-body"> <p>Wolfram/Alpha currently works on its own database of curated information. I can&#8217;t wait for the day when you can apply your technology to the entire uncurated database that is the Internet.</p> </div> <div class="comment-meta comment-byline">Kameike</div> <div class="comment-meta comment-date"><a class="comment-permlink" href="https://writings.stephenwolfram.com/2011/08/wolframalpha-comes-alive-with-cdf/#comment-5535">June 13, 2012 at 5:55 pm</a></div> </div> </li><!-- #comment-## --> </ol> <div class="comment-nav"> <div class="nav-left"></div> <div class="nav-right"></div> </div> </div> <input type='hidden' name='comment_post_ID' value='1515' id='comment_post_ID' /> <input type='hidden' name='comment_parent' id='comment_parent' value='0' /> <p style="display: none;"><input type="hidden" id="akismet_comment_nonce" name="akismet_comment_nonce" value="077347b9ac" /></p><p style="display: none;"><input type="hidden" id="ak_js" name="ak_js" value="27"/></p> </form> </div><!-- respond --> </div><!-- wrapper --> <script type="text/javascript"> function checkCommentFields() { if($(".socialLoggedIn").is(":visible")) return true; var ret = true; if($("#author").val().trim().length < 2) { $("#nameError").fadeIn(); ret = false; } else { $("#nameError").fadeOut(); } if(!validEmail($("#email").val().trim())) { $("#emailError").fadeIn(); ret = false; } else { $("#emailError").fadeOut(); } if($("#comment").val().trim().length < 5) { $("#commentError").fadeIn(); ret = false; } else { $("#commentError").fadeOut(); } return ret; } $(document).ready(function(){ $('.comment-author a').attr("target", "_blank"); if(window.location.href.indexOf("comment-page-1") > -1) { $('#comment-section').removeClass('hide'); } $("#author").keyup(function() { if($("#nameError").is(":visible") && $("#author").val().trim().length >= 2) $("#nameError").fadeOut(); }); $("#email").keyup(function() { if($("#emailError").is(":visible") && validEmail($("#email").val().trim())) $("#emailError").fadeOut(); }); $("#comment").keyup(function() { if($("#commentError").is(":visible") && $("#comment").val().trim().length >= 5) $("#commentError").fadeOut(); }); }); function validEmail(email) { signPos = email.indexOf("@"); dotPos = email.lastIndexOf("."); if (email.length < 6 || signPos == -1 || dotPos == -1 || (dotPos < signPos) || (dotPos - signPos == 1) || dotPos == email.length-1 ) { return false; } return true; } </script> <div id="footer_recent_posts"> <p class="sidebar-heading">Related Writings</p> <div class="sidebar_post_wrapper"> <div class="sidebar_thumbnail"> <a href="https://writings.stephenwolfram.com/2024/07/yet-more-new-ideas-and-new-functions-launching-version-14-1-of-wolfram-language-mathematica/" rel="bookmark" title="Permanent Link to Yet More New Ideas and New Functions: Launching Version 14.1 of Wolfram Language &#038; Mathematica" > <img width="128" height="108" src="https://content.wolfram.com/sites/43/2024/07/swblog-v14.1-icon.png" class="lazy wp-post-image" alt="" title="" /> </a> </div> <div class="sidebar_post"> <p><a href="https://writings.stephenwolfram.com/2024/07/yet-more-new-ideas-and-new-functions-launching-version-14-1-of-wolfram-language-mathematica/" rel="bookmark" title="Permanent Link to Yet More New Ideas and New Functions: Launching Version 14.1 of Wolfram Language &#038; Mathematica" >Yet More New Ideas and New Functions: Launching Version 14.1 of Wolfram Language &#038; Mathematica</a></p> <p><time datetime="2024-07-31">July 31, 2024</time></p> </div> </div> <div class="sidebar_post_wrapper"> <div class="sidebar_thumbnail"> <a href="https://writings.stephenwolfram.com/2024/01/the-story-continues-announcing-version-14-of-wolfram-language-and-mathematica/" rel="bookmark" title="Permanent Link to The Story Continues: Announcing Version 14 of Wolfram Language and Mathematica" > <img width="128" height="108" src="https://content.wolfram.com/sites/43/2024/01/swblog-v14.0-icon.png" class="lazy wp-post-image" alt="" title="" /> </a> </div> <div class="sidebar_post"> <p><a href="https://writings.stephenwolfram.com/2024/01/the-story-continues-announcing-version-14-of-wolfram-language-and-mathematica/" rel="bookmark" title="Permanent Link to The Story Continues: Announcing Version 14 of Wolfram Language and Mathematica" >The Story Continues: Announcing Version 14 of Wolfram Language and Mathematica</a></p> <p><time datetime="2024-01-09">January 9, 2024</time></p> </div> </div> <div class="sidebar_post_wrapper"> <div class="sidebar_thumbnail"> <a href="https://writings.stephenwolfram.com/2023/07/generative-ai-space-and-the-mental-imagery-of-alien-minds/" rel="bookmark" title="Permanent Link to Generative AI Space and the Mental Imagery of Alien Minds" > <img width="128" height="108" src="https://content.wolfram.com/sites/43/2023/07/ai-aliens-icon.png" class="lazy wp-post-image" alt="" title="" /> </a> </div> <div class="sidebar_post"> <p><a href="https://writings.stephenwolfram.com/2023/07/generative-ai-space-and-the-mental-imagery-of-alien-minds/" rel="bookmark" title="Permanent Link to Generative AI Space and the Mental Imagery of Alien Minds" >Generative AI Space and the Mental Imagery of Alien Minds</a></p> <p><time datetime="2023-07-17">July 17, 2023</time></p> </div> </div> <div class="sidebar_post_wrapper"> <div class="sidebar_thumbnail"> <a href="https://writings.stephenwolfram.com/2023/06/llm-tech-and-a-lot-more-version-13-3-of-wolfram-language-and-mathematica/" rel="bookmark" title="Permanent Link to LLM Tech and a Lot More: Version 13.3 of Wolfram Language and Mathematica" > <img width="128" height="108" src="https://content.wolfram.com/sites/43/2023/06/version-13.3-icon.png" class="lazy wp-post-image" alt="" title="" /> </a> </div> <div class="sidebar_post"> <p><a href="https://writings.stephenwolfram.com/2023/06/llm-tech-and-a-lot-more-version-13-3-of-wolfram-language-and-mathematica/" rel="bookmark" title="Permanent Link to LLM Tech and a Lot More: Version 13.3 of Wolfram Language and Mathematica" >LLM Tech and a Lot More: Version 13.3 of Wolfram Language and Mathematica</a></p> <p><time datetime="2023-06-28">June 28, 2023</time></p> </div> </div> </div> </article> </div> <div id="sidebar"> <form class="headerSearchBox" method="get" action="https://writings.stephenwolfram.com/" id="search"> <input class="searchboxsub" type="text" value="" name="s" id="query_1" placeholder="Search Writings" /> <input type="submit" class="headerSearchSubmit" value="" title="Search"> </form> <div class="sidebar-pod related-writings"></div> <div class="sidebar-pod recent-writings"> <p class="sidebar-heading">Recent Writings</p> <div class="sidebar-inner"> <div id="postContainer"> <div class="sidebar_post_wrapper"> <div class="sidebar_thumbnail"><a href="https://writings.stephenwolfram.com/2024/10/on-the-nature-of-time/" rel="bookmark" title="Permanent Link to On the Nature of Time" ><img src="https://content.wolfram.com/sites/43/2024/10/swblog-time-icon-v2.png" alt=""></a></div> <div class="sidebar_post"> <p><a href="https://writings.stephenwolfram.com/2024/10/on-the-nature-of-time/" rel="bookmark" title="Permanent Link to On the Nature of Time" >On the Nature of Time</a></p> <p><time datetime="2024-10-08">October 8, 2024</time></p> </div> </div> <div class="sidebar_post_wrapper"> <div class="sidebar_thumbnail"><a href="https://writings.stephenwolfram.com/2024/09/nestedly-recursive-functions/" rel="bookmark" title="Permanent Link to Nestedly Recursive Functions" ><img src="https://content.wolfram.com/sites/43/2024/09/swblog-recursive-icon.png" alt=""></a></div> <div class="sidebar_post"> <p><a href="https://writings.stephenwolfram.com/2024/09/nestedly-recursive-functions/" rel="bookmark" title="Permanent Link to Nestedly Recursive Functions" >Nestedly Recursive Functions</a></p> <p><time datetime="2024-09-27">September 27, 2024</time></p> </div> </div> <div class="sidebar_post_wrapper"> <div class="sidebar_thumbnail"><a href="https://writings.stephenwolfram.com/2024/08/five-most-productive-years-what-happened-and-whats-next/" rel="bookmark" title="Permanent Link to Five Most Productive Years: What Happened and What&#8217;s Next" ><img src="https://content.wolfram.com/sites/43/2024/08/swblog-5years-icon.png" alt=""></a></div> <div class="sidebar_post"> <p><a href="https://writings.stephenwolfram.com/2024/08/five-most-productive-years-what-happened-and-whats-next/" rel="bookmark" title="Permanent Link to Five Most Productive Years: What Happened and What&#8217;s Next" >Five Most Productive Years: What Happened and What&#8217;s Next</a></p> <p><time datetime="2024-08-29">August 29, 2024</time></p> </div> </div> <div class="sidebar_post_wrapper"> <div class="sidebar_thumbnail"><a href="https://writings.stephenwolfram.com/2024/08/whats-really-going-on-in-machine-learning-some-minimal-models/" rel="bookmark" title="Permanent Link to What&#8217;s Really Going On in Machine Learning? Some Minimal Models" ><img src="https://content.wolfram.com/sites/43/2024/08/swblog-ml-icon-v2.png" alt=""></a></div> <div class="sidebar_post"> <p><a href="https://writings.stephenwolfram.com/2024/08/whats-really-going-on-in-machine-learning-some-minimal-models/" rel="bookmark" title="Permanent Link to What&#8217;s Really Going On in Machine Learning? Some Minimal Models" >What&#8217;s Really Going On in Machine Learning? Some Minimal Models</a></p> <p><time datetime="2024-08-22">August 22, 2024</time></p> </div> </div> <div class="sidebar_post_wrapper"> <div class="sidebar_thumbnail"><a href="https://writings.stephenwolfram.com/2024/07/yet-more-new-ideas-and-new-functions-launching-version-14-1-of-wolfram-language-mathematica/" rel="bookmark" title="Permanent Link to Yet More New Ideas and New Functions: Launching Version 14.1 of Wolfram Language &#038; Mathematica" ><img src="https://content.wolfram.com/sites/43/2024/07/swblog-v14.1-icon.png" alt=""></a></div> <div class="sidebar_post"> <p><a href="https://writings.stephenwolfram.com/2024/07/yet-more-new-ideas-and-new-functions-launching-version-14-1-of-wolfram-language-mathematica/" rel="bookmark" title="Permanent Link to Yet More New Ideas and New Functions: Launching Version 14.1 of Wolfram Language &#038; Mathematica" >Yet More New Ideas and New Functions: Launching Version 14.1 of Wolfram Language &#038; Mathematica</a></p> <p><time datetime="2024-07-31">July 31, 2024</time></p> </div> </div> </div> </div> <a href="/all-by-date" class="all-by-date chevron-after">All by date</a> </div> <div class="sidebar-pod popular-categories"> <p class="sidebar-heading">Popular Categories</p> <div class="categories-list-row sidebar-inner"> <ul class="categories-list"> <li><a href="/category/artificial-intelligence">Artificial Intelligence</a></li><li><a href="/category/big-picture">Big Picture</a></li><li><a href="/category/companies-and-business">Companies &amp; Business</a></li><li><a href="/category/computational-science">Computational Science</a></li><li><a href="/category/computational-thinking">Computational Thinking</a></li><li><a href="/category/data-science">Data Science</a></li><li><a href="/category/education">Education</a></li><li><a href="/category/future-perspectives">Future Perspectives</a></li><li><a href="/category/historical-perspectives">Historical Perspectives</a></li><li><a href="/category/language-and-communication">Language &amp; Communication</a></li><li><a href="/category/life-and-times">Life &amp; Times</a></li><li><a href="/category/life-science">Life Science</a></li><li><a href="/category/mathematica">Mathematica</a></li><li><a href="/category/mathematics">Mathematics</a></li><li><a href="/category/new-kind-of-science">New Kind of Science</a></li><li><a href="/category/new-technology">New Technology</a></li><li><a href="/category/personal-analytics">Personal Analytics</a></li><li><a href="/category/philosophy">Philosophy</a></li><li><a href="/category/physics">Physics</a></li><li><a href="/category/ruliology">Ruliology</a></li><li><a href="/category/software-design">Software Design</a></li><li><a href="/category/wolfram-alpha">Wolfram|Alpha</a></li><li><a href="/category/wolfram-language">Wolfram Language</a></li><li><a href="/category/other">Other</a></li> </ul> </div> </div> <div class="sidebar-pod writings-by-year"> <p class="sidebar-heading">Writings by Year</p> <div class="sidebar-archive sidebar-inner"> <ul> <li><a href="/all-by-date/#2024">2024</a></li><li><a href="/all-by-date/#2023">2023</a></li><li><a href="/all-by-date/#2022">2022</a></li><li><a href="/all-by-date/#2021">2021</a></li><li><a href="/all-by-date/#2020">2020</a></li><li><a href="/all-by-date/#2019">2019</a></li><li><a href="/all-by-date/#2018">2018</a></li><li><a href="/all-by-date/#2017">2017</a></li><li><a href="/all-by-date/#2016">2016</a></li><li><a href="/all-by-date/#2015">2015</a></li><li><a href="/all-by-date/#2014">2014</a></li><li><a href="/all-by-date/#2013">2013</a></li><li><a href="/all-by-date/#2012">2012</a></li><li><a href="/all-by-date/#2011">2011</a></li><li><a href="/all-by-date/#2010">2010</a></li><li><a href="/all-by-date/#2009">2009</a></li><li><a href="/all-by-date/#2008">2008</a></li><li><a href="/all-by-date/#2007">2007</a></li><li><a href="/all-by-date/#2006">2006</a></li><li><a href="/all-by-date/#2004">2004</a></li><li><a href="/all-by-date/#2003">2003</a></li> <li><a href="/all-by-date/">All</a></li> </ul> </div> </div> <span id="side-images"> <a href="https://www.amazon.com/What-ChatGPT-Doing-Does-Work/dp/1579550819"><img src="https://content.wolfram.com/sites/43/2023/03/book-chatGPT.png" width="254" height="" alt=""/></a> </span> </div> </div><!-- end of "inner" --> <footer id="footer"> <div class="inner"> © Stephen Wolfram, LLC <span class="footer-sep">|</span> Open content: <a href="//creativecommons.org/licenses/by-sa/4.0/" target="_blank"> <svg id="icon-cc-by-sa" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 110 32"> <g transform="translate(76 0)"> <path d="M15.7,0.9c4.2,0,7.7,1.5,10.7,4.4c2.9,2.9,4.4,6.4,4.4,10.6c0,4.2-1.4,7.7-4.3,10.6c-3,3-6.6,4.4-10.7,4.4 c-4.1,0-7.6-1.5-10.6-4.4C2.2,23.5,0.7,20,0.7,15.9c0-4.1,1.5-7.6,4.4-10.6C8.1,2.3,11.6,0.9,15.7,0.9z M15.8,3.6 c-3.4,0-6.3,1.2-8.7,3.6c-2.4,2.5-3.7,5.4-3.7,8.7c0,3.3,1.2,6.2,3.6,8.6c2.4,2.4,5.3,3.6,8.7,3.6c3.3,0,6.2-1.2,8.7-3.7 c2.4-2.3,3.5-5.2,3.5-8.6c0-3.4-1.2-6.3-3.6-8.7C22.1,4.8,19.2,3.6,15.8,3.6z M9.1,13.8c0.3-1.8,1-3.3,2.2-4.3 c1.2-1,2.7-1.5,4.4-1.5c2.4,0,4.2,0.8,5.6,2.3s2.1,3.5,2.1,5.8c0,2.3-0.7,4.2-2.2,5.7c-1.4,1.5-3.3,2.3-5.6,2.3 c-1.7,0-3.2-0.5-4.4-1.5c-1.2-1-2-2.5-2.2-4.3h3.8c0.1,1.8,1.2,2.7,3.3,2.7c1.1,0,1.9-0.5,2.5-1.4c0.6-0.9,1-2.1,1-3.6 c0-1.6-0.3-2.8-0.9-3.6c-0.6-0.8-1.4-1.2-2.5-1.2c-2,0-3.1,0.9-3.4,2.7h1.1l-3,3l-3-3L9.1,13.8L9.1,13.8z" fill="currentColor"></path> </g> <g transform="translate(5 0)"> <path d="M59.4,5.2c-2.9-2.9-6.4-4.3-10.7-4.3c-4.1,0-7.7,1.4-10.6,4.3c-2.9,3-4.4,6.6-4.4,10.7s1.5,7.6,4.4,10.6 c3,2.9,6.5,4.4,10.6,4.4c4.1,0,7.7-1.5,10.7-4.5c2.9-2.8,4.3-6.3,4.3-10.5C63.7,11.7,62.3,8.1,59.4,5.2z M57.5,24.5 c-2.5,2.4-5.4,3.7-8.7,3.7c-3.4,0-6.2-1.2-8.7-3.6c-2.4-2.4-3.6-5.3-3.6-8.6c0-3.3,1.2-6.2,3.7-8.7c2.4-2.4,5.2-3.6,8.7-3.6 c3.4,0,6.3,1.2,8.7,3.6c2.4,2.4,3.6,5.3,3.6,8.7C61.1,19.3,59.9,22.2,57.5,24.5z" fill="currentColor"></path> <path d="M46.7,8.3c0-1.4,0.7-2.1,2.1-2.1s2.1,0.7,2.1,2.1c0,1.4-0.7,2.1-2.1,2.1C47.3,10.4,46.7,9.7,46.7,8.3z" fill="currentColor"></path> <path d="M52.8,18.3h-1.7v7.3h-4.7v-7.3h-1.7c0,0,0-4.1,0-6.1c0-0.6,0.4-1,1-1c2,0,4,0,6,0c0.6,0,1,0.4,1,1 C52.8,14.2,52.8,18.3,52.8,18.3z" fill="currentColor"></path> </g> <g id="cc-logo"> <path d="M15.7,0.9c4.2,0,7.8,1.5,10.7,4.4c1.4,1.4,2.5,3,3.2,4.8c0.7,1.8,1.1,3.7,1.1,5.8c0,2.1-0.4,4-1.1,5.8 c-0.7,1.8-1.8,3.4-3.2,4.8c-1.4,1.4-3.1,2.6-5,3.3c-1.8,0.8-3.8,1.2-5.8,1.2c-2,0-3.9-0.4-5.7-1.1c-1.8-0.8-3.5-1.9-4.9-3.3 c-1.4-1.4-2.5-3.1-3.3-4.9c-0.8-1.8-1.1-3.7-1.1-5.7c0-2,0.4-3.9,1.1-5.7c0.8-1.8,1.9-3.5,3.3-4.9C8,2.3,11.6,0.9,15.7,0.9z M15.8,3.6c-3.4,0-6.3,1.2-8.7,3.6C6,8.3,5,9.7,4.4,11.2c-0.6,1.5-1,3.1-0.9,4.7c0,1.6,0.3,3.2,0.9,4.6C5,22,6,23.4,7.1,24.5 c1.1,1.1,2.5,2.1,4,2.7c1.5,0.6,3,0.9,4.7,0.9c1.6,0,3.2-0.3,4.7-0.9c1.5-0.6,2.9-1.6,4.1-2.7c2.3-2.3,3.5-5.2,3.5-8.6 c0-1.7-0.3-3.2-0.9-4.7c-0.6-1.5-1.5-2.8-2.7-4C22.1,4.8,19.2,3.6,15.8,3.6z M15.6,13.4l-2,1c-0.2-0.4-0.5-0.8-0.8-0.9 c-0.3-0.2-0.6-0.3-0.9-0.3c-1.3,0-2,0.9-2,2.7c0,0.8,0.2,1.4,0.5,1.9c0.3,0.5,0.8,0.7,1.5,0.7c0.9,0,1.5-0.4,1.9-1.3l1.8,0.9 c-0.4,0.7-0.9,1.3-1.6,1.7c-0.7,0.4-1.5,0.6-2.3,0.6c-1.3,0-2.4-0.4-3.2-1.2c-0.8-0.8-1.2-2-1.2-3.4c0-1.4,0.4-2.6,1.2-3.4 c0.8-0.8,1.9-1.3,3.1-1.3C13.4,11.2,14.8,11.9,15.6,13.4L15.6,13.4z M24.2,13.4l-2,1c-0.2-0.4-0.5-0.8-0.8-0.9 c-0.3-0.2-0.6-0.3-0.9-0.3c-1.3,0-2,0.9-2,2.7c0,0.8,0.2,1.4,0.5,1.9c0.3,0.5,0.8,0.7,1.5,0.7c0.9,0,1.5-0.4,1.8-1.3l1.9,0.9 c-0.4,0.7-1,1.3-1.7,1.7c-0.7,0.4-1.5,0.6-2.3,0.6c-1.4,0-2.4-0.4-3.3-1.2c-0.8-0.8-1.2-2-1.2-3.4c0-1.4,0.4-2.6,1.2-3.4 c0.8-0.8,1.9-1.3,3.1-1.3C22.1,11.2,23.4,11.9,24.2,13.4L24.2,13.4z" fill="currentColor"></path> </g> </svg> </a> (code: <a href="//creativecommons.org/licenses/by-nc-sa/4.0/" target="_blank"> <svg id="icon-cc-by-nc-sa" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 146 32"> <g transform="translate(5 0)"> <path d="M59.4,5.2C56.5,2.3,53,0.9,48.7,0.9c-4.1,0-7.7,1.4-10.6,4.3c-2.9,3-4.4,6.6-4.4,10.7s1.5,7.6,4.4,10.6 c3,2.9,6.5,4.4,10.6,4.4s7.7-1.5,10.7-4.5c2.9-2.8,4.3-6.3,4.3-10.5C63.7,11.7,62.3,8.1,59.4,5.2z M57.5,24.5 c-2.5,2.4-5.4,3.7-8.7,3.7c-3.4,0-6.2-1.2-8.7-3.6c-2.4-2.4-3.6-5.3-3.6-8.6s1.2-6.2,3.7-8.7c2.4-2.4,5.2-3.6,8.7-3.6 c3.4,0,6.3,1.2,8.7,3.6s3.6,5.3,3.6,8.7C61.1,19.3,59.9,22.2,57.5,24.5z" fill="currentColor"></path> <path d="M46.7,8.3c0-1.4,0.7-2.1,2.1-2.1s2.1,0.7,2.1,2.1s-0.7,2.1-2.1,2.1C47.3,10.4,46.7,9.7,46.7,8.3z" fill="currentColor"></path> <path d="M52.8,18.3h-1.7v7.3h-4.7v-7.3h-1.7c0,0,0-4.1,0-6.1c0-0.6,0.4-1,1-1c2,0,4,0,6,0c0.6,0,1,0.4,1,1 C52.8,14.2,52.8,18.3,52.8,18.3z" fill="currentColor"></path> </g> <g transform="translate(76 0)"> <path d="M53.9,0.9c4.2,0,7.7,1.5,10.7,4.4c2.9,2.9,4.4,6.4,4.4,10.6s-1.4,7.7-4.3,10.6c-3,3-6.6,4.4-10.7,4.4s-7.6-1.5-10.6-4.4 c-3-3-4.5-6.5-4.5-10.6s1.5-7.6,4.4-10.6C46.3,2.3,49.8,0.9,53.9,0.9z M54,3.6c-3.4,0-6.3,1.2-8.7,3.6c-2.4,2.5-3.7,5.4-3.7,8.7 s1.2,6.2,3.6,8.6c2.4,2.4,5.3,3.6,8.7,3.6c3.3,0,6.2-1.2,8.7-3.7c2.4-2.3,3.5-5.2,3.5-8.6s-1.2-6.3-3.6-8.7 C60.3,4.8,57.4,3.6,54,3.6z M47.3,13.8c0.3-1.8,1-3.3,2.2-4.3S52.2,8,53.9,8c2.4,0,4.2,0.8,5.6,2.3c1.4,1.5,2.1,3.5,2.1,5.8 s-0.7,4.2-2.2,5.7c-1.4,1.5-3.3,2.3-5.6,2.3c-1.7,0-3.2-0.5-4.4-1.5c-1.2-1-2-2.5-2.2-4.3H51c0.1,1.8,1.2,2.7,3.3,2.7 c1.1,0,1.9-0.5,2.5-1.4c0.6-0.9,1-2.1,1-3.6c0-1.6-0.3-2.8-0.9-3.6c-0.6-0.8-1.4-1.2-2.5-1.2c-2,0-3.1,0.9-3.4,2.7h1.1l-3,3l-3-3 L47.3,13.8L47.3,13.8z" fill="currentColor"></path> </g> <g id="cc-logo"> <path d="M15.7,0.9c4.2,0,7.8,1.5,10.7,4.4c1.4,1.4,2.5,3,3.2,4.8s1.1,3.7,1.1,5.8s-0.4,4-1.1,5.8s-1.8,3.4-3.2,4.8 c-1.4,1.4-3.1,2.6-5,3.3c-1.8,0.8-3.8,1.2-5.8,1.2s-3.9-0.4-5.7-1.1C8.1,29.1,6.4,28,5,26.6s-2.5-3.1-3.3-4.9S0.6,18,0.6,16 s0.4-3.9,1.1-5.7C2.5,8.5,3.6,6.8,5,5.4C8,2.3,11.6,0.9,15.7,0.9z M15.8,3.6c-3.4,0-6.3,1.2-8.7,3.6C6,8.3,5,9.7,4.4,11.2 s-1,3.1-0.9,4.7c0,1.6,0.3,3.2,0.9,4.6C5,22,6,23.4,7.1,24.5s2.5,2.1,4,2.7s3,0.9,4.7,0.9c1.6,0,3.2-0.3,4.7-0.9s2.9-1.6,4.1-2.7 c2.3-2.3,3.5-5.2,3.5-8.6c0-1.7-0.3-3.2-0.9-4.7s-1.5-2.8-2.7-4C22.1,4.8,19.2,3.6,15.8,3.6z M15.6,13.4l-2,1 c-0.2-0.4-0.5-0.8-0.8-0.9c-0.3-0.2-0.6-0.3-0.9-0.3c-1.3,0-2,0.9-2,2.7c0,0.8,0.2,1.4,0.5,1.9s0.8,0.7,1.5,0.7 c0.9,0,1.5-0.4,1.9-1.3l1.8,0.9c-0.4,0.7-0.9,1.3-1.6,1.7c-0.7,0.4-1.5,0.6-2.3,0.6c-1.3,0-2.4-0.4-3.2-1.2c-0.8-0.8-1.2-2-1.2-3.4 s0.4-2.6,1.2-3.4c0.8-0.8,1.9-1.3,3.1-1.3C13.4,11.2,14.8,11.9,15.6,13.4L15.6,13.4z M24.2,13.4l-2,1c-0.2-0.4-0.5-0.8-0.8-0.9 c-0.3-0.2-0.6-0.3-0.9-0.3c-1.3,0-2,0.9-2,2.7c0,0.8,0.2,1.4,0.5,1.9s0.8,0.7,1.5,0.7c0.9,0,1.5-0.4,1.8-1.3l1.9,0.9 c-0.4,0.7-1,1.3-1.7,1.7c-0.7,0.4-1.5,0.6-2.3,0.6c-1.4,0-2.4-0.4-3.3-1.2c-0.8-0.8-1.2-2-1.2-3.4s0.4-2.6,1.2-3.4 c0.8-0.8,1.9-1.3,3.1-1.3C22.1,11.2,23.4,11.9,24.2,13.4L24.2,13.4z" fill="currentColor"></path> </g> <g id="cc-nc"> <path d="M91.7,1c4.2,0,7.8,1.4,10.7,4.3c2.9,2.9,4.4,6.4,4.4,10.7c0,4.2-1.4,7.7-4.3,10.5c-3,3-6.6,4.5-10.7,4.5 c-4.1,0-7.6-1.5-10.6-4.4c-2.9-2.9-4.4-6.5-4.4-10.6c0-4.1,1.5-7.7,4.4-10.7C84.1,2.5,87.6,1,91.7,1z M80.1,12 c-0.4,1.2-0.7,2.6-0.7,4c0,3.3,1.2,6.2,3.6,8.6c2.4,2.4,5.3,3.6,8.7,3.6c3.4,0,6.3-1.2,8.7-3.7c0.9-0.8,1.6-1.7,2.1-2.6l-5.7-2.5 c-0.2,0.9-0.7,1.7-1.4,2.3c-0.8,0.6-1.7,0.9-2.7,1v2.3h-1.7v-2.3c-1.7,0-3.2-0.6-4.6-1.8l2.1-2.1c1,0.9,2.1,1.4,3.3,1.4 c0.5,0,1-0.1,1.3-0.3c0.4-0.2,0.5-0.6,0.5-1.2c0-0.4-0.1-0.7-0.4-0.9l-1.4-0.6l-1.8-0.8l-2.4-1C87.8,15.4,80.1,12,80.1,12z M91.8,3.7c-3.4,0-6.3,1.2-8.7,3.6c-0.6,0.6-1.1,1.3-1.7,2l5.7,2.6c0.2-0.8,0.7-1.4,1.4-1.9c0.7-0.5,1.5-0.7,2.4-0.8V6.9h1.7v2.3 c1.4,0.1,2.6,0.5,3.8,1.4l-2,2c-0.8-0.6-1.7-0.9-2.6-0.9c-0.5,0-0.9,0.1-1.2,0.3c-0.4,0.2-0.6,0.5-0.6,0.9c0,0.1,0,0.2,0.1,0.4 l1.9,0.9l1.3,0.6l2.4,1.1l7.7,3.4c0.2-1.1,0.4-2.1,0.4-3.2c0-3.4-1.2-6.3-3.6-8.7C98.1,4.9,95.2,3.7,91.8,3.7L91.8,3.7z" fill="currentColor"></path> </g> </svg> </a>) <a href="//en.wikipedia.org/wiki/Wikipedia:Citing_sources" target="_blank"> <svg id="icon-wiki" xmlns="http://www.w3.org/2000/svg" viewBox="101 0 44 32"> <g transform="translate(0 0)"> <path id="wikipedia" d="M129.6,4.5l0.3,0h0.5l0.2,0h0.4l0.2,0l0.5,0h0.2l0.1,0.1v0.7c0,0.2-0.1,0.3-0.3,0.3c-1.1,0-1.3,0.2-1.7,0.7 c-0.2,0.3-0.6,1-1.1,1.7l-3.7,7l-0.1,0.2l4.6,9.4l0.3,0.1l7.2-17.1c0.3-0.7,0.2-1.2-0.1-1.5c-0.3-0.3-0.6-0.4-1.4-0.5l-0.7,0 c-0.1,0-0.2,0-0.2-0.1c-0.1,0-0.1-0.1-0.1-0.2V4.6l0.1-0.1h8.1l0.1,0.1v0.7c0,0.2-0.1,0.3-0.3,0.3c-1.1,0-1.9,0.3-2.4,0.7 c-0.5,0.4-0.9,1-1.2,1.7c0,0-2.2,5-4.4,10.1l-0.4,0.9c-1.6,3.6-3.2,7.2-4.1,9.2c-0.9,1.7-1.7,1.5-2.5,0c-0.6-1.2-1.6-3.3-2.5-5.5 l-0.7-1.4c-0.4-0.8-0.8-1.7-1.1-2.4c-1.5,3.2-3.6,7.4-4.7,9.4c-1,1.8-1.8,1.5-2.5,0c-2.3-5.4-7-15-9.3-20.3c-0.4-1-0.7-1.6-1-1.9 c-0.3-0.2-0.9-0.4-1.8-0.4c-0.3,0-0.5-0.1-0.5-0.3V4.6l0.1-0.1l0.8,0h1.4l1.4,0h0.4l2.5,0h0.3l1.3,0h0.8l0.1,0.1v0.7 c0,0.2-0.1,0.3-0.4,0.3l-0.9,0c-0.8,0-1.2,0.3-1.2,0.7c0,0.2,0.1,0.5,0.3,1c1.8,4.3,7.9,17.3,7.9,17.2l0.2,0.1l3.9-7.9 c-0.5-1.1-0.8-1.7-0.8-1.7L119,9.6c0,0-0.5-1.1-0.7-1.4c-1.2-2.4-1.2-2.5-2.4-2.6c-0.3,0-0.5-0.1-0.5-0.3V4.6l0.1-0.1h1l2.1,0h3.9 l0.2,0.1v0.7c0,0.2-0.1,0.3-0.4,0.3l-0.5,0.1c-1.3,0.1-1.1,0.6-0.2,2.3l2.6,5.3l2.9-5.7c0.5-1,0.4-1.3,0.2-1.5l0,0 c-0.1-0.1-0.5-0.4-1.3-0.4l-0.3,0c-0.1,0-0.2,0-0.2-0.1c-0.1,0-0.1-0.1-0.1-0.2V4.6l0.1-0.1l1.2,0H129.6z" fill="currentColor"></path> </g> </svg> </a> <span class="footer-sep">|</span> <a href="/terms" target="_blank">Terms</a> <span class="footer-sep">|</span> <a href="/feed/" target="_blank">RSS</a> </div> </footer></div><!-- end of "outerWrap" --> <script type='text/javascript' src='https://writings.stephenwolfram.com/wp-content/plugins/akismet/_inc/form.js?ver=3.2'></script> <script type='text/javascript' src='https://writings.stephenwolfram.com/wp-includes/js/comment-reply.min.js?ver=4.7.2'></script> <script type='text/javascript' src='https://writings.stephenwolfram.com/wp-includes/js/wp-embed.min.js?ver=4.7.2'></script> <!--noscript.en.html--> <style> #_noscript, #_noscript * { box-sizing: border-box; margin: 0; outline: 0; padding: 0; z-index: 99999999999; } #_noscript { background: #fff6aa; border-bottom: 1px solid #eeca48; bottom: 0; color: #4c4c4c; display: block; font-size: .875rem; font-style: italic; left: 0; min-width: 320px; position: fixed; right: 0; width: 100%; z-index: 99999998 !important; /* place it beneath the global header */ } #_noscript > div { align-items: center; display: grid; gap: .5rem; grid-template-columns: 28px auto; height: 40px; justify-content: center; margin: 0 1rem; } #_noscript svg { display: inline-block; height: 25px; vertical-align: middle; width: 28px; } #_noscript a { color: #222; font-style: normal; text-decoration: none; } #_noscript a:hover { color: #ef621a; } </style> <noscript id="_noscript" class="gl-noscript-standalone remove__ready"> <div> <div><svg class="_noscript-warning"><use href="#_noscript-warning"></use></svg></div> <div>Enable JavaScript to interact with content and submit forms on Wolfram websites. <a href="http://www.enable-javascript.com/" target="_blank" data-walid="GUIFooter">Learn how&nbsp;»</a></div> </div> </noscript> <div style="height: 0; width: 0; position: absolute; visibility: hidden; top: -999999999999px;"> <svg xmlns="http://www.w3.org/2000/svg"> <g id="_noscript-icons"> <symbol id="_noscript-warning" viewBox="0 0 28.21 25"> <path d="M27.91,21.7L16.01,1.1c-.84-1.47-2.96-1.47-3.81,0L.3,21.7c-.85,1.47,.21,3.3,1.9,3.3H26c1.69,0,2.75-1.83,1.91-3.3ZM15.75,7.44l-.46,9.42h-2.37l-.48-9.42h3.31Zm-1.65,14.25c-1.12,0-1.87-.81-1.87-1.89s.77-1.89,1.87-1.89,1.83,.79,1.85,1.89c0,1.08-.73,1.89-1.85,1.89Z" fill="#f47821"/> <polygon points="15.77 7.47 15.31 16.89 12.94 16.89 12.46 7.47 15.77 7.47" fill="#fff"/> <path d="M14.1,21.69c-1.12,0-1.87-.81-1.87-1.89s.77-1.89,1.87-1.89,1.83,.79,1.85,1.89c0,1.08-.73,1.89-1.85,1.89Z" fill="#fff"/> </symbol> </g> </svg> </div> <!--/noscript.en.html--> <script>var baselang = '';</script> <script src="https://writings.stephenwolfram.com/wp-content/themes/sw-writings/clipboard.js"></script> <script src="/common/js/clipboard/2.0/clipboard.js"></script> <script src="/common/js/c2c/1.0/WolframC2C.js"></script> <script src="/common/js/c2c/1.0/WolframC2CGui.js"></script> <script src="/common/js/c2c/1.0/WolframC2CDefault.js"></script> <link rel="stylesheet" href="/common/js/c2c/1.0/WolframC2CGui.css.en"> <script> let c2cWrittings = new WolframC2CDefault({'triggerClass':'writtings-c2c_above', 'uniqueIdPrefix': 'writtings-c2c_above-'}); </script><script type="text/javascript"> if ( location.hash!="" && Number.isInteger( Number( location.hash.substring(1) ) ) ) { var jumplink = Number( location.hash.substring(1) ) - 1; document.getElementsByClassName('InCell')[jumplink].scrollIntoView(true); } </script> <!-- begin framework footer en --> <div id ="IPstripe-wrap"></div> <script src="/common/stripe/stripe.en.js"></script> <!-- end framework footer en --> </body> </html>

Pages: 1 2 3 4 5 6 7 8 9 10