{"id":52285,"date":"2026-04-06T13:34:38","date_gmt":"2026-04-06T13:34:38","guid":{"rendered":"https:\/\/kingarthur.com\/songwriter\/?p=52285"},"modified":"2026-04-06T13:34:38","modified_gmt":"2026-04-06T13:34:38","slug":"the-secret-formula","status":"publish","type":"post","link":"https:\/\/kingarthur.com\/songwriter\/2026\/04\/06\/the-secret-formula\/","title":{"rendered":"The Secret Formula"},"content":{"rendered":"<p>[Silence]<br \/>\n[Instrumental, Guitar, Piano, Organ, Synth, Bass, Percussion, Drums]<\/p>\n<p>[Intro]<br \/>\n[Instrumental Intro: Pulsing Synth, Dark Organ, Distorted Guitar Harmonics]<br \/>\n[Minimal Beat, Sub Bass, Spoken Vocal]<br \/>\n(Quick!)<br \/>\nWhat&#8217;s the trick?<br \/>\n(What&#8217;s the scheme?)<br \/>\nWhat&#8217;s the cost?<br \/>\n(Of the dream?)<br \/>\nBefore all&#8217;s lost&#8230;<\/p>\n<p>[Verse 1]<br \/>\nThey wanted profit<br \/>\nWe wanted more<br \/>\nThey dug too deep<br \/>\nInto the core<br \/>\nWe burned tomorrow<br \/>\nFor today<br \/>\nAnd smiled while taking it away<\/p>\n<p>[Pre-Chorus]<br \/>\nEvery barrel<br \/>\n(Brings on peril)<br \/>\nEvery shortcut<br \/>\n(But, but, but)<br \/>\nMe, my, mine!<br \/>\n(Every mine)<br \/>\nCrossed the line<\/p>\n<p>[Chorus]<br \/>\nOh well<br \/>\n(If you&#8217;re gonna tell&#8230;)<br \/>\nHere&#8217;s the secret formula:<br \/>\nDoubling time equals<br \/>\nThe time-dependent growth constant<br \/>\nTimes the natural logarithm of 2<br \/>\n(It&#8217;s true)<\/p>\n<p>[Bridge]<br \/>\n&#8220;The Secret Formula&#8221;<br \/>\n(Featuring Princess Earth)<br \/>\n&#8230; and man staring as Dracula<br \/>\nOh well<br \/>\n(If you&#8217;re gonna sell&#8230;)<br \/>\nHere&#8217;s the hidden mechanism<br \/>\n(Princess Earth)<br \/>\n&#8230; trapped inside the prism<\/p>\n<p>[Instrumental]<br \/>\n[Guitar Solo]<br \/>\n[Heavy Bass Pulse, Organ Stabs, Drum Fills]<\/p>\n<p>[Verse 2]<br \/>\nThe hotter it gets<br \/>\nThe more things break<br \/>\nThe more things break<br \/>\nThe more heat they make<br \/>\nThe ice retreats<br \/>\nThe oceans rise<br \/>\nThe smoke fills up the darkened skies<br \/>\nThe forests burn<br \/>\nThe methane climbs<br \/>\nAnd every decade outruns time<\/p>\n<p>[Bridge]<br \/>\nSucking out the lifeblood<br \/>\n(Up to our ears in mud)<br \/>\nDraining every artery<br \/>\n(Blood becomes the flood)<br \/>\nSucking out the lifeblood<br \/>\n(Trading life for blood)<br \/>\nEvery warning buried<br \/>\n(Underneath the mud)<\/p>\n<p>[Breakdown]<br \/>\n[Minimal Percussion, Low Drone, Spoken Vocal]<br \/>\nThe faster it goes<br \/>\n(The faster it grows)<br \/>\nThe shorter the time<br \/>\n(Before it shows)<br \/>\nThe smaller the gap<br \/>\n(Between cause and effect)<\/p>\n<p>[Final Chorus]<br \/>\nOh well<br \/>\n(If you&#8217;re gonna tell&#8230;)<br \/>\nHere&#8217;s the secret formula:<br \/>\nDoubling time equals<br \/>\nThe time-dependent growth constant<br \/>\nTimes the natural logarithm of 2<br \/>\n(It&#8217;s true)<\/p>\n<p>[Bridge]<br \/>\n&#8220;The Secret Formula&#8221;<br \/>\n(Featuring Princess Earth)<br \/>\n&#8230; man staring as Dracula<br \/>\nOh well<br \/>\n(If you&#8217;re gonna sell&#8230;)<br \/>\nHere&#8217;s the hidden mechanism<br \/>\n(Princess Earth)<br \/>\n&#8230; trapped inside the prism<br \/>\nOh well<br \/>\n(Now the numbers swell&#8230;)<br \/>\nHere&#8217;s the shrinking doubling time<br \/>\n(Princess Earth)<br \/>\n&#8230; falling out of line<\/p>\n<p>[Outro]<br \/>\n[Slow Piano, Fading Synth, Wind FX]<br \/>\nWhat&#8217;s the trick?<br \/>\n(What&#8217;s the scheme?)<br \/>\nWhat&#8217;s the cost?<br \/>\n(Of the dream?)<br \/>\n[Fade Out]<\/p>\n<p>About the Song<br \/>\nThis song is about feedback loops and shrinking doubling times in the climate system. As warming increases, it triggers other processes that add even more warming: melting ice reduces reflectivity, fires release carbon, thawing permafrost releases methane, and warmer oceans intensify storms and reduce carbon absorption.<\/p>\n<p>The key mathematical idea (&#8220;secret formula&#8221;) is that doubling time depends on the growth constant:<br \/>\nWhen growth processes are governed by feedbacks, the doubling time is:<br \/>\nTd\u200b(t)=k(t)ln(2)\u200b<\/p>\n<p>Where:<br \/>\nTd\u200b(t) = doubling time<br \/>\nk(t) = time-dependent growth constant<br \/>\nln(2) = natural logarithm of 2<br \/>\nIf feedback amplification increases<br \/>\nk(t), doubling times shrink.<\/p>\n<p>As feedback loops strengthen, k(t) rises and doubling times shrink. That means impacts compound faster and faster. Instead of a slow, linear trend, climate change becomes an accelerating cascade where each destabilized system amplifies the next.<\/p>\n<p>From the album <strong>&#8220;<a href=\"\/albums\/Laboratory\/\">Laboratory<\/a>&#8220;<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>[Silence] [Instrumental, Guitar, Piano, Organ, Synth, Bass, Percussion, Drums] [Intro] [Instrumental Intro: Pulsing Synth, Dark Organ, Distorted Guitar Harmonics] [Minimal Beat, Sub Bass, Spoken Vocal] (Quick!) What&#8217;s the trick? (What&#8217;s the scheme?) What&#8217;s the cost? (Of the dream?) Before all&#8217;s lost&#8230; [Verse 1] They wanted profit We wanted more They dug too deep Into the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-52285","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts\/52285","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/comments?post=52285"}],"version-history":[{"count":2,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts\/52285\/revisions"}],"predecessor-version":[{"id":52287,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts\/52285\/revisions\/52287"}],"wp:attachment":[{"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/media?parent=52285"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/categories?post=52285"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/tags?post=52285"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}