{"id":142,"date":"2008-05-26T20:26:12","date_gmt":"2008-05-27T04:26:12","guid":{"rendered":"http:\/\/www.oeconomist.com\/blogs\/daniel\/?p=142"},"modified":"2009-09-23T19:47:28","modified_gmt":"2009-09-24T03:47:28","slug":"mistaking-a-map-for-the-territory","status":"publish","type":"post","link":"https:\/\/www.oeconomist.com\/blogs\/daniel\/?p=142","title":{"rendered":"Mistaking a map for the territory"},"content":{"rendered":"<p>A while back, I got a copy of <cite>Circuit Analysis<\/cite> by Robbins and Miller, to review material that I'd forgot, and to fill-in lacun&aelig; here and there.  On the whole, I think that it's a pretty good book, though somewhat slow-moving for my tastes.<\/p> <p>But to-day I hit a passage that bugs me: <blockquote>Although we use phasors to represent sinusoidal waveforms, it should be noted that sine waves and phasors are not the same thing.  Sinusoidal voltages and currents are real &mdash; they are actual quantities that you measure with meters and whose waveforms you see on oscilloscopes. <em>Phasors, on the other hand, are mathematical abstractions that we use to help visualize relationships and solve problems.<\/em><\/blockquote><\/p> <p>Okay, now, for those of you unfamiliar with phasors, these are two-dimensional vectors or complex numbers whose magnitude corresponds to the amplitude of a sinus wave, and whose direction corresponds to the phase of the wave.  In the case of a wave with an amplitude of 1 unit, a phasor would be a radial line on a unit circle, bearing the familiar relationship to a sine wave.<\/p> <p>There is an <em>isomorphism<\/em> between the set of phasors and any representation of sinus waves.  That is to say that for every representation of sinus waves and operations there&uuml;pon, one can find equivalent phasors and operations there&uuml;pon, and <span style=\"font-style: italic ;\">vice versa<\/span>, such that a one-to-one correspondence between operands and results is maintained.  From the perspective of mathematics, a phasor just <em>is<\/em> a representation of a sinus wave.<\/p> <p>This last point does not contradict what Robbins and Miller have said, but now consider <em>how<\/em> and <em>why<\/em> we see wave-forms on an oscilloscope.  The most familiar <em>graphical representation<\/em> of sinus waves looks very much like some of the waves that we observe in water, but electricity isn't water.  We cannot look at an ordinary circuit and <em>see<\/em> its voltage or current; instead, we use devices whose visible behaviour changes to <em>represent<\/em> voltage or current.  These devices <em>might<\/em> represent that behaviour in <em>various<\/em> ways; the ways in which they do are determined by various <em>cost considerations<\/em> (including cultural expectations).<\/p> <p>An oscilloscope is designed to present a particular sort of <em>graphical representation<\/em> of wave-forms.  It could instead be designed to present a <em>different<\/em> sort of graphical representation.  If it only had to represent sinus waves, then it could do this with stable phasors.  And if it had to represent non-sinus waves, then it <em>could<\/em> perhaps do this with time-varying phasors (giving the viewer an animated Fourier analysis), though I don't know that this would be as helpful to us.<\/p> <p>The representation of the oscilloscope is a <em>map<\/em>.  As Korzybski noted, <em>the map is not the territory<\/em>.  The phasor is not the voltage or the current, but <em>neither is the representation on the oscilloscope<\/em>; neither is more or less <em>real<\/em> than is the other.<\/p>","protected":false},"excerpt":{"rendered":"A while back, I got a copy of Circuit Analysis by Robbins and Miller, to review material that I'd forgot, and to fill-in lacun&aelig; here and there. On the whole, I think that it's a pretty good book, though somewhat slow-moving for my tastes. But to-day I hit a passage that bugs me: Although we [&hellip;]","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"footnotes":""},"categories":[6,66,175,4],"tags":[218,219,220,221],"class_list":["post-142","post","type-post","status-publish","format-standard","hentry","category-commentary","category-electronics","category-philosophy","category-public","tag-representation","tag-scientific-instruments","tag-semantics","tag-waves"],"_links":{"self":[{"href":"https:\/\/www.oeconomist.com\/blogs\/daniel\/index.php?rest_route=\/wp\/v2\/posts\/142","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oeconomist.com\/blogs\/daniel\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oeconomist.com\/blogs\/daniel\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oeconomist.com\/blogs\/daniel\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oeconomist.com\/blogs\/daniel\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=142"}],"version-history":[{"count":0,"href":"https:\/\/www.oeconomist.com\/blogs\/daniel\/index.php?rest_route=\/wp\/v2\/posts\/142\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.oeconomist.com\/blogs\/daniel\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=142"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oeconomist.com\/blogs\/daniel\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=142"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oeconomist.com\/blogs\/daniel\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=142"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}