{"id":2287,"date":"2009-03-30T10:29:32","date_gmt":"2009-03-30T17:29:32","guid":{"rendered":"http:\/\/blogs.discovermagazine.com\/cosmicvariance\/2009\/03\/30\/why-cant-we-visualize-more-than-three-dimensions\/"},"modified":"2009-03-30T10:29:32","modified_gmt":"2009-03-30T17:29:32","slug":"why-cant-we-visualize-more-than-three-dimensions","status":"publish","type":"post","link":"https:\/\/preposterousuniverse.com\/blog\/2009\/03\/30\/why-cant-we-visualize-more-than-three-dimensions\/","title":{"rendered":"Why Can&#8217;t We Visualize More Than Three Dimensions?"},"content":{"rendered":"<p>Physicists and mathematicians who think about higher-dimensional spaces are, if they allow their interest to somehow become public knowledge, inevitably asked:  &#8220;How can you <em>visualize<\/em> more than three dimensions of space?&#8221;  There are at least three correct answers:  (1) You can&#8217;t.  (2) You don&#8217;t have to; manipulating abstract symbols is enough to help you figure things out.  (3)  There are tricks to help you pseudo-visualize higher-dimensional objects by cleverly projecting them into three dimensions; see <a href=\"http:\/\/www.sciencenews.org\/view\/generic\/id\/35740\/title\/Math_Trek__Seeing_in_four_dimensions\">here<\/a> and <a href=\"http:\/\/scitalks.wordpress.com\/2007\/08\/14\/visualizing-4-dimensions\/\">here<\/a>.<\/p>\n<p>But really, why can&#8217;t we visualize things in more than three dimensions of space?  Could a Flatlander, living in a world with only two spatial dimensions, learn to visualize our three-dimensional world?  Could we somehow, through practice or direct intervention in the brain, train ourselves to truly visualize more dimensions?<\/p>\n<p>I can think of a couple of explanations why it&#8217;s so hard, with different ramifications.  One would be simply that our imaginations aren&#8217;t good enough to project our consciousness into a constructed world so very different from our own.  Could you, for example, really imagine what it&#8217;s like to live in <em>two<\/em> dimensions?   Sure, you can visualize Flatland from the outside, but what about asking what it&#8217;s like to really be a Flatlander?  The best I can do is to imagine a line, flickering with colors, surrounded by darkness on either side.  But the darkness is still there, in my imagination.<\/p>\n<p>The other possible explanation is that the process of visualization takes up a three-dimensional space in our actual brain, preventing us from &#8220;tuning a dimensionality knob&#8221; on our imaginations.  The truth is certainly more complicated than that (and I&#8217;m not experts, so anyone who is should chime in); the <a href=\"http:\/\/preposterousuniverse.blogspot.com\/2005\/02\/hallucinatory-neurophysics.html\">visual cortex<\/a> itself is effectively two-dimensional, but somehow our brain reconstructs a three-dimensional image of the space around us.<\/p>\n<p>Maybe this could be a new tantric discipline:  visualization in higher dimensions.  Or maybe the <a href=\"http:\/\/blogs.discovermagazine.com\/cosmicvariance\/2007\/03\/15\/maharishi-mathematics\/\">Maharishi<\/a> already offers a course?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Physicists and mathematicians who think about higher-dimensional spaces are, if they allow their interest to somehow become public knowledge, inevitably asked: &#8220;How can you visualize more than three dimensions of space?&#8221; There are at least three correct answers: (1) You can&#8217;t. (2) You don&#8217;t have to; manipulating abstract symbols is enough to help you figure [&hellip;]<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[48],"tags":[],"class_list":["post-2287","post","type-post","status-publish","format-standard","hentry","category-math"],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/posts\/2287","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/comments?post=2287"}],"version-history":[{"count":0,"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/posts\/2287\/revisions"}],"wp:attachment":[{"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/media?parent=2287"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/categories?post=2287"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/tags?post=2287"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}