{"id":171,"date":"2006-04-07T08:06:52","date_gmt":"2006-04-07T08:06:52","guid":{"rendered":"http:\/\/scienceblogs.com\/principles\/2006\/04\/07\/visualize-it-in-n-dimensions-a\/"},"modified":"2006-04-07T08:06:52","modified_gmt":"2006-04-07T08:06:52","slug":"visualize-it-in-n-dimensions-a","status":"publish","type":"post","link":"http:\/\/chadorzel.com\/principles\/2006\/04\/07\/visualize-it-in-n-dimensions-a\/","title":{"rendered":"Visualize It In N Dimensions, And Let N Go to Four"},"content":{"rendered":"

Mark Chu-Carroll has a very nice discussion of what “extra dimensions” actually mean<\/a> in theories like string theory. It’s not the same thing that hack SF authors mean when they talk about “dimensions” in which the Nazis won WWII (that’s “multiverse theory” or possibly “landscapeology” or possibly “late-night stoner bullshit”):<\/p>\n

\n

A better way to explain, but a slightly less intuitive one is to not separate dimensions quite so much. The set of dimensions in a space is the number of pieces of information that you need to identify a unique location in that space.<\/p>\n

On a plane, you can put down a coordinate grid, and identify any point on the grid with only two numbers. In a region of three dimensional space, you can specify any location in that space using only three numbers. But getting beyond three, we start to have some trouble.<\/p>\n

Try thinking about the colors on your computer screen. Basically, for each pixel on your screen, there are three lights that can be turned on in different brightnesses: one red, one green, one blue. The color of each pixel is determined by the brightnesses of three lights for a pixel: if all of the lights are completely off, the pixel is black; if the blue light is on very bright, the red light is on halfway, and the green light is off, you’ll get a bright bluish-violet; if the red light and the green light are on full brightness, and the blue light is on halfway, you’ll get a sort of pastel green. So the colors of your computer screen have three dimensions.<\/p>\n

Try thinking about the flavors of food. It’s commonly asserted that we humans have the ability to perceive sweet, salty, bitter, and sour flavors. Every flavor that we can experience is some combination of sweet, salty, bitter, and sour. Therefore, flavor has four dimensions.<\/p>\n<\/blockquote>\n

Really getting an intuitive grasp of anything beyond three dimensions is a tough problem. I can’t do it myself, but I can appreciate a good attempt at explaining it.<\/p>\n","protected":false},"excerpt":{"rendered":"

Mark Chu-Carroll has a very nice discussion of what “extra dimensions” actually mean in theories like string theory. It’s not the same thing that hack SF authors mean when they talk about “dimensions” in which the Nazis won WWII (that’s “multiverse theory” or possibly “landscapeology” or possibly “late-night stoner bullshit”): A better way to explain,… Continue reading Visualize It In N Dimensions, And Let N Go to Four<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"1","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11,14],"tags":[],"class_list":["post-171","post","type-post","status-publish","format-standard","hentry","category-science","category-string_theory","entry"],"_links":{"self":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/171","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/comments?post=171"}],"version-history":[{"count":0,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/171\/revisions"}],"wp:attachment":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/media?parent=171"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/categories?post=171"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/tags?post=171"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}