{"id":13908,"date":"2013-12-07T23:18:50","date_gmt":"2013-12-08T04:18:50","guid":{"rendered":"http:\/\/blog.kenperlin.com\/?p=13908"},"modified":"2013-12-07T23:18:50","modified_gmt":"2013-12-08T04:18:50","slug":"2-%c3%97-2-%c3%97-2-%c3%97-2","status":"publish","type":"post","link":"http:\/\/blog.kenperlin.com\/?p=13908","title":{"rendered":"2 \u00d7 2 \u00d7 2 \u00d7 2"},"content":{"rendered":"

In my periodic quest to understand what four dimensions are like, this week I decided to reduce it down to the simplest four dimensional world I can think of.<\/p>\n

My basic reasoning was like this: If you want to understand what two dimensions are like, this simplest thing you can make is a 2 × 2 arrangement of squares. In this tiny world, you can travel between top<\/b> and bottom<\/b>, and you can also travel between left<\/b> and right<\/b>. The world you can explore this way is kind of boring, since it has only four rooms to visit, corresponding to the four corners of a square:<\/p>\n

<\/p>\n\n\n
\n\n\n\n\n\n
Top
Left<\/th>\n		\nTop
Right<\/th>\n<\/tr>\n
 <\/th>\n  <\/th>\n <\/th>\n<\/tr>\n
 <\/th>\n  <\/th>\n <\/th>\n<\/tr>\n
Bottom
Left<\/th>\n		\nBottom
Right<\/th>\n<\/tr>\n<\/table>\n<\/td>\n<\/tr>\n<\/table>\n

<\/center><\/p>\n

The equivalent in three dimensions is a 2 × 2 × 2 cube. Now you can also travel between front<\/b> and back<\/b>. This world is a little more interesting, since it has eight rooms to visit, corresponding to the eight corners of a cube.<\/p>\n

So I’ve been looking at what happens when you extend this idea to just one more dimension. Now you have a 2 × 2 × 2 × 2 hypercube. You can travel back and forth in any of four dimensions, which means you can visit sixteen different rooms.<\/p>\n

I started posing little puzzles to solve in this tiny world, and some of those puzzles have turned out to be surprisingly interesting. More on that tomorrow.<\/p>\n","protected":false},"excerpt":{"rendered":"

In my periodic quest to understand what four dimensions are like, this week I decided to reduce it down to the simplest four dimensional world I can think of. My basic reasoning was like this: If you want to understand what two dimensions are like, this simplest thing you can make is a 2 × … Continue reading “2 \u00d7 2 \u00d7 2 \u00d7 2”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/13908"}],"collection":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=13908"}],"version-history":[{"count":21,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/13908\/revisions"}],"predecessor-version":[{"id":13929,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/13908\/revisions\/13929"}],"wp:attachment":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13908"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13908"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13908"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}