{"id":4362,"date":"2010-08-12T23:33:30","date_gmt":"2010-08-13T04:33:30","guid":{"rendered":"http:\/\/blog.kenperlin.com\/?p=4362"},"modified":"2010-09-19T14:00:29","modified_gmt":"2010-09-19T19:00:29","slug":"another-dimension","status":"publish","type":"post","link":"http:\/\/blog.kenperlin.com\/?p=4362","title":{"rendered":"Another dimension"},"content":{"rendered":"

We’re still doing production on the little walking guy. But meanwhile my collaborator Eva Schindling and I managed to build a nice little working zoetrope<\/a> of a tumbling hypercube.<\/p>\n

For those of you who don’t know, a hypercube is something like a cube, only with four dimensions instead of three. As a cube is to a square, a hypercube is to a cube. I made a java applet<\/a> some years back that lets you play with them.<\/p>\n

Of course we don’t live in four dimensions, so it’s hard to get a feeling for what happens when you rotate four dimensional things. Eva and I thought that it would be cool, rather than looking at 4D things rotating on a computer screen, to create an animated sculpture<\/i> of a rotating hypercube. That way you could look around it from all directions (at least, all 3D directions) as it does its weird 4D rotation.<\/p>\n

Because a hypercube has four dimensions instead of three, it can rotate in some pretty fancy ways. A simple rotation only requires two dimensions. Since a hypercube has four dimensions, it can rotate one way in two of its dimensions, while rotating a different way in the other<\/i> two dimensions.<\/p>\n

In our zoetrope, we made our little hypercube tumble around a circular track (a movement that uses two dimensions), while also rotating a different way in the remaining two dimensions.<\/p>\n

Now, this is not going to look very intuitive to us poor 3D humans. In fact, it looks as strange to us as, say, a rotating cube would look to a Flatland<\/a> creature that lives its entire life in a two dimensional world.<\/p>\n

Such a 2D creature couldn’t really see a cube — but it could see the shadow a cube makes if its silhouette is projected into the two dimensional world of Flatland:<\/p>\n


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

To the Flatland creature staring at the shadow, it wouldn’t look like something rotating so much as something becoming distorted in all sorts of weird ways.<\/p>\n

And that’s pretty much what happens when you try to make sense of a rotating hypercube. As things rotate out of our little 3D world, they look like they are changing size and shape, rather than rotating.<\/p>\n

But see for yourself:<\/p>\n


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\n<\/center><\/p>\n","protected":false},"excerpt":{"rendered":"

We’re still doing production on the little walking guy. But meanwhile my collaborator Eva Schindling and I managed to build a nice little working zoetrope of a tumbling hypercube. For those of you who don’t know, a hypercube is something like a cube, only with four dimensions instead of three. As a cube is to … Continue reading “Another dimension”<\/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\/4362"}],"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=4362"}],"version-history":[{"count":17,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/4362\/revisions"}],"predecessor-version":[{"id":4652,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/4362\/revisions\/4652"}],"wp:attachment":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4362"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4362"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4362"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}