It’s very cool that we can rotate things in three dimensions just by playing with a circular disk. After all, a disk is flat!<\/p>\n
What’s also cool is that we can rotate things in four dimensions just by playing with a sphere. It’s not even that difficult to do — but it can be a little difficult to understand.<\/p>\n
Just as you can rotate 3D objects by putting a finger down on a disk on a computer touch-screen, then moving the finger around inside the disk, there’s an equivalent action for a spherical region floating in space in front of you.<\/p>\n
Namely, you can put your hand inside the sphere, pinch your fingers together to “grab” the sphere, then move your hand around inside the sphere (then unpinch your fingers to “ungrab”).<\/p>\n
One way to think about this operation is that the volume inside the sphere is kind of like the area inside a circle, except in one higher dimension. As you move your pinched fingers around inside the sphere, you’re essentially rotating a 4D trackball.<\/p>\n
But how do your movements inside that floating sphere translate to rotations in four dimensions? We’ll get to that tomorrow.<\/p>\n","protected":false},"excerpt":{"rendered":"
It’s very cool that we can rotate things in three dimensions just by playing with a circular disk. After all, a disk is flat! What’s also cool is that we can rotate things in four dimensions just by playing with a sphere. It’s not even that difficult to do — but it can be a … Continue reading “Rotating more stuff”<\/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":"https:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/12145"}],"collection":[{"href":"https:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=12145"}],"version-history":[{"count":5,"href":"https:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/12145\/revisions"}],"predecessor-version":[{"id":12150,"href":"https:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/12145\/revisions\/12150"}],"wp:attachment":[{"href":"https:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12145"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12145"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12145"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}