A number of the things I’ve been showing here recently come in two flavors — two dimensional and three dimensional. For example, I first showed the springy ball\/stick model in two dimensions, and then quickly moved it to three dimensions (which seemed to make it richer).<\/p>\n
I wonder what effect this would have on other things, like fractal Koch snowflakes, or musical candy button machines. It’s not clear that everything<\/i> would benefit from that third dimension. Certain things might actually have a natural affinity for two. In those cases, adding depth might break some important symmetry, or only add confusion.<\/p>\n
It seems like an interesting way to think about any particular thing: Some things might really want to live in only one dimension — others really require four or even more (which can be really problematic if you’re trying to look at them). It seems like a useful question to ask, whether you are talking about music or a snowflake: For any given object or idea, how many dimensions does it want<\/i> to have?<\/p>\n","protected":false},"excerpt":{"rendered":"
A number of the things I’ve been showing here recently come in two flavors — two dimensional and three dimensional. For example, I first showed the springy ball\/stick model in two dimensions, and then quickly moved it to three dimensions (which seemed to make it richer). I wonder what effect this would have on other … Continue reading “How many dimensions?”<\/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\/5913"}],"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=5913"}],"version-history":[{"count":4,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/5913\/revisions"}],"predecessor-version":[{"id":5916,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/5913\/revisions\/5916"}],"wp:attachment":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5913"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5913"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5913"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}