{"id":1986,"date":"2007-06-17T23:34:04","date_gmt":"2007-06-18T07:34:04","guid":{"rendered":"http:\/\/www.ogre.nu\/wp\/?p=1986"},"modified":"2018-02-25T01:32:55","modified_gmt":"2018-02-25T09:32:55","slug":"takana","status":"publish","type":"post","link":"https:\/\/bendwavy.org\/wp\/?p=1986","title":{"rendered":"Takana"},"content":{"rendered":"<p><img decoding=\"async\" align=right src=\"\/doodle\/takana.png\"> I had the idea to design a <a href=\"http:\/\/www.omniglot.com\/writing\/fictional.php\">fantasy script<\/a> from combinations of a small repertoire of features: namely, subsets of this set of twelve segments.  Using a fixed number of segments gives some built-in error-detection.  There are 924 subsets of six segments; discarding those that form disconnected graphs leaves 306, more than enough for a <a href=\"http:\/\/www.omniglot.com\/writing\/syllabaries.htm\">syllabary<\/a>.  (Syllabaries have been invented more often than other types of scripts, but they&#8217;re underrepresented in fantasy.)<!--more--><\/p>\n<p>These figures can be considered as points on an oblique hyperplane bisecting a 12-dimensional hypercube; this hyperplane has 11 dimensions.  I hoped to find a neat projection of that arrangement into 2 or 3 dimensions, but <\/p>\n<p align=center><img decoding=\"async\" src=\"\/doodle\/skewrune.png\"><\/p>\n<p> none has turned up yet.<\/p>\n<p>I provisionally call these characters <i>Takana<\/i>: like Japanese <i>kana<\/i> they are intended to represent syllables (though I haven&#8217;t bothered to make assignments yet); and the superset figure resembles the <i>kanji<\/i> pronounced <i>ta<\/i> (meaning &#8216;field&#8217;).<\/p>\n<p>Having written the above, I now think I see how to look for a good projection: list the 46665 points on the projective hypersphere that represent directions of lines joining two of the 306 nodes, <a href=\"http:\/\/www.qhull.org\/\">find the Voronoi centers<\/a> of those points, and choose three such centers roughly at right angles to each other.<\/p>\n<p><strong>Later:<\/strong> That&#8217;s still not right.  What I want is a (n-3)-dimensional hyperplane in projective space that maximizes its minimum angle from any of the 46665 lines; collapsing the dimensions of that hyperplane should reduce the figure to 3 dimensions without collisions.  But how to find that hyperplane, I have no idea.  In higher dimensions my intuition stinks.<\/p>\n<p><strong>2008:<\/strong> <a href=\"?p=2140\">Takana go goth<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>I had the idea to design a fantasy script from combinations of a small repertoire of features: namely, subsets of this set of twelve segments. Using a fixed number of segments gives some built-in error-detection. There are 924 subsets of &hellip; <a href=\"https:\/\/bendwavy.org\/wp\/?p=1986\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,12],"tags":[],"class_list":["post-1986","post","type-post","status-publish","format-standard","hentry","category-language","category-mathematics"],"_links":{"self":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/1986","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1986"}],"version-history":[{"count":6,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/1986\/revisions"}],"predecessor-version":[{"id":4389,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/1986\/revisions\/4389"}],"wp:attachment":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1986"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1986"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1986"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}