{"id":2856,"date":"2015-04-02T10:30:10","date_gmt":"2015-04-02T17:30:10","guid":{"rendered":"http:\/\/theoryofeverything.org\/MyToE\/?p=2856"},"modified":"2015-04-02T10:30:10","modified_gmt":"2015-04-02T17:30:10","slug":"a-3d-projection-of-e8-binary-coordinates-to-pascal-triangle-related-columns","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2015\/04\/02\/a-3d-projection-of-e8-binary-coordinates-to-pascal-triangle-related-columns\/","title":{"rendered":"A 3D projection of E8 (binary coordinates) to Pascal triangle related columns"},"content":{"rendered":"<p>This uses &#8220;binary&#8221; vertices of E8 (all 0&#8217;s or 1&#8217;s) from the Pascal triangle \/ Clifford algebra construction.<br \/>\nNotice the 8 excluded &#8220;generator&#8221; vertices are the axis 1-8, which show the projection orientation {X,Y,Z} vectorx. These sometimes are added to the 240 vertex &#8220;dimension count&#8221; of E8. There are a number of overlaps in the vertices in some columns, which are indicated by the color of the vertex.<\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=2857\" rel=\"attachment wp-att-2857\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/04\/pascal-e8.png\" alt=\"pascal-e8\" width=\"500\" class=\"alignnone size-full wp-image-2857\" \/><\/a><\/p>\n<p>Just for good measure, here is a 2D 16&#215;16 matrix projection of the same &#8220;binary&#8221; E8 vertices. It shows the particle physics label with the E8 vertex number.<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=2861\" rel=\"attachment wp-att-2861\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/04\/BinSquare.png\" alt=\"BinSquare\" width=\"500\" class=\"alignnone size-full wp-image-2861\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This uses &#8220;binary&#8221; vertices of E8 (all 0&#8217;s or 1&#8217;s) from the Pascal triangle \/ Clifford algebra construction. Notice the 8 excluded &#8220;generator&#8221; vertices are the axis 1-8, which show the projection orientation {X,Y,Z} vectorx. These sometimes are added to the 240 vertex &#8220;dimension count&#8221; of E8. There are a number of overlaps in the &hellip; <a href=\"https:\/\/theoryofeverything.org\/theToE\/2015\/04\/02\/a-3d-projection-of-e8-binary-coordinates-to-pascal-triangle-related-columns\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">A 3D projection of E8 (binary coordinates) to Pascal triangle related columns<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[8,4],"class_list":["post-2856","post","type-post","status-publish","format-standard","hentry","category-physics","tag-3d","tag-e8"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/2856","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/comments?post=2856"}],"version-history":[{"count":0,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/2856\/revisions"}],"wp:attachment":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/media?parent=2856"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/categories?post=2856"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/tags?post=2856"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}