{"id":5976,"date":"2022-12-22T15:46:21","date_gmt":"2022-12-22T22:46:21","guid":{"rendered":"https:\/\/theoryofeverything.org\/theToE\/?p=5976"},"modified":"2025-08-30T09:55:25","modified_gmt":"2025-08-30T16:55:25","slug":"a-new-and-improved-e8-hasse-visualization","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2022\/12\/22\/a-new-and-improved-e8-hasse-visualization\/","title":{"rendered":"A New and Improved E8 Hasse Visualization"},"content":{"rendered":"\n<p>This uses the latest Mathematica version 13.2 with code tweaks to better understand what is being presented, including the E8 Algebra roots, weights, and heights. This is used on the <a href=\"https:\/\/en.wikipedia.org\/wiki\/E8_(mathematics)\" target=\"_blank\" rel=\"noopener\">E8 group theory page of WikiPedia<\/a>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/e8-100-dynkin-physics-b.svg\" target=\"_blank\" rel=\"noreferrer noopener\"><img decoding=\"async\" src=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/e8-100-dynkin-physics-b.svg\" alt=\"\"\/><\/a><\/figure>\n\n\n\n<p>For a more graphic intensive E8 Hasse visualization, see below with both positive and negative roots and more node information and graphics. See <a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/E8doubleHasse.nb\" title=\"\">here<\/a> and <a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/E8doubleHasse.pdf\" target=\"_blank\" rel=\"noopener\" title=\"\">here<\/a> for the Mathematica notebook and PDF respectively.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/E8doubleHasse.svg\" target=\"_blank\" rel=\" noreferrer noopener\"><img decoding=\"async\" src=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/E8doubleHasse.svg\" alt=\"\"\/><\/a><figcaption class=\"wp-element-caption\">Double Hasse E8 Visualization<\/figcaption><\/figure>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>This uses the latest Mathematica version 13.2 with code tweaks to better understand what is being presented, including the E8 Algebra roots, weights, and heights. This is used on the E8 group theory page of WikiPedia. For a more graphic intensive E8 Hasse visualization, see below with both positive and negative roots and more node &hellip; <a href=\"https:\/\/theoryofeverything.org\/theToE\/2022\/12\/22\/a-new-and-improved-e8-hasse-visualization\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">A New and Improved E8 Hasse Visualization<\/span> <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":[3],"tags":[18,4,26,14],"class_list":["post-5976","post","type-post","status-publish","format-standard","hentry","category-physics","tag-dynkin","tag-e8","tag-hasse","tag-math"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/5976","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=5976"}],"version-history":[{"count":7,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/5976\/revisions"}],"predecessor-version":[{"id":7290,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/5976\/revisions\/7290"}],"wp:attachment":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/media?parent=5976"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/categories?post=5976"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/tags?post=5976"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}