{"id":2489,"date":"2022-11-27T12:04:21","date_gmt":"2022-11-27T20:04:21","guid":{"rendered":"https:\/\/enfascination.com\/weblog\/?p=2489"},"modified":"2023-10-19T18:56:54","modified_gmt":"2023-10-20T02:56:54","slug":"all-the-sator-squares-in-english-with-code","status":"publish","type":"post","link":"https:\/\/enfascination.com\/weblog\/post\/2489","title":{"rendered":"All the SATOR squares in English, with code"},"content":{"rendered":"<figure id=\"attachment_2490\" aria-describedby=\"caption-attachment-2490\" style=\"width: 1070px\" class=\"wp-caption alignnone\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/enfascination.com\/weblog\/wp-content\/uploads\/2022\/11\/Sator_Square_at_Oppe\u0300de.jpg\" alt=\"\" width=\"1070\" height=\"1060\" class=\"size-full wp-image-2490\" srcset=\"https:\/\/enfascination.com\/weblog\/wp-content\/uploads\/2022\/11\/Sator_Square_at_Oppe\u0300de.jpg 1070w, https:\/\/enfascination.com\/weblog\/wp-content\/uploads\/2022\/11\/Sator_Square_at_Oppe\u0300de-150x150.jpg 150w, https:\/\/enfascination.com\/weblog\/wp-content\/uploads\/2022\/11\/Sator_Square_at_Oppe\u0300de-300x297.jpg 300w, https:\/\/enfascination.com\/weblog\/wp-content\/uploads\/2022\/11\/Sator_Square_at_Oppe\u0300de-768x761.jpg 768w, https:\/\/enfascination.com\/weblog\/wp-content\/uploads\/2022\/11\/Sator_Square_at_Oppe\u0300de-1024x1014.jpg 1024w\" sizes=\"(max-width: 1070px) 100vw, 1070px\" \/><figcaption id=\"caption-attachment-2490\" class=\"wp-caption-text\">OLYMPUS DIGITAL CAMERA<\/figcaption><\/figure>\n<p>Using code for recreational word play is very fun. Having fun with a housemate we drunkenly built a list of all 4- and 5- sided SATOR squares. <\/p>\n<p>These squares are special because they read the same left-to-right, top-to-bottom, and both directions in reverse.  The famous one is an ancient one from Latin<\/p>\n<blockquote><p>SATOR<br \/>\nAREPO<br \/>\nTENET<br \/>\nOPERA<br \/>\nROTAS<\/p><\/blockquote>\n<p>In the ancient world these were used both as magic spells and possibly the first memes. They pop up all over Western history, and into today: the movie Tenet is a reference to this square. <\/p>\n<p>Here are the 70 5-letter squares:<\/p>\n<blockquote><p>\n&#8216;assam&#8217;, &#8216;shama&#8217;, &#8216;sagas&#8217;, &#8216;amahs&#8217;, &#8216;massa&#8217;<br \/>\n&#8216;assam&#8217;, &#8216;shama&#8217;, &#8216;samas&#8217;, &#8216;amahs&#8217;, &#8216;massa&#8217;<br \/>\n&#8216;assam&#8217;, &#8216;shaya&#8217;, &#8216;sagas&#8217;, &#8216;ayahs&#8217;, &#8216;massa&#8217;<br \/>\n&#8216;assam&#8217;, &#8216;shaya&#8217;, &#8216;samas&#8217;, &#8216;ayahs&#8217;, &#8216;massa&#8217;<br \/>\n&#8216;asses&#8217;, &#8216;slive&#8217;, &#8216;simis&#8217;, &#8216;evils&#8217;, &#8216;sessa&#8217;<br \/>\n&#8216;asses&#8217;, &#8216;slive&#8217;, &#8216;siris&#8217;, &#8216;evils&#8217;, &#8216;sessa&#8217;<br \/>\n&#8216;asses&#8217;, &#8216;state&#8217;, &#8216;sagas&#8217;, &#8216;etats&#8217;, &#8216;sessa&#8217;<br \/>\n&#8216;asses&#8217;, &#8216;state&#8217;, &#8216;samas&#8217;, &#8216;etats&#8217;, &#8216;sessa&#8217;<br \/>\n&#8216;asses&#8217;, &#8216;stime&#8217;, &#8216;simis&#8217;, &#8217;emits&#8217;, &#8216;sessa&#8217;<br \/>\n&#8216;asses&#8217;, &#8216;stime&#8217;, &#8216;siris&#8217;, &#8217;emits&#8217;, &#8216;sessa&#8217;<br \/>\n&#8216;asses&#8217;, &#8216;swone&#8217;, &#8216;solos&#8217;, &#8216;enows&#8217;, &#8216;sessa&#8217;<br \/>\n&#8216;ayahs&#8217;, &#8216;yrneh&#8217;, &#8216;anana&#8217;, &#8216;henry&#8217;, &#8216;shaya&#8217;<br \/>\n&#8216;cares&#8217;, &#8216;amene&#8217;, &#8216;refer&#8217;, &#8216;enema&#8217;, &#8216;serac&#8217;<br \/>\n&#8216;dedal&#8217;, &#8216;enema&#8217;, &#8216;deked&#8217;, &#8216;amene&#8217;, &#8216;laded&#8217;<br \/>\n&#8216;dedal&#8217;, &#8216;enema&#8217;, &#8216;deled&#8217;, &#8216;amene&#8217;, &#8216;laded&#8217;<br \/>\n&#8216;dedal&#8217;, &#8216;enema&#8217;, &#8216;dered&#8217;, &#8216;amene&#8217;, &#8216;laded&#8217;<br \/>\n&#8216;dedal&#8217;, &#8216;enema&#8217;, &#8216;dewed&#8217;, &#8216;amene&#8217;, &#8216;laded&#8217;<br \/>\n&#8216;derat&#8217;, &#8216;enema&#8217;, &#8216;refer&#8217;, &#8216;amene&#8217;, &#8216;tared&#8217;<br \/>\n&#8216;gater&#8217;, &#8216;amene&#8217;, &#8216;tenet&#8217;, &#8216;enema&#8217;, &#8216;retag&#8217;<br \/>\n&#8216;gnats&#8217;, &#8216;nonet&#8217;, &#8216;anana&#8217;, &#8216;tenon&#8217;, &#8216;stang&#8217;<br \/>\n&#8216;hales&#8217;, &#8216;amene&#8217;, &#8216;lemel&#8217;, &#8216;enema&#8217;, &#8216;selah&#8217;<br \/>\n&#8216;hales&#8217;, &#8216;amene&#8217;, &#8216;level&#8217;, &#8216;enema&#8217;, &#8216;selah&#8217;<br \/>\n&#8216;laded&#8217;, &#8216;amene&#8217;, &#8216;deked&#8217;, &#8216;enema&#8217;, &#8216;dedal&#8217;<br \/>\n&#8216;laded&#8217;, &#8216;amene&#8217;, &#8216;deled&#8217;, &#8216;enema&#8217;, &#8216;dedal&#8217;<br \/>\n&#8216;laded&#8217;, &#8216;amene&#8217;, &#8216;dered&#8217;, &#8216;enema&#8217;, &#8216;dedal&#8217;<br \/>\n&#8216;laded&#8217;, &#8216;amene&#8217;, &#8216;dewed&#8217;, &#8216;enema&#8217;, &#8216;dedal&#8217;<br \/>\n&#8216;lares&#8217;, &#8216;amene&#8217;, &#8216;refer&#8217;, &#8216;enema&#8217;, &#8216;seral&#8217;<br \/>\n&#8216;massa&#8217;, &#8216;amahs&#8217;, &#8216;sagas&#8217;, &#8216;shama&#8217;, &#8216;assam&#8217;<br \/>\n&#8216;massa&#8217;, &#8216;amahs&#8217;, &#8216;samas&#8217;, &#8216;shama&#8217;, &#8216;assam&#8217;<br \/>\n&#8216;massa&#8217;, &#8216;ayahs&#8217;, &#8216;sagas&#8217;, &#8216;shaya&#8217;, &#8216;assam&#8217;<br \/>\n&#8216;massa&#8217;, &#8216;ayahs&#8217;, &#8216;samas&#8217;, &#8216;shaya&#8217;, &#8216;assam&#8217;<br \/>\n&#8216;pelas&#8217;, &#8216;enema&#8217;, &#8216;lemel&#8217;, &#8216;amene&#8217;, &#8216;salep&#8217;<br \/>\n&#8216;pelas&#8217;, &#8216;enema&#8217;, &#8216;level&#8217;, &#8216;amene&#8217;, &#8216;salep&#8217;<br \/>\n&#8216;resat&#8217;, &#8216;enema&#8217;, &#8216;sedes&#8217;, &#8216;amene&#8217;, &#8216;taser&#8217;<br \/>\n&#8216;resat&#8217;, &#8216;enema&#8217;, &#8216;seles&#8217;, &#8216;amene&#8217;, &#8216;taser&#8217;<br \/>\n&#8216;resat&#8217;, &#8216;enema&#8217;, &#8216;semes&#8217;, &#8216;amene&#8217;, &#8216;taser&#8217;<br \/>\n&#8216;resat&#8217;, &#8216;enema&#8217;, &#8216;seres&#8217;, &#8216;amene&#8217;, &#8216;taser&#8217;<br \/>\n&#8216;resat&#8217;, &#8216;enema&#8217;, &#8216;sexes&#8217;, &#8216;amene&#8217;, &#8216;taser&#8217;<br \/>\n&#8216;retag&#8217;, &#8216;enema&#8217;, &#8216;tenet&#8217;, &#8216;amene&#8217;, &#8216;gater&#8217;<br \/>\n&#8216;salep&#8217;, &#8216;amene&#8217;, &#8216;lemel&#8217;, &#8216;enema&#8217;, &#8216;pelas&#8217;<br \/>\n&#8216;salep&#8217;, &#8216;amene&#8217;, &#8216;level&#8217;, &#8216;enema&#8217;, &#8216;pelas&#8217;<br \/>\n&#8216;selah&#8217;, &#8216;enema&#8217;, &#8216;lemel&#8217;, &#8216;amene&#8217;, &#8216;hales&#8217;<br \/>\n&#8216;selah&#8217;, &#8216;enema&#8217;, &#8216;level&#8217;, &#8216;amene&#8217;, &#8216;hales&#8217;<br \/>\n&#8216;serac&#8217;, &#8216;enema&#8217;, &#8216;refer&#8217;, &#8216;amene&#8217;, &#8216;cares&#8217;<br \/>\n&#8216;seral&#8217;, &#8216;enema&#8217;, &#8216;refer&#8217;, &#8216;amene&#8217;, &#8216;lares&#8217;<br \/>\n&#8216;sesey&#8217;, &#8216;edile&#8217;, &#8216;simis&#8217;, &#8216;elide&#8217;, &#8216;yeses&#8217;<br \/>\n&#8216;sesey&#8217;, &#8216;edile&#8217;, &#8216;siris&#8217;, &#8216;elide&#8217;, &#8216;yeses&#8217;<br \/>\n&#8216;sesey&#8217;, &#8216;elide&#8217;, &#8216;simis&#8217;, &#8216;edile&#8217;, &#8216;yeses&#8217;<br \/>\n&#8216;sesey&#8217;, &#8216;elide&#8217;, &#8216;siris&#8217;, &#8216;edile&#8217;, &#8216;yeses&#8217;<br \/>\n&#8216;sessa&#8217;, &#8217;emits&#8217;, &#8216;simis&#8217;, &#8216;stime&#8217;, &#8216;asses&#8217;<br \/>\n&#8216;sessa&#8217;, &#8217;emits&#8217;, &#8216;siris&#8217;, &#8216;stime&#8217;, &#8216;asses&#8217;<br \/>\n&#8216;sessa&#8217;, &#8216;enows&#8217;, &#8216;solos&#8217;, &#8216;swone&#8217;, &#8216;asses&#8217;<br \/>\n&#8216;sessa&#8217;, &#8216;etats&#8217;, &#8216;sagas&#8217;, &#8216;state&#8217;, &#8216;asses&#8217;<br \/>\n&#8216;sessa&#8217;, &#8216;etats&#8217;, &#8216;samas&#8217;, &#8216;state&#8217;, &#8216;asses&#8217;<br \/>\n&#8216;sessa&#8217;, &#8216;evils&#8217;, &#8216;simis&#8217;, &#8216;slive&#8217;, &#8216;asses&#8217;<br \/>\n&#8216;sessa&#8217;, &#8216;evils&#8217;, &#8216;siris&#8217;, &#8216;slive&#8217;, &#8216;asses&#8217;<br \/>\n&#8216;shaya&#8217;, &#8216;henry&#8217;, &#8216;anana&#8217;, &#8216;yrneh&#8217;, &#8216;ayahs&#8217;<br \/>\n&#8216;stang&#8217;, &#8216;tenon&#8217;, &#8216;anana&#8217;, &#8216;nonet&#8217;, &#8216;gnats&#8217;<br \/>\n&#8216;start&#8217;, &#8217;tiler&#8217;, &#8216;alula&#8217;, &#8216;relit&#8217;, &#8216;trats&#8217;<br \/>\n&#8216;tared&#8217;, &#8216;amene&#8217;, &#8216;refer&#8217;, &#8216;enema&#8217;, &#8216;derat&#8217;<br \/>\n&#8216;taser&#8217;, &#8216;amene&#8217;, &#8216;sedes&#8217;, &#8216;enema&#8217;, &#8216;resat&#8217;<br \/>\n&#8216;taser&#8217;, &#8216;amene&#8217;, &#8216;seles&#8217;, &#8216;enema&#8217;, &#8216;resat&#8217;<br \/>\n&#8216;taser&#8217;, &#8216;amene&#8217;, &#8216;semes&#8217;, &#8216;enema&#8217;, &#8216;resat&#8217;<br \/>\n&#8216;taser&#8217;, &#8216;amene&#8217;, &#8216;seres&#8217;, &#8216;enema&#8217;, &#8216;resat&#8217;<br \/>\n&#8216;taser&#8217;, &#8216;amene&#8217;, &#8216;sexes&#8217;, &#8216;enema&#8217;, &#8216;resat&#8217;<br \/>\n&#8216;trats&#8217;, &#8216;relit&#8217;, &#8216;alula&#8217;, &#8217;tiler&#8217;, &#8216;start&#8217;<br \/>\n&#8216;yeses&#8217;, &#8216;edile&#8217;, &#8216;simis&#8217;, &#8216;elide&#8217;, &#8216;sesey&#8217;<br \/>\n&#8216;yeses&#8217;, &#8216;edile&#8217;, &#8216;siris&#8217;, &#8216;elide&#8217;, &#8216;sesey&#8217;<br \/>\n&#8216;yeses&#8217;, &#8216;elide&#8217;, &#8216;simis&#8217;, &#8216;edile&#8217;, &#8216;sesey&#8217;<br \/>\n&#8216;yeses&#8217;, &#8216;elide&#8217;, &#8216;siris&#8217;, &#8216;edile&#8217;, &#8216;sesey&#8217;\n<\/p><\/blockquote>\n<p>To generate them yourself (and the fours), here is code that you can run by pressing Play.<br \/>\nhttps:\/\/colab.research.google.com\/drive\/14gaONdrLuxc3Pzz6M8y1RWpTLIdLY7H0?usp=sharing<br \/>\nFor words we used the official Scrabble list. The tests are hard to read but they check the symmetries of the square.<\/p>\n<p>The interesting findings are that <\/p>\n<ul>\n<li>there are 70 5-letter ones in English, <\/li>\n<li>494 in 4 letters, <\/li>\n<li>none use only familiar words, <\/li>\n<li>few make technically readable sentences, <\/li>\n<li>we did surprisingly well building 4-letter ones by hand without the help of code, but<\/li>\n<li>building 5 letter ones by hand is very very hard<\/li>\n<li>They are counter-intuitive and having code made it a lot easier to think about them and understand the constraints they have to satisfy<\/li>\n<\/ul>\n<p>The basic rules in building them are that<\/p>\n<ul>\n<li> all n words have to be n letters long, <\/li>\n<li>each should be reversible (form a word in both directions),\n<ul>\n<li>if there is a middle word (for 3- and 5- and other odd lengths), it should be a palindrome (e.g. &#8220;TENET&#8221;; palindromes are a special case of reversible words), and <\/li>\n<\/ul>\n<\/li>\n<li>at least one should begin with a vowel\n<ul>\n<li>in english the only vowels that appeared in legal 5-letter vowel-ended words in our SATOR squares were <em>a<\/em> and <em>e<\/em>, with a&#8217;s accounting for the majority.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>The next challenge would be to build a SATOR cube (filled or hollow\u2014n slices of cube or a cube with one square on each face).  Probably there are none in 5 letters (if there are any, I&#8217;d guess there is just one), a couple in 4 letters, and several in 3 letters, with filled obviously more rare than hollow.<\/p>\n<p>Another challenge would be to find words that I want to include that aren&#8217;t on the Scrabble list and see if they change anything.<\/p>\n<!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content --><!-- AddThis Related Posts generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"<p>Using code for recreational word play is very fun. Having fun with a housemate we drunkenly built a list of all 4- and 5- sided SATOR squares. These squares are special because they read the same left-to-right, top-to-bottom, and both directions in reverse. The famous one is an ancient one from Latin SATOR AREPO TENET &hellip; <a href=\"https:\/\/enfascination.com\/weblog\/post\/2489\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">All the SATOR squares in English, with code<\/span><\/a><!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt --><!-- AddThis Related Posts generic via filter on get_the_excerpt --><\/p>\n","protected":false},"author":1,"featured_media":2490,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"wpupg_custom_link":[],"wpupg_custom_link_behaviour":["default"],"wpupg_custom_image":[],"wpupg_custom_image_id":[],"footnotes":""},"categories":[33,15,16],"tags":[],"_links":{"self":[{"href":"https:\/\/enfascination.com\/weblog\/wp-json\/wp\/v2\/posts\/2489"}],"collection":[{"href":"https:\/\/enfascination.com\/weblog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/enfascination.com\/weblog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/enfascination.com\/weblog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/enfascination.com\/weblog\/wp-json\/wp\/v2\/comments?post=2489"}],"version-history":[{"count":3,"href":"https:\/\/enfascination.com\/weblog\/wp-json\/wp\/v2\/posts\/2489\/revisions"}],"predecessor-version":[{"id":2493,"href":"https:\/\/enfascination.com\/weblog\/wp-json\/wp\/v2\/posts\/2489\/revisions\/2493"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/enfascination.com\/weblog\/wp-json\/wp\/v2\/media\/2490"}],"wp:attachment":[{"href":"https:\/\/enfascination.com\/weblog\/wp-json\/wp\/v2\/media?parent=2489"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/enfascination.com\/weblog\/wp-json\/wp\/v2\/categories?post=2489"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/enfascination.com\/weblog\/wp-json\/wp\/v2\/tags?post=2489"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}