{"id":95861,"date":"2026-09-07T02:02:06","date_gmt":"2026-09-07T00:02:06","guid":{"rendered":"https:\/\/beithazohar.com\/abraham-aboulafia-discovery-anticipated-modern-mathematics-centuries\/"},"modified":"2026-09-07T02:04:20","modified_gmt":"2026-09-07T00:04:20","slug":"abraham-aboulafia-discovery-anticipated-modern-mathematics-centuries","status":"publish","type":"post","link":"https:\/\/beithazohar.com\/en\/abraham-aboulafia-discovery-anticipated-modern-mathematics-centuries\/","title":{"rendered":"Abraham Aboulafia: the discovery that anticipated modern mathematics by centuries"},"content":{"rendered":"<style>.kb-row-layout-id_aboulafia-author > .kt-row-column-wrap{align-content:start;}:where(.kb-row-layout-id_aboulafia-author > .kt-row-column-wrap) > .wp-block-kadence-column{justify-content:start;}.kb-row-layout-id_aboulafia-author > .kt-row-column-wrap{column-gap:var(--global-kb-gap-md, 2rem);row-gap:var(--global-kb-gap-md, 2rem);padding-top:var(--global-kb-spacing-sm, 1.5rem);padding-bottom:var(--global-kb-spacing-sm, 1.5rem);}.kb-row-layout-id_aboulafia-author > .kt-row-column-wrap > div:not(.added-for-specificity){grid-column:initial;}.kb-row-layout-id_aboulafia-author > .kt-row-column-wrap{grid-template-columns:minmax(0, 1fr) minmax(0, 6fr) minmax(0, 1fr);}.kb-row-layout-id_aboulafia-author > .kt-row-layout-overlay{opacity:0.30;}@media all and (max-width: 1024px){.kb-row-layout-id_aboulafia-author > .kt-row-column-wrap > div:not(.added-for-specificity){grid-column:initial;}}@media all and (max-width: 1024px){.kb-row-layout-id_aboulafia-author > .kt-row-column-wrap{grid-template-columns:minmax(0, 1fr) minmax(0, 6fr) minmax(0, 1fr);}}@media all and (max-width: 767px){.kb-row-layout-id_aboulafia-author > .kt-row-column-wrap > div:not(.added-for-specificity){grid-column:initial;}.kb-row-layout-id_aboulafia-author > .kt-row-column-wrap{grid-template-columns:minmax(0, 1fr);}}<\/style><div class=\"kb-row-layout-wrap kb-row-layout-id_aboulafia-author alignnone wp-block-kadence-rowlayout\"><div class=\"kt-row-column-wrap kt-has-3-columns kt-row-layout-center-exwide kt-tab-layout-inherit kt-mobile-layout-row kt-row-valign-top\">\r\n\r\n<style>.kadence-column_aboulafia-left > .kt-inside-inner-col{border-top-width:0px;border-right-width:0px;border-bottom-width:0px;border-left-width:0px;}.kadence-column_aboulafia-left > .kt-inside-inner-col,.kadence-column_aboulafia-left > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column_aboulafia-left > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column_aboulafia-left > .kt-inside-inner-col{flex-direction:column;}.kadence-column_aboulafia-left > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column_aboulafia-left > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column_aboulafia-left{position:relative;}@media all and (max-width: 1024px){.kadence-column_aboulafia-left > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}@media all and (max-width: 767px){.kadence-column_aboulafia-left > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}<\/style>\r\n<div class=\"wp-block-kadence-column kadence-column_aboulafia-left inner-column-1\">\r\n<div class=\"kt-inside-inner-col\">\u00a0<\/div>\r\n<\/div>\r\n\r\n\r\n<style>.kadence-column_aboulafia-center > .kt-inside-inner-col{border-top-width:0px;border-right-width:0px;border-bottom-width:0px;border-left-width:0px;}.kadence-column_aboulafia-center > .kt-inside-inner-col,.kadence-column_aboulafia-center > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column_aboulafia-center > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column_aboulafia-center > .kt-inside-inner-col{flex-direction:column;}.kadence-column_aboulafia-center > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column_aboulafia-center > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column_aboulafia-center{position:relative;}@media all and (max-width: 1024px){.kadence-column_aboulafia-center > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}@media all and (max-width: 767px){.kadence-column_aboulafia-center > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}<\/style>\r\n<div class=\"wp-block-kadence-column kadence-column_aboulafia-center inner-column-2\">\r\n<div class=\"kt-inside-inner-col\"><div class=\"intervenant-article-wrap\"><article class=\"linked-post-block\"><a class=\"linked-post-thumb-wrap\" href=\"https:\/\/beithazohar.com\/en\/speaker\/yehonathan-sharvit\/\"><img width=\"209\" height=\"300\" src=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/yehonathan-sharvit-209x300.png\" class=\"linked-post-thumb wp-post-image\" alt=\"Yehonathan Sharvit\" loading=\"lazy\" decoding=\"async\" srcset=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/yehonathan-sharvit-209x300.png 209w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/yehonathan-sharvit-715x1024.png 715w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/yehonathan-sharvit-768x1100.png 768w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/yehonathan-sharvit-21x30.png 21w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/yehonathan-sharvit-52x75.png 52w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/yehonathan-sharvit-77x110.png 77w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/yehonathan-sharvit-112x160.png 112w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/yehonathan-sharvit-349x500.png 349w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/yehonathan-sharvit-1072x1536.png 1072w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/yehonathan-sharvit-35x50.png 35w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/yehonathan-sharvit-70x100.png 70w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/yehonathan-sharvit-140x200.png 140w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/yehonathan-sharvit.png 1160w\" sizes=\"auto, (max-width: 209px) 100vw, 209px\" \/><\/a><div class=\"linked-post-body\"><h3 class=\"linked-post-title\"><a href=\"https:\/\/beithazohar.com\/en\/speaker\/yehonathan-sharvit\/\">Yehonathan Sharvit<\/a><\/h3><\/div><\/article><\/div>        <style>\n        .intervenant-article-wrap{margin-top:12px;padding:10px 12px;text-align:center;max-width:380px;margin-left:auto;margin-right:auto}\n        .linked-post-block{display:flex;flex-direction:column;align-items:center;justify-content:center;gap:12px}\n        .linked-post-thumb-wrap{display:block;width:140px;height:140px;border-radius:50%;overflow:hidden;flex:0 0 auto;box-shadow:0 6px 18px rgba(0,0,0,0.08);background-color:#f6f6f6}\n        .linked-post-thumb-wrap img{width:100%;height:100%;display:block;object-fit:cover}\n        .linked-post-title{font-family:serif;font-size:1.25rem;margin:0;font-weight:600;line-height:1.1}\n        .linked-post-title a{color:inherit;text-decoration:none}\n        .linked-post-title a:hover{text-decoration:underline}\n        @media (max-width:900px){.intervenant-article-wrap{max-width:320px}.linked-post-thumb-wrap{width:120px;height:120px}}\n        @media (max-width:480px){.intervenant-article-wrap{max-width:260px}.linked-post-thumb-wrap{width:92px;height:92px}}\n        <\/style>\n        <\/div>\r\n<\/div>\r\n\r\n\r\n<style>.kadence-column_aboulafia-right > .kt-inside-inner-col{border-top-width:0px;border-right-width:0px;border-bottom-width:0px;border-left-width:0px;}.kadence-column_aboulafia-right > .kt-inside-inner-col,.kadence-column_aboulafia-right > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column_aboulafia-right > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column_aboulafia-right > .kt-inside-inner-col{flex-direction:column;}.kadence-column_aboulafia-right > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column_aboulafia-right > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column_aboulafia-right{position:relative;}@media all and (max-width: 1024px){.kadence-column_aboulafia-right > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}@media all and (max-width: 767px){.kadence-column_aboulafia-right > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}<\/style>\r\n<div class=\"wp-block-kadence-column kadence-column_aboulafia-right inner-column-3\">\r\n<div class=\"kt-inside-inner-col\">\u00a0<\/div>\r\n<\/div>\r\n<\/div><\/div>\r\n\r\n\r\n<div class=\"wp-block-uagb-advanced-heading uagb-block-aboulafia-author\">\r\n<h3 class=\"uagb-heading-text\">Article by <a href=\"https:\/\/beithazohar.com\/en\/speaker\/yehonathan-sharvit\/\" data-type=\"intervenant\" data-id=\"82958\">Yehonathan Sharvit<\/a><\/h3>\r\n<div class=\"uagb-separator\">\u00a0<\/div>\r\n<\/div>\r\n\r\n\r\n\t\t\t\t<div class=\"wp-block-uagb-table-of-contents uagb-toc__align-left uagb-toc__columns-1  uagb-block-aboulafia-toc      \"\n\t\t\t\t\tdata-scroll= \"1\"\n\t\t\t\t\tdata-offset= \"30\"\n\t\t\t\t\tstyle=\"\"\n\t\t\t\t>\n\t\t\t\t<div class=\"uagb-toc__wrap\">\n\t\t\t\t\t\t<div class=\"uagb-toc__title\">\n\t\t\t\t\t\t\tTable Of Contents\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"uagb-toc__list-wrap \">\n\t\t\t\t\t\t<ol class=\"uagb-toc__list\"><li class=\"uagb-toc__list\"><a href=\"#tserouf\" class=\"uagb-toc-link__trigger\">Tserouf<\/a><li class=\"uagb-toc__list\"><a href=\"#suffix-reversals\" class=\"uagb-toc-link__trigger\">Suffix reversals<\/a><li class=\"uagb-toc__list\"><a href=\"#the-symmetry-of-the-world\" class=\"uagb-toc-link__trigger\">The symmetry of the world<\/a><\/ol>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\r\n\r\n\r\n<p class=\"has-drop-cap has-text-align-left wp-block-paragraph\"><em>At the end of his major work, the thirteenth-century kabbalist <a href=\"https:\/\/beithazohar.com\/en\/the-light-of-the-intellect-rabbi-abraham-aboulafia\/\">Abraham Aboulafia<\/a> presents the method of Tserouf, the true foundation of his teaching. Yet the method appears deceptively simple. It took a combinatorics paper published in 1984 to reveal the mathematical power hidden in this ordering.<\/em><\/p>\r\n\r\n\r\n\r\n<h4 class=\"has-ast-global-color-0-color has-text-color wp-block-heading\"><strong>Tserouf<\/strong><\/h4>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">In <em><a href=\"https:\/\/beithazohar.com\/en\/books\/the-light-of-intellect-rabbi-abraham-aboulafia\/\">The Light of the Intellect<\/a><\/em>, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Abraham_Abulafia\" target=\"_blank\" rel=\"noopener\">Abraham Aboulafia<\/a>, a thirteenth-century kabbalist and an avid reader of <em>The Guide for the Perplexed<\/em>, develops a bold thesis: because language and the cosmos obey the same fundamental principle, human beings can approach the divine through the manipulation of letters.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">Contrary to what is often said, the secret of prophecy does not lie in the letters themselves but in the mechanical practice of arranging them. Aboulafia calls this practice <em>Tserouf<\/em>, the methodical <a href=\"https:\/\/en.wikipedia.org\/wiki\/Permutation\" target=\"_blank\" rel=\"noopener\">permutation<\/a> of letters. For it to work, however, Tserouf must be practiced and mastered according to a very precise method.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">He introduces his method as follows:<\/p>\r\n\r\n\r\n\r\n<figure class=\"wp-block-table\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>This rule is easy to understand, and although it has no end that we can apprehend, it necessarily has an end. [&#8230;]<\/td>\r\n<td>\u05d6\u05d4 \u05d4\u05db\u05dc\u05dc \u05d4\u05d5\u05d0 \u05e7\u05dc \u05dc\u05d4\u05d1\u05d9\u05e0\u05d5<br \/>\u05d5\u05d0\u05e3 \u05e2\u05dc \u05e4\u05d9 \u05e9\u05d0\u05d9\u05df \u05dc\u05d5 \u05e1\u05d5\u05e3 \u05de\u05d5\u05e9\u05d2 \u05dc\u05e0\u05d5 \u05d0\u05d1\u05dc \u05d9\u05e9 \u05dc\u05d5 \u05e1\u05d5\u05e3 \u05d1\u05d4\u05db\u05e8\u05d7 [&#8230;]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>And this is why all its parts are included in its general name, which is the Tserouf of the letters; it is also called the reversal of the letters, for all is one. [&#8230;]<\/td>\r\n<td>\u05d5\u05e2\u05dc \u05db\u05df \u05db\u05dc \u05d7\u05dc\u05e7\u05d9\u05d4 \u05e0\u05db\u05dc\u05dc\u05d5 \u05d1\u05e9\u05de\u05d4 \u05d4\u05db\u05dc\u05dc\u05d9 \u05d5\u05d4\u05d5\u05d0 \u05e9\u05dd \u05e6\u05d9\u05e8\u05d5\u05e3 \u05d4\u05d0\u05d5\u05ea\u05d9\u05d5\u05ea<br \/>\u05d0\u05d5 \u05e0\u05e7\u05e8\u05d0\u05d4 \u05d4\u05e4\u05d5\u05da \u05d4\u05d0\u05d5\u05ea\u05d9\u05d5\u05ea \u05e9\u05d4\u05db\u05dc \u05d0\u05d7\u05d3 [&#8230;]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>And this is why the letters were set in rotation, front and back, as it is written in the <a href=\"https:\/\/beithazohar.com\/en\/books\/sefer-yetsirah-facsimile-and-translation-of-the-manuscript-heb-763\/\">Sefer Yetsirah<\/a><\/td>\r\n<td>\u05d5\u05e2\u05dc \u05db\u05df \u05d4\u05ea\u05d2\u05dc\u05d2\u05dc\u05d5 \u05d4\u05d0\u05d5\u05ea\u05d9\u05d5\u05ea \u05d1\u05e4\u05e0\u05d9\u05dd \u05d5\u05d0\u05d7\u05d5\u05e8 \u05db\u05de\u05d5 \u05e9\u05db\u05ea\u05d5\u05d1 \u05d1\u05e1\u05e4\u05e8 \u05d9\u05e6\u05d9\u05e8\u05d4.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/figure>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">He then asks us first to master the Tserouf of two letters:<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">AB BA<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">Then, for three letters, the six arrangements must be listed in this order:<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">ABC ACB BCA BAC CAB CBA<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">He establishes this order so that:<\/p>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\">\r\n<li>The last word, CBA, is the reversal of the first, ABC<\/li>\r\n\r\n\r\n\r\n<li>The first letter remains fixed for as long as possible<\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">He does not explicitly explain why, unlike alphabetical order, BCA must come before BAC.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">For a four-letter word, there are 24 possible arrangements, and they must be listed according to the following four block headings:<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">The block beginning with A, followed by the six permutations of BCD<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">The block beginning with B, followed by the six permutations of CDA<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">The block beginning with C, followed by the six permutations of DAB<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">The block beginning with D, followed by the six permutations of ABC<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">His method seems so simple to him that he does not even bother to provide the full list of 24 permutations. He simply gives the following general recursive rule:<\/p>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\">\r\n<li>Keep the first letter fixed and perform the Tserouf on the last three letters<\/li>\r\n\r\n\r\n\r\n<li>Return to the beginning of the block<\/li>\r\n\r\n\r\n\r\n<li>Rotate the word by moving the first letter to the end<\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">Aboulafia guarantees that if this method is applied, no error will be made regardless of the number of letters.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">Indeed, applying his method to a five-letter word produces the following five block headings:<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">The block beginning with A, followed by the 24 permutations of BCDE<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">The block beginning with B, followed by the 24 permutations of CDEA<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">The block beginning with C, followed by the 24 permutations of DEAB<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">The block beginning with D, followed by the 24 permutations of EABC<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">The block beginning with E, followed by the 24 permutations of ABCD<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">Reading this text, I asked myself the following questions:<\/p>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\">\r\n<li>Why does he speak of a \u201creversal of the letters\u201d when the letters are being rotated?<\/li>\r\n\r\n\r\n\r\n<li>What exactly does he mean by \u201cset in rotation, front and back\u201d?<\/li>\r\n\r\n\r\n\r\n<li>Why does he not explicitly explain why BCA comes before BAC?<\/li>\r\n\r\n\r\n\r\n<li>Is it the order of the permutations that opens the way to prophecy, or simply the idea of permutation itself?<\/li>\r\n\r\n\r\n\r\n<li>Given the many algorithms now available for generating permutations, what makes Aboulafia\u2019s order special?<\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">Surprisingly, modern mathematics and computer science allow us to answer these questions and understand why mastering the order of Tserouf is so fundamental to Kabbalah.<\/p>\r\n\r\n\r\n\r\n<h4 class=\"has-ast-global-color-0-color has-text-color wp-block-heading\"><strong>Suffix reversals<\/strong><\/h4>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">In 1984, mathematician Shmuel Zaks published a short paper on algorithms for generating <a href=\"https:\/\/en.wikipedia.org\/wiki\/Permutation\" target=\"_blank\" rel=\"noopener\">permutations<\/a>, entitled <em><a href=\"https:\/\/cris.technion.ac.il\/en\/publications\/a-new-algorithm-for-generation-of-permutations\/\" target=\"_blank\" rel=\"noopener\">A New Algorithm for Generation of Permutations<\/a><\/em>.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">In his paper, Zaks gives a simple, efficient, and elegant procedure for generating every permutation of a word using only one operation: a suffix reversal, that is, reversing the order of the final letters of the word.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">The lengths of the suffixes to reverse follow an easy-to-remember rhythm: <br \/><br \/>232324<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">232324<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">232324<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">23232<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">Zaks\u2019s deceptively simple procedure attracted the attention of mathematicians, who studied an object known as the Pancake Graph. In this graph,<\/p>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\">\r\n<li>the vertices are all possible arrangements of a word with n letters<\/li>\r\n\r\n\r\n\r\n<li>the edges connect vertices that differ only by a suffix reversal<\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">This graph has remarkable properties that are especially interesting in network theory:<\/p>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\">\r\n<li>self-similarity<\/li>\r\n\r\n\r\n\r\n<li>maximum fault tolerance<\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">More surprisingly still, Zaks\u2019s procedure generates precisely Aboulafia\u2019s order.<\/p>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\">\r\n<li>Reversing the last two letters of ABCD gives ABDC<\/li>\r\n\r\n\r\n\r\n<li>Reversing the last three letters of ABDC gives ACDB<\/li>\r\n\r\n\r\n\r\n<li>and so on\u2026<\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<figure class=\"wp-block-image aligncenter size-large\"><img decoding=\"async\" width=\"936\" height=\"572\" class=\"wp-image-95837\" src=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-renversements-suffixe.png\" alt=\"Sequence of the 24 permutations of four letters obtained by suffix reversals according to Zaks\u2019s algorithm\" srcset=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-renversements-suffixe.png 936w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-renversements-suffixe-300x183.png 300w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-renversements-suffixe-768x469.png 768w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-renversements-suffixe-30x18.png 30w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-renversements-suffixe-75x46.png 75w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-renversements-suffixe-110x67.png 110w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-renversements-suffixe-160x98.png 160w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-renversements-suffixe-500x306.png 500w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-renversements-suffixe-50x31.png 50w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-renversements-suffixe-100x61.png 100w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-renversements-suffixe-200x122.png 200w\" sizes=\"(max-width: 936px) 100vw, 936px\" \/>\r\n<figcaption class=\"wp-element-caption\">Zaks\u2019s suffix reversals reproduce the order of Abraham Aboulafia\u2019s Tserouf.<\/figcaption>\r\n<\/figure>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">A single operation is used: <strong>reversal<\/strong>. This answers the first question: Tserouf is a sequence of <strong>partial reversals<\/strong> that eventually leads to the complete reversal of the word.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">There are many algorithms for enumerating all permutations of a word, but none is as simple and elegant as Zaks\u2019s.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">But there is more\u2026<\/p>\r\n\r\n\r\n\r\n<h4 class=\"has-ast-global-color-0-color has-text-color wp-block-heading\"><strong>The symmetry of the world<\/strong><\/h4>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">Computer science allows us to draw the structure of <em>Tserouf<\/em> by visualizing the Pancake Graph in Aboulafia\u2019s order using Zaks\u2019s formula.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">Each word is placed at equal intervals around a circle in Aboulafia\u2019s order, and each word is connected to its mirror image.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">For four letters, we obtain the following graph:<\/p>\r\n\r\n\r\n\r\n<figure class=\"wp-block-image aligncenter size-large\"><img decoding=\"async\" width=\"636\" height=\"652\" class=\"wp-image-95838\" src=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-4-lettres.png\" alt=\"Graph of Abraham Aboulafia\u2019s Tserouf for four letters and their 24 permutations\" srcset=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-4-lettres.png 636w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-4-lettres-293x300.png 293w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-4-lettres-30x30.png 30w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-4-lettres-73x75.png 73w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-4-lettres-107x110.png 107w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-4-lettres-156x160.png 156w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-4-lettres-488x500.png 488w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-4-lettres-50x50.png 50w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-4-lettres-98x100.png 98w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-4-lettres-195x200.png 195w\" sizes=\"(max-width: 636px) 100vw, 636px\" \/>\r\n<figcaption class=\"wp-element-caption\">Order of the 24 Tserouf permutations for four letters.<\/figcaption>\r\n<\/figure>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">For six letters:<\/p>\r\n\r\n\r\n\r\n<figure class=\"wp-block-image aligncenter size-large\"><img decoding=\"async\" width=\"936\" height=\"958\" class=\"wp-image-95839\" src=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-6-lettres.png\" alt=\"Circular visualization of Abraham Aboulafia\u2019s Tserouf for six letters\" srcset=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-6-lettres.png 936w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-6-lettres-293x300.png 293w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-6-lettres-768x786.png 768w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-6-lettres-30x30.png 30w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-6-lettres-73x75.png 73w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-6-lettres-107x110.png 107w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-6-lettres-156x160.png 156w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-6-lettres-489x500.png 489w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-6-lettres-50x50.png 50w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-6-lettres-98x100.png 98w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-6-lettres-195x200.png 195w\" sizes=\"(max-width: 936px) 100vw, 936px\" \/>\r\n<figcaption class=\"wp-element-caption\">Structure of Abraham Aboulafia\u2019s Tserouf for six letters.<\/figcaption>\r\n<\/figure>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">So far, nothing very surprising. But when we draw the graph for seven letters, something happens.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">Take a moment to look at it\u2026<\/p>\r\n\r\n\r\n\r\n<figure class=\"wp-block-image aligncenter size-large\"><img decoding=\"async\" width=\"936\" height=\"996\" class=\"wp-image-95840\" src=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-7-lettres-symetrie.png\" alt=\"Visualization of Abraham Aboulafia\u2019s Tserouf for seven letters revealing dihedral symmetry\" srcset=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-7-lettres-symetrie.png 936w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-7-lettres-symetrie-282x300.png 282w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-7-lettres-symetrie-768x817.png 768w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-7-lettres-symetrie-28x30.png 28w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-7-lettres-symetrie-70x75.png 70w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-7-lettres-symetrie-103x110.png 103w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-7-lettres-symetrie-150x160.png 150w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-7-lettres-symetrie-470x500.png 470w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-7-lettres-symetrie-47x50.png 47w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-7-lettres-symetrie-94x100.png 94w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/abraham-aboulafia-tserouf-graphe-7-lettres-symetrie-188x200.png 188w\" sizes=\"(max-width: 936px) 100vw, 936px\" \/>\r\n<figcaption class=\"wp-element-caption\">For seven letters, rounded patterns emerge from a graph made of straight lines.<\/figcaption>\r\n<\/figure>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">Rounded patterns seem to emerge from a graph made entirely of straight lines.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">This does not occur with the other known permutation-generation algorithms considered here. It is a distinctive property of Aboulafia\u2019s order.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">With the help of a mathematician friend, we were able to prove this formally in a <a href=\"https:\/\/arxiv.org\/abs\/2607.04658\" target=\"_blank\" rel=\"noopener\">paper<\/a> published in July 2026.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">The chords of the graph seem to point in chaotic directions, yet they organize themselves according to a dihedral symmetry: precisely the symmetry of a regular polygon with as many vertices as the Tserouf has letters. In other words, the graph can be rotated by one seventh of a turn without changing, and when reflected in a mirror it remains invariant.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">This seems to capture precisely the meaning of the introductory phrase about <em>Tserouf<\/em>: \u201cthe letters were <strong>set in rotation, front and back<\/strong>.\u201d<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">And this is not trivial, because the same kind of dihedral symmetry appears throughout the natural world.<\/p>\r\n\r\n\r\n\r\n<figure class=\"wp-block-image aligncenter size-large\"><img decoding=\"async\" width=\"250\" height=\"250\" class=\"wp-image-95841\" src=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-hexagonale-flocon-neige.png\" alt=\"Snowflake illustrating hexagonal symmetry\" srcset=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-hexagonale-flocon-neige.png 250w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-hexagonale-flocon-neige-150x150.png 150w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-hexagonale-flocon-neige-30x30.png 30w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-hexagonale-flocon-neige-75x75.png 75w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-hexagonale-flocon-neige-110x110.png 110w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-hexagonale-flocon-neige-160x160.png 160w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-hexagonale-flocon-neige-50x50.png 50w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-hexagonale-flocon-neige-100x100.png 100w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-hexagonale-flocon-neige-200x200.png 200w\" sizes=\"(max-width: 250px) 100vw, 250px\" \/>\r\n<figcaption class=\"wp-element-caption\">Hexagonal symmetry in the branches of a snowflake.<\/figcaption>\r\n<\/figure>\r\n\r\n\r\n\r\n<figure class=\"wp-block-image aligncenter size-large\"><img decoding=\"async\" width=\"502\" height=\"502\" class=\"wp-image-95842\" src=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-octogonale-tulipe.png\" alt=\"Pink flower illustrating radial symmetry\" srcset=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-octogonale-tulipe.png 502w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-octogonale-tulipe-300x300.png 300w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-octogonale-tulipe-150x150.png 150w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-octogonale-tulipe-30x30.png 30w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-octogonale-tulipe-75x75.png 75w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-octogonale-tulipe-110x110.png 110w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-octogonale-tulipe-160x160.png 160w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-octogonale-tulipe-500x500.png 500w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-octogonale-tulipe-50x50.png 50w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-octogonale-tulipe-100x100.png 100w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-octogonale-tulipe-200x200.png 200w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/>\r\n<figcaption class=\"wp-element-caption\">The arrangement of the petals illustrates radial symmetry in nature.<\/figcaption>\r\n<\/figure>\r\n\r\n\r\n\r\n<figure class=\"wp-block-image aligncenter size-large\"><img decoding=\"async\" width=\"424\" height=\"428\" class=\"wp-image-95843\" src=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-citron-octogonale-decagonale.png\" alt=\"Citrus cross-section illustrating radial symmetry\" srcset=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-citron-octogonale-decagonale.png 424w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-citron-octogonale-decagonale-297x300.png 297w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-citron-octogonale-decagonale-150x150.png 150w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-citron-octogonale-decagonale-30x30.png 30w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-citron-octogonale-decagonale-75x75.png 75w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-citron-octogonale-decagonale-110x110.png 110w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-citron-octogonale-decagonale-50x50.png 50w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-citron-octogonale-decagonale-100x100.png 100w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-citron-octogonale-decagonale-198x200.png 198w\" sizes=\"(max-width: 424px) 100vw, 424px\" \/>\r\n<figcaption class=\"wp-element-caption\">A citrus cross-section reveals the radial organization of its segments.<\/figcaption>\r\n<\/figure>\r\n\r\n\r\n\r\n<figure class=\"wp-block-image aligncenter size-large\"><img decoding=\"async\" width=\"488\" height=\"490\" class=\"wp-image-95844\" src=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-hexadecagonale-meduse-rayonnee.png\" alt=\"Natural radiating pattern illustrating radial symmetry\" srcset=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-hexadecagonale-meduse-rayonnee.png 488w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-hexadecagonale-meduse-rayonnee-300x300.png 300w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-hexadecagonale-meduse-rayonnee-150x150.png 150w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-hexadecagonale-meduse-rayonnee-30x30.png 30w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-hexadecagonale-meduse-rayonnee-75x75.png 75w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-hexadecagonale-meduse-rayonnee-110x110.png 110w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-hexadecagonale-meduse-rayonnee-160x160.png 160w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-hexadecagonale-meduse-rayonnee-50x50.png 50w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-hexadecagonale-meduse-rayonnee-100x100.png 100w, https:\/\/beithazohar.com\/wp-content\/uploads\/2026\/09\/symetrie-hexadecagonale-meduse-rayonnee-200x200.png 200w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/>\r\n<figcaption class=\"wp-element-caption\">A natural radiating pattern illustrates symmetrical organization around a center.<\/figcaption>\r\n<\/figure>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">Since the nineteenth century, one device has made dihedral symmetry visible: the kaleidoscope.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">Its name tells us what it does:<\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u03ba\u03b1\u03bb\u03cc\u03c2 (<em>kalos<\/em>)\u00a0\u2014 beauty,<\/li>\r\n\r\n\r\n\r\n<li>\u03b5\u1f36\u03b4\u03bf\u03c2 (<em>eidos<\/em>)\u00a0\u2014 form<\/li>\r\n\r\n\r\n\r\n<li>\u03c3\u03ba\u03bf\u03c0\u03b5\u1fd6\u03bd (<em>skopein<\/em>)\u00a0\u2014 to look<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">A kaleidoscope is an instrument for looking at beautiful forms. The secret of their beauty is dihedral symmetry, created by an arrangement of mirrors that repeatedly reverse a pattern according to a simple but precise method.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">This symmetry has the power to transform any pattern into a harmonious form.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">The mirrors reverse the pattern again and again, just as Tserouf reverses the letters.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\">Aboulafia can thus be seen as having constructed a literary kaleidoscope centuries ahead of its time. In his teaching, this practice is linked to access to prophecy, and he provides the method for reconstructing it.<\/p>\r\n\r\n\r\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\r\n\r\n<div class=\"ast-related-posts-title-section\"><h2 class=\"ast-related-posts-title\">Our other Articles<\/h2><\/div>\r\n\r\n\n\t\t\t<div class=\"wp-block-uagb-post-grid uagb-post-grid  uagb-post__image-position-background uagb-post__image-enabled uagb-block-3f8a17d6     uagb-post__items uagb-post__columns-3 is-grid uagb-post__columns-tablet-2 uagb-post__columns-mobile-1 uagb-post__equal-height\" data-total=\"6\" style=\"\">\n\n\t\t\t\t\t\t\t\t\t\t\t\t<article class=\"uagb-post__inner-wrap\">\t\t\t\t\t\t\t\t<h4 class=\"uagb-post__title uagb-post__text\">\n\t\t\t\t<a href=\"https:\/\/beithazohar.com\/en\/heykhalot-zohar-peqoudey-2\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">Heykhalot Zohar Peqoudey<\/a>\n\t\t\t<\/h4>\n\t\t\t\t\t\t<div class='uagb-post__text uagb-post-grid-byline'>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"uagb-post__text uagb-post__cta wp-block-button\">\n\t\t\t\t<a class=\"wp-block-button__link uagb-text-link\" style=\"\" href=\"https:\/\/beithazohar.com\/en\/heykhalot-zohar-peqoudey-2\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">Read this article<\/a>\n\t\t\t<\/div>\n\t\t\t\t\t\t<div class='uagb-post__image'>\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/beithazohar.com\/en\/heykhalot-zohar-peqoudey-2\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\"><img decoding=\"async\" width=\"300\" height=\"169\" src=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2023\/04\/Heykhalot-300x169.jpg\" class=\"attachment-medium size-medium\" alt=\"Heykhalot Zohar, les Palais du Zohar\" srcset=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2023\/04\/Heykhalot-300x169.jpg 300w, https:\/\/beithazohar.com\/wp-content\/uploads\/2023\/04\/Heykhalot-1024x577.jpg 1024w, https:\/\/beithazohar.com\/wp-content\/uploads\/2023\/04\/Heykhalot-768x433.jpg 768w, https:\/\/beithazohar.com\/wp-content\/uploads\/2023\/04\/Heykhalot-30x17.jpg 30w, https:\/\/beithazohar.com\/wp-content\/uploads\/2023\/04\/Heykhalot-75x42.jpg 75w, https:\/\/beithazohar.com\/wp-content\/uploads\/2023\/04\/Heykhalot-110x62.jpg 110w, https:\/\/beithazohar.com\/wp-content\/uploads\/2023\/04\/Heykhalot-160x90.jpg 160w, https:\/\/beithazohar.com\/wp-content\/uploads\/2023\/04\/Heykhalot-500x282.jpg 500w, https:\/\/beithazohar.com\/wp-content\/uploads\/2023\/04\/Heykhalot-50x28.jpg 50w, https:\/\/beithazohar.com\/wp-content\/uploads\/2023\/04\/Heykhalot-100x56.jpg 100w, https:\/\/beithazohar.com\/wp-content\/uploads\/2023\/04\/Heykhalot-200x113.jpg 200w, https:\/\/beithazohar.com\/wp-content\/uploads\/2023\/04\/Heykhalot-1536x865.jpg 1536w, https:\/\/beithazohar.com\/wp-content\/uploads\/2023\/04\/Heykhalot.jpg 1640w\" sizes=\"(max-width: 300px) 100vw, 300px\" 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class='uagb-post__image'>\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/beithazohar.com\/en\/heykhalot-zohar-bereshit-2\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\"><img decoding=\"async\" width=\"300\" height=\"169\" src=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2023\/04\/Heykhalot-300x169.jpg\" class=\"attachment-medium size-medium\" alt=\"Heykhalot Zohar, les Palais du Zohar\" srcset=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2023\/04\/Heykhalot-300x169.jpg 300w, https:\/\/beithazohar.com\/wp-content\/uploads\/2023\/04\/Heykhalot-1024x577.jpg 1024w, https:\/\/beithazohar.com\/wp-content\/uploads\/2023\/04\/Heykhalot-768x433.jpg 768w, https:\/\/beithazohar.com\/wp-content\/uploads\/2023\/04\/Heykhalot-30x17.jpg 30w, https:\/\/beithazohar.com\/wp-content\/uploads\/2023\/04\/Heykhalot-75x42.jpg 75w, https:\/\/beithazohar.com\/wp-content\/uploads\/2023\/04\/Heykhalot-110x62.jpg 110w, https:\/\/beithazohar.com\/wp-content\/uploads\/2023\/04\/Heykhalot-160x90.jpg 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href=\"https:\/\/beithazohar.com\/en\/the-three-degrees-of-shabbat\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">The Three Degrees of Shabbat<\/a>\n\t\t\t<\/h4>\n\t\t\t\t\t\t<div class='uagb-post__text uagb-post-grid-byline'>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"uagb-post__text uagb-post__cta wp-block-button\">\n\t\t\t\t<a class=\"wp-block-button__link uagb-text-link\" style=\"\" href=\"https:\/\/beithazohar.com\/en\/the-three-degrees-of-shabbat\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">Read this article<\/a>\n\t\t\t<\/div>\n\t\t\t\t\t\t<div class='uagb-post__image'>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\n\t\t\t\t\t\t\t\t<a class=\"uagb-post__link-complete-box\" href=\"https:\/\/beithazohar.com\/en\/the-three-degrees-of-shabbat\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\"><\/a>\n\t\t\t\t\t\t\t<\/article>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<article class=\"uagb-post__inner-wrap\">\t\t\t\t\t\t\t\t<h4 class=\"uagb-post__title uagb-post__text\">\n\t\t\t\t<a href=\"https:\/\/beithazohar.com\/en\/sefer-yetsirah-nahmanides\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">Sefer Yetsirah \u2013 Nahmanides<\/a>\n\t\t\t<\/h4>\n\t\t\t\t\t\t<div class='uagb-post__text uagb-post-grid-byline'>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"uagb-post__text uagb-post__cta wp-block-button\">\n\t\t\t\t<a class=\"wp-block-button__link uagb-text-link\" style=\"\" href=\"https:\/\/beithazohar.com\/en\/sefer-yetsirah-nahmanides\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">Read this article<\/a>\n\t\t\t<\/div>\n\t\t\t\t\t\t<div class='uagb-post__image'>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\n\t\t\t\t\t\t\t\t<a class=\"uagb-post__link-complete-box\" href=\"https:\/\/beithazohar.com\/en\/sefer-yetsirah-nahmanides\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\"><\/a>\n\t\t\t\t\t\t\t<\/article>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<article class=\"uagb-post__inner-wrap\">\t\t\t\t\t\t\t\t<h4 class=\"uagb-post__title uagb-post__text\">\n\t\t\t\t<a href=\"https:\/\/beithazohar.com\/en\/zohar-commentary\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">Zohar Commentary<\/a>\n\t\t\t<\/h4>\n\t\t\t\t\t\t<div class='uagb-post__text uagb-post-grid-byline'>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"uagb-post__text uagb-post__cta wp-block-button\">\n\t\t\t\t<a class=\"wp-block-button__link uagb-text-link\" style=\"\" href=\"https:\/\/beithazohar.com\/en\/zohar-commentary\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">Read this article<\/a>\n\t\t\t<\/div>\n\t\t\t\t\t\t<div class='uagb-post__image'>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\n\t\t\t\t\t\t\t\t<a class=\"uagb-post__link-complete-box\" href=\"https:\/\/beithazohar.com\/en\/zohar-commentary\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\"><\/a>\n\t\t\t\t\t\t\t<\/article>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<article class=\"uagb-post__inner-wrap\">\t\t\t\t\t\t\t\t<h4 class=\"uagb-post__title uagb-post__text\">\n\t\t\t\t<a href=\"https:\/\/beithazohar.com\/en\/zohar-document-en\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">Zohar<\/a>\n\t\t\t<\/h4>\n\t\t\t\t\t\t<div class='uagb-post__text uagb-post-grid-byline'>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"uagb-post__text uagb-post__cta wp-block-button\">\n\t\t\t\t<a class=\"wp-block-button__link uagb-text-link\" style=\"\" href=\"https:\/\/beithazohar.com\/en\/zohar-document-en\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">Read this article<\/a>\n\t\t\t<\/div>\n\t\t\t\t\t\t<div class='uagb-post__image'>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\n\t\t\t\t\t\t\t\t<a class=\"uagb-post__link-complete-box\" href=\"https:\/\/beithazohar.com\/en\/zohar-document-en\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\"><\/a>\n\t\t\t\t\t\t\t<\/article>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<article class=\"uagb-post__inner-wrap\">\t\t\t\t\t\t\t\t<h4 class=\"uagb-post__title uagb-post__text\">\n\t\t\t\t<a href=\"https:\/\/beithazohar.com\/en\/zohar-mantua\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">Zohar Mantua<\/a>\n\t\t\t<\/h4>\n\t\t\t\t\t\t<div class='uagb-post__text uagb-post-grid-byline'>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"uagb-post__text uagb-post__cta wp-block-button\">\n\t\t\t\t<a class=\"wp-block-button__link uagb-text-link\" style=\"\" href=\"https:\/\/beithazohar.com\/en\/zohar-mantua\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">Read this article<\/a>\n\t\t\t<\/div>\n\t\t\t\t\t\t<div class='uagb-post__image'>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\n\t\t\t\t\t\t\t\t<a class=\"uagb-post__link-complete-box\" href=\"https:\/\/beithazohar.com\/en\/zohar-mantua\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\"><\/a>\n\t\t\t\t\t\t\t<\/article>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<article class=\"uagb-post__inner-wrap\">\t\t\t\t\t\t\t\t<h4 class=\"uagb-post__title uagb-post__text\">\n\t\t\t\t<a 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class='uagb-post__image'>\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/beithazohar.com\/en\/zohar-yitro\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\"><img decoding=\"async\" width=\"126\" height=\"126\" src=\"https:\/\/beithazohar.com\/wp-content\/uploads\/2020\/06\/white-126.png\" class=\"attachment-medium size-medium\" alt=\"logo Beit Ha zohar\" \/>\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\n\t\t\t\t\t\t\t\t<a class=\"uagb-post__link-complete-box\" href=\"https:\/\/beithazohar.com\/en\/zohar-yitro\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\"><\/a>\n\t\t\t\t\t\t\t<\/article>\n\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\n\n<div class=\"bhz-related-view-all\"><a class=\"ast-button\" href=\"\/?page_id=23572\">See all Articles<\/a><\/div>","protected":false},"excerpt":{"rendered":"<p>At the end of his major work, Abraham Aboulafia presents the method of Tserouf. 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