# Sefirot and Torah:

## The Sefirot is a pattern of 10vertices linked by 22 lines.

This diagram of the Sefirot (and the English words for eachvertex) come from a figure on page 193 of the book The Jew in theLotus, by Rodger Kamenetz (HarperCollins 1994). I added the 3 colorsfor the lines. There exist other, slightly different, arrangements ofthe 22 lines, such as those shown on the webpages of Michael Graffam.

The Sefirot has some structure that is similar to the structure ofSingularities.

The 22 lines can be put in correspondence with the 22 letters ofthe Hebrew alphabet.

The Hebrew alphabet has 22 letters (compare the 0 plus 21 Major Arcana of the Tarot); 3 are Elementary (compare quaternion imaginaries)(green Sefirot lines); 7 are Double (compare octonion imaginaries)(red Sefirot lines); and the remaining 12 are Simple (compare the 12 Branches)(cyan Sefirot lines); as shown in this table that lists a correspondence with ASCII characters that can be used in an internet version of the Torah:
Elementary Double Simple Final ALEF A BET B GIMEL G DALET D HEY H VAV V ZAYIN Z HET X TET + YUD Y KAF K LAMED L MEM M NUN N SAMEH \$ AYIN O PEH P TZADE C QOF Q RESH R SHIN/SIN S TAV T KAF SOFIT k MEM SOFIT m NUN SOFIT n PEH SOFIT p TZADE SOFIT c
The 12 Simple letters correspond to the 12 vertices (both concave and convex) of the Mogan David:
/\____/__\____\ / \ /\/ \//\ /\/__\____/__\\ /\/

### Sefirot and Singularities

The Sefirot has some structure that issimilar to the structure of Singularities:

Crown/Keter has 3 lines, and the unimodalsingularities have have a 3-suffix series plus 14 (corresponding tothe Lie group G2) exceptional families.

Beauty/Tiferet has 8 lines, and the bimodal singularitieshave 8 infinite series plus 14 (corresponding to the Liegroup G2) exceptional families.

Yesod/Foundation has 3 lines (plus 1 other line toMalkhut/Kingdom), and there are 3 H singularities (H2, H3, H4) plusthe I2(k) singularities.

Malkhut/Kingdom has 3 lines, and the simple singularitiesare A, D, and E (if the E is thecentral line up to Yesod/Foundation, it is a connection between E andH).

The 6 outer vertices, 2 sets of 3 (like ijk and IJK of the1ijkEIJK octionions, are connected toeach other by a network of 7 lines (like the 7 imaginary octonions).

According to the book Singularities of Differentiable Maps, VolumeI, by V. I.Arnold, S. M. Gusein-Zade, A. N. Varchenko (Birkhauser 1985):

• "... The quasihomogeneous unimodal singularities are obtained from automorphic functions connected with 14 distinguished triangles on the Lobachevskii plane and three distinguished triangles on the Euclidean plane in precisely the same way as
• simple singularities are connected with regular polyhedra ...
• ... The quasihomogeneous bimodal singularities are associated with the 6 quadrilaterals and the 14 triangles on the Lobachevskii plane (in the latter case one must consider automorphic functions wiht automorphy factors corresponding to 2-, 3-, or 5- sheeted coverings) ...".

What about Torah study by non-Jews?

"... a non-Jew who studies the details of the seven Noahide laws,which are incumbent on him, deserves the honors due a Kohen Gadol(Sanhedrin 59a). The study of the seven Noahide laws may lead him tostudy most of the precepts of the Torah (Meiri to Sanhedrin 59a; seeResponsa, Rama section 10). ...

... Noahide Laws - the seven commandments given to Noah and hissons, which are binding upon all gentiles. These laws include theobligation to have a body of civil law, and the prohibitions againstidolatry, immorality, bloodshed, blasphemy, stealing and robbing, andeating limbs from a live animal. ...". (From Talmud Bavli / TractateChagigah, The Gemara, The ArtScrollSeries / Schottenstein Edition, Mesorah Publications Ltd. (1999) 13a3)