Mem is the thirteenth letter and its value is forty. It has two forms: the open mem, at the beginning and in the middle of a word, and the closed mem, shut on every side, at the end. The Talmud reports the view of Rabbi Yirmeyah, or of Rabbi Chiya bar Abba: the final forms mem, nun, tzadi, peh, kaf, "the Seers said them." The Gemara objects that a prophet may not innovate, and that Rav Chisda teaches that the mem and the samekh of the tablets stood by a miracle. It concludes: both forms already existed, but it had been forgotten which goes in the middle and which at the end, and the Seers fixed the rule: "open in the middle of a word, closed at the end." Rav Chisda adds that the writing on the tablets could be read from inside and from outside; one understands that the center of the closed mem, fully enclosed, had nothing to hold it.
For Sefer Yetzirah, mem is one of the three mother letters, alef, mem, shin, "a great secret, wondrous and hidden." From mem comes water, from shin fire, and air, alef, decides between them, like the pointer between the two pans of a scale. "He made the letter mem king over water, He bound a crown to it," and formed through it earth in the world, cold in the year and the belly in the soul; for "the earth was created from water." In the classification of sounds, mem belongs to the letters of the lips, bet, vav, mem, peh.
Among the children of the study hall, whom the Talmud quotes before Rabbi Yehoshua ben Levi, the two mems are read together: "open mem, closed mem: an open saying, a closed saying." The Torah contains what is explained to all and what remains sealed.
The Alphabet of Rabbi Akiva tells that the letters, engraved on the crown of the Holy One, blessed be He, each came to ask that the world be created through it. Mem pleaded: through me the inhabitants of the world will say "Your kingship is the kingship of all worlds," and the beginning of Your name, Melekh, King, is in me. The answer was no, for through it would come a "day of tumult," mehumah. Another version of the same Alphabet describes the two mems standing by the throne of glory: when the Presence descends, the open mem sings "Your kingship is the kingship of all worlds," the closed mem answers "and Your dominion in every generation," and the Holy One, blessed be He, embraces them and binds to each two crowns, of kingship and of glory.
Mem thus has two faces: water, for Sefer Yetzirah; the open saying and the closed saying, for the children; kingship sung in two voices, for Rabbi Akiva. One can bring these readings together: the revealed part and the hidden part of the Torah together proclaim the kingship of G-d, and the closed mem, which stood by a miracle in the tablets, is no less solid than the other.