Mem is the thirteenth letter of the Hebrew alphabet.

The gematria of Mem is 40.

Forty is the number of days it rained upon the earth during the Flood. Forty is also the num­ber of days Moses spent on Mount Sinai. Moses actually ascended the mountain three separate times. The first forty-day sojourn took place when he received the Torah. Then Moses descended with the Tablets, but shattered them when he saw the Golden Calf that the people had made in his absence. The following morning Moses returned to the mountain for another forty days to pray on behalf of the Jewish people. When Moses returned to the encampment, G‑d called out for him to return to the mountain, this time, with his own tablets. So Moses dug under his tent and found two sapphire stones. He brought them up with him to Mount Sinai for the third and final forty days, and G‑d engraved the Ten Commandments on them. It was the tenth of the month of Tishrei when Moses came down from the mountain with G‑d’s law after these final forty days. G‑d declared, “I have forgiven [the Jewish people] as you have asked.” The culmination of these three forty-day periods, the tenth of Tishrei, Yom Kippur, is thus the day we as the Jewish people fast and pray to atone for our sins.

There are other significant references to forty in the Torah: Moses’ spies scouted the land for forty days. The Jews were in the desert for forty years. And a mikveh, a ritual bath, is made up of forty se’ah (about 200 gallons).

What is the concept of forty? Forty represents a metamor­phosis, a transformation. After forty days, the embryo of a child begins to assume a recognizable form.

Additionally, a mikveh (with its forty se’ah) has the ability to change an individual from a state of impurity to purity. And if one wants to undertake a conversion,11 one must immerse in a mikveh, whereupon his or her Jewish soul is revealed.

G‑d brought a flood upon this world for forty days and forty nights. The waters of the flood were not for revenge, as is commonly assumed, but for atonement, to purify and transform the world, in much the same way a mikveh purifies a person.

Each of Moses’ forty-day sojourns in heaven signified a trans­formation. The first forty days was to receive the Torah, and when an individual learns Torah, he or she develops the ability to change for the better. The second trip was for prayer, tefillah. When a person prays, he or she can change an evil decree; in this case, G‑d’s intention to annihilate the Jewish people. Indeed, because of Moses’ supplications, G‑d was will­ing to bestow His mercy and once again offer them His Torah. The final ascent represented teshuvah (repentance)—also a transformation—because once a person has repented, he is no longer the same person he was when he sinned. When Moses finally returned to the Jewish people with G‑d’s law, they were at a level of atonement—and thus finally prepared to become G‑d’s nation.

Furthermore, the words Torah, tefillah and teshuvah begin with a tav, which has the numerical value of 400, or 40x10 (i.e., serving G‑d with all of one’s 10 faculties for 40 days).

The forty years that the Jews spent in the desert also consti­tuted a transformation. The nation that had rebelled against G‑d had metamorphosed into a nation that was ready to adhere to His word.