Who knows forty?
Please cite/link your sources, if possible. At some point after Shabbat, I will:
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Forty days before a baby is formed, it is determined in Heaven who the baby will marry.
40 generations from Moshe Rabbeinu to Rabbeinu HaKadosh (Rabi Yehudah HaNasi).
40 Sa'ah (usually given as 200 gallons) is equivalent to 3 cubic Amah (cubits), and is the minimum volume of a mikvah.
A mikvah must be big enough to immerse an average person (estimated at 1 Amah wide x 1 Amah deep x 3 Amah tall).
Knowing those facts, the Gemara in Arvei Pesachim computes the Reviis-Halog (from units of volume to cubic length) as 2 x 2 x 2.7 etzbaos. The computation is pretty straightforward, but many Rishonim do it in all sorts of convoluted ways -- as they try to avoid decimals!
40 are the days Moshe Rebbeinu was on Har Sinai receiving the Torah (Shemos 24:18) "Moshe arrived in the midst of the cloud and ascended the mountain; and Moses was on the mountain forty days and forty nights."
Forty days from an egg's fertilization at which point it's Halachically called a fetus. (Before that, it's "just water.")
Some interesting applications of this:
Some poskim use this source to allow some cases of abortion before this point, though R' Moshe Feinstein vehemently disagrees.
R' Ahron Soloveichik uses the above source to argue that Halachic motherhood is determined by womb and not egg, "as before 40 days the Halacha treats the egg no differently than a synthetic substance made in Japan."
When the Mishna in Avos talks about decrees made "40 days before the fetus is fashioned", that's usually interpreted as the moment of conception = (fashioning minus 40).
The Flood waters rage for 40 days and nights, as the world needs to be re-born, so to speak. Similarly, Moses is on Mount Sinai 40 days and nights, at which point he's reborn at a higher spiritual level (so to speak).
The Gemara (Nida 30b, see Rashi) records the results of some human experimentation conducted by non-Jews that involved impregnating women and later cutting them open to see whether a fetus' gender is visible by the 40-day-point. This seems to imply that Judaism is willing to make use of scientific knowledge even if it was obtained unethically. (Heard on a Rabbi Frand tape.)
40 cubits is the radius of a circle, centered on a vegetable or grain planted in a vineyard, in which (in some cases) all of the plants within the circle become forbidden for use and must be burned. (Rambam, Hil. Kilayim 6:2. Very timely, incidentally; this was the daily portion of Rambam, according to the one-chapter-a-day cycle, two days ago.)
Rabbi Tzadok fasted for 40 years (days only) to stave off the destruction of Jerusalem (Bavli, Gittin 56b). (Interestingly, the Ostrovtzer Rebbe is reputed to have fasted 40 years before the Holocaust, as well!)
40 years wandering in the Desert. (It's so obvious, that nobody said it!)
At 40 days, the fetus is considered to have a human form, and for some purposes it becomes like murder to abort it at this point. It also has ramifications for Ritual Purity (Mapelet Shilya). Hence, the moment of conception is sometimes referred to as "40 days before the formation of the child".
The Maharal considers 40 as the number of formation, so he considers the Jewish people as having been "formed" during their desert experience.
Each stone that they set up in the Jordan River (in Yehoshua) weighed 40 Seah.
40 years before the destruction of the Beis Hamikdash the Sanhedrin moved from the Hewn Chamber to a place called Chanus. (Sanhedrin 41a)
The torah says a person gets 40 lashes per transgression of a typical prohibition. Rabi Yehudah takes this literally. (Makkos 22a) The Tana Kamah holds that a man can only get 39 per sin.
40 are the days Yechezkel lay on his right side for the sins of the Southern Kingdom (Eze. 4:6).
40 are the days Goliath presented himself for battle with Israel, before David arrived and ultimately slayed him (Shmuel I 17:16).
Kayin and Hevel were 40 years old when they brought their Korbanos (Midrash Tanchuma, Bereishis 9)