It is a step beyond the natural, the number that transcends nature

AS the Maharal (1526–1609) points out in many of his works, seven represents this world, as exemplified by the seven days of creation. That number permeates discussions of this physical universe. There are seven gates to the netherworld; seven different punishments descend onto this world for seven types of sins (Avos V:10); seven days of various tumah defilements, including the seven-day Red Heifer-Parah Adumah defilement; seven Noachide mitzvos, and dozens of other sevens that point to it as the this-material-world number.
The number eight, by contrast, represents that which is nonphysical, spiritual, and otherworldly. It is a step beyond the natural, the number that transcends nature.
For example, says the Maharal, the bris milah of a newborn infant must take place ideally only on the eighth day, and not on any other day. That a newborn male comes into this world uncircumcised is perfectly natural. The bris milah ushers him and his soul into a realm beyond the natural, via the number eight.
Or consider Chanukah. It marks an eight-day miracle not only because the vial of oil miraculously lasted that long, but also the reverse: perhaps the vial lasted eight days because eight is the realm of transcendence beyond the normative laws of nature, beyond the reality of this world.
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