What makes a person alive? Is life something that either is, or isn’t? Or, Are some people more alive than others? If so, how is it determined?
In the Mishna on Amud Aleph, Hillel uses a melitza to back up a rabbinic decree. Hillel holds that a convert who converted on Passover eve cannot partake from the Paschal sacrifice and instead must undergo the same purification rituals as one who comes in contact with a corpse. That is, to be sprinkled by the ashes of the Red heifer on the third and seventh day and then immersion in the Mikvah. It is only a requirement because actually as a gentile when he was exposed to the corpse he does not become virtually impure. The reason for the rabbinic degree is so that the following year that convert will not make a mistake and assume that he can partake of the Paschal sacrifice despite having been in contact with a corpse only a day before.
However the meliltza (figurative expression) used by Hillel is הפורש מין הערלה כפורש מין הקבר, One who separates from the foreskin by being circumcised is ritually impure, like one who separates from the grave after coming in contact with a corpse. Consequently, he must first observe the seven-day purification process necessary to remove ritual impurity imparted by a corpse.
It is too juicy a statement to be taken as a mere legalism and is taken by certain mystical commentaries as Omnisignificant (See Ramchal Derech Etz Chaim 24 and Kli Yakkar Vayikra 12:2). It is noted that the Bris that occurs after 7 days on day 8 is similar to the 7 day purification period that is required after contact with a corpse.
In general, the number 7 is invoked by the tradition in many liminal rituals that involve the transition from life to death, or greater degrees of life from lesser states. Existence itself occurred over 7 days, marriage is celebrated in 7 days, death is marked, menstrual impurity (which is a symbolic loss of a potential baby) and mourning occurs over 7 days.
Our tradition is acutely aware of the passage of time and its significance. The importance of mindfully recognizing that we pass from states of life to death and death to life cannot be underestimated. The person who chooses to transition into Judaism, or to transition into marriage or even who completes a week of (hopefully) accomplishment and celebrates shabbos is moving away from death and toward life. If we don’t mark time and are not mindful of transitions in life, we lose awareness and even can be said to be less alive. Going through the motions without paying attention to what happens to us and how we grow is a small kind of dying that we should avoid.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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