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Steinsaltz writes:
Someone who accepts nezirut without specifying the amount of time remains a nazir for 30 days (in the language of the Mishna, “Stam nezirut sheloshim yom.“). This law appears in the Mishna on our page with no explanation.
The Gemara demands a source for this rule. Rav Matana suggests that the source is a gematria – that it is based on the numerical value of the letters of the word yihiyeh. Gematria assigns a numeric value to each of the Hebrew letters. The first ten letters (aleph through yod) are valued at 1-10. The next nine letters (kaf through kuf) are valued at 20-100. The final three letters (resh through taf) are the numbers 200, 300 and 400.
The Torah teaches (Bamidbar 6:5) that someone who accepts nezirut “will be holy” – kadosh yihiyeh. Taking the value of the letters:
י – yod = 10
ה – heh = 5
י – yod =10
ה – heh = 5
we arrive at a total of 30.
We explore the An Israelite Self-Offering A New Perspective on the Nazirite by Eliezer Diamond.