Why does a boy become Bar Mitzva at thirteen years old?

Regarding the verse “The wise man has his eyes on his head”[1] one can ask an obvious question: is it just the wise man who has eyes on his head, everyone has eyes on their head! Even animals! So what has wisdom have to do with eyes on one’s head? To understand the meaning behind this cryptic verse the Zohar explains that a man is not permitted to walk four amos without a head covering since the Shechina (Heavenly Presence) rests on the head of every Jew. With this understanding, the Zohar reads the posuk as follows: “The wise man has his eyes focused on what is on his head”, namely – the Shechina, and by constantly focusing on the fact that he is in Hashem’s presence he will surely become wise.

The Zohar further explains that when the Shechina rests on the head of a person, that person glows and becomes a lamp of Hashem, and every lamp needs oil to fuel its light and this oil is the Mitzvos and good deeds that a person does[1].

With this information we are on the way to answer our question why a boy becomes Bar Mitzva at thirteen years old.

When a baby is born, his height is generally five tefachim[2], at Bar Mitzva he is ten tefachim and as a fully grown adult he is generally fifteen tefachim[3].  The Gemora explains that the Shechina dwells at but never descends lower than ten tefachim from the ground[4].  Therefore we see that at thirteen years old the average Bar Mitzva boy is ten tefachim tall at which point he finally reaches the height where the Shechina can rest on his head.  Therefore, in order to keep the glow of the Shechina there, he needs to fuel his lamp by doing Mitzvos and good deeds (the oil) – which is why he becomes obligated in Mitzvos at that age.

(Based on the Leviyas Chein, a grandson of the Bach)

[1] This is the intention behind the Posuk “Your head should never lack oil” (Koheles 9:8)

[2] One amah

[3] The Alshich in Parshas Bechukosai explains that the height of man is proportional to his spiritual stature, and at each of these ages a person develops greater spiritual potential.  See there for a full explanation.

[4] Succa 5a