הכתב והקבלה — שלוש פעמים בשנה יראה כל זכורך... בחג המצות ובחג השבעות ובחג הסכות

Q — What does 'חג' actually mean? Rav Hai Gaon (cited by R. Nathan in the Aruch and Radak): from root חגג = motion of dancing in joy. HaKtav rejects this: (1) if 'chag' = dance/joy, what distinguishes חגיגה from שמחה (Chagigah 6b lists them as separate mitzvot)? (2) If joy/dance is the Torah-mandated essence of yom tov, how could Chazal forbid dancing on yom tov (Beitzah 36b)? Chazal can't override an explicit Torah requirement.

A — HaKtav VeHaKabbalah relocates the motion. 'חג' refers not to dance on the festival itself but to the *motion of pilgrimage* — the joyful travel from one's hometown to the chosen place, leaving home and comfort behind for crowded lodging, makeshift bedding, uncertain food. The proof-text: 'כִּי אֶעֱבֹר בַּסָּךְ אֶדַּדֵּם עַד בֵּית אֱלֹהִים בְּקוֹל רִנָּה וְתוֹדָה הָמוֹן חוֹגֵג' (Tehillim 42:5) — the 'חוגג' is the procession, the journey. The festival is named after the *going* in joy despite the discomforts. The arrival-celebrations (chagigah, simchah) are separate mitzvot, and Chazal's prohibition on dancing affects them, not the chag itself.