Vidyārambha and Upanayana — the beginning of study
The popular claimTwo rites for one threshold: the first letters, and the giving of the thread that made a student.
The sixteen mark the body's passages — birth, food, hair — until they reach the mind, and there the tradition marks the passage twice.
Vidyārambha — the first letters
The older sūtras do not have it. Vidyārambha, also called Akṣarābhyāsa, appears in the later Smṛti literature and the nibandhas as a rite for a child of five, or at the earliest three: the child is seated, Gaṇeśa and Sarasvatī are invoked, and the child's hand is guided to write the first letters — traditionally Oṁ, then the alphabet, or the phrase Om namaḥ siddham — in a tray of rice or on a slate. That is the rite. It takes a few minutes. Many families perform it on Vasanta Pañcamī, the fifth of Māgha's bright half, because that day is Sarasvatī's and removes the need to choose one; in Kerala it is the eḻuttiniruttu on Vijayādaśamī, when thousands of children write their first letters in temples on the same afternoon.
Upanayana — the thread
This is the rite the sūtras spend their pages on. Upanayana — upa-nī, to lead near — is the initiation by which a boy was brought to a teacher and became a brahmacārī, a student of the Veda. Manu gives the ages by varṇa: the eighth year from conception for a brāhmaṇa, the eleventh for a kṣatriya, the twelfth for a vaiśya, with outer limits of sixteen, twenty-two and twenty-four beyond which the rite lapsed.
Āśvalāyana's description runs through several sections. The boy is shaved, bathed, dressed in a new garment and a girdle of muñja grass; he is given the staff; the yajñopavīta, the sacred thread, is placed over his left shoulder; the teacher takes his hand and asks his name; the boy is made to step on a stone, to be firm as the stone; the teacher then imparts the Gāyatrī — Ṛgveda 3.62.10 — which the boy has not been permitted to hear before this moment. Then the boy begs his first food, from his mother first. The whole is followed by the beginning of Vedic study, and the rite's name for the boy from then — dvija, twice-born — is the idea that this is a second birth, into learning.
The Gāyatrī at the centre
The rite exists to transmit one verse, and it is worth being exact about which. Ṛgveda 3.62.10, in the gāyatrī metre, to Savitṛ, asking that he impel our thoughts. It is the verse a Vedic student would recite at dawn and dusk for the rest of his life. The reason it was withheld until Upanayana was not secrecy for its own sake: the tradition held that the verse was to be received, from a teacher, at a threshold, not overheard. This site has a page on the verse itself under Stotra.
What became of the two
Vidyārambha is alive and unchanged: a child, a tray of rice, a first letter, a grandparent's hand over the small one. Upanayana is alive but transformed. The initiation into a teacher's household has gone, because the household school has gone; what remains is the thread ceremony, kept by brāhmaṇa families and some others, often performed a day or two before a wedding to satisfy the sequence, or on a chosen day in childhood, with the Gāyatrī imparted by a priest or a father. The thread is worn; the study it was the gate to mostly is not. That gap is real and this page does not paper over it.
Two honest notes. The rite as the texts give it was for boys; the texts are explicit and so is this page. And it was restricted by varṇa, with the ages above; the tradition has moved on that in many communities, and the movement is the tradition's own. A reader should know what the text says and what is now done, and that the two differ.
Timing
The muhūrta treatises give Upanayana its own long table: the Sun in Uttarāyaṇa, the months of Māgha to Jyeṣṭha preferred, the boy's birth nakṣatra and the eighth from it avoided, Jupiter and Venus visible, a nakṣatra from the group associated with learning, and the bright half of the month. Vidyārambha's table is shorter and is on the page for occasions.
What this page does not say
It does not say that a person without the thread is unfit for learning, and it does not say that a child whose first letters were written on an ordinary Tuesday has begun badly. The two rites mark a threshold the tradition thought worth marking twice. What crosses it is the child.
Source — Ashvalayana Grihyasutra 1.19–1.22 and Paraskara Grihyasutra 2.2–2.5 on Upanayana; the Manusmriti 2.36–38 on the ages; the later Smriti and nibandha sources on Vidyarambha (Aksharabhyasa); the Rigveda 3.62.10 for the Gayatri
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