4 ideas
In the tenth century the vizier Ibn Muqla made Arabic letter shapes measurable. He fixed the alif's height as a set number of rhombic dots, which are the square marks the pen makes when pressed at its full width, and derived every other letter's dimensions from that alif and dot. Because the unit comes from the pen itself, beauty became a matter of proportion that could be taught, checked and reproduced rather than left to individual taste.
A calligrapher learned by repeatedly copying a master's model sheets (mashq) under direct correction, often for years. He had to learn to prepare the reed pen, ink and burnished paper as part of the discipline. Mastery was certified by an ijaza, a written license from the teacher permitting the student to sign his own work, so authority passed through a documented chain of teachers rather than through self-declaration.
Persian, Turkish and Urdu poets read the alphabet as a figurative vocabulary for the human form. The beloved's upright stature is an alif, curling locks are a jim or dal, the mouth is a tiny mim, and the down on a cheek is 'script' written by the divine calligrapher. Read this way, a face becomes a text and a text becomes a portrait, so the aesthetic of the page and the aesthetic of love share one grammar.
In Sufi thought the alif is the first letter, a single vertical stroke with no connection to the letter that follows. It is therefore read as a symbol of God's oneness, and every other letter is understood as a bending or unfolding of it. Mystics accordingly held that whoever truly understood the one alif needed no further book, because all multiplicity of letters, and of creation, is contained in that one stroke.