The numbering is a reading instruction, not an accident
A braille cell is a grid: two columns, three rows. Six possible dot positions, and every position has a fixed number. Dots 1, 2, and 3 run down the left column, top to bottom. Dots 4, 5, and 6 run down the right column, top to bottom. That is the whole system — and it is worth understanding why it is arranged that way rather than any other.
The numbering was standardised to match the way a trained reader encounters a cell. When a finger lands on a braille cell, it sweeps downward and slightly across. The left column comes first, and within each column the topmost dot is registered first. Numbering the dots 1–2–3 down the left and 4–5–6 down the right encodes that reading direction directly. A transcriber writing dot patterns in shorthand — dots 1, 4, 5, for instance — can visualise the cell immediately without a lookup table. The notation describes the physical layout.
There is also a mnemonic consequence. In the original French literary braille that Louis Braille published in 1829 and refined by 1837, the letters of the alphabet are built systematically from the top of the cell downward. The first ten letters — a through j — use only the top four positions: dots 1, 2, 4, and 5. The second decade repeats those patterns with dot 3 added; the third adds dots 3 and 6. Dot 6 alone, in the bottom-right position, carries a specific grammatical load in many codes, serving as an indicator sign; in English braille, for example, it marks a capital letter. Numbering that position 6 rather than, say, 3 keeps the decades of the alphabet in predictable numeric ranges, which simplifies both teaching and code design.