The Terrain
Draft for the author's reading. A map, not an argument: the same ground as Chapter 3, walked station by station.
Begin in flatland, because that is where the abstraction begins: one strand, one direction, a row of letters. The map below starts on that line and climbs off it. Each station is a place where the molecule refuses to stay flat — and each refusal is a dimension the description has to add or lose the information.
The terrain — walk from the line outward. Pick a station.
The Pairing
Across — strand to strand
A faces T, G faces C. Each strand can rebuild the other from its complement, so the information no longer lives in either string — it lives in the match between them. A relationship satisfied in both directions at once is already a second dimension, before any geometry appears.
Breaks flatland because: the unit that persists is not a letter but a pair — a relation. A one-dimensional reading keeps the letters and discards the match.
One alphabet, working in every dimension at once
Along
Order of letters
Across
Complement pairs
Around
Groove edge patterns
In space
Shape a protein fits
The same four letters are doing all four jobs simultaneously. That is the cross-dimensional relationship the linear view cannot hold: remove any one dimension and the other three still carry information the line never recorded.
The order of the stations is the order of the breaks. The pairing fails the line first: the match between strands is a relation, and a relation is not a point on a line. The alphabet fails it second: four letters that each carry their complement and their grip are a pairing system, not a row of beads. The helix and its grooves fail it third: the letters now present a surface pattern, readable from outside, that exists only in three dimensions. The fold fails it last: the line's own measure of distance stops predicting what touches what.
Nothing here contradicts the linear reading as far as it goes. It goes exactly as far as the first station — and no further.
Walked with the argument in Chapter 3 — The Pairing: Beyond Flatland.