Phyllotaxis
the spirals are counted, not admired
Concept

Held cut — where it appears

A cut that neither heals nor leaves a countable arrangement behind it. It is the third thing an ablation can do, between recovering and wrecking, and it is visible only on the bands where nothing wrecks at all, since the census that reads the others records only whether a cut wrecked.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The two bands that answer nothing, 586 stems and no wreck anywhere. The g35 and L34 bands cut at every rise, with one row per offset tried and one cell per rise, coarse on the left. A pale cell is a cut whose stem recovers and a mid cell is one that neither recovers nor leaves an orbit to count; the warm tone means a cut that wrecks, and it appears on the reference row below, which is offset 4 of the Lucas 4/7 wrecking at 83 of its 86 rises. g35 grew 490 stems across 70 rises at seven offsets and L34 grew 96 stems across 16 rises at six offsets, and wrecked none of them, so this is a zero that was measured rather than a band nobody cut. The dashed rule on each block is that band's own handover, where its two contact steps change places.

Two bands that wreck nothing

The census that reads a band refuses two of the six, and the refusal is correct: a band with no wrecked cut has no surviving family, so it has no answer to change. Cutting them anyway turns a refusal into a measurement, and the measurement has a third tone in it that the census cannot see.

cylinder · Rung interior Four accounts scored on the four bands of six that can score them. One column per band of the ladder and one row per candidate account of why a band's wrecking cuts change the family they leave standing. Each cell is what that account predicts of that band, in plain type where the band agrees with it and pale where it does not, and the header of each column is what the band actually does. The two bands with no wrecked cut are shown silent, because a band with no surviving family has no answer to change; over the four that can answer, the branch the band sits on is right 4 times of 4 and the other three are wrong twice each. A warm block marks each cell where the account and the band disagree.

Six bands, one table

Every rung of this ladder that carries a handover now has a band grown on it and cut at every rise it holds, and four accounts of which bands change their answer are scored on all six at once. The survivor is right on every band that can test it, and the same table read one cell differently kills it.

cylinder · Rung interior

Named alongside it

The objects these essays reach for when they reach for this one.

AblationCensus designContact familyHandoverHonest limitsNegative resultRungClaim testingConfoundingControlEvidenceLattice offset

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