Phyllotaxis
the spirals are counted, not admired
Concept

Confounding — where it appears

Two properties that vary together across every case available, so that no measurement can say which of them is acting. The branch a band sits on decides its divergence, its counted pairs and its rung spacing at once, so a result that follows the branch follows all of them and the design cannot separate them.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

How far each rearrangement is from closing, against the lag it kept. One bar per excluded cut, its length the distance from the displacements summing to nothing, ordered smallest first, and each labelled with the lag the cut left standing. The seven shortest bars are the cuts that kept a lag of 7 or 8 and the six longest are the cuts that kept 4 or 5, with a gap of 6.3 degrees between the two groups and no row in it. The rule sorts every one of them.

The lag decides whether it closes

Seven of the thirteen excluded rows have displacements that cancel and six do not. Every row that closes kept a lag of seven or eight and every row that does not kept four or five, thirteen times out of thirteen — and then a lattice nobody had cut broke it.

mechanism · Damage shape Four accounts of which bands speckle, scored on the three cut whole. Each candidate explanation of why one band's cuts change the family they keep and another's do not, against what the three bands cut whole actually do. A tick is an account that puts that band on the side the sweep does. The branch the band sits on is right on all three; the size of the counted pair, the number of wrecking offsets and how much of its rung the band spans are each wrong on two. Three bands can eliminate and cannot confirm, and this eliminates three of the four.

The branch is what is left

Four accounts of why one band's cuts change what they keep and another's do not were written down before a third band was cut. Three of them are now wrong on a band each, and the survivor is the one with no mechanism behind it.

cylinder · Rung interior The Lucas 4/7 band cut at every one of its 86 rises. One row per wrecking offset on each band, one cell per rise, coarse on the left, with each band's width in proportion to the rises it holds. A pale cell is a rise at which that offset's cut recovers and has no survivor to report; a dark cell keeps one of the band's own counted pair and a warm cell keeps a family off it, so a change of answer is where the tone changes. The Lucas 4/7 is the test the branch account most needed: 86 rises, 774 stems, 144 wrecks across two offsets and not one change of the surviving family. Across the one bands drawn, 144 cuts wreck of 774 grown. The dashed rule on each row is that band's own handover, where its two contact steps change places.

The fourth band, cut whole

Three bands cut at every rise left one account of which bands change their answer standing, and the account was the one nobody had a reason to prefer. The band that would have killed it has now been cut, and it did not kill it.

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.

Claim testingContact familyHonest limitsHandoverNegative resultParastichy pairAblationCensus designPredictionReplicationRungUnderdetermination

All concepts