Phyllotaxis
the spirals are counted, not admired
Concept

Settling criterion — where it appears

The stated rule for whether a run counts as settled: every later divergence within a tolerance of a final value. Applying it unchanged to wrecked runs is what keeps those runs comparable with intact ones, and loosening it to admit them would make the settling table a statement about the criterion.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

Predicted 29 of 63 settle; 17 do. The 63 wrecked runs of the slot design regrown to 1200 organs and put to the settling table's own criterion, unchanged in every tolerance. Rows are whether the 300-organ endpoint sat within 1 degree of a destination; columns are whether the regrown run settles. The prediction written down before the sweep was that the 29 agreeing runs would settle: 12 of them do and 17 refuse, and the whole set settles 17 rather than 29. Agreement carries information without being a rule — 41.4 per cent of the agreeing runs settle against 14.7 per cent of the others, an odds ratio of 4.09 and a phi coefficient of 0.300 — so an agreeing run is still likelier to refuse than to settle.

A destination or a refusal

Sixty-three wrecked runs were regrown to twelve hundred organs and put to the settling table's own criterion, unchanged in every tolerance. The prediction written down before the sweep said twenty-nine would settle; seventeen do, and the prediction is wrong on its own side of the table as well as in its total.

mechanism · Settling The endpoint over four times the run: 60 of 63 do not move at all. One cell per wrecked run, dark where the divergence reported as its endpoint at 300 organs is the same divergence at 1200, warm where it moved. It moves on three of 63 runs, by a median of 0.0000 degrees and a worst of 0.0039. That worst is 128 times smaller than the 0.5 degrees at which two settled values are counted as one destination, and the movement has no sign — 1 up, 2 down. The short reading is precise about where a run finishes; it is silent about whether the run stays there.

Like with like

Seventeen wrecked runs settle when regrown to four times their length, and every one of them settles at the divergence the short run already reported. The endpoint moves by four thousandths of a degree at worst, which makes the short reading precise about where and silent about whether.

mechanism · Settling The same verdict at every length from 300 organs to 1200. The settling criterion applied to the first 300, 400, 600, 800, 1000, 1200 organs of each of the 63 regrown runs. It accepts 17 at every one of them and refuses 46 at every one, and not one run changes sides. A truncated twelve-hundred-organ run is the shorter run organ for organ, so this is a comparison of lengths rather than of growths. The slowest arrival in the whole set is 138 organs, so 140 is the measured requirement and 300 carries a factor of 2.1. The column drawn dark is 300 organs, where the verdict is 17 settled and 46 refused.

What a run length was hiding

The settling criterion returns an identical verdict on all sixty-three wrecked runs at every length from three hundred organs to twelve hundred, so run length explains nothing. What the sweep does find is that an endpoint is a mean over an orbit, and thirty-four refusers never come within a degree of their own reported endpoint.

mechanism · Settling

Named alongside it

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

Claim testingEndpointHonest limitsNegative resultSettlingSummary statisticAttractorDestinationMeasurementOrbitRefusalAblation

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