Phyllotaxis
the spirals are counted, not admired
Concept

Branching exponent — where it appears

The power p for which a junction's parent radius satisfies r0^p = r1^p + r2^p, three under Murray's law and two under Da Vinci's.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

1101001000100000.2000.4000.6000.8001daughter ratio — the smaller branch over the largerjunctions needed to tell Murray's rule from Da Vinci'san even fork — one is enougha twig — 2195the same tree, built at an exponent of 3, measured twicethe truth — 350 even forks3.0150 twigs1.692% error per radius · 47% of twigs impossiblemargin 0.11% against 2.8% noise

Which junctions say anything

Da Vinci's rule and Murray's law differ by 12% at an even fork and by a tenth of a per cent at a twig. So one even fork settles which is right, and two thousand twigs do not — a factor of two thousand across a tree, decided entirely by the shape of the junction and not by how carefully it is measured.

branching · exponent 1101001000100000.2000.4000.6000.8001daughter ratio — the smaller branch over the largerjunctions needed to tell Murray's rule from Da Vinci'san even fork — one is enougha twig — 2195the same tree, built at an exponent of 3, measured twicethe truth — 350 even forks3.0150 twigs1.692% error per radius · 47% of twigs impossiblemargin 0.11% against 2.8% noise

A sample that is confidently wrong

Fifty lopsided junctions from a tree built at an exponent of exactly 3 return 1.7, with an interval that excludes 3 and excludes 2 as well. The sample carrying almost no information does not give a wide answer — it gives a narrow wrong one, and the cause is a selection nobody applies on purpose.

branching · exponent mean sides per cell(forced to six)mean squared departure from six(not forced)whorled, 144°5.9860.023golden, 137.508°5.9900.253rational, 137.5°5.9900.255Lucas, 99.502°6.0360.255137.0°5.9900.291Poisson5.9691.830six433–637 interior cells each, inside 86% of the radiussame cells, same cut, two statistics

What a summary throws away

Four statistics this collection has relied on turn out to be incapable of varying with the thing they describe — one is invariant to shuffling, one is fixed by a theorem, one is a parameter that stopped mattering, one is a fitted number selected into being wrong. In each case the second statistic was free and nobody had taken it.

wrong · second statistic

Named alongside it

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

MeasurementSamplingSpecimenSummary statisticSurveyAllometryBiasDa Vinci's ruleFittingMurray's lawSelectionTransport

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