Concept

Transport — where it appears

The movement of fluid through a branching network, and the cost whose minimisation gives Murray's law.

Named by 6 essays across 4 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
-0.50000.500125810131621242629lag, in internodescorrelation between a divergence and the one that many internodes later816245132129reads 8/13 · no rule in itmain 0.514 · band 0.073sampling bandkinematic lattice · 759 anglesgenerated from a stated rule, not drawn to look right

Errors that pass between organs

An organ's neighbours are the ones eight and thirteen places back — that is what a parastichy pair is. So a disturbance transmitted by contact is correlated at exactly the two lags the readout examines, and it does not have to be told them. Driven into a lattice with no rule in it, it returns the counted pair on eight stems out of eight.

mechanism · noise transport
0.4000.6000.80011.201.40-0.30100.1760.3010.4770.699how much more strongly the error is inherited from the 8-neighbour than from the 13-neighbourthe second comb's strength as a fraction of the main comb'sthe placement rule: 0.65equal combs1:21:11.5:12:13:15:1at 3:1 the ratio is 0.75kinematic lattice · 3 seeds a pointgenerated from a stated rule, not drawn to look right

What a forgery has to know

A lattice with transported errors reproduces the comb and the pair, so one quantity is left: the two combs' relative strength. Weighted by distance the forgery puts more in the second comb than the first; the rule does the opposite. It matches only if the coupling is turned three to one towards the further neighbour, which no falloff supplies.

mechanism · noise transport
stemwhat the angles say18/10not the lattice's pair28/12not the lattice's pair3refused48/10not the lattice's pair58/12not the lattice's pair68/12not the lattice's pair78/12not the lattice's pair88/11not the lattice's pairthe positions say 8/13kinematic lattice · error of period 8generated from a stated rule, not drawn to look right

The control a survey would need

A comb no longer shows that a plant computes its pattern, so the survey this site has been specifying for five phases has to change. What it loses is its headline; what it gains is a measurement a botanist can actually make — six requirements, four of them already in the specification, and a quantity nobody has ever reported.

wrong · control spec
three sampling bandsthe placement rule0.6428/13independent errors0.031refusedan error with a memory0.014refusedan error that repeats0.4338/10, 8/12errors passed between neighbours0.5538/13one rule, four kinematic latticesgenerated from a stated rule, not drawn to look right

The comb was never the rule

A control is only as strong as the alternative it builds, and the previous phase built one that varied the rule while holding the disturbance fixed at independence. Five phases of the angle-sequence thread, with what each claimed and what still stands — and why the next evidence has to come from an intervention rather than from a longer stem.

cylinder · noise transport

Named alongside it

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

MeasurementAutocorrelationDiscriminationEvidenceHonest limitsNull modelIdentifiabilityNoiseParastichy pairThe placement ruleSpecimenSurvey

All concepts