Fitting — where it appears
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.
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.
What one exponent reports
Fit a single shape exponent to an organ that has four of them and it returns a real quantity — the harmonic mean of what its individual steps report. Harmonic means sit below arithmetic ones, so the fit understates, systematically, in a known direction, and invisibly.
Named alongside it
The objects these essays reach for when they reach for this one.
SpecimenAllometryBranching exponentDa Vinci's ruleMeasurementMurray's lawSamplingSummary statisticSurveyTransportBiasCone