Phyllotaxis
the spirals are counted, not admired
Concept

Prior — where it appears

What is believed about the answer before a measurement is read: the possibilities allowed and the weight each is given. A reading that uses one inherits it, so a recount aimed from the belief that heads are Fibonacci finds Fibonacci readings more often whether or not they are there.

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

What a divergence picked at random gives, at a rise of 0.100. Fibonacci pairs take 59.6% of the circle at this rise, and the share falls as the rise does. The claim that Fibonacci counts are what nature "prefers" needs the preference to come from somewhere, and it is not from the geometry being generous.

How often is it Fibonacci

The claim that plant spirals come in consecutive Fibonacci numbers is stated as a near-universal. Asked of the geometry, the answer collapses with scale — at a coarse rise 67% of divergences give Fibonacci pairs, and at a fine one 15%, with whorled and unnamed pairs taking the rest.

wrong · Frequency What one recount reads after 34/55 was first read as 34/54, for each belief the counter aims from. A head whose true pair is 34/55, first read as 34/54 with closing errors spread over 7.2°, recounted once; the two closings of the head are correlated by 0.9. Each bar is one counter, split into the recount reading 34/55, announcing itself again, and reading another pair silently: unaimed, aiming +0.0°, 41.8% right, 55.2% announced, 3.0% silent; expects Fibonacci, aiming +3.8°, 69.6% right, 30.2% announced, 0.2% silent; expects Fibonacci, capped at 2σ, aiming +3.8°, 69.6% right, 30.2% announced, 0.2% silent; expects any spiral, aiming −4.5°, 5.5% right, 62.7% announced, 31.8% silent; expects nothing, aiming +0.3°, 44.7% right, 52.8% announced, 2.5% silent.

The recount aims where the counter expects

A counter who recounts an announced reading knows it went wrong, and if the same habit spoils both counts of a head, the first error says where to aim the second. But the reading alone does not say which way the first erred: a reading of 34/54 is as well explained by a whorled 34/54 read right, or by 34/53 read long, as by 34/55 read short. The direction comes from what the counter expects. Expecting Fibonacci, an aimed recount at 7.2° and a habit correlated at 0.9 reads 34/55 69.6 per cent of the time where an unaimed one reads it 41.8, and the census needs seven specimens rather than fifteen. Expecting only a spiral, it aims the wrong way and reads 34/55 5.5 per cent of the time. The belief that helps is the hypothesis the census is testing: uncapped, it reads the geometry's whorled 3/6 heads as 3/5 and a census of a hundred rejects a true null 40 per cent of the time; capped, it still reads a silent 33/53 as Fibonacci twice as often. And no aimed recount spends fewer counts than 13/21 counted once.

wrong · Sample size

Named alongside it

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

CensusParastichy pairBiasBranchBranch selectionContinuityDivergence angleFibonacciFrequencyHonest limitsMeasureMeasurement error

All concepts