Phyllotaxis
the spirals are counted, not admired
Concept

Error propagation — where it appears

Carrying the uncertainty on a measured quantity through into whatever is computed from it. It does not always reach the answer: a wall located by which swept rises bracket a crossing has ends that are sweep positions, so halving the error bar behind it left the wall's own uncertainty where it was.

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

Every bracket on the wall at a half, before the refinement and after. One pair of bars per falloff exponent: above, the rises consistent with that exponent's crossing on forty starting angles and the 5 published rises; below, the same on eighty angles and 9 rises. Two of the four have an open end before — at a half that is the coarse end, where no published rise has a share confidently above the level — and none is open after, the widest closing at 1.57 times. The four walls sit inside a factor of 1.111 of one another, against 1.624 on the reading that could not locate them, so they came closer together rather than further apart.

Four walls closer than they looked

Two of the four falloff exponents had a wall with no upper end at all, and the other two were located to factors of two and a half and nearly four. Nine rises at eighty starting angles close every bracket — and the four walls turn out to sit inside a factor of 1.111 of one another, which is narrower than the narrowest bracket.

mechanism · Falloff exponent The bracket at each of the four corners of the refinement, at a half. The geometric mean bracket at each corner, and under it how much of the joint narrowing each half of the refinement accounts for. It is taken over the two exponents whose bracket is closed at every corner, with the two halves of the refinement crossed against each other. The rule across the bars is 1.54, the narrowest bracket the published rise list can express at all. On forty starting angles and the published rises it is 3.06 times with two of the four brackets closed; doubling the angles alone gives 1.96, halving the rise spacing alone gives 1.46, and both together give 1.44. In the logarithm, where the two effects add, the rises account for 98.8 per cent of the joint narrowing and the angles for 59.3 per cent — summing to 158.1 per cent, which is what overlapping causes look like and not two independent factors of two.

Two refinements that do not multiply

The design that located the wall did two things at once — doubled the starting angles and halved the rise spacing — and the arithmetic behind it assumed each would buy about a factor of two. The finer rises did ninety-nine per cent of the narrowing and the doubled angles added under one, because a bracket's ends are rises and no error bar can move them.

mechanism · Falloff exponent

Named alongside it

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

BracketClaim testingFalloff exponentHonest limitsMeasurement errorResolutionRiseSamplingSettlingDiscretisationFactorial designIdentifiability

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