Concept

Tolerance — where it appears

7 essays name this object, across 4 fields. What follows is each of them, and the objects they name alongside it.
upstream of the choicethe neighboursalready placedthe profileenergy by azimuththe choicethe least of itthe recordwhat a ruler readsfield noisejostle noiseplacement noiseone rule, three entry pointsthe order is the argument

The noise that arrives through the neighbours

The two kinds of noise this site had were idealisations that bracket the rule's choice. The realistic disturbance is neither: a primordium is placed exactly, and then the organ grows, so by the time the next one forms its neighbours have moved. That is a third kind, and it is invisible in every measurement a plant offers.

mechanism · noise entry
placement noise, at 1°2.00°field noise, at 0.015 of the barrier1.68°no noise at all0.64°largest divergence scatter still holding a latticethe two differ by 0.33° — a fifth of what either toleratesand by 2.9× more than a noiseless run scatters65 nodes per rung · 10 runs per amplitude2.00° against 1.68°

Two degrees of scatter

A lattice tolerates about two degrees of wander in its divergence angle, and two kinds of noise sharing no code agree on the number to within a third of a degree. It is not a constant: carried finer, the same stem survives 0.8°, and the tolerance tracks the band of angles that produce its pair at all.

emergence · scatter tolerance
-0.20000.2000.4000.6000.5000.75011.251.50divergence scatter, in degrees — the one quantity a plant offerscorrelation between one divergence and the next4 runs per point · band ±0.13every point is a lattice

What a quiet plant is worth

Almost every measurement gets easier as the effect gets larger. This one gets harder — a stem's divergence sequence stops carrying information about its noise at precisely the scatter where the noise becomes obvious. The specimens worth measuring are the ones that look least interesting.

wrong · survey spec
-0.20000.2000.4000.6000.5000.75011.251.50divergence scatter, in degrees — the one quantity a plant offerscorrelation between one divergence and the next4 runs per point · band ±0.13every point is a lattice

What one angle says about the next

A tenth of a degree of placement noise moves a stem's divergence scatter from 0.50° to 0.62°, which nobody would report. It takes the correlation between consecutive angles from 0.54 to below zero. The other two kinds of noise, at scatters where no measurement can separate them, leave it at 0.6.

cylinder · sequence
loop cut at 3/√h, p = 133%27.78° of scatterexponential cut-off, p = 1100%0.68° of scatterexponential cut-off, p = 3100%0.82° of scatter6 runs each, separated by 0.2° of placement noisehalf-weight radius 1.5 spacings

The fragility belonged to the window

A pattern that exists only because the rule cannot see far was expected to be held together by that cut, and to fall over when nudged. It does — while the cut is a loop bound. Written down as a falloff at the same range, the same rule keeps every run under the same nudge, at a scatter an inverse-cube rule cannot be told from.

emergence · noise amplitude
field 0.0052.10.70° of scatterfield 0.00750.01.00° of scatterfield 0.010.01.12° of scatterjostle 0.22.10.89° of scatterjostle 0.41.10.87° of scatterjostle 0.81.11.12° of scatterplacement 0.20.00.78° of scatterplacement 0.40.00.94° of scatterplacement 0.80.01.42° of scatter3 runs each · a basin change is half a local spacingplacement noise: zero by construction

Which minimum was chosen

The rule takes an argmin, so there are two completely different things noise can do to it: move the answer, or move the question. One of them can change what is chosen and the other cannot, ever — and the difference is exactly zero against one or two placements in a thousand, at amplitudes where every other measurement says the two are identical.

emergence · noise entry
field1.64°intact to 0.015, broken by 0.02jostle1.72°intact to 1, broken by 1.4placement1.42°intact to 0.8, broken by 13 runs per amplitudescatters 19% apart

The boundary belongs to the pattern

Three kinds of noise, in three incommensurable units, destroy a lattice at the same place — about a degree and a half of divergence scatter. The previous phase measured that of two kinds and called it a scale rather than a constant. With a third it looks less like a coincidence and more like a property of what a lattice is.

emergence · scatter tolerance

Named alongside it

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

Divergence angleNoiseEnsembleIdentifiabilityMeasurementThe placement ruleBasinAutocorrelationDiscriminationEquilibriumMeasurement errorMetastability

All concepts