Phyllotaxis
the spirals are counted, not admired
What a plant might be doing

The drift goes the other way

A rule that corrects what its neighbourhood shares should let through any disturbance slower than its own reach, and should suppress anything faster — a crossover, tracking the depth. Swept over a neighbourhood that changes by a factor of sixty, there is no crossover anywhere, and the deep rule passes nearly four times as much as the shallow one. The prediction is not weakly supported; it is backwards.
24 min read 14 figures State the claim, state the testForm is not mechanismTwo routes, one number

Worth reading first: A disturbance with a memory · How far a primordium reaches · The sequence has a memory.

The prediction is a filter and it is worth writing out before it fails, because the reasoning is good and the failure is instructive.

A placement rule puts each organ where the repulsion from the organs already there is least. If every organ in that neighbourhood is displaced by the same amount, the whole profile shifts and the minimum shifts with it, so the rule places the next organ in the displaced position and the error passes through untouched. If the organs are displaced by different amounts, the profile changes shape, the minimum moves less than the disturbance did, and the error is partly corrected.

A disturbance correlated over few organs looks like the second case to any neighbourhood deeper than its correlation length. A disturbance correlated over many organs looks like the first case to any neighbourhood shallower than it. So the rule should be a high-pass filter whose corner sits where the correlation length meets the depth of the neighbourhood, and the prediction is a crossover that tracks the depth.

The depth is measurable — the number of organs carrying nine tenths of the profile the rule minimises — and it can be varied by a factor of sixty by changing the exponent of the falloff. The correlation length is a parameter of the disturbance. Nothing had varied them together.

A deeper rule passes more of a drift, not lessThe wander left in a stem's divergences, against how many organs its disturbance stays correlated over, for rules whose neighbourhoods run from 3 organs to 182. The prediction under test said a rule should pass a drift once the drift outlasts its neighbourhood, so the shallow rules should be the leaky ones and each line should turn where its own depth is crossed. Every line rises smoothly and the deepest rule is the highest of them at every correlation length — 82 against 22 at the longest drift. There is no crossover anywhere in the sweep.02550750102030how many organs the disturbance stays correlated overwander at a block of 64182 organs120 organs30 organs8 organs3 organsneighbourhood measured as the organs carrying 90% of the profileno crossover at any depth
Fig. 1 The sweep. The wander left in a stem’s divergences, against how many organs its disturbance stays correlated over, for rules whose neighbourhoods run from three organs to a hundred and eighty-two.
A memory manufactures nothingThe largest comb mean found in a kinematic lattice whose azimuth errors are an AR(1) process, against the coefficient of that process, over eight seeds at each point. The dashed line is where the rule's own stems sit, at 0.64; the shaded strip is three sampling bands. Every point is inside the strip — 0.028, 0.026, 0.022, 0.014 at ρ = 0.3, 0.5, 0.7, 0.9 — and the readout returns nothing on 32 runs out of 32. A correlated error is not a periodic one.00.2000.4000.6000.3000.5000.7000.900how strongly each error remembers the last, ρthe largest comb mean anywhere in the thirty lagsthe rule's own stems: 0.64three sampling bands0.0280.0260.0220.014kinematic lattice · AR(1) errorgenerated from a stated rule, not drawn to look right
Fig. 2 The disturbances the sweep is driven by, read at lags rather than at block sizes. A memory of this kind leaves no comb, which is why the wander is the observable it has to be measured with.

How the sweep is built

Two things have to be held still for the sweep to mean anything, and both are worth stating because getting either wrong would produce the observed result without any physics in it.

The disturbance is the same size at every correlation length. A correlated stream built by the obvious recursion has a larger variance than an uncorrelated one, so comparing at equal nominal amplitude would compare a disturbance with one nearly twice its size and report the difference as an effect of correlation. Every stream here is divided by its own measured standard deviation, so a jostle of a quarter degree is a quarter degree of displacement per organ at every setting.

The stems are the same pattern. Every run in the sweep is counted at 8/13 by a blind counter shown its positions, at every depth and every correlation length. A depth at which the rule grew a different lattice would be comparing two objects rather than one, and the exponents at the ends of this sweep are chosen inside the range where the lattice holds.

What a lattice survives depends on the colour of the disturbance, sixfoldfive stems for each of seven disturbances at each of six displacements, every stream normalised by its own measured spread so that a displacement of half a degree is half a degree in every row. A filled mark is a stem that still has a lattice — a divergence scatter under 2° — and an open one is a stem that does not. Independent errors survive to 0.5°; errors that remember the last one to 1.5°; errors inherited from the contact neighbours only to 0.25°. The number beside each row is the scatter a protractor would record where the lattice is standing, and it is the quantity that explains the table: what destroys a lattice is not how far an organ moves, but how far it moves relative to the organs it is placed against.displacement per organ0.25°0.5°1°1.5°2°3°independent0.57–1.03°a memory, ρ = 0.50.38–0.68°a memory, ρ = 0.90.28–0.98°a memory, ρ = 0.970.26–1.31°repeating every 80.63–0.93°inherited, a = 0.50.97–0.97°inherited, a = 0.71.15–1.94°scattera latticeno lattice left5 stems a cell · rise 0.005generated from a stated rule, not drawn to look right
Fig. 3 Why the second condition needs checking rather than assuming: a disturbance of the wrong size or the wrong colour costs a stem its lattice entirely, and the amplitude used throughout this thread is inside where every colour survives.

Three seeds are averaged at every cell, and the spread between them is carried through the figures as a band rather than reported once. At the white control that spread reaches a factor of four, which is why the companion null in this thread is stated against it rather than against a constant.

The memory of a divergence sequence, at 0.75° of scatterWith no noise at all the lag-one correlation is 0.54: the rule corrects itself, so a lattice arrives with a memory in it. Matched at the same recorded scatter, placement noise leaves -0.10, jostle noise leaves 0.66, field noise leaves 0.47. The band is ±0.13, which is what an uncorrelated sequence of this length gives.-0.25000.2500.500123456lag, in nodescorrelation between a divergence and the one that many nodes laterno noiseplacement noisejostle noisefield noisesampling band4 runs each · 243 divergences per runmatched at 0.75° of scatter
Fig. 4 What correlation in a sequence of divergences looks like when there is some. The sweep below asks whether a rule’s depth decides how much of it survives into the sequence.

No crossover, at any depth

The first thing to say about the figure is what is missing from it.

Every line rises smoothly with the correlation length. None of them has a knee, a plateau, a step or a turn. There is no correlation length at which any of the five rules stops suppressing and starts passing, and no ordering among the lines that changes anywhere in the sweep.

That absence is checked rather than eyeballed: at every depth, the wander must be strictly larger at each longer correlation length than at the one before, and the sweep must contain correlation lengths shorter than the neighbourhood, where a filter would have suppressed them. At a depth of a hundred and eighty-two organs, every correlation length in the sweep — 2.8, 9.5 and 32.8 organs — is comfortably inside the neighbourhood, and all three pass.

The disturbance with the largest wander leaves none in the sequenceHow much of a divergence sequence's variance survives being averaged over blocks, on kinematic lattices. The vertical quantity is B² times the variance of the block means divided by the variance of the sequence, which is one at every block size for independent errors — the arithmetic is normalised for a *differenced* stream, since a divergence is the difference of two organs' errors. A line that climbs is a sequence with power at frequencies below one per block. The disturbances that remember the last error climb to 32 at a block of 128. The ones inherited between touching organs do not climb at all — 1.06 and 0.83 at the same block — although their own deviates carry ×5 and ×49 an independent stream's variance in exactly this statistic. What they do instead is dig a hole: at block sizes of 8 and 13, which are the offsets they couple at, the statistic falls to 0.22 and 0.21.10.11024813163264128block size, in organsvariance of the block means, against independent errorsindependenta memory, ρ = 0.5a memory, ρ = 0.9a memory, ρ = 0.97inherited, a = 0.5inherited, a = 0.7shared once, a = 0.76000 organs · 6 runs eachgenerated from a stated rule, not drawn to look right
Fig. 5 What the statistic looks like when there is structure in it: on a kinematic lattice, where the disturbance is visible directly, the shape of the curve carries the disturbance’s own correlation. Through the rule there is no shape to read.
Two combs, at a rise of 0.005The autocorrelation of 760 divergence angles from one stem held at a rise of 0.005. The filled teeth are the lags at multiples of 8; the open teeth are the second comb, at the same spacing offset by 5. Reading the spacing off the first and the offset off the second gives the pair 8 and 13, which is what the position counter reports for the same stem — from angles alone, with no coordinate anywhere in the calculation.-0.50000.500125810131621242629lag, in internodescorrelation between a divergence and the one that many internodes later816245132129spacing 8 · offset 5pair 8/13 — counter says 8/13the shaded strip is the sampling bandone stem · 760 divergences · disturbance 0.25generated from a stated rule, not drawn to look right
Fig. 6 The other observable for the structure of a disturbance, on the same machinery. A comb reads a correlation at a lag and a wander reads one at a block size, so a claim made in either has to be checkable in the other.

What the numbers are, line by line

The figure compresses five sequences and they are worth reading out, because the regularity in them is stronger than the headline.

At an exponent of 1.5 — a hundred and eighty-two organs — the wander runs 0.98, 10.03, 30.59, 82.26 across independent errors and correlation lengths of 2.8, 9.5 and 32.8 organs. At an exponent of 2, a hundred and twenty organs: 0.82, 7.24, 27.61, 68.51. At 3, thirty organs: 0.91, 5.05, 19.08, 46.47. At 4, eight organs: 0.69, 4.80, 15.06, 35.70. At 6, three organs: 0.60, 3.42, 10.94, 22.37.

Two things fall out of the columns rather than the rows.

The white column is close to one at every depth, which is the calibration working: independent errors give one by construction of the statistic, and a column that drifted with depth would mean the normalisation was itself depth-dependent and nothing else in the table could be read. It runs 0.98, 0.82, 0.91, 0.69, 0.60 — sagging slightly at the shallow end, by a factor of 1.6 across a depth range of sixty, which is inside the seed spread.

The ordering is preserved down every column. It is not that the deep rule wins at the longest drift and the ordering shuffles elsewhere; the deep rule is highest at 2.8 organs, at 9.5, at 32.8, and the shallow rule is lowest at all three. A filter would produce crossings between the lines somewhere in that range, since each line’s corner would sit at its own depth, and the depths differ by a factor of sixty.

What the sequence sees that the scatter cannotEach point is an ensemble at one amplitude, placed at the scatter it produces. A stem at three quarters of a degree of scatter has a lag-one correlation near zero if its noise arrived after the primordium was placed, and near 0.7 if it arrived before — and no measurement of the scatter can tell those apart. The separation closes above about a degree, because what the other two kinds preserve is the correlation of a lattice.-0.20000.2000.4000.6000.5000.75011.251.50divergence scatter, in degrees — the one quantity a plant offerscorrelation between one divergence and the nextplacement noisejostle noisefield noise4 runs per point · band ±0.13every point is a lattice
Fig. 7 How much of a sequence’s spread sits between adjacent terms. That is the part a placement rule corrects, and it is the part the deep rule corrects best — which is the fact the ratio in these figures is dividing by.

And the direction is reversed

The second thing is worse for the prediction than the first.

At a correlation length of 32.8 organs, the wander runs 82.3, 68.5, 46.5, 35.7, 22.4 from the deepest rule to the shallowest. The rule that looks at a hundred and eighty-two organs passes 3.7 times as much as the one that looks at three.

The filter reading says the opposite. A shallow rule should be the leaky one: a disturbance correlated over thirty-three organs is a uniform translation to a neighbourhood of three, so a three-organ rule should pass all of it, and a hundred-and-eighty-two-organ rule should see the variation within the drift and correct most of it.

Which arrangements carry a comb, and what each one reportsThe largest comb mean in five arrangements at a rise of 0.005, all read by the same instrument at the same length, with the sampling band of 0.073 marked. Only the first is a placement rule; the other four are kinematic lattices with no rule in them, differing from one another only in how their azimuth errors are structured. Independent errors and errors with a memory leave nothing to read. A repeating error puts up a comb and names a partner that is not the lattice's. Errors inherited from the contact neighbours reproduce both the comb and the pair.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
Fig. 8 The same disturbances read the other way, at lags rather than at block sizes. What separates the shapes here is which organs share an error, and that is the property the filter reading is about.

The measured ordering is not marginal and it is not a seed. It is monotone across all five depths, at every correlation length in the sweep including the shortest, and the ratio between the ends is far outside the seed-to-seed spread.

Where each kind's lattice gives wayThe largest amplitude at which every run still has a lattice, and the scatter it produces there. The amplitudes are incomparable — field 0.015 (fraction of the barrier), jostle 1 (degrees of azimuth), placement 0.8 (degrees of azimuth) — and the scatters agree to 19%. The boundary belongs to the pattern rather than to the disturbance: a lattice fails at about a degree and a half of scatter, and which of three mechanisms produced it does not move where.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
Fig. 9 How much disturbance a stem takes before it stops being a lattice, by the kind of disturbance. Everything in this sweep is run well inside that, so no row is measuring a stem that has fallen apart.

The prediction was about the wrong quantity

The account of what went wrong is the subject of the next rung and is worth stating here in outline, because otherwise the result looks like a mystery rather than an error.

The wander is a ratio. Its numerator is how much the block means of the divergences move, which is what “how much drift got through” ought to mean. Its denominator is the variance of the divergences themselves — the scatter between neighbours.

A deeper rule suppresses the relative part of a disturbance better than a shallow one, because it has more neighbours to compare against. That is the denominator falling. If the numerator barely moves, the ratio rises — and it rises for a reason that has nothing to do with how much drift the rule let through.

The wander climbs because its denominator fallsThree quantities across the same sweep of the rule's depth, each divided by its own value for the shallowest rule so that they share an axis. The wander rises by a factor of 3.7 as the neighbourhood goes from 3 organs to 182. The scatter between neighbouring divergences falls by 1.57, because that is the part of a disturbance a placement rule corrects and a deeper rule corrects it better. What is left — how many degrees of slow drift actually reach the divergences — changes by 1.20, from 1.52 to 1.82 degrees. The rule barely filters a drift at any depth.012342.262.081.480.9030.477organs in the neighbourhoodagainst the shallowest rulewanderscatterdrift througha drift correlated over 33 organs · 3 seeds a pointdrift through: 1.52° to 1.82°
Fig. 10 The decomposition, ahead of the essay that makes it: the wander, the scatter under it and the degrees of drift that actually reach the divergences, across the same sweep.

So the sweep did test something, and what it tested was not what it was built to test. The filter reading is a claim about the numerator and the statistic is dominated by the denominator.

Three cut-offs at the same nominal width of 2 spacingsThe weight the interaction is multiplied by, against distance. They halve at 1.39 (exponential), 1.67 (gaussian), 2.00 (hard) spacings — so a rule described as "cut off at 2 spacings" is three different rules until the falloff is named. Every later figure is read in half-weight radii for that reason.00.2500.5000.7501012345distance from the candidate, in local spacingsweight the interaction is multiplied byhalf weightexponentialgaussianhardweight = f(d / 2√h)window runs to 4 widths
Fig. 11 What “how deep the rule looks” could mean, drawn as weight against distance. The exponent is the only one of these knobs that changes the shape rather than the edge, which is why it is the one the sweep uses.

Why the prediction was worth making anyway

It is tempting, having found the error, to say the experiment was ill-posed. It was not, and the distinction matters for what gets built next.

The filter reading came out of a measurement rather than out of nowhere: a rule driven by a correlated jostle leaves more wander than a kinematic lattice driven by the same jostle, while cutting the neighbour-to-neighbour scatter by more than half. Both halves of that were measured. The reading assembled them into a mechanism — the rule corrects the relative part and passes the shared part — and the mechanism is, as far as this sweep can tell, correct.

The wander is in the disturbance and not in what a plant lets you measureEach disturbance measured twice, in the same statistic. On the left, the variance of the block means of the disturbance's own deviates, over blocks of 100, as a multiple of what independent draws would give; on the right, the same quantity for the divergence sequence those deviates produce, over blocks of 128. The left column is what this site measured when it proposed a slow wander as a second observable. The right column is what a botanist would have: a divergence is the difference of two organs' errors, and differencing is exactly the operation that removes power at low frequencies. The disturbance inherited between touching organs goes from ×49.1 — the largest here — to 0.83, which is what independent errors give. The one with a memory in time keeps most of its own.in the disturbanceblocks of 100in the divergencesblocks of 128the horizontal rule is what independent errors giveindependent×0.930.96a memory, ρ = 0.9×16.2410.25inherited, a = 0.7×49.090.83shared once, a = 0.7×2.550.956000 organs · 6 runs eachgenerated from a stated rule, not drawn to look right
Fig. 12 The measurement the reading came from: what is in a disturbance, and what survives into the sequence of divergences a plant hands over. The shape with the largest wander in the stream leaves none in the sequence, because a divergence is a difference.

What the reading got wrong is the step from a mechanism to a prediction about a particular number. It assumed that if the rule corrects the relative part, then a statistic that is supposed to measure the shared part will show the correction turning on and off with the depth. That step needed the statistic to be a measurement of the shared part alone, and it is not.

The general form is worth keeping: a mechanism can be right and every prediction derived from it through a ratio can be wrong, because the ratio’s denominator is also a function of the mechanism.

What would have shown the crossover

If the filter is real, the place to look is the numerator on its own — how many degrees of slow drift reach the divergences, without dividing by anything.

That measurement is available from the same runs and it is the next rung’s subject. The short version is that it is nearly flat across the whole sweep: a neighbourhood sixty times deeper passes about a fifth more drift, where the ratio moves by a factor of 3.7. So the filter, measured directly, is very weak rather than sharply tuned, and there is no corner in it either.

Two combs, at a rise of 0.005The autocorrelation of 760 divergence angles from one stem held at a rise of 0.005. The filled teeth are the lags at multiples of 8; the open teeth are the second comb, at the same spacing offset by 5. Reading the spacing off the first and the offset off the second gives the pair 8 and 13, which is what the position counter reports for the same stem — from angles alone, with no coordinate anywhere in the calculation.-0.50000.500125810131621242629lag, in internodescorrelation between a divergence and the one that many internodes later816245132129spacing 8 · offset 5pair 8/13 — counter says 8/13the shaded strip is the sampling bandone stem · 760 divergences · disturbance 0.25generated from a stated rule, not drawn to look right
Fig. 13 The other observable this thread has for a disturbance’s structure. A comb reads correlation at a lag; a wander reads it at a block size; the same function underlies both, which is why a claim made in one has to be checkable in the other.

That is a second negative and it is the honest place to leave the filter reading: the rule does correct what is relative and does pass what is shared, and the amount it passes is almost independent of how deep it looks — which is not what a filter with a corner does.

The comparison against no rule at all

There is one more control worth putting beside the sweep, because it answers a question the sweep alone leaves open: is the rule doing anything to the drift, or is the whole table simply the disturbance showing through?

The comparison is a kinematic lattice — organs placed at a fixed divergence plus the same disturbance, with no placement rule anywhere in it. That is what “all of it gets through” looks like, and at a correlation length of 32.8 organs it gives a wander of about 36, over three seeds whose individual answers run from 22 to 58.

What the positions say, and what the angles sayEach row is one stem at one rise. The left column is the parastichy pair counted from the coordinates; the right is the single number read out of the divergence angles alone, over 5 runs. On the Lucas ladder — 3/4, 4/7, 7/11 — the readout returns the smaller number too, so it is reading the lattice rather than Fibonacci. The last row is the one that matters: at a rise of 0.05 the positions give an unarguable 2/3 and the angles give 4, 23, 12, 2, 9 — all five wrong, and all five refused.counted from the pointsread from the anglesgolden, rise 0.0323 / 535/5 clear · peak 0.72golden, rise 0.0135 / 855/5 clear · peak 0.59golden, rise 0.0058 / 1385/5 clear · peak 0.78Lucas, rise 0.0323 / 435/5 clear · peak 0.52Lucas, rise 0.024 / 745/5 clear · peak 0.45Lucas, rise 0.0087 / 1175/5 clear · peak 0.59golden, rise 0.052 / 34, 23, 12, 2, 9refused — peak 0.13 under 0.345 runs per rise · the readout sees a list of angles and nothing elsethe refusal is the gate working
Fig. 14 The two objects being compared, in general: a lattice with errors written onto it, and a stem the rule grew. They can be made to agree on many statistics, which is why the ones they disagree on are worth finding.

The rule at an exponent of three gives 46.5, which is above the no-rule control. The rule at an exponent of six gives 22.4, which is below it. So the rule is not uniformly a filter or uniformly an amplifier of this statistic; where it sits relative to no rule at all depends on how deep it looks.

That is a strange thing for a filter to do and an entirely ordinary thing for a ratio to do. A rule that suppresses relative scatter shrinks the denominator below the kinematic lattice’s, and a deep rule shrinks it enough to push the ratio above one even though the numerator is not larger. The control does not rescue the filter reading; it makes the case for looking at the numerator alone, which is what the next rung does.

It is also worth saying that the control is noisy — a factor of two and a half between its own seeds at three seeds — so it is used here to bracket rather than to measure. Sharpening it would mean many more runs of a lattice nobody is otherwise interested in.

What this does not say

It does not say the rule does not correct anything. It corrects a great deal: the scatter between neighbouring divergences falls from 0.32° to 0.21° across the depth sweep, which is the correction happening and being measured.

It does not say there is no crossover anywhere. It says there is none across correlation lengths from 2.8 to 32.8 organs at neighbourhoods from 3 to 182. A disturbance correlated over thousands of organs, or a neighbourhood of one, are not reached.

It does not say the exponent only changes the depth. It changes how sharp the profile’s minimum is as well, and the companion sweep of the loop bound — which changes the number of organs and nothing else, and does nothing — is the control for that rather than a proof.

And it does not say a plant’s inhibition falls as any of these exponents. The exponent here is being used as a handle on depth, not proposed as a measurement. What a real inhibitor’s range is remains this collection’s most testable open quantity and is untouched by this.

What is left of the filter

Something survives, and it is worth separating from what does not.

The mechanism survives: a rule places against neighbours, so it responds to what differs between them and is blind to what they share. That is not a hypothesis about plants, it is a property of taking a minimum over a sum, and it is why a drift passes through where a jitter does not.

The tuning does not survive. The filter reading implied that the rule has a characteristic scale — its own depth — separating what it corrects from what it does not, and that moving the scale moves the separation. Across a factor of sixty in the depth, no separation appears at any correlation length in the sweep.

The reason is visible once the question is asked in the right units. The depth of the neighbourhood is a number of organs, and the correlation length of the disturbance is a number of organs, but the rule does not compare organs at equal weight. Thirty organs carry nine tenths of the profile at an exponent of three, and the nearest half dozen of those carry most of the thirty. So the scale that would set a corner is not the depth as measured; it is something much shorter and much less sensitive to the exponent, which is exactly what a nearly-flat sweep looks like.

That is a claim this thread does not test and states rather than proves. It is written down because a negative result with no account of why the prediction failed is an invitation to make the same prediction again with a different parameter.

The check that would refuse it

Three assertions, and they are arranged so that the negative cannot be satisfied by a sweep that failed to sweep.

The first is that the neighbourhood really varies: the number of organs carrying the profile must fall at every step of the exponent sweep, and the range must span at least a factor of ten. It spans sixty-one.

The second is the absence of a crossover, stated as monotonicity: at every depth, the wander must be strictly larger at each longer correlation length. A crossover would show as a violation somewhere. The same assertion requires that the sweep include at least one correlation length shorter than the neighbourhood at every depth, since a filter can only be refuted where it predicts suppression.

The third is the reversal: at the longest correlation length, the wander must fall at every step as the rule is made shallower, and the ratio between the ends must be at least two. That is the assertion that turns “the prediction is unsupported” into “the prediction is backwards”, and it is the one that would fail first if the effect were noise.

Where this goes next

020406015295785organs in the loopwander at a block of 64independentℓ = 2.8ℓ = 9.5ℓ = 32.83 seeds a point · vertical bars are the spread between themnothing depends on the loop bound The window was not the neighbourhood A placement rule corrects what is relative between neighbours and passes what moves them all together, so how much of a slow disturbance gets through should depend on how deep the neighbourhood is. The obvious knob is how many organs the rule sums over. Swept across a factor of six, it changes nothing at all — and a parameter that is not binding produces exactly the flat sweep a robust result produces. 10.11024813163264block size, in organsvariance of the block means, against independent errorsindependenta memory, ρ = 0.9a memory, ρ = 0.97inherited, a = 0.5inherited, a = 0.7900 organs · jostled at 0.25° · 3 stems eachgenerated from a stated rule, not drawn to look right What the rule does to a drift A placement rule was supposed to leave no slow wander in a divergence sequence, because its errors are corrections rather than inheritances. Driven by a disturbance that drifts, it leaves a larger one than a lattice with no rule in it at all — while cutting the per-organ scatter by more than half. The rule removes what is relative between neighbours, and a drift is not. 012342.262.081.480.9030.477organs in the neighbourhoodagainst the shallowest rulewanderscatterdrift througha drift correlated over 33 organs · 3 seeds a pointdrift through: 1.52° to 1.82° What the ratio was hiding The statistic that says a rule sharpens a drift rises by a factor of nearly four across a sweep of the rule's depth. Undo the normalisation and ask instead how many degrees of drift actually reach the divergences, and the answer changes by a fifth. Nearly all of the effect was in the denominator, and the denominator is the thing the rule is good at.

Shares its objects with

Essays that name at least two of the same things, and that neither author linked.

  • Errors that pass between organs — both name autocorrelation, discrimination, honest limits, measurement, noise, null model, the placement rule, self correction
  • The comb was never the rule — both name autocorrelation, discrimination, falsifiability, honest limits, measurement, null model, the placement rule, self correction
  • The disturbance that travels — both name autocorrelation, discrimination, honest limits, measurement, noise, the placement rule, repulsion, self correction
  • The ratio was never about the rule — both name autocorrelation, discrimination, falsifiability, honest limits, measurement, noise, null model, the placement rule
  • What a forgery has to know — both name autocorrelation, discrimination, honest limits, measurement, noise, null model, the placement rule, repulsion
  • A comb is evidence of a rule — both name autocorrelation, discrimination, falsifiability, measurement, noise, the placement rule, self correction

Named objects

A flat tag is an object no other essay names yet.

AutocorrelationDiscriminationDriftFalsifiabilityHonest limitsMeasurementNegative resultNeighbourhoodNeighbourhood depthNoiseNull modelThe placement rulePredictionRepulsionSelf correction