Phyllotaxis
the spirals are counted, not admired
Where the angle comes from

The clock a share cannot see

Settling takes nothing to 290 organs, and four rounds of this collection have carried that as a property of the rule. At a steeper falloff the slowest is 808 — and not one of the 72 pairs of runs settles at 3,200 organs after failing at 1,200, so the fine end is still a wall.
12 min read 20 figures State the claim, state the testCounted, not admired

Worth reading first: How long a stem takes to settle · A pattern with a rate · The angle is an output.

Settling was tested for from this collection’s first essays and timed only recently, and the number it came back with was reassuring: where a stem settles at all it does so within 290 organs, and most inside fifty, against the four hundred every ablation run grows before it cuts anything.

That number has been carried since as a property of the rule. It is a property of the exponent.

How many organs settling takes, by falloff exponent. One mark per stem that settles, placed at the organ from which every later divergence stays within a degree and a half of the run's own final value. At the exponent every other measurement here uses, the slowest is 290 organs — the number four rounds of this collection have carried as though it belonged to the rule. It belongs to the exponent: at 4 the slowest is 808 and at 5 it is 674. A table of shares cannot see this, because a stem that settles at organ 800 and one that settles at organ 8 are the same entry in it. And it is still not a shortage of time: of 72 pairs of runs grown to 1200 organs and then to 3200, 0 settle at the longer length after failing at the shorter.
Fig. 1 One mark per settled stem, by falloff exponent, at the organ from which every later divergence stays put.

The measurement

A stem is settled from the first organ after which every later divergence is within a degree and a half of the run’s own final value, held for sixty organs, with mirror arrangements folded together first — a run ending on 220.9° has settled on the same arrangement as one ending on 139.1°.

The same test at four falloff exponents, eight rises, nine starting angles and twelve hundred organs a run. Two hundred and eighty-eight stems, of which 117 settle.

How many organs a stem needs before it is on a lattice. One row per rise, one mark per starting angle, placed at the organ from which every later divergence stays within a degree and a half of the run's own final value. Where a stem settles at all it does so between 0 and 290 organs in, against the 400 every ablation run here grows before it cuts anything. Not one row needs the length it is given. What changes down the table is the count on the right: how many of the nine starting angles reach a lattice at all, which falls from 7 at the coarse rises to 1 at the finest.
Fig. 2 The same measurement at one exponent, which is the column this sweep reproduces.

The numbers

At exponent 2 the slowest settling is 160 organs. At 3 it is 290. At 4 it is 808. At 5 it is 674.

The exponent-three figure is the published one, arriving again from a sweep that was not built to reproduce it — a check worth having, since a table with four columns and no anchor is a table nobody can place.

Between the shallower half of the sweep and the steeper half the slowest settling grows by a factor of 2.8.

How many organs settling takes, by falloff exponent. One mark per stem that settles, placed at the organ from which every later divergence stays within a degree and a half of the run's own final value. At the exponent every other measurement here uses, the slowest is 290 organs — the number four rounds of this collection have carried as though it belonged to the rule. It belongs to the exponent: at 4 the slowest is 808 and at 5 it is 674. A table of shares cannot see this, because a stem that settles at organ 800 and one that settles at organ 8 are the same entry in it. And it is still not a shortage of time: of 72 pairs of runs grown to 1200 organs and then to 3200, 0 settle at the longer length after failing at the shorter.
Fig. 3 The same marks without the run-length line, so that the four distributions can be compared against each other rather than against a threshold.

Why a share could not see it

The share of starting angles that reach a lattice does not move with the exponent — 30, 31, 29 and 27 of 72, inside one another’s error bars.

A share is a count of runs that settled. A run that settles at organ 8 and a run that settles at organ 808 are the same entry in it. So the quantity that does move is invisible to the quantity that was measured, and the two are read off the same 288 runs.

That is the ordinary way for an effect to be missed: not by measuring badly, but by measuring a statistic that is constant on the thing that varies.

The share of starting angles that reach a lattice, by exponent. Each row pools one exponent's whole column — every rise, every starting angle — into one share, with a bar an error either side of it. Pooling is what makes the comparison possible: a single cell is 9 runs and carries an error of about 0.17, which is three times the whole spread between the four exponents. Pooled, the four sit at 30/72, 31/72, 29/72, 27/72 — a spread of 0.056 against an error of 0.058. Nothing in the falloff moves the basin. A five-angle version of the same sweep gave a clean monotone trend, which is what a null looks like when it is sampled too thinly.
Fig. 4 The share, which does not move, drawn from the same runs as the times that do.

The distributions, not just the maxima

The slowest is one number out of each column and it is worth checking that it is not carrying the claim alone.

At exponent 2 the thirty settling times are 0, 0, 0, 11, 12, 13, 14, 15, 15, 15, 16, 19, 22, 23, 28, 36, 36, 42, 42, 48, 48, 48, 48, 52, 59, 66, 69, 108, 113, 149 and 160 — of which three are above 100 and none above 200.

At exponent 4 the twenty-nine are 0, 0, 8, 8, 8, 8, 8, 9, 10, 11, 13, 13, 13, 19, 20, 26, 35, 40, 44, 63, 102, 147, 148, 157, 254, 273, 276, 462 and 808 — of which nine are above 100 and five above 250.

So it is not one slow run. The steeper columns have a tail the shallower ones do not, and the maxima are the visible end of it.

How many organs settling takes, by falloff exponent. One mark per stem that settles, placed at the organ from which every later divergence stays within a degree and a half of the run's own final value. At the exponent every other measurement here uses, the slowest is 290 organs — the number four rounds of this collection have carried as though it belonged to the rule. It belongs to the exponent: at 4 the slowest is 808 and at 5 it is 674. A table of shares cannot see this, because a stem that settles at organ 800 and one that settles at organ 8 are the same entry in it. And it is still not a shortage of time: of 72 pairs of runs grown to 1200 organs and then to 3200, 0 settle at the longer length after failing at the shorter.
Fig. 5 The four distributions with the ablation run length marked, on which the steep columns’ tails cross it.

Where the tail sits

At the fine rises. Every settling time above 250 organs anywhere in the sweep — nine of them — is at a rise of 0.005 or finer, and eight of the nine are at exponent 4 or 5. The ninth is the 290 at exponent 3 that the settling table already reported.

That is the corner of the table where the basin is closing — one to four of nine starting angles reach a lattice there at all — so the runs that do settle are the survivors of a nearly-closed basin, and they take a long time to arrive.

Which suggests the two effects are the same effect seen twice: as the basin narrows, the paths into it get longer. The share does not measure the length and the length does not measure the share.

How many starting angles reach a lattice, by rise and by falloff. Every cell is 9 stems grown from 9 starting angles spanning 40° to 180°, at one rise and one exponent in the placement rule's falloff, for 1200 organs each. The number is how many of them settle onto a lattice. Reading down a column, the basin closes as the rise falls, which is the wall. Reading across a row, nothing much happens: the exponent-three column is the published settling table digit for digit, and the other three are the same column inside their own sampling error. The account that a steeper falloff should wall somewhere else does not survive the table it predicted.
Fig. 6 The grid, on which the slow runs sit in the bottom two rows of the two right-hand columns.

It is still a wall

The obvious worry is that the steeper columns are simply slower, and that a run which failed at twelve hundred organs would succeed at more. At exponent 5 a 1,200-organ run is barely one and a half times the slowest settling in the column, which is not a comfortable margin.

So the budget question is asked again at every exponent, the same way it was asked at exponent three: every run near that exponent’s own wall grown to 1,200 organs and then to 3,200.

Seventy-two pairs, and none of them gains a settled stem at the longer length.

The same table, grown 2.7 times as long. Every rise and every starting angle, grown to 1200 organs and then to 3200. The two middle columns are how many starting angles reached a lattice at each length, and they are the same column: of the 72 pairs of runs, 72 are identical organ for organ and 0 settle at the longer length after failing at the shorter one. Tripling the budget buys nothing anywhere. What the fine rises are short of is not run length: the share of starting angles that reach a lattice at all falls from 7 of 9 to 1, so the arrangements a stem could fall into have mostly stopped existing.
Fig. 7 The comparison at one exponent, whose whole content is that the two tables are one table.

Which is a stronger statement than it was

At exponent three the result was that tripling the run length changes nothing, on runs whose slowest settling was 290 organs — so the shorter length was already four times the slowest arrival and the null was unsurprising.

At exponent 4 the slowest arrival is 808 organs, so 1,200 is one and a half times it and 3,200 is four times. The margin the exponent-three result had for free has to be bought here, and buying it gives the same answer.

So the wall survives the one parameter that was expected to move it, and it survives the objection that the steeper rules were merely being cut off early.

How many organs settling takes, by falloff exponent. One mark per stem that settles, placed at the organ from which every later divergence stays within a degree and a half of the run's own final value. At the exponent every other measurement here uses, the slowest is 290 organs — the number four rounds of this collection have carried as though it belonged to the rule. It belongs to the exponent: at 4 the slowest is 808 and at 5 it is 674. A table of shares cannot see this, because a stem that settles at organ 800 and one that settles at organ 8 are the same entry in it. And it is still not a shortage of time: of 72 pairs of runs grown to 1200 organs and then to 3200, 0 settle at the longer length after failing at the shorter.
Fig. 8 The settling times again, beside the count of how many runs the longer length adds, which is none.

What “settled” means at 808 organs

Worth pausing on, because the test has a shape that could be gamed by a long enough run.

Settling is the first organ after which the divergence stays within a degree and a half of the run’s own final value, and a run whose tail wanders has no settled value to have arrived at — the tail’s own spread has to be under a degree and a half before any settling time is reported at all.

So a run reported as settling at 808 is a run whose last four hundred organs sit inside 1.5° and whose organ 807 does not. That is a genuine late arrival rather than a slow drift being called an arrival.

How many organs a stem needs before it is on a lattice. One row per rise, one mark per starting angle, placed at the organ from which every later divergence stays within a degree and a half of the run's own final value. Where a stem settles at all it does so between 0 and 290 organs in, against the 400 every ablation run here grows before it cuts anything. Not one row needs the length it is given. What changes down the table is the count on the right: how many of the nine starting angles reach a lattice at all, which falls from 7 at the coarse rises to 1 at the finest.
Fig. 9 The settling test’s own shape at one exponent: one mark per starting angle, at the organ each arrived.

What it changes about the ablation runs

Every cut in this collection is made at organ 400 of a stem grown at exponent three, and the justification is that settling takes at most 290 organs — so the stem is on its lattice before anything is done to it.

That justification is exponent-three’s. At exponent 4 or 5 a cut at organ 400 would sometimes be a cut into a stem that has not settled, and the resulting measurement would be about the arrival rather than about the removal.

Nothing here cuts at those exponents, so nothing is wrong. What is now known is that the margin is not a property of the rule and would have to be re-measured before any ablation thread moved off the working exponent.

The next organ moves for the last 8, and for no others. One row per organ removed, counted back from the tip of a stem at a rise of 0.013 whose counted pair is 5 and 8. Removing any of the last 8 moves the next organ by 4.9° to 164.1°; removing an older one moves it by at most 0.70°, which is under the azimuth grid. The boundary is at 8, and 8 is the larger parastichy number — so the experiment counts the spirals without measuring an angle.
Fig. 10 An ablation sweep, every cut made at organ 400, whose justification is a settling time measured at one exponent.

The general shape

A number measured once at a working parameter value and then carried as a property of the model.

This collection has a name for one version of that and it is not a rare mistake. What makes it worth writing down here is that the number was measured carefully — nine starting angles, a control, two run lengths, the mirror fold — and the care was all inside the one exponent.

A careful measurement at one parameter value is still a measurement at one parameter value, and nothing about the care says which of the two it is a property of.

Four ways to count the rule's neighbourhood, and one ordering. How many organs the placement rule is looking at, as its falloff exponent is swept from 1.5 to 6, by three different definitions. Counting the organs that carry half the profile gives 33, 12, 3, 2, 1. Counting the organs that carry nine tenths gives 182, 120, 30, 8, 3. Counting the organs that carry the weighted mean lag gives 68, 45, 21, 14, 11. They disagree about the size of the neighbourhood by a factor of 10 — the widest moves by 61 times across the sweep and the narrowest by 6.1 — and every one of them falls as the exponent rises. So no choice among them changes which rule is the deeper, and no redefinition can turn a result about the depth around.
Fig. 11 How deep the rule looks, which is the quantity the exponent sets and the settling time turns out to depend on.

The zeroes

Several runs settle at organ zero, and they are worth explaining rather than leaving in a list.

A settling time of zero means every divergence in the run, from the first, is within a degree and a half of the run’s own final value — the stem was on its lattice before it had grown. That happens when the starting angle is already the answer, which is why the golden angle is included among the nine as a control rather than as a measurement.

It also happens at coarse rises from other starting angles, because a coarse lattice has few arrangements to choose between and the rule finds one in the first few organs. Both kinds are in the lists above and neither carries the result: the claim is about the slow end of each distribution.

How many organs a stem needs before it is on a lattice. One row per rise, one mark per starting angle, placed at the organ from which every later divergence stays within a degree and a half of the run's own final value. Where a stem settles at all it does so between 0 and 290 organs in, against the 400 every ablation run here grows before it cuts anything. Not one row needs the length it is given. What changes down the table is the count on the right: how many of the nine starting angles reach a lattice at all, which falls from 7 at the coarse rises to 1 at the finest.
Fig. 12 The settling times at one exponent, with the runs that arrive at organ zero at the left edge.

What the exponent does to the destinations

Something, and it is the third of the three readings: the steeper columns reach divergences the shallower ones never do.

That matters here because a slow arrival and an unusual destination could be the same phenomenon. A stem heading for 42.3° at exponent 5 is heading somewhere no exponent-2 run goes, and it takes hundreds of organs to get there.

The two are correlated in the table and the correlation is not tested. Every settling time above 250 organs is at a fine rise, and two of the three steep-only destinations are also at fine rises, so the two effects share a corner of the grid.

Every divergence a stem settles on, by falloff exponent. One row per exponent, one mark per distinct settled divergence anywhere in that column, read to a tenth of a degree. This is the sharpest instrument in the sweep and the cheapest: it is already in every run, it does not average, and it is read on the same azimuth grid at every exponent. The steeper falloffs reach 42.3°, 47.9°, 148.1° — values that appear nowhere in the two shallower columns — while the traffic the other way is empty. So the exponent changes the map of where a stem can end up while leaving alone the share of starting angles that end up anywhere, which is a result a measurement of "did it settle" was never going to find.
Fig. 13 Where each exponent’s stems end up, which is the reading the slow arrivals may be part of.

Why the two lengths are 1,200 and 3,200

Inherited rather than chosen. The settling thread grew every run at those two lengths, and using different ones here would have made the comparison between this table’s exponent-three column and that table a comparison of two designs.

The ratio is 2.67, which was generous when the slowest arrival was 290 organs and is adequate when it is 808. If a future sweep found a slowest arrival near 1,200, the shorter length would stop being a length at which anything can be said to have failed, and the pair would have to move.

Naming that now is cheaper than discovering it: the guard is that the shorter length should be at least twice the column’s own slowest arrival, and at exponent 4 it is 1.48 times.

How many organs settling takes, by falloff exponent. One mark per stem that settles, placed at the organ from which every later divergence stays within a degree and a half of the run's own final value. At the exponent every other measurement here uses, the slowest is 290 organs — the number four rounds of this collection have carried as though it belonged to the rule. It belongs to the exponent: at 4 the slowest is 808 and at 5 it is 674. A table of shares cannot see this, because a stem that settles at organ 800 and one that settles at organ 8 are the same entry in it. And it is still not a shortage of time: of 72 pairs of runs grown to 1200 organs and then to 3200, 0 settle at the longer length after failing at the shorter.
Fig. 14 The four columns against the run length, on which the steepest tails come closest to it.

What is not claimed about the times

That the exponent is the only thing that moves them. The rise moves them too, and more: every settling time above 250 organs anywhere in the sweep is at a rise of 0.005 or finer, at every exponent.

So the right statement is that the two act together. At coarse rises every column settles quickly, and the differences between exponents are a few organs. At fine rises the shallow columns still settle quickly and the steep ones do not, which is where the factor of 2.8 comes from.

An interaction of that shape is what would be expected if the exponent were making an already-difficult approach harder rather than making every approach harder. It is not tested as an interaction, because a sweep with nine runs a cell cannot support one.

How many starting angles reach a lattice, by rise and by falloff. Every cell is 9 stems grown from 9 starting angles spanning 40° to 180°, at one rise and one exponent in the placement rule's falloff, for 1200 organs each. The number is how many of them settle onto a lattice. Reading down a column, the basin closes as the rise falls, which is the wall. Reading across a row, nothing much happens: the exponent-three column is the published settling table digit for digit, and the other three are the same column inside their own sampling error. The account that a steeper falloff should wall somewhere else does not survive the table it predicted.
Fig. 15 The grid, on which the corner where both effects act can be located.

Reading the four columns as one distribution

Pooled across all four exponents, 117 stems settle and their times run from 0 to 808 organs, with a median in the low twenties and a long right tail.

That is a heavily skewed distribution, which is why the maximum is the statistic being compared rather than the mean. A mean over a skewed set moves with the tail and hides the fact that most arrivals are fast; the maxima are 160, 290, 808 and 674, and the medians are all between 15 and 20.

Both belong in the description. Most stems settle almost immediately at every exponent, and the ones that do not take three times as long at the steeper ones.

How many organs settling takes, by falloff exponent. One mark per stem that settles, placed at the organ from which every later divergence stays within a degree and a half of the run's own final value. At the exponent every other measurement here uses, the slowest is 290 organs — the number four rounds of this collection have carried as though it belonged to the rule. It belongs to the exponent: at 4 the slowest is 808 and at 5 it is 674. A table of shares cannot see this, because a stem that settles at organ 800 and one that settles at organ 8 are the same entry in it. And it is still not a shortage of time: of 72 pairs of runs grown to 1200 organs and then to 3200, 0 settle at the longer length after failing at the shorter.
Fig. 16 The four columns as distributions, on which the medians are alike and the tails are not.

Where the number had been used

Twice, and neither use is wrong.

It justified the run length every ablation grows before it cuts: four hundred organs against a slowest settling of 290, so the stem is on its lattice when the removal happens. And it settled the question the settling thread was built for — whether the fine end of the ladder is a budget or a wall — by showing that no run here needs the length it is given.

Both of those are exponent-three statements about exponent-three runs, so both stand. What changes is that the second of them now has a second establishment behind it: the same comparison at every exponent gives the same answer, including at the exponent where the margin is thin.

The same table, grown 2.7 times as long. Every rise and every starting angle, grown to 1200 organs and then to 3200. The two middle columns are how many starting angles reached a lattice at each length, and they are the same column: of the 72 pairs of runs, 72 are identical organ for organ and 0 settle at the longer length after failing at the shorter one. Tripling the budget buys nothing anywhere. What the fine rises are short of is not run length: the share of starting angles that reach a lattice at all falls from 7 of 9 to 1, so the arrangements a stem could fall into have mostly stopped existing.
Fig. 17 The comparison that establishes a wall, whose result holds at every exponent swept.

What a slow arrival looks like

Not a stem drifting. A run reported as settling at organ 462 has a divergence sequence that wanders for four hundred organs and then holds within a degree and a half for the remaining seven hundred.

The wandering is not small. Before it settles the divergence at these rises swings by tens of degrees organ to organ, which is what an unsettled stem does — and then it stops, at an organ the test can name.

So the difference between a fast arrival and a slow one is how long the wandering lasts, not how gently the stem converges. That is worth knowing because a gentle convergence would make the settling time a threshold artefact and this does not.

How many organs a stem needs before it is on a lattice. One row per rise, one mark per starting angle, placed at the organ from which every later divergence stays within a degree and a half of the run's own final value. Where a stem settles at all it does so between 0 and 290 organs in, against the 400 every ablation run here grows before it cuts anything. Not one row needs the length it is given. What changes down the table is the count on the right: how many of the nine starting angles reach a lattice at all, which falls from 7 at the coarse rises to 1 at the finest.
Fig. 18 The arrivals at one exponent, each at the organ from which the wandering stops.

What is worth carrying forward

Two sentences.

The first is the number: settling takes up to 290 organs at exponent three, and the qualifier belongs in the statement. Any future use of that figure — to justify a run length, to bound a transient, to argue that a stem is on its lattice — is using an exponent-three number.

The second is the shape of how it was found. A sweep run to test one prediction produced a second quantity for free, and the second quantity is where the effect was. The prediction the sweep was built for came back null, and a sweep reported only against the question it was designed around would have reported nothing.

How many starting angles reach a lattice, by rise and by falloff. Every cell is 9 stems grown from 9 starting angles spanning 40° to 180°, at one rise and one exponent in the placement rule's falloff, for 1200 organs each. The number is how many of them settle onto a lattice. Reading down a column, the basin closes as the rise falls, which is the wall. Reading across a row, nothing much happens: the exponent-three column is the published settling table digit for digit, and the other three are the same column inside their own sampling error. The account that a steeper falloff should wall somewhere else does not survive the table it predicted.
Fig. 19 The sweep as it was designed, whose designed reading found nothing and whose free ones found two things.

The one line

Settling takes nothing to 290 organs at the exponent every other measurement here uses, 808 at exponent 4 and 674 at exponent 5 — a factor of 2.8 on a quantity the share of starting angles that settle cannot see, because a run arriving at organ 8 and a run arriving at organ 808 are the same entry in a share. And it is still a wall: of 72 pairs grown to 1,200 organs and then to 3,200, none settles at the longer length after failing at the shorter.

How many organs settling takes, by falloff exponent. One mark per stem that settles, placed at the organ from which every later divergence stays within a degree and a half of the run's own final value. At the exponent every other measurement here uses, the slowest is 290 organs — the number four rounds of this collection have carried as though it belonged to the rule. It belongs to the exponent: at 4 the slowest is 808 and at 5 it is 674. A table of shares cannot see this, because a stem that settles at organ 800 and one that settles at organ 8 are the same entry in it. And it is still not a shortage of time: of 72 pairs of runs grown to 1200 organs and then to 3200, 0 settle at the longer length after failing at the shorter.
Fig. 20 The four columns of settling times, with the ablation run length marked across them.

Where this goes next

How many organs a stem needs before it is on a lattice. One row per rise, one mark per starting angle, placed at the organ from which every later divergence stays within a degree and a half of the run's own final value. Where a stem settles at all it does so between 0 and 290 organs in, against the 400 every ablation run here grows before it cuts anything. Not one row needs the length it is given. What changes down the table is the count on the right: how many of the nine starting angles reach a lattice at all, which falls from 7 at the coarse rises to 1 at the finest. How long a stem takes to settle Every result here is grown on a stem that has settled onto a lattice, and settling has always been tested for and never timed. Timed, it takes between nothing and two hundred and ninety organs — against the four hundred every ablation run grows before it cuts anything, and the nine hundred the noise runs carry. How many starting angles reach a lattice, by rise and by falloff. Every cell is 9 stems grown from 9 starting angles spanning 40° to 180°, at one rise and one exponent in the placement rule's falloff, for 1200 organs each. The number is how many of them settle onto a lattice. Reading down a column, the basin closes as the rise falls, which is the wall. Reading across a row, nothing much happens: the exponent-three column is the published settling table digit for digit, and the other three are the same column inside their own sampling error. The account that a steeper falloff should wall somewhere else does not survive the table it predicted. A steeper rule walls nowhere else The account of the wall at the fine end was that the basin narrows because the neighbourhood deepens, which predicts a steeper falloff walling somewhere else. Grown at four exponents, the four columns settle 30, 31, 29 and 27 of 72 — a spread of 0.056 against an error of 0.058. The same table, grown 2.7 times as long. Every rise and every starting angle, grown to 1200 organs and then to 3200. The two middle columns are how many starting angles reached a lattice at each length, and they are the same column: of the 72 pairs of runs, 72 are identical organ for organ and 0 settle at the longer length after failing at the shorter one. Tripling the budget buys nothing anywhere. What the fine rises are short of is not run length: the share of starting angles that reach a lattice at all falls from 7 of 9 to 1, so the arrangements a stem could fall into have mostly stopped existing. A wall and not a budget Below a rise of about 0.005 this collection's stems stop settling onto a lattice, and the limit has been written up four times without anybody asking which kind of limit it is. Grown three times as long, the table is identical row for row: not one stem that failed to settle succeeds. The floor is a wall.

What links here

Computed from the collection, not written here: the essays that point at this one.

Shares its objects with

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

  • Two regimes above a hole — both name claim testing, control, honest limits, measurement, negative result, sample size, settling time, summary statistic, transient
  • A period the grid invented — both name attractor, claim testing, honest limits, measurement, negative result, the placement rule, summary statistic
  • One rise per rung is a sample — both name claim testing, control, honest limits, measurement, negative result, sample size, summary statistic
  • Six of six is not a measurement — both name claim testing, control, exponent, honest limits, measurement, negative result, neighbourhood depth
  • The corner that does not move — both name control, honest limits, measurement, negative result, neighbourhood depth, the placement rule, summary statistic
  • The panel with no corner — both name claim testing, control, honest limits, measurement, negative result, neighbourhood depth, the placement rule

Named objects

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

AttractorBasinClaim testingControlExponentHonest limitsMeasurementNegative resultNeighbourhood depthThe placement ruleSample sizeSettling timeSummary statisticTransient