The control a survey would need

This site has been assembling a survey specification for five phases, and the thing it was for has just changed. The measurement was supposed to answer does this plant compute its pattern? It does not, and cannot, because a lattice whose errors are passed between contact neighbours produces the same reading with no rule in it.

So the specification has to be rewritten around what the measurement can still establish. This essay is that rewrite, and the surprise is how little of it moves: four of the six requirements are unchanged, one is new, and one gets harder in a way that is worth its cost.

What the measurement can still establish #

Three things, in descending order of how well they are established.

The parastichy pair, from the angles alone. This is solid and is what the whole instrument was built for. Two hundred and fifty divergence angles, no coordinates, and the readout returns two integers that a count on the same shoot confirms. Nothing in this phase touches it.

That the errors are not independent. A comb rules out an arrangement whose organ positions are independent draws around an ideal lattice. That is the null model a botanist would otherwise be arguing against, and ruling it out is worth having even though it is weaker than what was claimed.

And a constraint on how the transmission is weighted. The ratio of the second comb to the main one is 0.65 on stems the placement rule grew and 1.30 on a transport of errors weighted by distance. A plant’s measured ratio therefore discriminates between those two — not between “a rule” and “no rule”, but between two specific ways of getting the same correlation.

The six requirements #

One. Two hundred and fifty internodes of readable shoot per plant. From the phase that found the pair. Unchanged.

Two. A reading error under a quarter of a degree per organ. From the same phase, and still the binding constraint: half a degree takes the length to 400 and three quarters to 1,100, because the cost goes as the fourth power of the error once it passes the pattern’s own scatter.

Three. A shoot slower than about 250 nodes to the rung. From the mixture phase. Now checkable from the reading rather than assumed, which is this phase’s contribution: two overlapping windows that agree certify it.

Four. The recorded scatter reported alongside every readout. From the measurement phase. Now doing a second job — separating a silent stem that is too orderly from one that is too disorderly, 0.38° against 56°.

Five. Two overlapping windows, and only agreement reported. New. It costs nothing beyond requirement one, since both windows come out of the same 250 internodes plus 125 more.

Six. Several plants of the same species, and a parastichy count on each. This is the one that gets harder, and the two reasons are the two forgeries.

Why several plants, and how many #

A single stem cannot distinguish a lattice from a disturbance that repeats.

The periodic forgery names a partner drawn from its own disturbance rather than from the arrangement, so it names a different one on each stem — 10, 10, 12 and 12 across the four that report. The rule’s stems name the same pair every time. Reading three plants and requiring agreement removes the crude forgery entirely.

The comb ratio needs more. It is 0.65 on the rule’s stems with a spread from 0.58 to 0.79 across five, and it is being compared against 1.30. Separating those with a per-plant spread of about a third takes six plants comfortably and two not at all.

So requirement six is six plants, and that number comes from the spread of a ratio rather than from a general instinct that more is better. It is also the first requirement in this specification that is about the population rather than about a specimen, which is a change in kind: everything before it could be satisfied by finding one good plant.

The protocol, step by step #

Written as instructions rather than as requirements, because a specification that cannot be handed to somebody is not finished.

Choose six shoots of one species at one stage. They should be slow-growing — the requirement is 250 nodes to a rung, which for most plants means a shoot that has been extending for a season rather than a week — and each should have at least 375 internodes below the tip with organs still identifiable.

Record the divergence angle at every internode. From the tip downward, in order, to a quarter of a degree. The order matters more than the absolute azimuths: every quantity here is a correlation between positions in the sequence, and a shoot recorded out of order is a shoot with its comb destroyed.

Record a parastichy count on each shoot, at the height of the upper window, by the ordinary method of following contact rows around.

Read each shoot twice — the top 250 internodes, and the 250 starting 125 lower — and record the outcome as one of the six the previous essay lists.

Report, for the whole sample: the pairs from shoots that agreed and whose count confirmed the reading; the ratio of second comb to main for each of those; the recorded scatter of every shoot including the silent ones; and the counts of each outcome, including the discards.

That last item is the one most likely to be dropped and the one this thread has argued hardest for. The discards are measurements: how many shoots were too fast is a fact about the species and the season, and how many readings the instrument got wrong is a fact about the instrument.

What a result would look like #

Three outcomes are worth writing down in advance, because a specification that does not say what would count as which is not a test.

Pairs agreeing across six plants, ratio near 0.65. Consistent with a placement rule and with any transport whose coupling leans about three to one towards the smaller parastichy number. Not proof of a rule; a constraint on what a transport would have to look like.

Pairs agreeing, ratio near or above 1.30. Evidence against the placement rule as this site implements it, and consistent with error transport weighted by distance. This is the outcome that would be most interesting and it is the one nobody expects.

Pairs disagreeing across plants. Either the shoots are not all on the same rung — checkable, since the counts are recorded — or the comb is being manufactured by something that varies from plant to plant, which is the periodic forgery. Either way the reading is not a measurement of a lattice and the sample says so.

The point of writing those before any data exists is that all three are publishable. A specification whose interesting outcome is the one it expects has not been designed as a test.

What is no longer in the specification #

One thing, and removing it is a real gain.

Before this phase, a survey that found a comb would have needed to argue that the plant’s disturbances are not correlated from organ to organ — an argument nobody could make, since no one has measured a plant’s disturbance autocorrelation and doing so is harder than the measurement it would support.

That control is not needed. A disturbance with a memory of any length manufactures no comb and destroys none, at correlation coefficients up to 0.97, so finding a comb says nothing either way about correlation length and the survey does not have to control for it.

What the extra requirement is worth against what it costs #

Requirement six is six plants where the previous specification implied one, and a sixfold increase in field work deserves an accounting rather than an assertion.

What it buys, in order:

Three plants remove the crude forgery. A disturbance that repeats names its partner from its own shape, so three stems that agree have already excluded it — the probability of three independent draws naming the same wrong partner is small and is measured rather than argued, since the eight forged stems here produced three different answers between them.

Six plants make the ratio a measurement. The ratio’s per-plant spread is about a third of its value, and the two hypotheses it separates are a factor of two apart. Six brings the spread of the mean to about an eighth, which separates them cleanly; two brings it to a fifth, which does not.

And any number above one turns a refusal into a rate. With one plant, a silent stem is a failed measurement. With six, the fraction that were silent is a measurement of the population — how many shoots at this site in this season were growing too fast, or were too orderly to read.

That third one is free and was not designed for. It falls out of the requirement the other two forced, which is the ordinary way a specification improves: a control added for one reason turns out to answer a question nobody had asked.

What the specification cannot buy #

The question the whole thread was aimed at — is this plant computing its pattern? — is not on the list above, and no amount of stem or specimens puts it there.

The reason is structural rather than statistical. The two arrangements agree on every quantity computable from a list of angles or a list of positions: divergence, rise, parastichy pair, transitions, contact families, side-count distribution, hop lengths and both combs. More data improves the precision on each of them and adds nothing new to the list, because the list is closed by what a finished plant carries.

The next evidence has to come from an intervention: remove a primordium and measure where the next organ goes. A placement rule predicts a displacement, computable with nothing free once the interaction range is fixed; a transport of errors predicts none, because it has no opinion about where organs go. That is a real experiment — laser ablation of primordia has been done for decades — and it is a real prediction, and neither the prediction nor the experiment is in this phase.

Which plants could supply it #

The specification is finally specific enough to ask which species could satisfy it, which is a question this site has avoided because the answer needs horticulture rather than arithmetic. What can be said is which properties a candidate needs, and each is now a number.

Enough internodes. 375 with identifiable organs, which rules out most rosettes and every annual with a short season, and points at long monopodial shoots — conifer leaders, tall herbaceous stems that keep their leaf scars, climbing shoots that extend for months.

Slow enough. Fewer than a rung per 250 nodes, which is a statement about how fast the internode length falls along the shoot rather than about growth rate in time. A shoot whose parastichy pair is the same at the top and 375 internodes down satisfies it, and that is checkable by counting twice before any angles are recorded.

Measurable to a quarter of a degree. This is the hardest one and it is about the organs rather than the shoot: leaf scars with a definite centre, on a stem round enough that azimuth means something. It rules out flattened stems, organs that migrate after initiation, and anything where the scar is a ridge rather than a point.

And several of them alike. Six shoots at the same stage, which for a wild population means one site and one season.

None of those is exotic and no two of them are obviously compatible: the shoots long enough tend to be the ones whose organs are hardest to place, and the ones with crisp scars tend to be short. That tension is the actual reason this survey has not been done, and it is a better statement of the difficulty than eight phases of specification were previously able to give.

The dataset, for the eighth phase running #

This site has specified a survey it cannot do since the measurement phase, and the specification has grown each time. It is worth saying plainly what that means, because eight phases of specifying is either diligence or avoidance and the difference is whether the specification is converging.

It is. The first version asked for divergence angles down a stem. The current one asks for six things, five of which are properties of how the angles are recorded rather than new measurements, and the sixth is six plants instead of one. A botanist with a protractor, a slow-growing shoot and an afternoon could satisfy all six.

What has grown is not the cost. It is the number of ways the measurement was found to be able to go wrong quietly, each of which is now a stated requirement rather than an assumption — and every one of them was found by building the thing that would break it.