Phyllotaxis
the spirals are counted, not admired
Stems and cones

A change with nowhere to be

The claim this whole thread rests on is that a survivor does not change where the two contact steps change places. Nineteen located changes never put one there. The twentieth is flagged at a handover, and it is flagged because the offset stops wrecking for thirty-four rises.
15 min read 20 figures State the claim, state the testCounted, not admiredOne parameter, one family

Worth reading first: Where a handover sits.

A handover is the rise at which a lattice’s two contact steps change places: above it one family has the shorter hop across the surface and below it the other does. A band is the stretch of rise around one, over which the counted pair and the settled divergence hold still.

The claim the handover thread rests on is that the survivor does not change there. When a cut wrecks a stem, the family whose hop the wrecked run holds rigid is not decided by which hop is currently shorter — and the sharpest form of that is that the rise where the ordering changes is not the rise where the survivor does.

Offset 5 on the 5/8 band, and the change that cannot be placed. Every rise of the band, coarse on the left, with offset 5's cut drawn at each: pale where it recovers, dark where it wrecks and keeps 5, warm where it wrecks and keeps 20. It keeps the off-pair family at two rises above the handover and then does not wreck again for 34 rises, so its return is bracketed across a stretch that contains the handover. The flag that says a change sits at a handover fires here for the first time, and it is a statement about where the offset stops wrecking rather than about the handover.
Fig. 1 The one offset on the third band whose answer changes, drawn against the band’s own handover.

What the claim had behind it

Nineteen located changes on the golden 8/13 band, none of them at its handover. Zero changes on the Lucas 7/11 band, which contributes a vacuous confirmation and was reported as vacuous rather than counted.

That is a strong negative. The changes on the first band sit seven to fifty-seven rises below the handover, at three separate rises for the three offsets that change, and none of them is nearer than seven rises to the crossing. The same band’s alternation turned out to be speckle rather than a period, so the changes are not evenly spread either — they cluster below the crossing and thin out further down.

Nineteen chances to land on one rise and none of them did. Under a coin that puts a change anywhere on a 126-rise band, that is unremarkable — the handover is one rise of 126 — which is why the claim is stated as a negative rather than as a surprise.

Every rise of the 8/13 band, cut at every offset. One column per rise of the band, coarse on the left and fine on the right, and one row per offset that wrecks anywhere on it. A filled cell is the family the cut stem keeps; a pale cell is an offset that recovers at that rise and has no survivor to report. The band holds 126 rises and 1890 cut stems. three of the six offsets change their answer somewhere inside, three never do, and the vertical rule is the handover — the rise where the two contact steps change places. Not one of the 19 changes is at it.
Fig. 2 The first band’s nineteen changes at full resolution, none of them at the rise its two contact steps cross.

The flag

The sweep marks a change at the handover when the two rises it is bracketed between sit either side of the handover rise. That is the only test available: a change is not observed at a rise, it is observed between two rises where the answer differs.

Across two bands the flag never fired. On the third band it fires once, and the firing is the subject of this essay.

The bracket is not two adjacent rises. It runs from 0.01605 to 0.01497 — a hundred and eight steps of the grid the rises are named on, twenty rises of the band — and the handover at 0.01558 is inside it because nearly everything on the band is inside it.

Offset 5 across the 5/8 band, rise by rise. The family this one offset keeps at each of the band's 112 rises, coarse on the left. It wrecks at 28 of them and keeps the 5-family and the 20-family at different rises. The ticks below mark no island: the answer changes once and stays changed. The handover is the taller rule and the change of answer is nowhere near it.
Fig. 3 The offset whose change is flagged, drawn across every rise the band holds.

Why the bracket is so wide

Because a change of surviving family can only be bracketed between two rises at which that offset wrecks, and offset 5 on this band wrecks at 28 of 112 rises.

At 0.01605 it wrecks and keeps 20. Then it recovers at every rise for the next thirty-four, which carries it past the handover and well below it. At 0.01497 it wrecks again and keeps 5.

Nothing was observed in between because there was nothing to observe. A cut that recovers leaves a stem with no rigid lag to report, so those thirty-four rises are not rises where the answer was 5 or 20; they are rises where the question has no answer.

Which offsets wreck across the Lucas 7/11 band. One row per offset and one column per rise, with a mark where a single removal at that offset wrecks the stem. The set is not the same at every rise: on this band one offset wrecks at only 27 of its 124 rises, in several separate stretches, while others wreck at all of them. So a census taken at one rise of a band and a census taken at another are censuses of different sizes, and every claim of the form "at every offset that wrecks" is quantified over a set the rise decides.
Fig. 4 The wrecking set moving across a band, which is what decides where an answer exists at all.

What is at the handover rise itself

One wrecking cut. At 0.01558 the only offset that wrecks is 4, and it keeps 5 — as it does at the rise above and the rise below and at 111 of the band’s 112 rises.

So the direct reading at the handover is available and it shows nothing changing. The offset that changes is not wrecking there; the offset that is wrecking there does not change.

That is the honest summary and it is neither a confirmation nor a counterexample. The band has one changing offset and it is silent across its own handover.

All one bands cut at every rise, offset by offset. One row per wrecking offset on each band cut whole, one cell per rise, coarse on the left. A pale cell is a rise at which that offset's cut recovers and has no survivor; a dark cell is a cut that wrecks and keeps one of the band's own counted pair; a warm cell is a cut that keeps a family off the pair. The vertical rule on each row is that band's handover, where its two contact steps change places. The golden 8/13 band changes the family it keeps 19 times, the golden 5/8 twice and the Lucas 7/11 not at all.
Fig. 5 The third band’s three offsets at every rise, with the handover marked and the changing offset silent across it.

The flag is measuring the wrecking set

Which is the finding. A test of the form does the answer change at the handover assumes the answer exists on both sides of it, close enough that a change between them is a change there.

On this band it does not. The flag fires because the bracket is wide, and the bracket is wide because the offset stops wrecking — so what the flag reports is a property of the wrecking set rather than of the survivor.

Nothing in the sweep distinguished the two cases before, because the first two bands never produced a wide bracket: on the golden 8/13 the changing offsets wreck at 123, 110 and 22 of 126 rises, so their brackets are one to a few rises wide.

Every rise of the 8/13 band, cut at every offset. One column per rise of the band, coarse on the left and fine on the right, and one row per offset that wrecks anywhere on it. A filled cell is the family the cut stem keeps; a pale cell is an offset that recovers at that rise and has no survivor to report. The band holds 126 rises and 1890 cut stems. three of the six offsets change their answer somewhere inside, three never do, and the vertical rule is the handover — the rise where the two contact steps change places. Not one of the 19 changes is at it.
Fig. 6 The first band’s changing offsets, which wreck densely enough that every bracket is narrow.

A distinction the instrument could not make

Two things can be true of a change, and until this band they had never come apart.

Located: the change is bracketed between two adjacent rises, so its position is known to one step of the grid and can be compared with the handover’s.

Flagged: the bracket contains the handover, whatever its width.

On nineteen changes both were available and the flag was never set. On the twentieth the flag is set and the location is not available, and the flag is what the sweep reported.

Offset 5 on the 5/8 band, and the change that cannot be placed. Every rise of the band, coarse on the left, with offset 5's cut drawn at each: pale where it recovers, dark where it wrecks and keeps 5, warm where it wrecks and keeps 20. It keeps the off-pair family at two rises above the handover and then does not wreck again for 34 rises, so its return is bracketed across a stretch that contains the handover. The flag that says a change sits at a handover fires here for the first time, and it is a statement about where the offset stops wrecking rather than about the handover.
Fig. 7 The distinction drawn: a change bracketed across twenty rises, against the handover it contains.

What a fixed instrument would say

That this band produces no test of the claim. Its one changing offset is silent across the handover, so the claim is neither supported nor contradicted here.

The tally therefore stands at nineteen tests, all negative, one band with nothing to say and one band with nothing to change. That is a weaker position than twenty of twenty, and it is the position the evidence supports.

Reporting it that way costs the round a confirmation it would have been entitled to claim under the old reading, which is the reason for writing it down rather than adjusting the flag quietly.

Where a rung's handover sits, over six rungs. The rise at which the two contact steps change places, as a fraction of the way down each rung from its coarse end, over every rung on both branches that has one. All six fall in the coarse half and none in the middle: the positions measure 6, 12, 15, 33, 35, 40 per cent. That is a fact about the arithmetic of the lattice rather than about any experiment run on it, because the crossing is where the two step lengths are equal and both are functions of the rise and the divergence alone.
Fig. 8 Where handovers sit inside their own rungs, which is the position a change would have to coincide with.

Why the test is hard to make at all

The two quantities live at different resolutions and neither can be moved much.

A handover is geometry. It is computed from hop lengths on an intact stem, so it can be located to any grid anybody cares to walk — on one Lucas rung it is now known to one part in ten thousand for the cost of a few hundred stems and no cuts at all.

A survivor is a cut. It exists only where a removal wrecks the stem, and where it wrecks is itself a function of the rise. So one side of the comparison is continuous and arbitrarily fine, and the other is a scatter of points whose spacing nobody controls.

What each band holds, and what it moves. One row per band. The counted pair is held by construction and the settled divergence is held to a twentieth of a degree; the quantity a band exists to move is which of the two contact steps is the shorter. five of the six do move it — the ordering changes hands exactly once inside, and at both ends the two steps differ by enough for an ordering to mean anything. The remaining one changes hands three times and its two steps are never more than 0.0 per cent apart, so it holds all three quantities and is a control rather than an experiment.
Fig. 9 The geometry a handover is read from, which is smooth and can be walked at any resolution.

Where the test can be made cleanly

On a band whose changing offsets wreck densely. The golden 8/13 is that band: its offset 8 wrecks at 123 of 126 rises, so every one of its thirteen changes is bracketed within a rise or two, and the comparison with the handover is a comparison of two well-located rises.

That is where the nineteen negatives come from, and it is worth noticing that they come from one band. The claim is scored on nineteen changes and one lattice family, which is a narrower base than the count suggests.

A fourth band with a densely wrecking changing offset would double the base. Whether the Lucas 4/7 provides one is not predictable from anything here.

A divergence that does not move across the 5/8 band. Measured at every rise of a band on the golden branch, where a counter returns 5 and 8 spirals throughout. The settled divergence moves by 0.0469 degrees across the whole band, which is a fraction of the azimuth grid step and a fortieth of the slide across the rung it sits in. The ratio of the two contact steps does move: it falls to 1.0013 and the ordering changes hands at a rise of 0.0156, so above that rise the shorter step belongs to the 5 family and below it to the 8 family. Two of the three quantities that vary along a rung are therefore held here and the third is not, which is what makes the ends of this band a matched pair.
Fig. 10 The band whose changing offsets wreck at nearly every rise, which is where the claim is tested.

The rung where both are located

There is one object on the ladder where both quantities are known to one step of the five-decimal grid, and it is not a band. On the Lucas 7/11 rung, the two contact steps cross between 0.00804 and 0.00803, and the rise at which a cut first keeps the larger family sits between 0.00640 and 0.00639.

Those are a hundred and sixty-four steps of the grid apart, which is 45 per cent of the rung’s whole span. Both are located to one step, so the separation is larger than the two locations put together by two orders of magnitude.

That is the cleanest form of the claim available anywhere on this site, and it is a rung rather than a band because a rung can be walked and a band is a fixed set of rises.

Two rises on the Lucas 7/11 rung, each located to one step of the grid. The whole of the Lucas 7/11 rung, coarse on the left, with the two rises this round located. The two contact steps change places between 0.00804 and 0.00803, found by walking all 378 rises of the rung and evaluating hop lengths, with no cut stems at all. The family a cut leaves standing changes between 0.0064 and 0.00639, found by cutting 89 stems. They are 164 steps of the grid apart, which is 45 per cent of the rung's whole span, so the geometry crossing is not what moves the survivor.
Fig. 11 The two rises located to one grid step each on one rung, and how far apart they are.

What the band design is actually good for

Counting. A band cut at every rise tells how many changes there are, which offsets have them, and whether they form islands — and none of that needs the changes to be located against anything.

Placing them against a handover is a second question the design answers only where the wrecking set cooperates. The design was not built for it: it was built to test whether the survivor is constant across a band, and the handover comparison came later.

So the right reading is that a band sweep produces a census of changes and, incidentally, a comparison with the handover on the changes whose brackets are narrow.

What nine rises find on each band, against what the whole band holds. The coarse design cuts nine rises of a band, evenly spaced in the logarithm of the rise, and asks whether the family a cut keeps changes anywhere. On the golden 8/13 it finds five of nineteen changes and on the Lucas 7/11 it finds none of none, so it had never been wrong about whether anything changes. On the golden 5/8 there are two changes and it finds neither, both of them at single rises with the offset recovering on either side. Its record on that question is now 2 of 3.
Fig. 12 What each band sweep counts, which is the question the design was built for.

The same shape, one level down

This is the second time in one round that an answer has turned out to exist only where a cut wrecks.

On the Lucas 7/11 rung, offset 8 changes the family it keeps and cannot be located — it keeps 7 at 0.0065 and 11 at 0.00637 and does not wreck at the three rises between. The rise the search does locate to one grid step is the rise at which the lattice first keeps the larger family anywhere, which is a different quantity.

Two different sweeps, two different questions, the same limit: an offset’s own answer is sampled at the rises where its cut wrecks, and that sampling is not under anybody’s control.

The Lucas 7/11 rung between 0.007 and 0.006, cut at every rise. One row per offset, one column per rise of the search, coarse on the left. A pale cell is a rise at which that offset's cut recovers; a dark cell is a cut that wrecks and keeps a lag of 7; a warm cell is one that keeps 11. The nine intermediate rises of the ten-thousandth grid were cut first and the nine of the hundred-thousandth grid inside the one bracket they opened. The change sits between 0.0064 and 0.00639, one step of the grid the ladder names its rises on, and above it no cut keeps 11 anywhere.
Fig. 13 The same limit on a rung: an offset’s answer exists only where its cut wrecks.

Why not sweep more finely

Because it would not help. The gaps are not gaps in the sampling; they are stretches where the cut recovers, and cutting at every hundred-thousandth instead of every two-thousandth would produce more rises at which offset 5 recovers.

The only thing that would fill them is a different offset, and a different offset is a different question — the answer at offset 4 across the handover is already known and it does not change.

That is what makes the limit structural rather than a matter of resources. It is the object that is silent, not the instrument.

The flat band, re-measured on a finer grid. A quantity that comes out constant is the first thing an azimuth grid should be suspected of, so the whole band is grown again on a grid of 6144 steps against the 1536 the site uses. The finer grid does resolve structure the coarse one flattened: a shallow minimum 0.0820 degrees deep, with its floor at a rise of 0.0158. What it does not do is separate the ends, which still agree to 0.0000 degrees while carrying opposite step orderings. The matched pair the band is for survives the check that would have broken it.
Fig. 14 The same band read at two grids, which changes how finely it is sampled and not where its cuts wreck.

What would change the answer

A band where an offset changes its family at two adjacent rises either side of a handover. That is a positive result and it would refute the claim outright, and nothing rules it out.

Or a fourth band with dense changing offsets and no change at its handover, which would move the claim from one lattice family to two.

Both are the same half-hour of machine time on the Lucas 4/7 band, and neither is predictable. That is the state a claim should be left in: with a stated test that could go either way and a cost attached to it.

The families left standing, on both sides of every handover. One row per band, with every offset cut at rises spread across it and always at both ends and at the handover itself. The last column is every family left standing anywhere on that band. On three of the four bands that wreck at all it is a single family, unchanged across a rise at which the two contact steps swap places — so the step ordering is not what decides which family survives, and the result now rests on four counted pairs rather than on two. The shortest-hop reading scores 44 of 114 across the whole set, which is what a reading looks like when the quantity it is stated over is not in the mechanism.
Fig. 15 The one band left that could produce either outcome, and the three that have been cut.

What a wrecked cut is, and why it can vanish

A removal wrecks a stem when the pattern above the hole never returns to the arrangement it had. Whether it does is not a property of the offset alone: the same offset at two rises a few thousandths apart can wreck at one and recover at the other, with the counted pair, the divergence and the front all unchanged.

That is the fact this essay is downstream of. Every band cut whole has shown it, and on the third band it is at its most thorough — not one of the three offsets wrecks at every rise, where the first band has one that does and the second has three.

So the set of rises at which a given offset has an answer is itself a scatter, and the scatter is what sets the resolution of every question about that offset’s answer. Nothing about the design chooses it.

The next organ moves for the last 8, and for no othersOne 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.organ removed, counted back from the tiphow far the next organ moves, in degrees1136.9°286.0°348.3°4164.1°526.2°692.3°7131.0°84.9°— the front ends here90.0°100.7°110.7°120.0°130.7°140.0°150.2°160.2°rise 0.013 · pair 5/8generated from a stated rule, not drawn to look right
Fig. 16 What each offset’s removal does at one rise, of which only some wreck and only those have a survivor.

The arithmetic of the bracket

Twenty rises of the band, which at a step of two parts in a thousand is a ratio of 1.041 in the rise — from 0.01605 down to 0.01497. The handover sits at 0.01558, which is 47 per cent of the way along that stretch in the logarithm.

Put differently: the bracket covers 18 per cent of the whole band, and the band covers 23 per cent of its rung. So the change is located to about four per cent of a rung, against a handover located to better than a tenth of a per cent of one.

A comparison between a quantity known to four per cent and one known to a tenth of a per cent is a comparison whose answer is decided by the first, and the first is not under control.

Two ways of predicting how wide a band is. A band ends where the settled divergence has moved 0.05° from its value at the handover, so the width should follow from how fast the divergence changes there. Reading that rate as the rung's average slope predicts widths that are wrong by factors of 0.20 to 5.92 — wrong in both directions, so no constant rescues it. Reading it as a curvature about a stationary point gives 0.41 to 1.08, with five of the six inside a third. The difference between the two is the difference between a curve and its average, and a band is exactly where the two are least alike.
Fig. 17 How much of its rung each band covers, which is the scale a change’s bracket has to be read against.

Why the flag was written that way

Because on the band it was written for, it was right. Every change on the golden 8/13 band is bracketed within a rise or two, so the bracket contains the handover and the change is at the handover were the same statement there, and the simpler one was coded.

That is the ordinary way a reading acquires a hidden assumption: it is written against the case in hand, it is correct there, and the assumption is invisible until a second case violates it. The same thing happened to the count of exceptional chains, where three or more exceptions and no balanced pair were treated as one description and turned out to differ on two rows.

The repair in both places is the same: separate the two readings, report both, and say which one a claim is being made on.

The 13 cuts the exchange sets aside, chain by chain. One row per wrecked cut with no balanced pair, one cell per chain of the lag it kept, and the chains displaced away from the common level filled. The lag is printed at the left and the sum of the displacements at the right, folded into half a turn either way. seven of the 13 sum to within 12 degrees of nothing and six do not, and every row that closes kept a lag of 7 or 8 while every row that does not kept 4 or 5. The rows are stacked by that lag.
Fig. 18 Another reading that carried a hidden assumption until a second case separated its two halves.

What the sweep does report correctly

Everything about the change itself. That it happens, that it is at offset 5, that the family it goes to and comes back from is 20, that it happens twice and that both rises sit above the handover.

The two rises at which offset 5 keeps 20 — 0.01625 and 0.01605 — are read directly and are not brackets. It is the return to 5 that is bracketed, because the offset is silent from 0.01605 to 0.01497.

So the picture is: two isolated rises with an unusual answer, a long silence, and then the ordinary answer again. What cannot be said is where inside the silence the ordinary answer resumed.

That is also why the nine-rise sample found nothing on this band: a sample that visits ten rises at a step of fourteen is very unlikely to land on either of two isolated rises, and it landed on neither.

The 17 rows of the exchange table, gathered by the lag they kept. One bar per surviving lag, its length the number of rows the table holds at that lag, with the hop that lag's stems keep written beside it. The hop is nearly constant inside a lag, so a correction fitted over 17 rows is fitted over four hops — which is the denominator that matters and is much smaller than the row count suggests. Adding a lag to the table is worth more than adding rows at a lag already in it.
Fig. 19 The families a cut has been seen to keep, including the one this band’s offset 5 keeps at two rises.

The general shape of the limit

A quantity that exists only where something else happens can be sampled no more finely than that something else. Here the quantity is the family a cut keeps and the something else is the cut wrecking, and the wrecking set is not under anybody’s control.

That is not a resolution problem and cutting more rises does not fix it. Cutting every hundred-thousandth of the band instead of every two-thousandth would produce more rises at which offset 5 recovers, and its silence across the handover would be just as complete.

The same limit turns up one level down in the same round, on a rung rather than a band, where an offset changes the family it keeps and cannot be located because it is silent at three consecutive rises inside its own bracket. Two sweeps, two questions, one structural constraint — and naming it in both places is worth more than either instance.

What could be tested instead

The claim is about a handover, and a handover is geometry: it can be located to any grid anybody cares to walk, for the cost of one grown stem per rise and no cuts.

So the useful move is to pick the object where the other side is also well located. On the Lucas 7/11 rung both the crossing and the rise at which a cut first keeps the larger family are known to one step of the five-decimal grid, and they are 164 steps apart. That is a test of the same claim with neither side bracketed, and it is the strongest form of it anywhere on this site.

A band gives the better-controlled comparison — the divergence is held still — and a rung gives the better-located one. Neither subsumes the other, which is the argument for keeping both.

What is recorded

That a change of surviving family was flagged at a handover for the first time across three bands cut whole; that the change is bracketed across twenty rises and a hundred and eight steps of the grid; and that the handover is inside the bracket because the offset does not wreck anywhere near it.

That the claim is therefore untested on this band rather than confirmed or contradicted, and that the tally is nineteen located changes, all negative, from one band.

And that the flag as written cannot tell a change at a handover from a change bracketed across one, which is a defect in the reading rather than in the sweep, found by a band that produced the case.

Offset 5 on the 5/8 band, and the change that cannot be placed. Every rise of the band, coarse on the left, with offset 5's cut drawn at each: pale where it recovers, dark where it wrecks and keeps 5, warm where it wrecks and keeps 20. It keeps the off-pair family at two rises above the handover and then does not wreck again for 34 rises, so its return is bracketed across a stretch that contains the handover. The flag that says a change sits at a handover fires here for the first time, and it is a statement about where the offset stops wrecking rather than about the handover.
Fig. 20 The case that separated the two readings, which is one change on one offset of one band.

Where this goes next

All three bands cut at every rise, offset by offset. One row per wrecking offset on each band cut whole, one cell per rise, coarse on the left. A pale cell is a rise at which that offset's cut recovers and has no survivor; a dark cell is a cut that wrecks and keeps one of the band's own counted pair; a warm cell is a cut that keeps a family off the pair. The vertical rule on each row is that band's handover, where its two contact steps change places. The golden 8/13 band changes the family it keeps 19 times, the golden 5/8 twice and the Lucas 7/11 not at all. The third band, cut whole Two bands cut at every rise disagreed about whether the family a cut keeps ever changes, and three explanations were available for a difference between two things. The cheapest third band settles which of them survives, and it settles it against the account nobody was betting on. Offset 7 across the 8/13 band, rise by rise. The family this one offset keeps at each of the band's 126 rises, coarse on the left. It wrecks at 126 of them and keeps the 4-family and the 8-family at different rises. The ticks below mark one islands — runs of 2 rises where the coarse family comes back inside the fine one. The handover is the taller rule and the change of answer is nowhere near it. Three offsets, three crossings The claim the band design rests on is that the survivor does not change where the two contact steps change places. It holds at full resolution: nineteen changes and not one at the handover. Where they are is three different rises, eight, nineteen and twenty-nine below it. What nine rises find on each band, against what the whole band holds. The coarse design cuts nine rises of a band, evenly spaced in the logarithm of the rise, and asks whether the family a cut keeps changes anywhere. On the golden 8/13 it finds five of nineteen changes and on the Lucas 7/11 it finds none of none, so it had never been wrong about whether anything changes. On the golden 5/8 there are two changes and it finds neither, both of them at single rises with the offset recovering on either side. Its record on that question is now 2 of 3. Nine rises were not enough A coarse sample of a band had never been wrong about whether anything changes inside it, and that record was the argument for trusting a negative from it. The third band cut whole makes it two of three, and the missed feature is one rise wide.

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.

  • A period the grid invented — both name ablation, artefact, claim testing, discretisation, honest limits, measurement, negative result, refusal, resolution
  • A band with nothing inside it — both name ablation, claim testing, contact family, handover, honest limits, negative result, resolution
  • A list that was a rounding — both name artefact, claim testing, discretisation, honest limits, measurement, negative result, resolution
  • A median that is an exception — both name artefact, claim testing, honest limits, instrument setting, measurement, negative result, refusal
  • A removal that changes nothing — both name ablation, artefact, claim testing, discretisation, measurement, negative result, resolution
  • A window nobody aligned — both name ablation, artefact, claim testing, honest limits, measurement, negative result, resolution

Named objects

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

AblationArtefactClaim testingContact familyDiscretisationHandoverHonest limitsInstrument settingMeasurementNegative resultRefusalResolution