Reading window — where it appears
Named by 13 essays across 2 fields — each of them below, with the objects they name alongside it.
The window nobody varied
Every parastichy pair reported for the settling table was counted over the top two hundred organs of a run, and that number had never been moved. Moved seventeen ways across a factor of forty, on all three hundred and eighty-four settled runs, it changes nothing at all.
A plateau the instrument should have had
The counting window decides nothing on the settling table, and it has two bounds that decide everything outside it. A window one organ too narrow returns the previous rung of the same ladder, a family past the offset ceiling is reported as a coarser rung at every width there is, and neither failure produces a refusal, noise or a wide error bar.
How many organs a pair needs
A count taken over too few organs does not fail. It returns the rung below, which is a perfectly good pair, and nothing anywhere says so. The window that avoids it is not a constant but the counter's own arithmetic, and 384 settled runs sit exactly where that arithmetic puts them.
A sequence that was a reading
One of the settling table's additive sequences rested on a single count that skipped a term, and the account of it was that the count had been taken over the wrong patch. It was not. The counter works out whether its two families wind opposite ways and the reading throws the answer away, on five runs in three hundred and eighty-four.
A counter that cannot be slid
The counter that needs no order of arrival follows each family into chains and counts them, and on an ideal lattice it agrees with the counter that does. On a stem whose rise falls it works only inside a band of widths, and outside the band it returns a pair rather than refusing: the rung below when the band is too narrow for the larger count, a pair on no rung when the band spans more than about a third of a rung of rise. The upper edge moves with the rate, so a width that is right on one stem is wrong on another, and on the fastest bijugate stem measured no width works at all.
A band that follows the rise
The index-free counter reads a growing stem only inside a band of widths, and the upper edge is a third of a rung of rise rather than a number of organs — so a width right on one stem is wrong on another. A counter that fits the decay of the rise through the spacings of its own band's whorls, and takes the band spanning a third of a rung, chooses 49, 97 and 193 organs on stems falling over 150, 300 and 600. Given no width at all it reads within eight points of the best of eighteen fixed widths on six of the seven stems, matching it exactly on one and beating it on two. Refusing any band too narrow to have shown the rung above the pair it counted removes every reading of the rung below, on every stem — and costs between five and fifty-one points of correct reading to do it.
The window was not carrying it
The ratio of a Lucas seed's rate edge to its length rose from 2.05 at fifteen whorls to 2.20 at eighty, and the suspect was the counting window, which is most of a short seed. Read through windows of 20, 26, 39 and 52 folded nodes, seventeen of the eighteen stems lose the seed at exactly the same organ of rate, so the window carries almost none of it. Part of the rise was the grain of rate the edge was found on, worth up to six hundredths of the ratio. What is left rises by a tenth below thirty whorls and has stopped by sixty, at a level an ordinary stem reaches about one and a half per cent lower than a bijugate or trijugate one — and a trijugate edge is not always a line.
A band that follows a curving rise
The index-free counter that sizes its own band was built on stems whose rise falls by a constant factor per organ, so the decay it fits through its band's spacings was one number and the fit a straight line. On stems whose rise falls as a cone's does, fast near the base and slowing sixfold, or as an ogive's, slow and then speeding up, the straight line still recovers the local decay to within half a per cent at every band, and every band it chooses spans a third of a rung of rise, 0.324 to 0.333, with no excess at either end. Its width runs from 84 organs to 272 up a cone and from 139 to 58 up an ogive. A fixed width reads one end of such a stem and fails at the other: 49 organs returns the rung below on almost all of a cone's tip, 193 a pair on no rung on almost all of its base. Where the self-sized band fails, at an ogive's fastest end, it refuses, and it never returns the rung below.
A counter built on a falling rise
A shoot starting to flower has a rise that falls and then climbs again. Read through that turn, the index-free counter that sizes its own band is right on nine bands in ten going down and one in eight coming back, and on a quarter of those it returns a pair on no transition at all. The fit it depends on is fine. It reads a negative decay perfectly and treats it as no decay, so it holds its widest band over more than a whole step of rise between transitions. Sized from the magnitude of the decay it reads the climb as well as the fall, at 94 per cent on every stem. And the stem itself goes back down the transitions it went up, at the same rises, to the width of a band.
A wider window buys back a shaken stem
On exact stems the counting window decides nothing once it clears a small floor, which leaves it looking like a setting nobody needs. Move every organ and it becomes the instrument. A pair that a twenty-organ window reads on an ideal lattice needs one or two hundred organs with each organ moved by half a spacing, four to eight hundred at four fifths, and up to twelve hundred at a whole spacing, where the organs have left their places altogether and the pair is still there to be counted. The price is steep, close to the two-and-a-half power of the error, and at one and a half spacings no window up to sixteen hundred organs holds the pair. When it goes, it goes upward: the wrong answer is the next pair, not the one below.
A spread that grows with its window
A spread over a sample of a steady quantity does not depend on how big the sample is. These spreads triple when the window triples, on nearly every row of the census, which means the classes this thread calls steady are sliding — slowly, and invisibly at any single window.
The window nobody moved
Three instrument settings sit between the ablation census and every statement it makes. Two have been varied and both decided answers. The third is a hundred and twenty organs at the top of a run, it has never been moved, and moving it changes the verdict on three rows.
Three rows a window moves
Three of the census's thirty cuts are periodic when a hundred and twenty organs are read and not when a hundred and eighty are. Their spreads do not grow in proportion to the window, they grow by twenty and forty times, and the reason is that a window is the tail of a run.
Named alongside it
The objects these essays reach for when they reach for this one.
Honest limitsInstrument settingClaim testingParastichy pairRiseSilent failureMeasurement errorRefusalCounting blindChain countingRungThreshold