Concept

Matched design — where it appears

A set of comparisons built so that everything but the quantity under test is held fixed by construction rather than by argument. Two stems on different lattices at one rise is one; seven such pairs, across which the ordering reverses, is what makes it a design rather than an anecdote.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

456781011121.621.701.801.8922.102.22rise (falling to the right)how deep the front is, in organs3/53/44/75/87/118/13goldenLucas7 rises · both branches settled to under 0.5°4 reversals

Seven rises and two seeds

One organ removed from a stem is felt out to the larger of its two spiral counts. Every test of that has confounded the count with the rise, because on one branch the two move together. Grow a second branch beside the first at the same rise and they come apart — and doing it at seven rises turns a matched pair into a design whose last column changes hands four times.

cylinder · branch choice
010201.502how far below its rung's own boundary the stem sitsdisplacement at that offset (°)golden 3/5Lucas 4/7golden 5/8Lucas 7/11golden 8/13felt above 2.5°rung boundaries solved, not fittedgenerated from a stated rule, not drawn to look right

The front that reads one short

Eleven cells of a fourteen-cell design put the boundary exactly at the larger spiral count. Three put it one offset earlier, and the tempting move is to lower the threshold until all fourteen agree. Measured instead of tuned, the three turn out to be the three cells nearest below their own rung's boundary — and the last offset of a front is weak because it has only just arrived.

cylinder · branch choice
Lucas, rise 0.0243/4 · front 4103°golden, rise 0.023/5 · front 5134°Lucas, rise 0.014/7 · front 797°golden, rise 0.0085/8 · front 8139°03691215offset, in organs back from the tipincoming countband: the front · open circle: the incoming countgenerated from a stated rule, not drawn to look right

The hole on the other branch

Near a transition, the run of offsets a stem notices stops being a run: there is quiet past the front and then one isolated offset, felt as hard as anything inside it. Where that offset sits was pinned down on Fibonacci lattices, where the numbers to check it against are 5, 8 and 13. On the Lucas branch they are 4, 7 and 11 — and the rule holds there too.

cylinder · branch choice

Named alongside it

The objects these essays reach for when they reach for this one.

AblationBranchHonest limitsLadderMeasurementParastichy pairRungDiscriminationFalsifiabilityFibonacciIdentifiabilityLucas numbers

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