Phyllotaxis
the spirals are counted, not admired
Concept

Azimuth grid — where it appears

The finite set of directions an organ may be placed at, here 1,536 samples of the circle at a quarter of a degree apart. Every angle this collection reports is a multiple of that step, so a quantity smaller than one step is the grid rather than a measurement, and a block that is the grid rounding a constant is a period nothing has.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Three chains, each moved a third of a turn, on g008 cut at offset 6. The eight chains of a stem that kept a lag of 8, set round the circle, with the three that are displaced marked and their displacements written on. Each is about a third of a turn the same way round, and they sum to -359.6 degrees — one whole turn to within half a degree, on an azimuth grid whose step is a quarter of a degree. A rearrangement that closes by going once round sums to a turn, not to nothing, which is why the test it was set had the wrong number in it.

A cycle sums to a whole turn

The test proposed for whether three displaced chains are a three-cycle was that their displacements sum to zero. Three chains rotating into one another's places each move about a third of a turn the same way round, and a third of a turn three times is a whole turn — which the unfolded test calls the worst row in the census.

mechanism · damage shape What is the same at 0.00998 and at 0.00997. Six quantities read on the two rises the transition sits between. Five of them are identical: the two walls the slot has, the divergence the intact stem settles to, the block the cut opens, which of the three removals wreck the stem, and the lags the doubled cut leaves rigid. The sixth is how far the first organ placed after the doubled cut moves, and it goes from 163.59 to -9.14 degrees. The lattice is the same on both sides; where one organ goes is not.

A transition and not a slope

The question was whether a fourth cell's cost declines smoothly to nothing or falls in one step. It falls in one step, and the answer decides whether a word in the collection names something or is a threshold on a continuum.

cylinder · both walls

Named alongside it

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

ArtefactClaim testingHonest limitsBoth wallsCycleDamage profileDisplacementExceptional chainExchangeFalsifiabilityFoldingInteraction

All concepts