Concept

Slip — where it appears

How far a disturbed lattice's mean divergence has moved from the one it was disturbed out of. It is not an arbitrary angle: over the period of the family that survived, the accumulated slip is a whole number of turns, and almost always exactly one.

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

30°60°90°12345678910111213141516lag, in organshow much that hop moves (°)lag 8: 0.09°golden, rise 0.005 · organ 4 back · block 8the surviving lag is 8

The hop that survived

A stem that never repairs after an organ is removed settles into an exactly repeating block of angles, and the period of that block is a spiral count of the lattice it was cut from. Nobody could say why. Read the wrecked stem by lags rather than by neighbours and the answer is one line: one family of the original lattice is still standing, organ by organ, and the block is its period.

emergence · ablation
0360720051015the wrecked offsets, six latticessurviving lag × slip (°)largest departure from a whole turn: 2.97°19 wrecked offsets · slips 0.0° to 102.8°generated from a stated rule, not drawn to look right

One turn per survivor

If a wrecked stem keeps one family of its old lattice exactly, then the angle it settles at is not free. Over the period of the family that survived, the pattern has to come back to where that family left it — which means the whole change in the divergence is a whole number of turns spread over a small whole number of organs. Measured, it is one turn, at seventeen of nineteen.

emergence · ablation
cut from136.99°lag 5 kept · 0 turnscounted 5/11175.01°no lag keptcounted 2/6189.96°no lag keptcounted 4/6208.80°lag 5 kept · 1 turncounted 5/12235.00°no lag keptcounted 3/6280.43°lag 5 kept · 2 turnscounted 5/9140°180°220°260°settled divergence after the cutrise 0.013 · 6 destinations over cuts of one to five organs3 are slips of the lattice cut from

A wreck has a short list

Cuts of one organ through five, over two hundred and forty-six stems that never came back, land on six settled divergences between them. Removing five organs instead of one wrecks nearly everything and reaches nowhere the single cut had not already found — and half the list turns out to be the old lattice slipped by a turn, while the other half is not the old lattice at all.

emergence · dose

Named alongside it

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

AblationCounting blindEquilibriumFalsifiabilityHonest limitsLatticeMeasurementParastichy pairThe placement ruleRigid hopLattice offsetRise

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