Depth

Ladders — page 5

A field says what an essay is about. A ladder says what else there is to say about it — the distinct arguments that stand against one idea, from the one that introduces it to the one that assumes all the others.

A stem unrolled: 28 nodes at 137.51° with a rise of 0.090 circumferences. The counter is shown these coordinates and the circumference, and finds 2 parastichies one way and 3 the other. The faint strips left and right are the same stem: a family leaving one edge re-enters at the other.

Stem lattice

1 A stem is a cylinder

1 rung · cylinder

The plane of stems: divergence across, rise up. Each shade is one parastichy pair. The marked points are the lattices where three families are equally short — the forks — and the Fibonacci ones run up the middle towards 137.51°.

The tree not the angle

5 The angle is not the object

1 rung · wrong

The lag between two rates, measured against the rate. Each dot is one rate: the mean gap between where the grown pattern changed its count and where the static ladder puts that transition, in rungs. Over rates from 9 to 135 nodes per rung the worst is 0.087 of a rung. A lag of one rung would put a dot on the top line.

Tracking

4 The lag that is not there

1 rung · emergence

The spiral counts, band by band, in one head. The same flower gives 13/21, 21/34, 34/55, 55/89 at different radii. A caption saying "34 and 55 spirals" is a statement about one annulus.

Transitions

2 The counts change with radius

1 rung · lattices

Three organs, and the exponent each has at each place. Left: the meridian of a cone, an ogive of arc radius 12, and a spherical cap of radius 40, each scaled to its own length. Right: d log r / d log s along it. The cone sits at 1 the whole way; the ogive starts near 2 at its blunt tip and falls to 0.23 by the end of the 100 per cent shown; the cap starts at 1 and falls slowly.

Varying exponent

5 An organ has no single exponent

1 rung · cylinder

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