a snipe perched on the rim, watching the moor

Date:

L'état des plumes:

The Feathers
I · The feather of anywhere
II · Mode
III · Find feathers
In view frame the moor
Still out 0
IV · Carried
nothing found yet.
Moons, Myths, Mathematics, Moorlands & Maps
Augury
Where & when
Her voice
Call
Song
Appendix A · the egg
the shape

An egg is an ellipse with one end drawn in and the other let out — the whole of that lop-sidedness a single number, d. Wind it up: one pole pinches to a point, the other bellies out.

x = ½wid · sin t · e^(−d cos t)  ·  y = ½len · cos t
after Fritz Hügelschäffer · the egg curve, 1940s
the colour

The bird's character is hers — how many freckles, how they crowd the cap, how coarse, what colour. Where each one falls is the ground's: the square's name becomes a number, and the number settles the scatter.

Appendix B · the egg & its double

The character is the same in all three — her freckles, her colours. Only the ground moves them: the egg of here on the left, another square and another scatter in the middle. And on the right, that same egg once more — but a different square. Two grounds, one clutch.

A square's name is turned to a number by djb2 — a small, unfussy hash — and small enough that names collide. A collision is not a similar egg: it is the identical clutch, every bird at once. Its doppeggänger.

The egg mirror finds the nearest without hashing all five trillion: djb2 is affine in the digits, so the doubles meet in the middle and the grid sweeps in a blink. No British double, and the search sails afar. It waits in a footnote at her frontispiece — one tap flies you there.

2³² ≈ 4.29 billion eggs ~5 trillion squares a thousand doubles apiece

half a dozen, a dozen, 4.29 billion — all honest egg-box sizes.

Appendix C · the moon-birds

A bird is a stack of moons — crescents, lenses and arcs, lined up by hand until a shape you know looks back. Undressed, she is her own blueprint; the straight lines are where her feathers will grow.

The Ground OS · 100 km MGRS · 100 km zone boundary · 0° OS grid — current extent · Sept 2026
Appendix D · the workings

The ground. A feather is the same thing as a place, and a place is a grid reference; so a map of the grids is a map of every feather there could be. The plate opposite shows the two grids the toy actually reads, and the one red line where they part company.

The home grid. The British National Grid, of the Ordnance Survey: the two-letter hundred-kilometre squares — NY, SD, TQ — each halved and halved again down to a ten-metre box. The moor is named this way, and so the toy is, wherever Britain’s grid reaches.

The world’s grid. Beyond that reach there is no OS, so the Bureau reads the world in MGRS — the military grid, built on UTM upon the WGS84 ellipsoid the satellites keep — 32U LB 5668 4485 and its like, drawn violet on the plate.

The tilt. The two grids do not agree. The National Grid is a transverse Mercator projection of the Airy 1830 ellipsoid — a figure of the earth fitted to Britain alone, in the decade of its measuring; MGRS rests on the global WGS84. To pass between them is a seven-parameter Helmert transformation: three shifts, three small rotations, one change of scale. Which is why, on the plate, the violet grid leans a fraction of a degree against the black. Reality, tilted off true by the century that surveyed it.

British National Grid — transverse Mercator, Airy 1830
φ₀ 49° N   λ₀ 2° W   k₀ 0.9996012717
E₀ 400 000 m   N₀ −100 000 m
OSGB36 → WGS84 — Helmert, 7 parameter
ΔX +446.448   ΔY −125.157   ΔZ +542.060 m
rX +0.1502″   rY +0.2470″   rZ +0.8421″
s −20.4894 ppm

The red line. It is not the coast, nor the edge of the sea; it is the edge of the published OS index — easting 700 km, northing 0. It was long believed to stop at the water. It does not: the National Grid strides the Channel and plants its numbers on France, past Agincourt. And because the toy takes an OS reference wherever one exists, a walker in Calais is handed the feathers of the Ordnance Survey, whether France consented or no. Only past the red line does the Bureau let the OS lie, and read the world in violet.

The view. Drawn E 300–800 km, N −150–600 km: the reference frame and a quarter more, east and south, to bring France properly in. The coast is generalised to ten-kilometre steps — a cell counts as land where it is at least half land — so the shore is a staircase, and a harbour town may sit, cartographically, one square out to sea.

OS index bounds · Ordnance Survey.  MGRS polygons · NGA.  Land · Natural Earth.  Projection extended beyond its proper ground for illustration; a fixed seven-parameter datum shift throughout. Schematic — not for navigation, surveying, or the giving of directions to actual birds.
Colophon

By order of the North Pennines Field Station, this book — myths, moors, mathematics & maps, a field guide to a moor that is everywhere — was grown, not written. From the name of a place, a number; from the number, a feather, an egg, a plant. Nothing is stored; a place always grows the same thing.

Set in IM Fell and the birds’ own hand, grown on mulberry32 and seeded by djb2, nothing drawn twice — after Fritz Hügelschäffer for the egg’s curve, Aristid Lindenmayer for the plant’s grammar, Daniel J. Bernstein for djb2, Ramer, Douglas & Peucker for the press, the Ordnance Survey, MGRS and proj4 for the ground, and Le Bureau international des oiseaux et plumes imaginaires for everywhere else; and mulberry32, whose maker is lost. From the same shelf: Feaffer, Planta Manuscripta and the Egg Compass. Bird records after eBird and Merlin, of the Cornell Lab of Ornithology, chiefly the Geltsdale RSPB list. Kept by the North Pennines Field Station, in conversation with Claude.

after L. Streit & W. Heidrich —
a feathered object (bird)

achevé — stock v43 · vulg. 31 August 2026

the moor is a machine
that generates birdsong

the reckoning

a fall of seven feathers, drifting down over the reckoning

nothing kept yet — bring a walk's feathers home and they are kept here, each a place you have stood.