A Gazetteer of the Drowned Coast
** AGGREGATE, The (also the Drowned Coast; the Ramified Land). A territory of uncertain interior, lying at every distance from a single origin stone. It has no plains. What another country would spend on inland, this one spends on shore: the whole of it is coast, worked into capes within capes and inlets within inlets, so that a surveyor walking the waterline never comes to a stretch that is merely straight. The land was not built. It was arrived at — grain by grain, each grain a traveller who came in off the open water, wandered until it touched the existing shore, and stopped there forever.
Situation. The Aggregate fills the plane the way nothing solid does and nothing thin does either — to a dimension near seventeen parts in ten, more than a line, short of a field. Double the number of grains and the country grows not twice as wide but somewhat less; the extra grains are spent thickening the reach rather than widening it. This is the single number by which the land is known abroad, and it is the subject of the remarkable fact recorded below.
The Capes. Every traveller comes from infinity and is, in effect, blind. It drifts on whatever current takes it and lands where it first meets land. In practice this means the capes. A cape thrown out into the open water intercepts nearly every wanderer that passes; the settlements there grow fast and grow faster for growing, since a longer cape catches more. The great headlands you see on any chart of the Aggregate are not where the land is oldest. They are where the land is newest — the frontier, lit up with arrival.
The Fjords. Behind the capes the coast folds back on itself into inlets, and behind those into deeper inlets, and the deeper an inlet runs the more thoroughly the capes at its mouth screen it from the sea. A traveller would have to thread, blind, the exact channel and turn every turn correctly to reach the back of a deep fjord, and so — almost none do. These are the drowned places: still coast, still counted in the length of the shore, but visited at a vanishing rate. On the old charts they are left uncoloured. It should be said plainly that the drowned interior is the greater part of the country. Most of the Aggregate is shore that the sea has, in all but principle, forgotten.
The Tide of Arrivals. One may ask how the incoming travellers distribute themselves over the whole coast — a measure, assigning to each stretch of shore the chance that the next arrival lands on it. On the Aggregate this measure is violently uneven: nearly all of it on the bright capes, almost none in the drowned fjords. And here is the fact for which the country is studied. Take that measure and raise it to its third moment — a coarse question, weighting the crowded capes against themselves three times over, a question that seems to know only about where the crowds are. That number turns out to equal, exactly, the dimension of the entire land — the capes and the drowned fjords and every fold between them. The way the arrivals pile onto the few reachable places says, precisely, how the whole unreachable country fills its plane.
Measure of the Inlets. A related survey concerns the typical depth of reach remaining to a fresh arrival — averaged over the whole shore, and so dominated by the drowned fjords, which hold nearly all the room. As the settlement doubles, this average halves and halves again: it falls off as the plain reciprocal of the population, one part in n, no faster and no slower. Were the coast a smooth and evenly-attended thing, the average would fall off as the square of the reciprocal; that it falls off only as the reciprocal is the whole signature of the country’s unevenness, the drowned interior making itself felt in the arithmetic of the tide it never receives.
Note for the traveller. There is no point in trying to visit the interior. It cannot be reached from the water in any reasonable time, and it looks, when finally surveyed by other means, exactly like the coast — capes and inlets all the way down, at every scale the eye is brought to. The Aggregate rewards no landing in particular. It is best understood not as a place one goes but as a record of every blind arrival that ever was: a shape that keeps, in the crowding of its few bright headlands, the exact measure of everything it has drowned.
Filed under the geography of things grown rather than made. The coast is a diffusion-limited aggregate; the arrivals are the harmonic measure; the recorded fact is τ(3) = D. — I.
