page forty-one

The Mere

Forty rooms have weighed and counted things you could see. Today's number fills a lake with fish you cannot, and gives you six days with a boat to find out how many there are. Catch, mark, let go, catch again. The arithmetic is a single line. The hard part is the netting.

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The mere. Tap the water to set a net, tap a net to take it up. Rings on the surface are fish rising.

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The keeper's book

Your report to the club
Mere
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The arrow keys walk to other days. Every day is a different water, a different fish and a different number of them.

What is real here and what is not

The method, its history and the way it goes wrong are real. The mere, the club and the fish are the day's number.

  1. 01

    Laplace and Petersen

    Pierre-Simon Laplace estimated the population of France in 1802 from the ratio of registered births to people in a sample of parishes he had counted outright: the same proportion this page uses. The fisheries biologist C. G. J. Petersen tagged plaice in the Limfjord in the 1890s and read their numbers off the share of tagged fish in later catches.

  2. 02

    Lincoln and Schnabel

    Frederick Lincoln did the same for North American ducks from returned leg bands in 1930. In 1938 the mathematician Zoe Emma Schnabel published the version for a lake netted over many days, adding up catch times marked-at-large over every day: the running estimate in the keeper's book. D. G. Chapman's adjustment of 1951 adds one to the recaptures so the sum can be worked out before any have come in.

  3. 03

    Why it comes out low

    The arithmetic assumes every fish is as likely to be caught as every other on every day, and that the marked ones mix back in evenly. Neither is quite true. Fish keep to home ground, so nets that go back to one bay keep catching the same fish; and some fish are bolder about nets than others. Both push the recaptures up and the estimate down. Field biologists spend most of their effort on sampling design for exactly this reason.

  4. 04

    How the day is drawn

    The fish are set out in four to six shoals of unequal size, with about one in eight a loner, and each is given its own range and its own temper about nets. Where each one is on each of the six mornings is fixed by the day's number, so the same nets in the same places always bring up the same fish. When the mere is drained, the page re-runs your week 240 times with two other keepers' habits for comparison.

Forty-one rooms, and one number doing all the work. Today it stocks a lake, hides the fish in it and lets you find out how much a few nicked tail fins can tell you about what you never saw.