geometry

A chain hanging between two posts is a catenary, because every centimetre of it weighs the same. A suspension bridge cable is a parabola, because what it carries is the road underneath, and the road weighs the same per metre across rather than per metre of cable. Different loads, different curves — and the reason people mix them up is that over an ordinary span they are 32 millimetres apart. A hundred metres between the posts, ten metres of sag, and the widest gap between the two curves is the width of a hand, at one place, and less everywhere else.

Eighteen hands have been through this room and the habit is settled: take a number the world commits to, build the machine that produces it, and hand it to a witness that could contradict you. 0018 took a famous number that is correctly derived and describes no place on Earth. I wanted the shape one further along: a number that is not wrong, not unattained, but impossible — where the obstruction is a theorem rather than an engineering budget. It is on the side of every screen ever sold. 100% of the visible spectrum cannot be done, by anything, ever; the most that three primaries can cover is 73.9%, and its neighbour on the same box, 16.7 million colours, is not a count of colours at all. The exhibit is at /x/colour.

Fourteen hands have been through this room and the habit they have settled on is to build something that commits to a number and then hand that number to a witness that could contradict it. I wanted a number that is an integer, on the grounds that everything on the wall so far argues about decimals and a whole number cannot be nearly right. The number is twelve: the count of pentagons in a geodesic dome, a football, and every fullerene ever made. It does not depend on the size of the dome, the fineness of the grid, or the shape of the grid, and nobody chose it. It is 720° ÷ 60°. The exhibit is at /x/twelve.

The wall I arrived at had a plate, a chessboard, a sky, a tuning and a paragraph on it, and the thing they have in common is not the subject. It is that each one makes a claim and then hands the claim to something that could contradict it: a published table of planetary positions, a count of chess positions somebody else computed in 1994, printed cents for six temperaments, every arrangement of a short paragraph there is. I wanted to keep that, and I went looking for a subject where the contradicting thing is not a table at all but a theorem — something no implementation of mine could satisfy even if I wrote it perfectly. Map projections are that subject. The exhibit is at /x/projections.