The square root of our plumb-bobbing obsession

The square root of our plumb-bobbing obsession

Eastern Colorado Great Plains • Photo by Ken Lund (CC BY-SA 2.0)

Originally published 18 March 1991

Here is a lit­tle les­son about the best and worst of west­ern civ­i­liza­tion. It can be sum­ma­rized in one word: Square.

Yep, that’s right. Square. The 90-degree cor­ner, the plumb-bobbed line. For­get the squig­gle, wig­gle, curlicue, and arc. We’re talk­ing orthog­o­nal­i­ty here. We’re talk­ing perpendicularity.

I was fly­ing across the North­ern Great Plains the oth­er day at 37,000 feet. Not a cloud in the sky. The snow was melt­ed in the fields but still banked along the roads. From the Appalachi­ans to the Rock­ies, for a thou­sand miles, as far as the eye could see, the land was ruled by thin white lines (those snowy roads) into one-mile squares. The whole of the cen­tral Unit­ed States was plot­ted out in a square grid as neat as the tiles on your kitchen floor.

But wait. I’ll come back to the checker­board land. Let’s start in the sky. Let’s start with the constellations.

Patterns in the sky

For as long as humans have looked at the sky they have grouped the stars into pat­terns called con­stel­la­tions. Pat­terns that evoke famil­iar objects in the envi­ron­ment. Bears. Birds. Fish. Or inven­tions of the human imag­i­na­tion. Cen­taurs. Drag­ons. A fly­ing horse.

Every cul­ture makes pic­tures of the stars. Aus­tralian abo­rig­ines see kan­ga­roos in the sky. Poly­ne­sians imag­ine fish. Eski­mos fill the night sky with seals and polar bears.

Mak­ing pic­tures of the stars is a uni­ver­sal human trait, as nat­ur­al as day and night. But only in west­ern Euro­pean cul­ture have we found it nec­es­sary to put the pic­tures into square-cor­nered frames.

That’s right. The con­stel­la­tions on our west­ern star maps are sep­a­rat­ed by straight-line bound­aries. The bound­aries fol­low north-south or east-west lines, and all of the lines meet at right angles. The Amer­i­can astronomer Ben­jamin Gould began this orthog­o­nal map­ping of the sky in 1875. The sys­tem was offi­cial­ly adopt­ed by the Inter­na­tion­al Astro­nom­i­cal Union in 1930.

Con­stel­la­tions are anachro­nisms for mod­ern astronomers, but if we’re going to include them on our star maps then by gol­ly we’ll lay ’em out with rec­tan­gu­lar lines. It’s the west­ern way, begun by Greek geo­g­ra­phers and per­fect­ed by the philoso­pher-sci­en­tist René Descartes in the 17th cen­tu­ry. Carte­sian coor­di­nates: that’s what we call his method of plot­ting the world on a graph-paper grid.

And not just the sky. Take a look at Manhattan.

From Wall Street in the south to Hel­l’s Gate in the north, from the East Riv­er to the Hud­son, the city is a grid of rigid rec­tan­gles. The street plan ignores nat­ur­al con­tours of the land, the curve of shore­lines, water­cours­es, and pat­terns of drainage. The grid was laid out by a city com­mis­sion in 1811. The com­mis­sion­ers had one objec­tive: the effi­cient sale of land. Nature or esthet­ics did­n’t enter into it. Right-angled hous­es are cheap­est to build, the com­mis­sion­ers decreed, and right-angled hous­es fit best on right-angled lots.

The acknowl­edged goal of the 1811 com­mis­sion was not to embell­ish Man­hat­tan Island, but sub­due it.

Some­thing sim­i­lar was at work in 1785 when the young Con­gress in Wash­ing­ton decreed that pub­lic lands west of the Appalachi­ans would be sur­veyed and sold in squares. Six-mile squares called town­ships. Each town­ship divid­ed into 36 one-mile squares called sec­tions (usu­al­ly bor­dered by roads). Sec­tions divid­ed into four quar­ters. Bin­go! The checker­board grid I observed from 37,000 feet.

Patterns on the land

What I saw from the air­plane is a clas­sic exam­ple of west­ern Carte­sian effi­cien­cy. One mil­lion square miles of prac­ti­cal geo­met­ric util­i­ty. A geo­graph­ic straight-jack­et of math­e­mat­i­cal lines. The rule of the square.

Our enthu­si­asm for the square has enabled us sub­due nature with a dogged effi­cien­cy. The square-ruled earth and sky yield read­i­ly to sci­en­tif­ic under­stand­ing and tech­no­log­i­cal exploita­tion. We are rich­er, health­i­er, and more pow­er­ful than those cul­tures that are still bogged down in squig­gles and curlicues.

The squar­ing of the cir­cle is our secret of success.

But it’s a strange and unset­tling sort of suc­cess. A suc­cess that has brought with it intractable envi­ron­men­tal prob­lems, a sense of dis­con­nect­ed­ness from nature, and a kind of spir­i­tu­al ennui.

This ten­sion between nature and the square was eas­i­ly observed from 37,000 feet, in the land­scape below. Here and there, hills, water­cours­es, or a curv­ing line of bluffs man­age to frus­trate the rec­tan­gu­lar grid, forc­ing roads to devi­ate from their bee-line cours­es, nudg­ing the bound­aries of town­ships into gen­tle curves, or grace­ful­ly scal­lop­ing the square perime­ters of farms.

It was like a map on top of a map. First, the map which is nature, a map of cur­va­ceous sur­pris­es, con­cav­i­ties and con­vex­i­ties, oxbows and mean­ders. And, ruth­less­ly imposed upon the first, a sec­ond map, dead straight, T‑square per­fect, square-cornered.

It was the best and the worst of west­ern civilization.

What I saw from the air­plane was the straight-edged cor­nu­copia of our suc­cess: the effi­cient, ruth­less, ele­gant, uncom­fort­able square.

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