Two visions writ on the American landscape

 kw: book reviews, nonfiction, geography, cartography, surveying, history

Take a look in the lower right portion of this street map, around the name Anaheim:

Much of the map is gridded in a N-S, E-W pattern familiar to most Americans, but the older portion of the city of Anaheim, an area about 2.5 x 2.5 miles, is tilted 14.5° west of north. I used to think this was due to the city being originally laid out with a compass that wasn't corrected for declination, but the magnetic declination in this area is about 11° east of north, and over the past century it has been similar, never to the west. I haven't learned more about the original survey, but it was clearly done before the rest of the county, probably in the late 1800's.

Now look north of Anaheim, past Fullerton: There is no grid in much of this area. It is an area of suburbs with winding streets, which also includes a nature preserve, an arboretum, and a couple of large parks plus a long, skinny—and winding—golf course.

This one map encapsulates the tension written in America's landscape between the Cartesian vision of Thomas Jefferson and the more naturalistic vision of later city-and-landscape planners such as Frederick Law Olmsted, the planner of New York's Central Park. Some 2/3 of the United States is laid out in a grid with the squares one mile on a side, which facilitates agriculture, as seen in this satellite image of an area about 6 x 4 miles in size northwest of Edmund, OK.

We can see that where the suburbs are built into the agricultural landscape, even though within them the streets may wind about or run at different angle, the neighborhood boundaries fit neatly into a quarter section (1/2 x 1/2 mile) or a section (1 x 1 mile). The farmers in the area are free to divide up their land as they see fit, but they tend to use rectangles and squares parallel to the section boundaries.

Having lived in Oklahoma for nine years, I can testify that navigation is typically quite easy. Someone will say, "Just go 3 miles east and 6 miles north, and turn in at the next street on the left." Then they may need to tell of another turn or two. No GPS is typically needed. On the other hand, I once visited some relatives in North Carolina, in the days before GPS. I was instructed how to find the local police department. I went there and told them where I wanted to go. A patrolman drove ahead to lead me along the winding roads and around several turns. When we got to the house he said, "We'll show you how to find this place one more time, if you need it. After that you are on your own." Today, I'd use GPS, and arrive with no clue about how I actually would get there without it.

Liberty's Grid: A Founding Father, a Mathematical Dreamland, and the Shaping of America, by Amir Alexander, tells the story of how both the grid and the anti-grid came about. The first chapter (of six), plus most of the Introduction before it, leads a reader gently through the mathematical and philosophical background that led from the geometry of Euclid to the analytical geometry of Descartes and on to the esoteric geometry imagined by Newton. Euclidean geometry is constructive; objects such as triangles and circles and lines are constructed according to defined rules. Cartesian geometry is deductive; one may place Euclidean objects at will in a mathematical space. However, the X-Y grid we call the Cartesian coordinate system did not originate with Descartes, but was named in his honor a century later. To Descartes, the universe is filled to capacity by Euclidean objects with no gap between them. A modern thinker cannot imagine it, but it was "the way things are" to that generation of philosophers.

Newton instead imagined an empty and unbounded space, in which every location had an "address", a pair of X-Y coordinates, and a mathematical object was defined by the series of such "addresses" it encountered. Thus, three sets of coordinates defined a triangle's corners, and thereby the triangle itself, while any point on its boundary could be calculated from the corner coordinates and a measure of how far along one of the edges the point of interest happened to be. This infinite and empty mathematical space gave free rein to the mathematical imagination in a way that the filled space of Descartes could not. It led directly to Newton's invention of "fluxions", or The Calculus as it is now called.

Thomas Jefferson seized on Newton's Cartesian system as the perfect method for surveying the great continent of North America. We learn of the long struggle to get such an idea accepted by the Congress of the new United States. Jefferson, wary of cities and their evil effect on people, considered farmers, "honest yeomen, wedded to the soil," as the epitome of human perfection. He believed that, given the opportunity to obtain land with no history, no cultural meaning attached (Jefferson ignored the original inhabitants, with tragic results), farmers would build a republic on sound principles of ethics and responsibility.

Jefferson abhorred the model of power embodied in places such as the gardens of Versailles, seen here, with broad lanes radiating from the palace and the landscape constructed in homage to the tyrant-king Louis.

Mostly by the force of his personality, and the power he had as America's third President, Jefferson was able to get the project started, firstly in Ohio, and over the following 150-ish years, it developed across much of America, at least in arable lands, and many semi-arable areas.

Fast-forward a generation or so. There was a long struggle to prepare a plan for the island of Manhattan. Eventually, much of it was gridded, not according to the N-S, E-W grid in the Midwest and West, but parallel to the twin rivers, the Hudson and East Rivers. As this plan was being carried out, with dictatorial powers the city planners assumed (which would soon be shot down these days), an anti-grid movement began.

The first "win" in the anti-grid salvo was the planning and construction of Central Park in New York City, encompassing 877 acres. Although the boundaries are streets of the city grid, within all is sylvan, irregular, and naturalistic, with no right angle to be found. The success of its designers, Frederick Law Olmsted and Calvert Vaux, led to the design of smaller but equally attractive parks in major and medium-sized cities all over the country.

A partial compromise between the naturalism of Olmsted and the European vision embodied in Versailles (and many copycat royal gardens) was struck by the French designer Pierre Charles L'Enfant in his plan for Washington, DC.

The long central Capitol Mall, from the Lincoln Memorial at the west to the Washington Monument and the Capitol Building, and onward to the Lincoln Center at the east end, forms the axis of a series of avenues radiating from not just the Capitol and the White House but an additional fifteen figurative power centers, representing the fifteen U.S. states in existence prior to 1796. Note that the Jefferson Memorial, symmetrically opposed to the White house, is in an area without the gridded aspect of the rest of the city. A rebuke of Jefferson's vision, perhaps? I find it suggestive that later additions to the landscape, the two Lincoln-honoring "anchors" of The Mall, and the Jefferson Memorial, focus more on the Savior of the Union than on its initial architect.

We are complex creatures, we humans. The Grid is based on belief in human goodness. The Anti-Grid is in part a reaction to an understanding of universal human sinfulness and the restorative quality of natural, or naturalistic, landscapes. Not all farmers are "honest yeoman"…and there are tens of millions fewer family farms than existed a century ago. Not all city dwellers are the demons Jefferson imagined, which is a relief, given that 81% of Americans live in cities and "highly urban" areas, only 3% are farmers, and the rest live in suburban and semi-rural areas.

Today a new grid has been imposed, not just on America, but on the world. If you use Google Maps to view anyplace on Earth, and right-click on something, the top line on the menu that appears will be the geodetic coordinates, such as 39.94962, -75.15028 for the Liberty Bell in Philadelphia. On your phone, in the Maps app, zoom in on a place and press your finger to a point of interest for about a second. The coordinates (with an extra digit of precision) will be placed in the search bar. These numbers are not very meaningful to us, but they are critical to the function of your GPS navigator, whether in your phone or a standalone unit. Hint: if you need to go to a location that doesn't have a convenient address, and you can find it on the map, you can get its coordinates and make them a named "favorite" for later use. The navigator can steer you almost right to it, perhaps giving you an indication of a short walk if it's not right on a street.

I want to give kudos to the author and his editors. This book has the most thorough index I've ever seen in a book of 370+ pages. The book is very well written. While reading all the math history in the first chapter, I thought, "Oh, he's going to lose some folks here," but the writing carries one on. Not everyone will understand, but the review gives one a feel for the currents of history that led to Newton's breakthrough, and to Jefferson's geometrical obsession.