Measuring Space I

Avoiding a pitfall

This page illustrates problems with using area as a measure­ment of space—in other words, it tells how NOT to measure space. The next page demon­strates how TO measure space.

Area is a necessary ingredient of space, just as flour is a necessary ingredient of cake—but flour is not cake, and area is not space. Cake needs leavening, the stuff that makes it “light,” and space needs distance.
Area by itself does not measure space.

The idea of uninterrupted space

One of the key concepts at is that of uninterrupted space. All spaces have their limits or boundaries.1 Uninterrupted space captures the idea that these boundaries are, for much of the space, far away. Proper space measurement quantifies the amount of uninterrupted space.

Distance yields area

It turns out that if you have distance, then automatically you will have area, but the opposite is not true—if you have area, you will not necessarily have distance.

What does it mean to have distance? Here we do a little thought experiment. Imagine that you are standing somewhere in an open space, and the closest structure to you—including roads as a type of structure—is at a distance R. This means that a circle around you of radius R is free of structures because, if there were another structure inside this circle, then it would be closer than distance R—and we have said that this is not the case. So, there is a circle around you with area πR2 that is free of structures.

I-25 in Larimer County, Colorado Part of Interstate 25 in Larimer County, Colorado. The median of I-25 in this county has area of one half square mile, but has little space because it is all adjacent to a road.
Tap or click image to enlarge.

In the photo on this page2, you could choose any point that is 0.4 miles from all roads—and there are plenty of such points out there in this semi-arid, high plains environment—and you would be guaranteed to have a half square mile of roadless area around you (compare this to the example in the next section). From your chosen point, you could walk 0.4 miles in any direction and not encounter a road; this is credible open space. In this treeless environment, you also would have views out to 0.4 miles distance in all directions—and, in many directions, much farther than that—that would be unobstructed by human constructions. Distance guarantees a minimum area that is free of obstructions.

Area does not necessarily yield distance

On the other hand, a half square mile, even though it is devoid of human structures, may be so close to human “stuff” as to make a mockery of the term space. For example, the median strip of Interstate Highway 25 in Larimer County, Colorado, has an area of about one half square mile, but its average distance from a busy highway is a mere 14 feet (3 meters). This highway median—all grassland, with no structures—is an example of area without space.3

Area by itself does not imply space.

Area calculations do not reflect space

If we are to understand space loss, then it is critical to employ a measurement that adequately expresses losses in uninterrupted space. Losses in area do not do this.

“Area subtraction” illustrates the ineffectiveness of area as a space metric. When a new road penetrates to or crosses the center of a featureless tract, there is a significant reduction in the unobstructed freedom of movement within the tract. The area of the new road, however, is usually tiny compared to the area of the tract. Subtracting the area of the road from the area of the tract, therefore, may indicate an area loss of only a few percent, or less—while the loss of unobstructed movement within the tract is much more impaired than a few percent.

Roads are estimated to cover about 2% of the land area of the 48 con­ter­mi­nous states[4], which suggests—if we use area subtraction4—that we still have 98% of our space and have used up only 2%. It also suggests that 50% space loss will not happen until we have graded or paved half of the nation. If half of the nation were paved, say the eastern half, then space would be left in the western half. But if the paving were more or less evenly distributed, then 50% pavement would surely mean that space was dissected into tiny pieces and remaining spaciousness would be far less than 50% of the spaciousness in a roadless nation.

Area alone does not measure space.

Combine distance and area to measure space

We have demonstrated why we should avoid the pitfall of using area as a measure of space. On the next page we show how to combine distance and area to yield meaningful measurements of spaciousness.

Read more…

Measuring Space II

How to measure space with both distance and area.

What is Space?

Why distance is important to include in space concepts and measurements.

1 Some spaces have internal features that violate surrounding natural conditions; these are part of the boundary.
2 Image from Google Earth, 2016.
3 If you drive this highway today, you will see that there is an anti-collision fence in the center of the median. When this page was first written, the only constructed features in this median were interchange bridges and police cross-overs.
4 In this illustration, we use roads as a surrogate for all human features, which is only a rough approximation of developed area.