The Scale of Precision in Maps: Understanding Why an Inch-By-Inch Earth Map Does Not Exist

When we think about mapping the entire Earth, it might seem intuitive to imagine a map with one-inch precision, where every detail is perfectly captured. However, this notion overlooks the fundamental limitations of map scales and the practical considerations of map creation.

The Limitations of Map Scales

In cartography, the scale of a map does not imply the relative size at which features are displayed but rather the actual scale at which they are transferred from an existing reference. A map with a scale of 1:100,000 means that one unit of measurement on the map corresponds to 100,000 of the same units in the real world. This precision has significant implications for the practical application and usefulness of the map.

Understanding Map Scale

The scale of a map is crucial for understanding its precision and the relative size of elements on the map. As mentioned, a map with a scale of 1:20 means that one inch on the map represents 20 inches in the real world. This is a very small scale, and thus, it is not feasible to create a map at this scale for the entire Earth's surface. If an American sheet at 1 meter in width has 90 percent of points within 1mm of their real-world positions, this means that the map's accuracy diminishes significantly the larger the coverage area.

Let's consider a table with a cup on it in your patio. A map that shows the world inch by inch would have to magnify the table and the cup to such an extent that they appear much larger than just a few inches. Similarly, if you are sitting on a chair beside the table, the map would show your chair to be enormous. This is impractical and unhelpful for navigation or other real-world uses.

Practical Considerations and Cartographic Challenges

From a technical perspective, the scale of a map is not the relative size of things when zoomed in but the scale at which the map is drawn or printed. For cartography, a map is drawn on a drawing board approximately 0.9 meters by 0.6 meters, with 90 percent of points being within a millimeter of their real-world positions. This means that if the printed map is 1 meter wide, the precision of things located can have errors up to 1,000 times the size of the drawn map.

When the United States Geological Survey (USGS) says their map is "1:100,000," they mean that the precision when locating or drawing any point is 100 meters. Even with advanced technology and digitizers, the limitations of the underlying data and scale remain constraints. Magnifying a map can make it more detailed, but the base precision does not change.

Real-World Maps and Scale

At a scale of 1:20, when the map is drawn or printed on a standard size map paper (about 0.9 meters by 0.6 meters), there is a significant limitation. Approximately 90 percent of points must be within 1mm of their real-world positions, which translates to being just under 2cm apart in the real world or approximately one inch on the map.

For example, if 1 meter on the map represents 20 meters in the real world, then 1mm represents 2cm. With this scale, a regular-sized map of 90 cm by 60 cm can only fit approximately 0.00036 square kilometers (360 square meters) of the Earth's surface. This means that completely mapping the Earth with such precision would require an impractically large number of maps, covering an area equivalent to Russia.

A Historical Perspective: Borges' "Tl?n, Uqbar, Orbis Tertius"

Jorge Luis Borges, in his famous Fiction, presents a narrative that helps us understand the absurdity of trying to map every inch of the Earth. In the story, a cartographer guild creates a perfect map of a province, then the entire empire. Over time, these maps start to lose their purpose, and ultimately, are discarded.

Borges' text highlights the impracticality and futility of creating a map that matches the entire real world on a one-to-one basis. This absurdity underscores the challenges and limitations of cartography.

Shortly:

Map Scales: The scale of a map affects the precision in which features are represented. Real-World Examples: Practical considerations like the size of features and the need for maps at different scales. Historical Perspective: Borges' work illuminates the limitations and absurdity of attempting to map every inch of the Earth.

Understanding these principles can help us appreciate the complexity and artistry involved in cartography and why an inch-by-inch map of the Earth's surface is simply not feasible.