"The Perfect Map" is a paradox.
Where would we be without maps? They provide us with much information to give us directions, pinpoint locations, quantify distances and areas, and identify landmarks (roads, tracks, intersections, towns, cities, signs, etc.)
What exactly is a map? It is a scale drawing of the real world. It's purpose is to convey to the reader a picture of the reality it represents.
Different maps have different scales. Some maps, for instance, have scales where one inch on the drawing equals one mile in real world. If you measured 10" on the map, you would realize that on that scale, you were looking at a representation of 10 linear miles of the real world at that geographic location. And one square inch on the map (i.e. 1" x 1") = 100 square miles in reality (i.e. 10 x 10).
So now, what if you changed the map scale? Suppose that two inches on the map would represent the 10 linear miles. Or four square inches (i.e. 2" x 2") would equal the same 100 square miles in reality (i.e. 10 x 10).
From this we can deduce that when you double the square dimensions in, you actually make it possible to provide four times as much information, because you have four times the square inches available in the larger scale. For if the same four square inches on paper provides details on 100 square miles, that means you can include 4 times as much information as you would be able to if you had to draw information for 100 square miles in only one square inch.
What would happen if you used a scale of 10" on the map equals 10 linear miles. Or 100 square inches (i.e. 10" x 10") would equal the same 100 square miles in reality (10 miles x 10 miles)? This means you would now have ten times as much detailed information, because you have ten times the square inches available in the larger scale. For if the same one hundred square inches on paper provides details on 100 square miles, that means you can include 100 times as much information as you would be able to if you had to draw information for 100 square miles in only one square inch.
Therefore, the larger the scale, the more detail you can include on the map, the more accurately you can represent or depict reality on paper. Which means, the more detail you have on your map, the more useful and valuable it becomes in terms of the amount of information it can give you.
What then is the perfect map? What is the perfect scale?
The perfect scale would be when one mile on the map equals one linear mile in reality, or one square mile (i.e. 1 x 1) on paper equals one square mile in the real world. This is the perfect map, because this would provide sufficent space on the map to literally draw 100% of everything that was out there in the real world. No detail would be left out or missing, with the perfect map.
So here is the paradox: The minute you have created the perfect map, that is precisely the moment when you have created a map that is now completely useless. You no longer need the map, because you need only walk around in the real world to get all of the details you need. The perfect map is perfectly useless!
Rod P.