My friend and colleague Rob Pennock likes to illustrate the concept of representation, which is essential for understanding both cognition and the scientific method, using maps. One thing (for example a mental image of one’s grandmother or a scientific model of a natural phenomenon) insofar as a correspondence exists between the representation and the thing represented. Maps represent actual geographic patterns, but the particular nature of the representation depends heavily upon the function by which reality is encoded into the map. The function used to make the map depends in turn upon what the goals of the map, and map-maker, are.
A beautiful example can be seen in a series of maps of the results of the recent US presidential election. Check out this series from Mark Newman at the University of Michigan:
A few highlights:
The geographically “accurate” map* with states colored according to the outcome of Electoral College votes:
This map shows that the nation is mostly RED based on landmass–there is more landmass present in Republican-leaning states.
But let’s not forget that there are Democrats in “red” states, so let’s look at the results by county instead of by state:
This map shows islands of blue (cities) amid large regions of red. If anything this makes the country look even redder.
But votes are cast not by blades of grass but by people, so let’s re-size everything by population. In the next map, equal-sized areas on the map have equal-sized populations:
This is starting to resemble the political reality–a nation more blue than red–if not the geographical reality*.
*A caveat regarding “normal” map. Any projection of a portion of a globe onto a two-dimensional map is going to involve distortions. See this.