Both maps and models seek to take a complex reality and simplify it for better understanding, use and prediction. Today’s lesson introduces basic mapping and modeling concepts. We finish with a look at the 5 Themes of geography.

Maps are to the real world in geography what a sample is to a population in statistics. We can’t accurately represent the real world because it’s just too darn big, much like we are usually unable to survey our entire population in statistics. But if I take certain parts of the world and represent them on a map, the hope is my map will represent reality in the same way that I hope my sample will represent my population. Maps use a rule to assign selected objects in the observable world to a feature on the map (much like a function works in mathematics). Maps require two decisions: what am I trying to map and how detailed should it be (i.e. what do I leave in and what do I leave out?)

Mapping involving decisions – what to leave in and what to leave out. Mapping always involves tradeoffs. To get one thing, I must give up another. For scale, to get accuracy I need a small scale (1:10, 1:20 etc.). But such a small scale results in an unwieldy, inconvenient map. Large scales mean that I can easily get my map on a normal-sized piece of paper but I will sacrifice much detail as I will have to leave things out. Projection refers to the method I choose when mapping the spherical 3D Earth onto a 2D piece of paper. The tradeoff here is between accurate shapes of the continents and their relationships to other continents (known as “conformity” and very important for navigation versus accurate areas of the landmasses. The common Mercator sacrifices accurate area to get conformity. The Mollweide gives us perfectly proportioned areas at the sacrifice of shape. The Fuller Dymaxion gives us both but at the sacrifice of usability.

The most famous is the Mercator map. The projection distorts area at each pole so Greenland looks way bigger than it should. The Mercator gives us accurate shape and relation (conformal) but sacrifices accuracy in displaying area.

The Mollweide projection is an equal-area projection. The projection trades accuracy of angle and shape for accuracy of proportions in area, and as such is used where that property is needed, such as maps depicting global distributions.

The Fuller Dymaxion map is our spherical world mapped on to a 20-sided polygon called an icosahedron, which is then unfolded. It is very good at equal area and is conformal – but… it lacks cardinal directions so may be impractical for most cartographic uses.

Location maps merely map out a physical feature based on where it is in space. These are the general purpose maps we are all familiar with – road maps, street maps, atlases, topographic maps etc. Thematic maps use the location map as a base and then they overlay another map over it, the overlay map focuses on one parameter or one category of data. Thematic maps, as the name indicates, have a theme. They tell a story. In the example on the left, John Snow put a map of cholera deaths on top of a location map of London city streets to better understand a cholera outbreak. Thematic maps are also known as “quantitative maps”.

The John Snow cholera map is a good example of a dot map. Graduated circles use circles of various sizes to indicate amount or frequency. The final distinction is between isopleth and choropleth maps. Isopleth maps use isolines – lines that connect points of equal value. Think of the lines that show elevation on a topographic map or the lines that show areas of pressure on a weather map. Isopleth maps let the isolines cross the internal boundaries of the map (see example on right). A choropleth map (next page) assigns each internal map area a statistical value and lets the variation over areas be communicated through (usually) variations in shading. A map showing a one hour commute isoline from a city would be an isopleth. A map that shows per capita income by county with each level of income resulting in a county being shaded differently would be a choropleth map.

Here, the internal map division is at the county level. Dark blue means the most Clinton views, dark red the most Trump views. This is a choropleth map.

In a cartogram, the largest area on the map (in this case, CA) is the one with the highest statistical value (in this case, electoral votes).

Both remote sensing and GIS are in high demand. Businesses are beginning to use RS and GIS to get data about their competitors. Example: using satellite photos to count the number of cars in your competitors parking lot. Both fields are taught in college usually through geography departments.

Remote sensing technology (satellite or aerial photography) used to analyze the crowd size at the 2009 Inauguration versus the 2017 Inauguration.

A model is just a simplified version of the real world that helps us better see cause-and-effect relationships. Prediction is also an important function of the model. Thanks to the model of gravity, I can use simple equations to identify the most important objects in relation to gravity and I can use the model to predict motion. Models are never completely accurate – that is the trade-off. In simplifying the system, we sacrifice complete accuracy. In my gravity example, although every object attracts every other object, I disregard the pushes and pulls from distant objects and only take into account the larger forces (I make it a two-body problem). As for mental maps, they are subjective images regarding an area developed through an individual’s experiences, beliefs and prejudices.

Theories are sophisticated models. A theory known as environmental determinism says that the impact of the environment upon humans is far larger than the impact of humans on their environment. Here, the very shape of the continents is said to have either helped or hindered trade and the spread of agriculture. (This is the core of Jared Diamond’s book Guns, Germs and Steel). A determinist says that human outcomes are primarily determined by the environment. The competing theory, possibilism, says that humans possess skills that allow them to change their environment to best suit their own needs.

The Five Themes are a useful model for organizing geographic inquiry.