Analogies are powerful and dangerous. It is a good idea to not take more of it than what the analogy can offer. But the idea that building mathematical models can be compared to map making is a powerful one. If you look at the image featured in this post it is easy to realise that maps, like mathematical models, capture the assumptions and understanding of a community…even if they are wrong or incomplete.
Maps show us our biases. The image above (top left) shows the map using a conventional representation. It uses the Mercator projection where Greenland can be seen as a much bigger landmass than Australia. Which is not true. To the right you will seethe Gall-Peters projection which does a better job but is not perfect either. In general all these maps are wrong in one respect or the other but nobody should doubt that they are useful.
Here is another map:
It is a map of the subway system in London and as an example it captures one important aspect of mathematical modelling and map making: the important thing about a map like this is not only what it shows but what it chooses not to. This map is incredibly useful and a good part of that is because it shows only the information that a traveller needs in order to reach any corner of London served by the tube. Arguably it could not show less information (maybe the thick blue line showing the Thames river) but even more importantly: adding more information would likely make it a worse map. Some people might argue that there is a lot of information that is critical if we want to understand transportation in London. Maybe the nature of the terrain that had to be open for building the lines? The elevation? how congested those lines typically are? distance between stops (the map is not to scale), average travelling times? They all sound like good ideas but they would make the map more complicated and more difficult to navigate.