The only way to truly represent something is to reproduce it exactly. Since cartography attempts to take the entire world and map it into either a physical representation or a digital graphic, the challenges faced are huge. The first job is to obtain accurate measurements of distances, heights, and sizes. Then there’s the need to understand the shapes of natural features that aren’t idealized. There is no mountain that is a true triangle and no river follows a path of actual curves and angles. The natural world is much more imperfect.
Once things are measured, they have to be scaled to fit the size of the finished map and then the features, including cities, towns, roads, and other man-made objects, need to be plotted. Placing mountains, lakes and rivers on a colorado map can be further complicated by the need to represent elevation . Two symbols can’t occupy the same space, even if they are on the same mountain but at different elevations.
The most obvious challenge is how to depict a three dimensional, physical world on a flat, two-dimensional space. On the surface, globes seem to be the easy answer. However, most globes can only provide a spherical representation, showing how cities and places relate to each other across a circumference. They do not usually depict elevation or topographical features accurately.
In the end, the only way to accurately represent something is yet to be invented. But for now, maps, globes, and GPS systems will do their best to turn a living, changing planet into a physical reproductions that can give humans a glimpse at what it all looks like.