In essence a map is a representation of a topology or function. For example a formula such as X=2Y maps a value of Y to each value of X. Of course we all know that mathematicians are weird and sometimes hard to understand but have you ever seen a schematic map of a subway (underground railway) system? Have you ever seen the same network of rails illustrated on a more "normal" map of the city in which it is located? Different maps of the very same thing can look quite different.

When you make a map of a flat area - a "plan" or "elevation" - things are quite simple, but when you try to map a larger area, such as the surface of an entire planet, things can get quite complicated if you want your map to be flat. It is all very well to make a globe, but try turning the surface of that globe into a flat map! Ouch!

However you go about it, you end up with edge-effects. As I write this article I am actually engaged in programming map-generating programs intended to generate maps of fictional landscapes. I happen to be examining the map-generators that are included in the free, open-source (GNU GPL licensed) strategy game, FreeCiv. Edge effects are very apparent in such maps. The maps are basically rectangular, but you can choose to have them act like cylinders by "wrapping" left to right or top to bottom, or you can even have "wrap" in both directions. Most often people choose to use "wrap" only left to right, and block the top and bottom with "polar regions". Such simplistic "wrapping" makes for quite extreme distortion though if you try it with a real map of the world!

Have you ever seen a "family tree" diagram? That too is a kind of map! A map of family relationships. You might have also seen various diagrams of the evolution of species - a much larger-scale kind of "family tree". These are maps that include time as well as space! You might also have seen "timelines", which are yet another kind of map of time. Maps do not have to relate only to spatial dimensions!

Consider a dictionary, or the index of a book, or even the table of contents of a book. Those too are maps. The dictionary is an interesting case because in a way it is a kind of reverse-lookup map, in that the words have been arranged to fit the map! That is, the words have been put into a sequence determined by the map: the dictionary puts the words into alphabetic order for convenience of finding them. The Dewey Decimal System used in libraries is kind of like that too: it helps map where in the library the book you are looking for can be found.

In essence a map is a representation of relationships. But it is also true that representation is itself a map, because if you had no way of "mapping" (relating) the representation to whatever the representation represents you might not even realise that the representation is a representation at all! Think of the paintings of Pablo Picasso or Salvador Dali: pictures of things or people, yet distorted in some way. If you distorted a picture even more, eventually it could be so distorted that you could not tell by looking at it what it was intended to be a picture of; what it represents. Your eyes and mind have to be able to "map" the image to the thing in order to recognise what thing the image represents.

If you look at the actual file of .gif or .jpg or other "image file" used on the web for transmitting pictures to your browser; look at it not through an image-viewing tool such as the browser but just as a sequence of bits or bytes; you will probably have a very hard time recognising what it is a picture of. That is because it is a map of the picture. Your browser knows how to read that map, so it can use it to map it to your screen.

I could go on, rambling on about more and more obscure kinds of maps; but hopefully you get the point, which is simply that "maps" is a wide field, perhaps quite a lot wider than many people imagine it to be!