Saturday, January 28, 2012

Maps and Territories

If you are going to visit a city you might want a map of that city that will help you get around. Of course you have to be sure that you have the right map. A map of any city won't do. If the city you find yourself in is London and you try to follow a map of, let's say, New York your trip will be confusing. You might find some resemblances ("maybe this is this street and that corner over there is this, but wait - where is this square?"), but at some point you will find that the map doesn't fit the territory. You realize that for every city you need a specific unique map.

But maybe, you think, there is some way to make a map that will fit every city in the world. A Map of Everyplace - a MoE). One way of doing this would be to only include in the map such things that are common to all cities in the world. Roads for example - but you cannot tell where they are actually going. Buildings - but not where they are. Such a map will be useless you realize (a Map of Very Few Things).But what if, you think, you took all the cities in the world and made an average, a statistical median of all of them? Wouldn't this then be a Map of Everyplace? So you do it and find that this "citymap" doesn't help you travel in any city (It becomes a Map of No City).

Scientific theories and models are map-making. The notion that you can use one map (for example Einsteins theory of relativity) to fit everything (like quantum entanglement) doesn't work. It's like taking the "wrong" map (a map of NY when going to London) with you on a trip. Right and wrong here is contextual, of course. There might be nothing wrong  with the NY map but it still doesn't work in London.

The more generally applicable you try to make a map ( A GUT or ToE for example) the less useful. Science have a natural tendency to abstract away reality. The map is not the territory!