Representations matter. In my own work, I have lectured about the importance of having a plurality of representations to gain a better understanding of relationships in what is being represented. Hierarchies or networks are not "there" but are a function of a particular representation that utilizes pre-chosen criteria of value.
Maps of the world are a great example.
I happen to like the Gall-Peters projection:
"The Gall-Peters achieved considerable notoriety in the late 20th century as the centerpiece of a controversy surrounding the political implications of map design."
Recently one of my complex systems colleagues here at the University of Michigan, Mark Newman, has created some very interesting "cartograms" by varying the criteria upon which the representation is based, using a typical map of the world.
"It's possible, however, and sometimes very useful, to redraw the map with the sizes of countries made bigger or smaller in order to represent something of interest. Such maps are called cartograms and can be an effective and natural way of portraying geographic or social data."
In addition:
"Worldmapper is a collection of world maps, where territories are re-sized on each map according to the subject of interest. There are now nearly 600 maps."
In fact, now that I think about, the tagline in my email signature is "See differently, then you will act differently." That about says it. :-)
