Metaphoric landscapes, curved surfaces in space
Besides natural scenery, which is its foremost and everyday notion, what can be meant by the term“landscape“? Obviously, it involves some notion of space, some spatial configuration, structure. In the sciences, the landscape metaphor is recurrent: In biology for example, the “epigenetic landscape“ shall provide a simple picture for epigenetic phenomena such as cell differentiation, providing a means to explore by figurative analogy different aspects of the concept in question. In population genetics, the “fitness landscape“---be it adaptive or not---describes the fitness of individuals with certain genetic traits; physicists speak about “energy landscapes“ when they refer to a system’s potential energy as a function of space.
All metaphors just mentioned have something in common: They refer to curved surfaces in some coordinate space. So what does qualify those geometric surfaces as landscapes? It is the small layer where the earth meets the skies at the horizon, for that layer defines a two-dimensional surface in three-dimensional space. It thus provides the link between abstract geometric surfaces and actual landscapes: Where we skip some level of detail regarding the latter, we start to read the ups and downs of the former as hills and valleys.
Landscapes… Beautiful landscapes, of course: mountain ridges and beaches. The sea and the desert as they constantly evolve, retract & gain territory, change their very appearance. Did you know that not only does a wild sea roar but that dunes can sing? Landscapes are dynamic, and we‘re part of it.
Of birds and people and forces
Imagine you have a bird’s eye view of a public square full of people. Some of them stand together chatting, one or two sit on a bench reading the newspaper. Others are moving around, crossing the square hastily as to catch the bus on the other side or just because they overheard their alarm clock this morning, being in a hurry all day since; some stroll around without any apparent destination, changing their mind once in a while and turning direction. What makes all those people move, what determines their pace?
They move according to a global potential, they follow inevitably the line of steepest descent. The steeper the faster. This potential is invisible, of course --- but it defines a landscape, and in the following we will expose its dynamics, the dynamics of the unseen.
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