So I want to understand the illusion of being at the edge of the world at the Sleeping Bear Dunes in northern Michigan. Since I like doing mathematics I think of this as a mathematics problem; so, I figure, I need to put together some equations. Before I do that, I need to think of what I want the equations to represent, which is the part of the problem where I build a model of the dunes. In the process I should get at least a qualitative idea of the effect; later, I should be able to quantify that.
What’s a dune? Well, it’s a great whomping big pile of sand right next to the water. There’s more to a dune than that, but since all I’m interested in is how the dune looks, I don’t need to think about much more than what the dune’s shape is, and how it compares to the water beside it. If I wanted to understand the ecology of a dune, or fascinating things like how it moves, then I’d have to model it in greater detail, but for now I’m going to try out this incredibly simple model and see what it gets me.