Pretty much everyone (including me) thinks that the world is round, but very rarely is it obvious that this is the case: In our every day lives the world is for all intents and purposes flat. It strikes me as a little absurd that thinking that world is flat is taken to be so incredibly ignorant, when there is so little direct sensory evidence for it. If you haven’t gone to the sea and observed ships crossing the horizon, or performed some experiment to demonstrate it, thinking the world is round is really only taking other peoples word for it. The roundness of the earth is almost completely detached from what we experience and the fact that most of us have this knowledge is a real tribute to our ability for abstract thought.
The intangibility of the roundness of the earth is an excellent example for my ongoing campaign to make people aware of just how far our understanding of the world is from our direct experience of it. Considering the world at the level of our physical interactions with it seems to be ignored by our post-enlightenment mindset – I think it needs setting straight. And the best way of doing this is to represent familiar but abstract concepts in ways that relate to our basic interactions with the world (ecologically, to borrow J. J. Gibson‘s term)
This is my first demonstration of how unnatural thinking the world is round is: I will calculate how big a circle I need to walk in to decide with confidence that the world is round. We all have an intuitive grasp of how far it is to walk somewhere, so the question is: how affected should this understanding be by the curvature of the earth. This is based on the principle that circles are “smaller” on a sphere than they are on a flat surface, reflecting the formal definition of curvature (almost) exactly.