Before Pythagoras in 6th century BC, many people believed that the earth was flat. It's such common knowledge now, two and a half millennia later, that we don't even think about it twice.
Pragmatically speaking, however, I argue that we often experience the earth as flat and that it is better for us to live and work as if it were flat. Mathematically I can offer an argument that in essence the earth is flat to us.
Imagine flying off into in outer space, several hundreds of miles away from earth. Imagine, then, flying back closer and closer, until we're back on
terra firma.
Notice how earth essentially flattens as we approach closer and as we land back on solid ground. (Sure, there are curves, rolling surfaces, hills and mountains: The earth is not a perfectly smooth sphere. In fact, it's more of an oblate spheroid, extending out some from the equator.)
In our day-to-day lives, from how we construct our houses and buildings, to how we walk from place to place, we don't see these things and ourselves as situated on a big ball (i.e., something round). Instead we see it all as if we were on cardboard or plywood (i.e., something flat). If in fact we were to imagine being on that big ball, we would be concerned about toppling over or rolling off.
Occasionally I ask my friends to define a line in terms of a circle. Many are nowhere near as geeky as I am, so they're bemused at best and stumped at worst. It's this:
A line is a circle with infinite radius. Similarly a plane is a sphere with infinite radius. This is part of my mathematical argument: You see, our size as an individual vis-a-vis the earth is very tiny. In other words, the earth, compared to each of us, is of such massive heft, so as to be essentially infinite in its radius and thus essentially a plane (i.e., flat) to us. This size difference is what
flattens the earth as we return from outer space back on solid ground.
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