The past few nights there's been a lovely waxing crescent moon in the western sky. I know this "toenail" will grow fatter each evening 'til it's a half-moon overhead. And fatter still 'til it's full and rising in the east just after sunset. I know where I am on earth and I know what the moon's going to look like in the sky over time. It's nice and orderly, like this chart.In my imagination the sky is curved overhead. The sun is somewhere beneath my flat earth casting the earth's shadow on the moon. I can set this image in motion and see the crescent moon setting at midnight. With some effort I can even imagine the moon "under" the earth in the morning and I guess if I search in the eastern sky at midday I should be able to find the moon.
I try to visualize this from somewhere in space - on the plane of the earth's orbit around the sun for simplicity's sake. I block out the stars and other planets and see a flat western hemisphere. There I am at 42 degrees latitude with my feet pointed toward the center of the earth. The moon is setting to the left of the flat earth. The sun is behind my dark, flat western hemisphere and I'm moving toward the right. East? Counter clockwise?
Then I start to lose my grip on these inter-related concepts in four dimensions and I remember Flatland. Not only can I not visualize time as a fourth dimension. I'm absorbed in a two dimensional world in which I can't imagine the third dimension.
