We were learning about how the intersection of two planes forms a line today in math discussion. And letting my mind wander, as I often do, I started thinking about the nature of intersecting space. I figure, if two 1-dimensional objects (lines) intersect to form a 0-dimensioned object (point), and two 2-dimensional objects (planes) intersect to form a 1-dimensional object (line), shouldn't it follow that the intersection of two 3-dimensional objects (spaces?) should be a 2-dimensional object (plane)? But it's weird, cuz when you think about it, it seems like the intersecion of two spaces should just be another space, right? I spent a good portion of the rest of the day pondering this idea.

And I got to thinking... to get lines to intersect (and not just be identical lines), you have to see them in 2 dimensions; and to get planes to intersect, you have to see it in 3 dimensions; so I guess to properly visualize the intersection of spaces, you'd have to be able to visualize it in 4 dimensions. Man, I like strained my brain pondering the nature of the 4th dimension, and to very little success, obviously. Geez, I haven't been all WAAAAHHH thinking about higher order dimensions like this since I read Flatland back in 11th grade... "Upward, not Northward." Part 1 was sooooo boring, I almost didn't make it to Part 2, which is where all the good stuff is. A very thought-provoking read- I highly recommend it.