Davide P. Cervone
of Union College Mathematics Department.
Okay so like we live in a 3-D world. If you want, you can call us Spacelanders. We can go right and left, forward and backwards, up and down. And that's it.
But Flatlanders are stuck in a 2-dimensional world. They can go right and left, and they can go forward and backwards. And that's it.
They're straight lines, triangles, squares, pentagons, hexagons, etc., all the way up to circles, but they have no thickness; they live their entire existence travelling around within a plane.
From time to time, a Flatlander claims to have had a weird "encounter" with a strange 2-D shape that appears first as a point, then grows into a 2-D shape like a circle, triangle, square, polygon, then it shrinks again down to a point, then vanishes again. A Flatlander who has one of these bizarre experiences runs screaming to tell the Authorities all about what he saw. The Authorities immediately lock him up in an insane asylum for life.
What's really going on in these encounters is that a Solid 3-D object "falls" from above the Flatland Plane, intersects with the Plane, and then falls below the Plane again, vanishing from Flatland altogether. But while the Solid intersects the Plane, the Flatlander sees plane slices of the descending Solid.
"Flatland" by Edwin Abbott Abbott is a wonderful story about life in Flatland, as told by a Square who had one of these weird encounters with a Solid Object, and when he tried to explain the 3rd Dimension to his neighbors, he was immediately locked in an asylum for life.
If you Leave a Comment asking what the top image is, I'll report you to Homeland Security because you're probably a terrorist. The top image is of something that can't possibly exist intersecting through another thing that can't possibly exist. Everybody knows there's no such thing as dimensions greater than 3.