It just doesn't look right. Start with a bunch of identical, rectangular, flat blocks, like jewel cases or unopened packs of Trident. Stack them up flat, as neatly as possible. You only need 10 or so for a good demonstration, but 50 looks better.

Now slide the first one sideways so it's almost halfway off the second one. At this point, it makes sense. If it goes any farther its center of gravity will be unsupported and it'll fall right off.

Slide the second one in the same direction so a third of it is also hanging over empty space. Keep on going down the line, sliding each one by one fourth, one fifth, one sixth. By the tenth one, the top block isn't close to being above the bottom block.

Now, I vaguely understand the math here. It's an infinite sum from pre-calculus. 1/2 + 1/3 + 1/4 + 1/5 + ... = infinity. This means that the top block can be infinitely off to the side of the base of the tower!

That's not right. When I learned math, the real world problems always had a nice round answer like 1 or pi. Infinity in the real world is supposed to be reserved for grand phenomena like black holes and the size of the universe.
