Treating spaces as fiber bundles allows us to tame twisted beasts.
If we glue lines onto every point $b$ in a circle (or a circle to every point of a line), we get a cylinder. In other words, a cylinder is the product space $S^1 \times [0,1]$.
My mentor, Eric Weinstein, made up a lovely analogy which he permitted me to share.
Originally published at rin.io on July 21, 2014.