I bet you didn't recognize that image as the periodic table. Even now, there’s no consensus about how to draw the Periodic Table. For example, Hydrogen, the first and lightest element, has always been awkward: it tends to get plonked on top of the first column (the alkali metals), but it doesn’t really fit there—it’s not a metal, after all. In what other ways could we organize the elements, and how would that change our understanding?