That fossilized chart on every classroom wall — isn't that The Periodic Table? Isn't that what Mendeléev devised about a century ago? No and No. There are many ways of organizing the chemical elements, some of which are thought-provoking, and which reveal philosophical challenges. Where does hydrogen 'belong'? Can an element occupy more than one location on the chart? Which are the Group 3 elements? Is aluminum in the wrong place? Why is silver(I) like...