A dichotomy is a division into two mutually exclusive, opposed, or contradictory groups. Consider the reaction below. The bicyclic pentadiene on the left could in principle open on heating to give the monocyclic -annulene (blue or red) via what is called an electrocyclic reaction as either a six (red) or eight (blue) electron process. These two possibilities represent our dichotomy; according to the Woodward-Hoffmann (WH) pericyclic selection rules, they represent contradictory groups. Depending on the (relative) stereochemistry at the ring junctions, if one reaction is allowed by the WH rules, the other must be forbidden, and of course vice-versa. It is a nice challenge to ask students to see if the dichotomy can be reconciled.