Why are there two sexes, and how is the balance between the two maintained in evolution? The riddle is one that baffled Chales Darwin. He explicitly left it for later generations. It was eventually solved, with typical brilliance, by the great Ronald Fisher. The fundamental sexual inequality is an economic one. Eggs are hugely larger than sperm. From this much follows. Why do peacocks have such a ridiculously large, ornamental “tail”, when it obviouly must put them in danger? Do females go for male beauty for beauty’s sake (as Darwin thought, and Fisher explained)? Or are males advertising some useful quality (as AlfredWallace, Darwin's co-discoverer of natural selection, insisted). Is the peacock’s tail favoured in spite of being a handicap? Or could it be favoured precisely becuse it is a costly handicap? Does it have to be costly as a certificate of honesty? Do females only go for honest males? This is a talk I gave on a ship crusing the Galapagos archipelago.