This episode features reports from Cockburn in Greece and Italy elaborated by demonstrations from Hart-Davis, Jopson and expert guests that examine the ideas and inventions that emerged from Ancient Greece. * Geometry allowed for advances in engineering such as the Tunnel of Eupalinos visited by Cockburn on Samos. * Musical scales were invented by Pythagoras in a process explained by Hart-Davies that he applied to the universe. * The water organ was invented by Ctesibius of Alexandria using a devise reconstructed by Jopsom that was the first to use compressed air. * Mirrors were used by Archimedes in a process demonstrated by Jopsom to set fire to enemy ship at Syracuse. * Belly bow, demonstrated to Hart-Davies, was the first mechanical weapon and more powerful than a standard bow. * Communication devices, such as those reconstructed by Jopsom, allowed the secure transmission of messages. * Democracy was originally developed in the city of Athens visited by Cockburn. * The Kleroterion, reconstructed by Jopsom, secured the fair and democratic selection of juries. * The high-tech stagecraft of Heron of Alexandria, reconstructed by Jopsom, included the first robot, steam engine and automatic doors. * Ethylene was inhaled by the Oracle at Delphi, visited by Cockburn, prior to her predictions. * Advanced astronomical theories, explained by Hart Davies, were put forward by Pythagoras, Aristarchus of Samos and Eratosthenes. * Antikythera mechanism, demonstrated to Hart-Davies, was the world's first computer.