When Kristen explains "The Sword of Damocles" she states that Damocles was a king and that the gods hung a sword by a thread over the throne. Damocles was actually a courtier who exaggerated the kings happiness. The king, Dionysius, allowed Damocles to act as king for a day. The king hung the sword over the throne to demonstrate the constant threats that the king must survive.
When discussing the ropes, they discount the knitter's yarn because the rope used was synthetic. They assume her yarn is wool- not all yarn is wool, some is acrylic (synthetic).