"He collected about 4,000 vessels"
The Bay of Baiae
Public DomainThe Bay of Baiae - Credit: JMW Turner

Graves's account of Caligula's construction of a bridge across the Bay of Baiae is based partly on Suetonius's The Twelve Caesars and partly on Cassius Dio's Roman History. Suetonius's suggestion that Caligula thought this idea up "to outdo Xerxes, who excited much admiration when he threw a bridge over the rather more narrow Hellespont" seems like a deliberate spoiler, given the fact that Xerxes, far from being admired for his action, became one of the stock-examples of hubris (for example, in Aeschylus's The Persians). 

Graves's Claudius suggests that Caligula's real motivation was rather Thrassylus's prophecy (that Caligula was no more likely to rule the Empire than he was to cross the Bay of Baiae on a horse). Nonetheless he has him laughing at Xerxes, and berating the god Neptune as a coward, promising "to teach the old god an even sharper lesson" some time soon.