Smith conceived the song on board the ill-fated Italian cruise ship Costa Concordia during a trip she took with her guitarist Lenny Kaye in 2009. The singer-songwriter was asked by French auteur Jean-Luc Godard to appear in his movie Film Socialisme
and the film was partly set on the ship that two years later would hit the news headlines after it sank off the coast of Tuscany. The two musicians were scarcely used by Goddard, and spent their time sitting in the sun, reading and sketching out songs. "We went to Egypt, Cyprus and Turkey," remembered Smith to The Sun
. "It was quite a cruise despite the fact I had to hear everyone singing 'Volare
' all night. We wrote 'Seneca' and formed the ideas for 'Amerigo' during that time.