The Irish ancestry of Anna Patterson's husband Tom Costello sparked the name Cuil, which the company states is taken from a series of Celtic folklore stories involving a character, Fionn mac Cumhaill, they erroneously refer to as Finn MacCuil .
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The ensemble and the three main characters are introduced during the surreal prologue: Finn McCool (a non-dancing role played by Tony Kemp), high king of Ireland; Diarmuid (Colin Dunne), captain of the Fianna—Finn's army; and Grania (Jean Butler), Finn's betrothed.
She is one of the central figures in the Middle Irish text Finn and Gráinne and most famously, in the 17th-century tale The Pursuit of Diarmuid and Gráinne, which tells of her betrothal to Fionn mac Cumhaill, leader of the Fianna, and her subsequent elopement with Fionn's warrior Diarmuid Ua Duibhne.
In the play, a number of writers, historic, literary or public figures, and scientists are mentioned to illustrate O’Nolan’s colorful and over-populated universe, such as Marcel Proust, Oscar Wilde, Graham Greene, James Joyce, Fionn mac Cumhaill, Harry Rowohlt, Homer, Jonathan Swift, George Bernhard Shaw, the Marx Brothers, Brendan Behan, Éamon de Valera, Karl Kraus, Sherlock Holmes, and Erwin Schrödinger.
The area is heavy with legend, the name itself is supposed to have originated, when Fionn mac Cumhaill finally obtained justice by killing Goll mac Morna, the slayer of his father.