Yeats was capable of taking the long view of history. He uses the image of the gyre, a coil that continues to expand outward, as a symbol of the fragmentation of society. Also, he conceives of the "twenty centuries" since the birth of Christ as merely one night of "stony sleep." He thought that present events were always deeply rooted in the past, whether people realized it or not. Finally, he believed that great visionaries, like poets, had access to the entire communal memory of the human race through something called Spiritus Mundi, the world of the spirit. The vision that the speaker of the poem has in the second stanza is said to arise from the mystical connection to this collective "storage room," as it were, of eternal symbols.
If the falcon in the poem is a symbol of present-day society, then Yeats thinks Europe can no longer recognize the traditions that formed the "centre" of his own history.