After last week's visit to Croke Park by Queen Elizabeth and Prince Philip, the sight of the US president swinging a hurley this morning wasn't all that surprising. Barack Obama is the offspring of a mother from Kansas and a father from Kenya – neither of which is a hurling stronghold – but, like almost all modern US presidents, he has made a claim to Irish ancestry.

And so he today made his way to Moneygall, County Offaly, to pay tribute at the ancestral pile, which one ancestor, Falmouth Kearney, apparently left in 1850.

Ever since Kennedy, we almost expect a president to be a bit Irish. The last election campaign was a particularly good one for the Irish, with both Republican and Democrat candidates claiming Irish ancestry (leading to one ludicrous article in Prospect magazine that suggested that John McCain's Scots-Irish temperament could make him unsuitable for the job).

There is a question as to why, post-peace process, this type of thing still goes on. While Irish Americans tended to be vocal (and financially generous) in their support for republicans during the Troubles, it made sense for US politicians to claim a personal investment in the island.

But even now, with Northern Ireland functioning in relative peace, the love-in continues. Successive taoisigh still travel to the US for St Patrick's Day to present the president with a shamrock.

It's actually appropriate that the head of the government should be in the US on our national day – the first St Patrick's Day parade took place in north America, and the incarnation of the day as one of drinking, wacky hats and plastic bodhrans is largely an invention of the Irish American diaspora – as is much of Irish national identity.

Playwright Martin McDonagh (himself London Irish), memorably deals with this conundrum in the Cripple of Inishmaan, set during Robert J Flaherty's filming of Man of Aran.

The Aran islanders of the play continuously refer to "Irish" traits – talkativeness, friendliness – as dictated to them by the Irish Americans making the film: the choice of Man of Aran as a backdrop is significant. Flaherty, while marketing the film as a documentary on a way of life, in fact staged several scenes (as he had with his previous film, Nanook of the North), and even cast as a family islanders who were unrelated.

Irishness is a more diasporic identity than we care to admit: the amiable, rural Irish idyll that emerged in the late 19th and early 20th centuries had its genesis in London and New York. Upper class cultural revivalists such as WB Yeats in London, and first generation emigrants from the west of Ireland in the US, knowing they were unlikely to return, created an Ireland of the mind, green and welcoming and ancient. So embedded has this notion become that by 1943 (Irish American) Eamon de Valera practically made its attainment state policy with his St Patrick's Day address envisioning:

"A land whose countryside would be bright with cosy homesteads, whose fields and villages would be joyous with the sounds of industry, with the romping of sturdy children, the contest of athletic youths and the laughter of happy maidens, whose firesides would be forums for the wisdom of serene old age. The home, in short, of a people living the life that God desires that men should live."

A nation rendered as a Tin Pan Alley ballad.

Irishness is a shared creation, a project we've all had a hand in. As president of a country made up of diasporas, it may not merely be electioneering that leads Obama to Offaly, but something deep and genuine. We're part of them, and they're part of us.