Earlier this month, 1,000 nationalists - although their spokesman claimed they are not nationalists - signed an open letter to the Taoiseach, Leo Varadkar, calling on the Irish Government to set up a "citizens assembly" to discuss reunification.
In an advertisement listing the signatures in The Irish Times, they claimed: "Discussion about reunification of Ireland has moved centre stage. Many citizens are already involved in formal and informal discussions about this ... In recent years, a conversation about Ireland's future and the place of unionists in it is publicly taking place among unionists. This is a welcome development."
I contacted several prominent liberal unionists I know to ask them if they had ever heard of this public conversation. None of them had.
In the article accompanying the advertisement, the spokesman for the group (which calls itself "Ireland's Future"), Belfast solicitor Niall Murphy, clarifies that it is actually not a public conversation at all.
Privately, these conversations are happening, he says, "and whereas there might not be the confidence to articulate that out loud yet, we need to create a space where that can be done sensitively and constructively".
I talk to unionists and loyalists regularly and I'm pretty certain that no significant group of them are talking about unity. However, for the sake of argument, let us imagine what such a conversation might look like at the moment...
Nationalist: Let's start a conversation about Irish unity. "Ultimately, in a new Ireland, unionism is going to be there, they're our neighbours, they own this place, too, and they need to be accommodated. I would like to hear a warm embrace for the unionist tradition in an all-island constitutional entity." (These were Niall Murphy's exact words in his Irish Times interview.)
Unionist: But I don't want to talk about an all-island constitutional entity. That would be my worst nightmare. That is what I, my father and my grandfather have been fighting - politically and, occasionally, taking up arms - to prevent for the past 100 years and more.
Nationalist: But after Brexit - with its 56% vote for staying in the EU - and with Catholics probably becoming the largest social group in the 2021 northern census, you're going to have to start talking about the constitutional future of the north of Ireland some time soon.
Unionist: Talking about the constitutional future of Northern Ireland is one thing. But your language about embracing "the unionist tradition in an all-island constitutional entity" sounds to me like you have already decided the outcome of our conversation - and it is a unitary, all-Ireland state. Is "an all-island constitutional entity" the only future option for unionists, in your view?
Nationalist: It could be a federal Ireland with powers in the north devolved from Dublin to a Stormont-type Assembly and Executive, as is done presently from London under the Good Friday Agreement.
Unionist: But does it have to be solely within an all-Ireland framework? Why couldn't it be the continuation of Northern Ireland remaining part of the UK, with a power-sharing government in Belfast and a significant Irish dimension, as at present?
Nationalist: No - that won't work. The power-sharing Executive was shown to be unworkable, largely because of the arrogance, bigotry and corruption of the DUP, and the refusal of the British Government to confront them, because they needed their votes in Westminster. We have to move towards an all-island solution.
Republican: And, anyway, the northern state was always illegitimate, because it was carved out undemocratically after Ireland as a whole voted for independence in the 1918 election. It then systematically oppressed and discriminated against northern nationalists.
Unionist: I'm not going to talk to you. Your IRA killed members of my family in the Enniskillen and other bombings. After that, I want nothing to do with your hypocritical, self-serving arguments. Until you express remorse for the murderous campaign of the IRA, I won't be discussing anything with you, let alone the constitutional future of Northern Ireland.
And, anyway, what makes you think that a 50%+1 vote in a border poll for unity, leading to a large, alienated unionist minority in a so-called "united" Ireland, is going to make for a stable society anymore than a large, alienated nationalist minority did in Northern Ireland?
Nationalist: The probable break-up of the UK after Brexit (with Scotland voting eventually for independence) means you are going to have to talk about some form of Irish unity one of these days.
British politicians and people have made it clear they do not want you to be part of the future United Kingdom.
In a YouGov poll last month, more than four out of 10 British people questioned said they would not be concerned if the north of Ireland left the UK and a majority of both Leave and Remain voters said they would rather have their preferred Brexit outcome than see the north stay in the UK.
Unionist: I see very little sign of people south of the border saying they want us, the unionists, in their cosy little state.
Yet you're asking me to give up my country, the place where my home is, the place I feel I belong. What would your response be if I demanded that you gave up your country?
Nationalist: The two questions are not comparable. You are part of the Irish nation and always have been, whether you like it or not.
This island has been divided for too long by the British. In Wolfe Tone's words, it is time to substitute "the common name of Irishman [and Irishwoman] in place of the denominations of Protestant, Catholic and Dissenter".
We will do our best to be generous to you in a united Ireland, changing our symbols - our flag, anthem and constitution - to accommodate you.
Unionist: It seems to me that this is not an equal conversation at all. You are demanding that I sign up to an all-Ireland state, which is against everything I stand for.
All you are prepared to discuss and negotiate is the form of that all-Ireland state.
You are not prepared to discuss any kind of compromise short of that: something that would see both you and I suffering some pain for the sake of peace and reconciliation on this island, ie some in-between outcome which sees you postponing your dream of constitutional unity in return for me agreeing to reduce my 100% adherence to the United Kingdom.
Moderate unionist and moderate nationalist together: It's a pity you didn't think about that when you supported the UK leaving the EU. Until the 2016 Brexit referendum, we were precisely in that in-between territory, the Good Friday Agreement and the Single European Market allowing us to move towards a kind of economic unity while the constitutional forms remained essentially the same.
Extreme unionist: I want to make clear that, in the event of a 50%+1 vote for Irish unity, we will do all in our power (including the use of force) to prevent that happening in the areas we control.
Republican: And I want to make clear that, if a majority, however slim, votes in favour of unity in a border poll, we will do all in our power (including the use of force) to implement that democratic decision.
US facilitator: I think we should stop there. We are not getting anywhere with this line of argument. It seems to me that far from being a "new conversation", this is turning into the traditional dialogue of the deaf.
Andy Pollak was the founding director of the Centre for Cross Border Studies