Just a few years ago it would have seemed ridiculous to think of a British prime minister and the leader of the Irish republican movement having anything in common, or having any real personal relationship.
But listening to Gerry Adams, it is clear that a bond of sorts has been forged between the Sinn Fein leadership and Tony Blair, between the Falls Road and Downing Street.
A united Ireland is certainly not the goal of Mr Blair, while for Mr Adams it certainly is. And the Prime Minister, as he spelt out in his keynote Belfast speech last week, also wants the IRA to shuffle off the stage and become part of history.
The IRA was swift to chide Mr Blair for making "unrealistic demands" and Mr Adams shows no signs of departing from that position.
But the Prime Minister also made a point of commending the republican leader for trying to make the Good Friday Agreement work, and for taking "huge risks to try to bury the past". And the Sinn Fein president, in his initial reaction to the Blair speech, prefaces his remarks with praise for the Prime Minister: "Mr Blair has made a singular and exceptional contribution to the process. He understands as well as I do that it is a process, and that all of us need to apply ourselves and see beyond the difficulties of the moment. I have found that one of the qualities that he has brought has been his ability to think outside the frame and to appreciate the difficulties facing the different constituencies to this."
Yet there is clearly a monumental gap between the Adams view, which is that the IRA helped start the peace process and has helped keep it alive, and the Blair view, that the IRA's day has gone.
The Sinn Fein leader reports anger in republican ranks. "Whatever the content of the speech, the reality is that very few people will read the entire text. So people will make their minds up on the spin that is put on it, either by the media or the spin from the British themselves.
"I could imagine many republicans will just pick up the spin – I think that's regrettable and that will make our management of this a little bit more difficult.
"They will see, at a time of crisis, that ultimatums are made and they are aimed at republicans, while the British Government itself doesn't fulfil its obligations, and appears to have a different attitude towards the activities of its own forces and those of the Unionist paramilitaries.
"There's palpable anger – the anger wasn't just at the speech, it was that it came in the week of the suspension of the institutions.
"Allied to the anger there will be a grave disappointment at Mr Blair in some republican quarters, because they looked to him to be different, because he did have a different attitude, a different approach."
One of the Blair-Adams points of accord is that, battered though it may be, the Good Friday Agreement remains the only show in town. The suspension of its centrepiece, the Belfast Assembly and its power-sharing executive, came last week. No one is sure when, or even whether, the whole thing can be put together again.
With David Trimble about to pull his Ulster Unionist ministers out of the administration, the Government moved with evident regret to mothball the devolved government for the moment.
Mr Adams is highly critical of the move, arguing suspen-sion is outside the terms of the Agreement and thus undermines it. But what else could the Government have done to give things as soft a landing as possible? "If the Unionists wanted to walk out – and I don't think they should have – they should have been allowed to walk out," he maintains.
The argument here is that Unionists were wrong to leave government and that the British were wrong in facilitating them. The problem for republicans, however, is that most of the blame for the executive's downfall has been heaped on the IRA.
So what about the lengthy charge-sheet against the IRA – the break-in at Castlereagh Special Branch offices, the consorting with narco-terrorists in Colombia, the political spying at Stormont? The Prime Minister did not list these, but it was clearly continuing IRA activities which brought him to insist the organisation must now disappear, since otherwise there is little or no chance of building a new devolved coalition.
Mr Adams pauses before giving a considered answer, one which dwells on the general rather than the specific.
"We've had such a ferocious, consistent, relentless campaign, with such huge publicity around all of these allegations. So when the likes of me comes on, and almost being in a perpetual state of denying all of this, I'm very conscious that we can be accused of being in denial.
"One thing I can say assertively and definitively is that all of these matters are allegations, that none of them involves Sinn Fein. That – unlike the Unionist paramilitaries and indeed the British forces – the IRA cessation remains intact." His central argument is that the overall situation is far better than it has been for decades. He adds: "Mr Blair drew attention to the unacceptable number of deaths, but he compared the death toll this year to the far larger tolls over the past 30 years.
"That's all to the good, and I think that as we continue with the process we're going to continue to make that type of progress.
"Let's just be realistic about this – it might not be a perfect process, it may not even be a perfect peace, but it's a lot better than what's happening in the Middle East; and it's a lot better than what was happening in the North of Ireland over a long period.
"I would assert, I think without fear of contradiction, that 20 years ago, had we been able to spell out to people the possibilities that we now have and the progress that we have now achieved, people would have been grasping it with both hands. In fact it might not have been believed, at a time that we were told that all of this was intractable."
However, in addition to the gap between republicanism and the British Government, there is also a yawning chasm between Sinn Fein and Unionists, most of whom, according to opinion polls, do not want to go back into government with republicans.
Mr Adams gives his analysis: "One section of Unionism wants this Agreement to work, but its view is not represented anywhere within political Unionism.
"Then there is the quite fundamentally negative position of the [Rev Ian Paisley's] Democratic Unionist Party, which is against this Agreement and wants it to fail. It has set its face against the Agreement because it's against the process of change that it involves. And then you have an element of that attitude within the Ulster Unionists, and they don't trust the leader, David Trimble. But he has now moved hook, line and sinker into their camp."
Relations with Unionism are bad enough at the moment, but what if the polls are correct in suggesting that Mr Paisley could actually overtake Mr Trimble? "Nobody really knows," says Mr Adams, "but any Unionist in leadership will have to face up the same challenges. Whatever happens within Unionism it will have to do business with the rest of us – and that includes doing business with Sinn Fein."
The peace process clearly faces some daunting challenges ahead. There may be some element of trust between Mr Adams and Mr Blair but there is none between republicanism and Unionism and the idea of IRA disbandment is hugely problematic.
Tremendously difficult negotiations clearly lie ahead, with no obvious basis for compromise in sight. Can the crisis be overcome? "It's at times like this that I think of the old adage of the optimism of the will asserting itself over the pessimism of the intellect," Mr Adams replies.
"The progress that has been made this far has been remarkable, but all of this is work in hand, and all of this is work which has to be brought to completion right across all of the outstanding and unfinished items.
"All I can say is that you have to keep picking yourself up. I'm not just somebody who goes around with some naïve sense that destiny will prevail in all of these matters.
"It does require an awful lot of hard work. It is very daunting, it is very testing and it is very challenging, but we cannot afford to go back to where we have come from.
"We have seen what is possible. It may every so often slip out of our grasp, but we have seen that it is possible. We just have to keep going back at it and be dogged and determined."
"None of this is intractable – all of this can be sorted out. It might take time, it might take a bit of collective management and a bit of patience and a lot of tenacity, but it can all be sorted out."
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