We were never told what David Cameron gave Aung San Suu Kyi for lunch at Chequers. But we do know what the Queen was offered the day she shook hands with the former IRA leader Martin McGuinness. The traditional Irish menu concluded with a sweet honeycomb toffee, known in Ireland as yellow man.
It was bold of McGuinness to have allowed that. Yellow man is the kind of abusive nickname with which he might be labelled by the three hardline dissident Republican groups who on Friday announced that they were merging to re-form the IRA. It was a clear attempt to undermine the power-sharing government in which McGuinness has become deputy First Minister. This new IRA criticised the Good Friday peace agreement negotiated by McGuinness and Sinn Fein, saying "the Irish people have been sold a phoney peace, rubber-stamped by a token legislature in Stormont". Such are the perils of Sinn Fein's retreat from the purity of armed struggle into the messy reality of day-to-day politics.
Something similar is happening now to Aung San Suu Kyi, the woman who became a global symbol of human rights through almost a quarter of a century of imprisonment. The high expectations her heroism created now seem unsustainable as she makes the transition from long-term political prisoner to an agent of change in Burma's reform process.
Suu Kyi is facing a backlash from campaigners dismayed at her silence over the plight of the 800,000 Rohingya, whom the United Nations describes as one of the world's most persecuted minorities. In her first parliamentary speech last week, she called for laws to protect the rights of minorities. But many previous supporters criticised her for not mentioning the Rohingya by name.
Being locked up in house arrest, or locked into the certainties of armed struggle, was, in a perverse way, easier for Sui Kyi and McGuinness alike. Principled opposition is a lot less complicated than mainstream politics. But the latter is no less risky. At the back of McGuinness's mind must be the example of Michael Collins, the leader of the IRA in its war against Britain, who went to London to negotiate the treaty on Irish independence and was murdered by hardline republicans.
Real politics is a delicate balancing act, as McGuinness has shown. He followed his royal handshake with a strong attack on David Cameron for failing to move the peace process forward. He was backed by First Minister Peter Robinson, the Unionist leader, who also wants McGuinness investigated for his part in the Bloody Sunday killings.
A similar complexity embroils the heroine of Burma. The majority of ethnic Burmese are Buddhists, and many deeply resent the steady influx of the Muslim Rohingya from Bangladesh. Some critics have accused Suu Kyi of sharing that resentment; others say she does not want to alienate the majority community as the next presidential election approaches. "One has to be suspicious or concerned about what her views are," said Brad Adams, the Asia director of Human Rights Watch.
These are ignoble accusations against a woman who walked, alone and unarmed, directly toward the guns of a military junta. The criticism of both her and Martin McGuinness misunderstands the true nature of the accommodation which is an essential part of mainline politics.
Compromise is not necessarily about sacrificing principle; it can be about timing and the order in which things are done. Politics is the art of the possible because it understands the psychology of process, not just outcome. Adroit politicians must be good listeners if they are to find ways to reach agreements with opponents. Compromise is about forfeiting interests rather than ideals; it is not about dirty deals, but it is essential to the proper functioning of a democracy.
And it can demand more courage than the easy self-righteousness of opposition. The great heroes of our times – Nelson Mandela, Vaclav Havel and Aung San Suu Kyi – have all been brave. They have all shown a magnanimity characterised by an extraordinary lack of bitterness. And they have all been shrewd political pragmatists. "I strive to be as practical as my father was," Suu Kyi told the British Parliament, recalling that when a British general accused him of switching from the Japanese to the British side during the Second World War because the British were winning, he replied, "It wouldn't be much good coming to you if you weren't, would it?"
There will be many who would not want to place Martin McGuinness in such company, but there can be no doubt of his courage nor the prescience of his vision. Shaking hands with the Queen was a deliberate and symbolic way of offering the hand of friendship to all the unionists of Ulster. "We now operate in a new context," he said. "Dialogue has replaced conflict. Respect has replaced mistrust."
For that to increase, in Ireland and Burma alike, requires new thinking, new ideas and the dawn of new political realities. And that will mean further compromise.