The government of Myanmar (Burma) rejects any suggestion that they are its responsibility. The Rohingya, it claims, are not an indigenous people of Burma, but Bengali Muslims who migrated from neighbouring Bangladesh. The government of Bangladesh insists they are not Bangladeshi citizens either.
Indeed, the people calling themselves Rohingya are most likely the descendants of an early generation of Bengalis that the British brought to Burma from India during the colonial era.
The natural flow of people across the border would have swollen their numbers over the years, making it impossible to tell who is a recent migrant and who is a longtime settler. In any event, to the Burmese people, they are all the same. They are unwelcome guests in their land, and not entitled to Myanmar citizenship. This blatant racial discrimination calls attention to the fact that the Rohingya are not sprung from the same Mongoloid racial stock and are not Buddhist as most Burmese people are.
This was not an issue at all in the age of empire, when different races professing different religions and speaking different tongues lived peacefully among one another under the distant rule of the sovereign. But the rise of the modern nation-state, which fused language, ethnicity and culture in the "imagined community", changed the rules of the game.
Not every ethnic community in the postcolonial era was capable of forming a nation-state. Those that could not be assimilated into the dominant national community found themselves waging a futile struggle for self-determination, or leaving their homeland to escape genocide.
During the 1947 partition of the Indian subcontinent, the homeland of the Bengali people became part of East Pakistan, separated from West Pakistan by 1,400 kilometres of Indian territory. Bengali nationalist agitation led to independence from Pakistan in 1971 and to the formation of what is today known as Bangladesh.
With an estimated population of 160 million, Bangladesh is today the world's eighth most populous country. It is mostly hemmed in by India, its big neighbour, but it shares a border with Burma to its southeast. After the establishment of modern Bangladesh, the Rohingya remained in Arakan, now part of the Rakhine State in northwestern Burma.
In 1978, sectarian violence and Burmese military operations aimed against them forced many Rohingya to flee to Bangladesh.
The intermittent violence flared up again in 1991, driving them out of Arakan to seek new lives abroad, mostly as workers in the Middle East. In 2012, the unending exodus of the persecuted Rohingya came to a head, prompting the Bangladeshi government to close its borders. Those who make it across the border are detained in refugee camps in Bangladesh, Burma, or Thailand-where they are held as stateless persons.
The more than 6,000 boat people who cast out to sea at the beginning of 2015 have come mainly from these refugee camps.
The word "Rohingya" is clearly a self-description. The Rohingya consider themselves a minority group that has lived in Burma's Arakan Valley for generations. Refusing to be labelled Bengali Muslims, they insist they are not illegal migrants from Bangladesh.
Indeed, this self-identity appears to have become a crucial element in the current campaign for global humanitarian intervention on their behalf. These are people who are not just escaping from poverty but are being oppressed and prevented from pursuing normal lives in their country of origin. As victims of state-sponsored exclusion, they are covered by the existing international convention on refugees.
There is, however, a small complicating factor. Not everyone in those refugee boats that have drifted for months on the Andaman Sea and the Malacca Straits and recently landed in Aceh, Indonesia, and in the Malaysian resort island of Langkawi, is a Rohingya.
One report says that about half of them were, in fact, young Bangladeshis who have hitched their hopes for a better life abroad to the global sympathy and attention that the Rohingya cause has generated. This has been a source of conflict.
The presence of Bangladeshis in these boats has reinforced the Burmese argument that these are not their people. Deadly clashes over dwindling supplies of food and water between the Bangladeshis and the Rohingya sharing these boats have been reported.
One can imagine the horrific situation aboard those boats-people killing one another over food and water as they drift aimlessly on the open sea, enacting a scene from a barbaric and brutal age.
Those who sympathise with the Rohingya may feel differently about the Bangladeshis. The former are refugees from political persecution, while the latter are at best economic refugees. In an ideal world, that distinction should perhaps not be made at all.
But in a world of nation-states, where the principal responsibility for a nation's citizens lies with their government, it is reasonable to ask whose nationals these refugees are. If no government will acknowledge the Rohingya, then they become the charge of the whole international community.
The Philippines has recently signalled its readiness to take in its share of these boat people-a noble humanitarian gesture that puts to shame every nation that has ever pushed out boats laden with starving refugees back to sea.
But, this is a problem that no single country can realistically address by itself.
Having taken a bold moral position on this question, we now have to look for a sustainable solution within the ASEAN framework of co-operation, or, failing this, within the United Nations.