When is an Iranian also an Arab? When is an Iraqi not an Iraqi? Why do both Iranians and Iraqis trade accusations that the other is working for "US imperialism"?
The answers to these paradoxes underlay the recent dramatic siege in London where six Iranian Arabs seized the Iranian Embassy for several days, killing two hostages before British paratroopers regained control.
These paradoxes also underlie the growing tension along the 800-mile border between Iran and Iraq, and especially the growing ferment in the border's southern stretches, where it cuts through some of the world's richest oil-producing terrain.
Since the oil-producing regions of Kuwait and Saudi Arabia are not far from this nexus, the ideological ferment there could be of considerable importance to the West.
What seems to be happening is that the previous regional balance has been swept away, along with the Shah's peacock throne. Thus, the peoples of the region are seeking new opportunities to define and express their identities.
They are doing so, moreover, in a time when most nationalist Arab ideologies have been shown up as incapable of solving the vast problems facing the Arab world.
* The "Arab unity" proclaimed by populist Nasserites in Egypt and more conspiratorial Baathists in Syria or Iraq has proved to be a chimera when regimes following these ideologies have come to power.
* the "socialism" that was an essential part of the post-World War II ideologies usually has ended up with privileged political elites opening up their countries to private Western enterprise. Only in Iraq (and tiny, Marxist South Yemen) is there any continuing stress on developing the public sector.
* The secularism that was a banner for all the original ideologies when they first contested control with religious-dominated parties has given way in most cases to a policy of making concessions to religious interests emboldened by the new Islamic revival.
In both Egypt and Syria recent legislation has sought to strengthen Islamic customs, while even the sternly secularist Iraqis will admit that "we were wrong to ignore the contribution of Islam to the Arab culture."
* And, of course, the ideologies have proved themselves unable to solve the Arab-Israeli problem, which continues to eat up vast Arab (as well as Israeli) resources and appears as closely linked as ever to the stability of the whole region.
What is left, along a Fertile Crescent largely disillusioned with the traditional "Arabist" ideologies, are three major discernible alternatives (since Soviet communism does not seem to have much hold):
The peoples of the region may seek stability by looking to traditional Arab leaders, such as the Saudis of Saudi Arabia or the Hashemites of Jordan. They would do this as in ever greater numbers they leave their traditional roles in agriculture or small-scale manufacture for integration into the economic boom sweeping the region.
Or they can seek inspriration from the experiments in Islamic rule being tried out in nearby Iran.
Or they can work and wait quietly, as many of the educated class seem to be doing, for some new form of genuine democracy to gain real roots in the region.
But in the meantime, the peoples living round the northern end of the Persian Gulf have had to start asking themselves some very searching questions.
Those on the arid Iranian side of the border are mainly ethnic Arabs, who traditionally have railed against rule by the Persians of Tehran, Iran -- but who share with them their Shia Muslim faith.
So for them, is it more important to be Arab, to be part of the Iranian conglomerate, or to be Shiite? At least ten of the Iranian Arab prisoners whose release was demanded by the gunmen in London were reported to have petitioned against being released. Did this mean they were supporters of Ayatollah Ruhollah Khomeini?
Meanwhile, those living over the border in Iraq in the humid, baking south of the country are nearly all Shiites. They share a nominal Arab ethnic affiliation with their rulers in Baghdad, but not, it sometimes seems, very much else.
For them, again, is it more important to be Shiites, to be Arabs, or to be part of the Iraqi conglomerate, which also includes sizable numbers of non-Arab Kurds?
There are no easy answers to these questions. Different institutions on each side of the border compete to provide different answers.
The Shiites, whose traditions include respect for some democratic forms and creative interpretation of doctrine, maintain their own elaborate community organizations and institutions on both sides of the border. These include a network of community centers where discussion is encouraged, called the husseiniyehs, and a widely respected system of community taxes.
In Iran, these institutions are backed up by the embryo Islamic republic in trying to persuade people that their Islam should be their basic expression of identity. Ayatollah Khomeini has, indeed, gone further than saying his revolution is for all Shiites, but says it is for all muslims, wherever they are , and whether they are Shiite or more orthodox Sunnite Muslims.
In Iraq, meanwhile, the Baathist state apparatus and educational system try to persuade people, and especially the 65 percent of the population which is Shiite, that it is more important to be Arab (and specifically Baathist) than to be any kind of Muslim. The state apparatus in Baghdad is dominated by Baathists from the narrow layer of Sunni Arabs who live just north of Baghdad, who thus have some interest in seeing their argument accepted.
The official Iraqi media play up historical differences between the Arabs and Persians, referring to the regime in Tehran as "those Persian mobsters."
So the struggle for hearts and minds continues. It is most visible right now in Iraq and Iran because of the problems between those two societies.
But a similar struggle is also going on, in a lower key, in Saudi Arabia and the other oil-rich states of the Gulf. there the message of Islam has a direct impact hard to conceive in Western terms and substantial numbers of Shiites leaven the existing politico-religious equation.
So the future of the Gulf region ultimately may depend on a few thousand key thinkers in the lands around the upper Gulf working out their own answers to that age-old question:
Who am I?