THE POLITICS OF ISLAM.

The scenes have seldom if ever before been equalled in third-world history. They were a phenomenon of such extraordinary impact that they still cause those who experienced them to shake their heads at the memory.

Day after day literally a million or more people packed shoulder-to-shoulder in the capital city of a large, strategic neighbor of the Soviet Union, putting to rout one of the most heavily armed, pro-US rulers on earth with a reiterated roar that made the very streets pulsate:

''ALLAHU AKBAR'' - ''God is greatest.''

Today, five years later, the Islamic revolution in Iran still sends alarm bells through the West and in the East, and divides and electrifies the Muslim world itself.

Quite apart from threats to oil supply lines in the Persian Gulf, and from whether the Kremlin can somehow eventually gain at the West's expense, other basic questions persist:

What elements in Islamic, and especially in Iranian Muslim, thought helped bring about the revolution and sustain it far longer than its critics expected - even in the face of the long war with Iraq?

And might those elements spread to other Muslim countries, with incalculable effects if more mass revolts should break out against secular, Westernized rulers?

The answer to the second question depends, in part, on non-Islamic factors common to the third world: poverty, rapid population growth, mushrooming city slums, too few exports, too many imports, too many debts.

But it also has a great deal to do with a deep and important debate going on among Muslim scholars in a score of countries: What kind of government does Islam permit, or demand?

The debate was one of a number that arose in the wake of the Arab defeat by Israel in 1967. What happened in Iran galvanized it. Events that followed, including the war with Iraq, Muslim rebel resistance to Soviet troops in Afghanistan, chaos in Lebanon, and growing Saudi efforts to oppose Iran, have heated it still more.

The debate is not yet well known in the West.

Both West and East look at the Muslim world as it exists today and see a string of dictators and military rulers from Libya to Sudan to Syria to Pakistan to Indonesia.

More and more, however, those rulers are having to find ways of coping with Islam's appeal to the grass roots, while an increasing number of Muslim thinkers of various kinds - modernist and orthodox alike - stress that in their view, governments based on a lack of popular participation are in fact contrary to the Koran and the sayings and teachings of the Prophet Muhammad.

Iran has intensified the dilemma of Westernized, secular rulers, military men , dictators, and kings around the world of Islam: Should they try to compromise with the force of Islam's appeal (Pakistan, Bangladesh, Sudan, Turkey, Malaysia) or should they pay it little more than lip-service in public affairs (Egypt, Jordan, Morocco, Syria, Iraq, Tunisia, Indonesia, Afghanistan, South Yemen.)

(The House of Saud is unique. It tries to ride two horses at once: rapid Westernization, but internal Islamic orthodoxy accompanied by a massive anti-Iran, pro-Sunni orthodox missionary effort throughout the Muslim world as well as in the United States and Europe.)

''We Muslims are strong in spirit but weak in government,'' a prominent Egyptian says in Cairo. Quickly he asks that his name be withheld, because, he says, he still lacks full confidence in his own country's rule of law.

First - the role of Shia Muslim thought in the Iranian revolution:

Why was the revolution without a conventional strong man or political party? Why did it lack the support of either superpower?

Its timing lay in the Shah's own string of mistakes: his autocratic and Western ways, the brutality of his secret service, corruption, his use of oil wealth in ways that disillusioned rather than fulfilled.

But the bedrock, the form, the words of the revolution lay deep in the Islamic sect known as Shiism, as well as in its development inside Iran since the year 1502, when it became the official faith of the Persian state.

Most of the world's Muslims are Sunni - that is, they follow the Koran (said to be a divine revelation to the Prophet Muhammad) and the hadith (his other sayings and traditions). The hadith, together with accounts of his actions, forms the Sunna, or ''beaten path.''

A small minority - some 80 million in all - accept the Koran but differ somewhat in what they see as the Sunna. They consider that Muhammad's authority - temporal as well as spiritual - descends only through his son-in-law Ali, Ali's sons Hasan and Hussein, and a line of subsequent imams (leaders) numbering 12 in all.

The Shias derive their name from the Arabic words Shi'at Ali, or ''followers of Ali.''

From their belief in him and his sons they acquire two crucial characteristics.

The first: their passion for martyrdom. The second: a politically active caste of religious leaders, whose current chief is said to speak with an authority derived from the divine.

The sense of martyrdom goes back to Hussein, who was killed in AD 680 at the head of a handful of men in battle with a vastly superior force from the Umayyad dynasty, Muslims say.

To the Shia, Hussein is the supreme martyr who symbolizes man's struggle against tyranny: ''Every day in his (a man's) life is a day of battle in which he must seek either triumph or martyrdom,'' according to noted Muslim scholar Hamid Algar, professor of Persian and Islamic studies at the University of California at Berkeley.

Says Professor Hasan Askari, an Indian Shia now teaching at the Center for the Study of Islam in Birmingham, England, ''Shiism is all about protest against authority, passion, constant rebellion.''

Hence so many Iranians, including teen-agers, are apparenty ready to die in the war against Iraq. Hence the Ayatollah Khomeini spent most of his exile in Iraq, at the tombs of Ali and Hussein located there, hence millions of Shias weep and wail in the streets each year in Iran, Iraq, the Gulf, eastern Saudi Arabia, India, and elsewhere to mourn Hussein's death.

Political authority for contemporary imams derives from a belief that the 12 th and last ''true'' imam disappeared from human view in northern Syria in AD 874. He is said to be in ''occultation'' - hidden from view - until he returns to earth at an unknown time in the far distant future.

This is a vital point, Professor Algar has written.

Sunni Muslims also view Islam and politics as combined in individual experience, but see their own imams as outside secular rule. They recognize Muhammad's authority as having descended through the first three caliphs, or rulers, after his death, and only then through Ali, who was officially the fourth.

Thereafter, Sunnis see leadership as having passed into secular hands in dynasties based in Damascus and Baghdad. These dynasties expanded into North Africa, Spain, Turkey, Iran, and eastward to India. They were eventually conquered by Mongols and then Turks. Centuries of decline and European domination followed. In 1924 the caliphate was abolished by Turkey's Mustafa Kemal Ataturk in 1924.

The Sunni tends to accept secular authority - but the Shia does not. To the Shia, Professor Algar says, only the 12th imam has true political as well as ecclesiastical authority. In his absence, the leading Shia figure on earth is his regent.

Secular rule must be illegitimate, Persian Shias say. Only an Islamic state based on the Shariah and ruled in effct by the senior ayatollah (the title means ''sign of God''), will do until the 12th imam returns to earth. For hundreds of years in Persia, Shia imams stood apart from, and critical of, government.

Ayatollah Ruhollah Khomeini began attacking the Shah's Western ways in 1963. He opposed then, and still does, secular American influence (''Satan No. 1'') and the Soviet Union as well (''Satan No. 2'').

When the revolution reached a climax, he had another aspect of Shiism in Iran to fall back on: its network of workers at the grass roots and its sizable funds contributed by the faithful.

Some 180,000 village mosque leaders, all trained in the religious center of Qom, rapidly spread messages from the Ayatollah tape-recorded in Paris and telephoned to Iranian cities.

One other element: Many university students were swayed by the late Ali Shariati, an Iranian with a PhD in sociology from the Sorbonne in Paris who interpreted Islam as an ideology. He argued that Islam had the answers that Marxism and existentialism failed to provide.

Today, pro-Khomeini figures such as the director of the Muslim Institute in Britain, Kalim Saddiqui, break with conventional criticism in the West and point out that Iran has held nine elections and referendums since 1979. The new Majlis , or national assembly, is taking shape.

Islamic law is followed. Banks are to be forced to abandon interest. The bulk of the people still support the revolution, Dr. Saddiqui says, despite Western estimates of an inflation rate well over 25 percent, considerble middle-class unhappiness, and the human and economic drain of the war with Iraq.

''I don't like the way the war is going or what the Revolutionary Guards have done,'' says one traditional Muslim scholar in Cairo, ''but I have to say that Khomeini is devout, sincere, personally unostentatious....''

''Say what you like,'' says a Pakistani diplomat whose country is trying to stay neutral in the war. ''What Iran did was historic: a mass movement instead of a coup, and it worked.''

Charles A. Kimball, director of the Middle East office of the National Council of Churches in New York, says:''One can have reservations about various elements of what's going on, but the majority of Iranians definitely desire to turn away from the West, and the East, and to show that there is an Islamic way in the 20th century.... The revolution is painful and difficult in several ways, but it has vitality, and it's poorly understood in the West....''

On the other side, the conservative sheikh of al-Azhar (mosque and college) in Cairo, one of the most prominent Sunni Muslim leaders in the world, told the Monitor in an interview that Iran should have agreed to a cease-fire years ago. Modernist Islamic scholars agree: Ahmed Shalaby in Cairo was one of many who welcomed the revolution at first but who now see it ''going further and further away from Muslims and from Islam.''

Can the revolution be exported? Or is it merely a Persian, Shia phenomenon that can't even rouse the majority Shias in neighboring Iraq?

Javid an-Sari, general editor of the weekly Arabia magazine published in London, says the Ayatollah has failed to influence Shia communities in other countries such as Iraq (dominated by Saddam Hussein), Saudi Arabia, and the Gulf.

Iraq's Shias, actually in the majority, have been kept in check by Saddam Hussein, who has shot a number for alleged treason and has placated others by building new mosques and appealing to their Iraqi nationalism.

Sunni Saudi Arabia, historically opposed to Persian expansionism as well as being the site of the two holiest places in all of Islam (Mecca and Medina, where the Prophet Muhammad lived), fights the Ayatollah indirectly, through publications, missionaries, and funds abroad.

And yet in the longer term, Iran's impact can hardly be dismissed.

The Muslim world is in sharp and difficult transition from the colonial era to finding its own independent identity. The rule of law is largely absent. One-man rule is the norm, although many Muslims read the Koran as opposing violence or jihad (holy war) except in self-defense.

Muslim countries have too little money, too many people, too few exports, too much hunger. They are much more aware of their own history than is the West - of an Islam that dominated much of the world for 1,000 years until conquered by Mongols, Turks, and Europeans.

The only colonial power still occupying territory is the Soviet Union, in Central Asia. But resentment against the West is still strong. Islam looks increasingly attractive, not only as a personal alternative to Western secularism as well as Eastern atheism, but also as a national identity and culture.

The events in Iran have led to confident statements like this one made by Dr. Saddiqui:

''Talk to the bus drivers and the rickshaw pullers in the Muslim world, Shia and Sunni alike, and you'll find that they approve of what Khomeini has done in Iran.... They feel that Westernized elitist rulers have to go, in Saudi Arabia, the Gulf, Jordan, Iraq, Morocco, Indonesia, Sudan, Turkey, Somalia, and elsewhere.

''Iran now defines itself in Islamic terms.... Its frontiers are not physical but Islamic.... National boundary lines are artificial.... I don't know where the new revolutions will be, or when, but they are coming, some within the next 10 years.''

Many in the West would scoff. While interest in the forms and principles of Islam appears to be reviving in a number of prominent Muslim countries, it currently stops far short of following the Ayatollah Khomeini to the barricades.

In the long term, however, it remains very much an open question whether Islam, brought by Iran so dramatically front and center in world thought, might indeed provide the form, the language, the intensity, and the commitment to harness crowded, poor, urbanized post-colonial Muslim third-world grievances into significant revolt.

''Not only Arab states are worried that the idea of mass, representative government might spread,'' says Charles Kimball in New York, ''but many Latin Americans, too, look to Iran as an example of a popularly based revolt against a heavily armed ruler.''

Muslims are today arguing vehemently whether Islam calls for one-man, one-vote democracy, other forms of participation, or socialism. Almost all emphatically reject communism because it is atheist. Most define Islam as socialistic rather than socialist because it stresses an equitable division of wealth from rich to poor in accordance with Islamic law (Shariah).

Modernist Muslims see the Koran calling for Western-style human rights and the rule of law.

Reformists see a unique kind of Islamic government built around a strong central leader advised by a learned council and bound by the Shariah.

Radical fundamentalists turn to rejection and violence.

Thanks largely to Iran, the debate is not cooling, but heating up.