A woman in Riyadh, Saudi Arabia, may not drive a car. She may not hold a job. She is not supposed to travel anywhere without a male member of her family. She does not appear in public without an enveloping, floor-length black robe and a black veil pulled over her head (to comply with the Koran's injunction that women must be modest in public and avoid what one scholar calls ''the lustful glances of men'').

And several times a day, every day, streets are patrolled by bearded men belonging to Committees for the Propagation of Virtue and the Suppression of Vice. They tap on shop-fronts with canes, closing them down completely for ritual Islamic prayers.

From facts like these, Westerners assume that women generally in Islam are second-class citizens, and that Islam is based on 7th century practices with little relevance to the modern world.

Add a sketchy knowledge of the Shariah punishments (Islamic law based on the Koran, tradition, and jurisprudence which includes death for a married person proved to have committed adultery and the loss of a hand for theft). Throw in the Western belief that Muslim men have the automatic right to marry four women each, and distaste for Muslim customs is deepened.

The distaste reinforces the veil that prevents the West from fully understanding the way the Muslim world thinks, at a time when that world includes 70 countries and some 800 million people from Morocco to Indonesia, all searching with increasing restlessness for their own third-world identities.

Yet the Koranic and Shariah picture is not nearly so simple as it might seem from a distance:

* Muslim women across the Red Sea from Saudi Arabia in Egypt walk freely and unveiled. They follow a more liberal interpretation of the Koran, which says that a woman may maintain a modest appearance by covering shoulders, arms, and legs. So do women eastward across the Persian Gulf in Pakistan, especially in cosmopolitan Karachi. There, evidence of change includes a woman instructing pilots for the national airline, and 400 neatly uniformed girls at just one government vocational school repairing television sets, designing apartment blocks, and rewiring electric motors.

* The Koran itself says nothing about the veil and portrays women as equal with men in the sight of Allah. But it does urge women to be modest and sees them in roles different from men's. Cultural and tribal customs seclude many women in the name of Islam, while other traditions do not.

In Indonesia, for example, which is more than 90 percent Muslim, women are unveiled. (One area of West Sumatra is matriarchal.) The Islam that has emerged in Indonesia is of the moderate Shafi school, very different from the more conservative Islam in Saudi Arabia and Pakistan.

* Women in Pakistan are expected to offer their daily prayers at home and many smaller mosques don't provide places for women on Friday (the Muslim Sabbath). Women attend mosque in Egypt and in Indonesia, though they sit separately from men.

* Western-educated women in the Islamic world seem happy enough to be back in the Islamic world. Some say they accept its rules as a small price to pay for leaving behind the emphasis on feminine allure in much of the West's advertising , dress, entertainment, and behavior. Others prefer the freedoms of the West.

''I choose to veil my hair and wear Islamic dress (covering shoulders, arms, and legs),'' said Nadia, the daughter of an Islamic scholar in Cairo. ''I don't feel restricted. If I want my own way, I can get it in discussions with my father and brother.''

In an elegant pink Pakistani outfit in Islamabad, Oxford-educated Rehana Hyder said: ''Things are changing in Pakistan. Women are certainly freer.'' She herself has a good job with the local United Nations office. One restriction: no dates with young men. ''Our society wouldn't understand,'' she said.

* Neither the Koran nor the Shariah gives any automatic right to marry more than once, to amputate a thief's hand, or to kill an adulterer.

At a time when wars meant that women outnumbered men in Mecca and Medina, the Koran said a man could marry up to four women - provided he treated each with equal fairness. In one view, the aim of the central Koranic verse on the subject is to protect orphans.

In some countries, polygamy is banned by civil law unless the first wife gives permission. Muslim scholars point to another Koranic verse as virtually forbidding more than one wife because it says a man cannot be equal to all his wives, be he ''ever so eager.''

A man is still permitted by the Shariah to divorce by simple proclamation, but in Pakistan the local government council must be given the chance to reconcile the couple first. Some other countries have placed similar obstacles in a man's path: Tunisia has banned divorce by proclamation altogether. Women also have the right to seek divorce, though they must use special Shariah courts.

Devout Muslims also know that the Prophet Muhammad is reported to have said that of all actions permitted by Allah, divorce is the least acceptable.

Family ties are not weak but extremely strong in Islam.

As for adultery and theft, such stringent proof is required that the death penalty, amputation, and flogging are now rare in many countries.

Neither Egypt nor Pakistan has seen such punishments in recent history, but they do take place in Saudi Arabia. (Saudi Princess Misha was shot for adultery in Jeddah in July 1977 and her lover beheaded.)

A confession (said to have been obtained in the case of the Saudi princess) or the eye-witness of four just believers is required if a married person is to be killed for adultery - ''and four witnesses are impossible to find,'' says Gamal el-Din Mahmoud, senior Shariah judge in Cairo. ''And anyone giving false evidence may be flogged.''

For a hand to be amputated, two believers must testify, and the crime must fall outside 11 separate restrictions. These forbid amputation if the theft took place within a family, if the object is worth less than 17 grams of gold ($206 at today's prices), and if the owner failed to protect it properly. If it is shown that the thief stole from hunger, the authorities who failed to provide enough food are held responsible.

In Sudan, where President Jaffar Nimeiry is trying to enforce Islam throughout the country, a number of amputations have been ordered recently for theft and other crimes. In Indonesia, such punishments are seen as symbolic and the legal system is based on the Napoleonic Code. Islamic practice, then, as distinct from Islamic principles, varies widely and is hedged about with restrictions.

The principles are endlessly interpreted in light of different national traditions and cultures. The Koran and the Shariah are quoted and requoted to support opposite points of view.

In Saudi Arabia, which uses a strict interpretation of the law called Hanbali , king and taxi-driver alike are buried with simple headstones. Yet in Muslim Egypt, whose Pharaohs built the pyramids 47 centuries ago, families still vie to build elaborate mausoleums unsanctioned by Islam.

In Riyadh, a Saudi caught eating in public during daylight during the fasting month of Ramadan can be beaten. In Cairo, an Egyptian can eat or not, as he wishes.

The Koran specifically forbids the use of alcohol and pork but lays down no legal penalties. While devout Muslims obey, there are those who do not. The Koran forbids Muslims doing anything to harm their bodies, so Muslims must make up their own mind about the effects of smoking, which is not mentioned in the Koran.

Nonetheless, questions do persist about the Shariah as Westerners compare it to their own values of liberty, equality, democracy, and the rule of law.

The Western view of women in Islam, for instance, is reinforced by traditional conservatism in some poor, rural areas of Christian Europe - Spain, Italy, Greece, and Poland - that still seclude their women much as the European Middle Ages did.

Devout Muslims, however, reject women's lib and ''equality'' as Western concepts. They prefer what they see as Islam's solid guarantees of women's status based on equity, inheritance laws, and other legal rights. Most Muslim countries take a conservative view of women. They are to be modest, retiring, good mothers, and keepers of the home.

''I don't want to be equal with men,'' says quiet Kenyan mother Yasmin Muhammad, who lives with a seven-year-old daughter and five-year-old son in the Kibera district of Nairobi, a city with a substantial Muslim population. ''A man is the head of the family,'' she said, ''I have my rights - and I approve of family planning as well.''

On the other hand, even sympathetic observers such as Godfrey Jansen, author of the book ''Militant Islam,'' says women definitely are subordinate.

''Islam is tolerant,'' according to a saying in Pakistan, ''but Muslims are not.''

Illiteracy rates are far higher among rural women than rural men in Egypt and in Pakistan: Some blame this on Islam, while others see it as a common pattern in the third world.

Saudi Arabia preaches strict public observance of 7th-century rules, though critics say wealthy Saudi women change into chic Paris fashions when abroad, and that alcohol is available in many Saudi private homes.

Says noted Muslim scholar Muhammad Zaki Badawi in London, ''The three great monotheistic religions (Christianity, Judaism, Islam) are religions of men. Christ came as a man. Look at what St. Paul says in the New Testament'' (a reference in part to I Corinthians 11:1-9).

Dr. Badawi went on at once, however, to defend Islam's position: ''Before Muhammad, women had no rights in Arabia. They had few under the Greeks and Romans. Islam emancipated them. More than 1,000 years before British and American women were able to hold property, Islam gave women the right to work, to inherit, to own.''

So the Muslim world is a paradox. More than 90 percent of Pakistani village women are illiterate: Yet as Sabiha Hafeez, research director of the women's division of the Cabinet secretariat, works to change that, she points to a framed Koran verse on her office wall: ''Women have the same rights over men as men have over women.''

Two years ago Islamic scholars tried to prevent women in Pakistan sitting as judges or magistrates. They pointed to a verse in the Koran saying that in business, the witness of one man or two women was required because one woman might forget.

But the federal Shariah court in Pakistan threw the case out. Chief Justice Aftab Hussein used the same Koran to refute all the arguments.

Yes, he said, one verse states that ''men are in charge of women'' - but only in the sense of providers and guardians. The chief justice had previously held that the evidence of one woman in court is sufficient to try a case.

Today, many Muslims are not only happy with what they see as the stability and sense of order in the Shariah but also they want their secular rulers to adopt the Shariah without any reservations. No Muslim country does this completely, though Iran, Saudi Arabia, Pakistan, and Libya come closest.

Pakistan has just reviewed its laws to align them with the Shariah and has introduced special hadood laws to punish adultery, drinking alcohol, theft, and false witness. The Pakistani state collects the annual zakat alms tax for the poor and is eliminating interest from domestic banking by October 1985. But it will still float interest-bearing government bonds abroad to raise money.

The Egyptian legal code, based on Napoleonic law, breaks from the Shariah by allowing interest, trade in wine and pork, lotteries, and commodity futures.

Sudan's President Nimeiry backs his Islamic legal code with martial law. Advisers such as Hasan al-Tourabi defend him, while others see his use of the Shariah as political expediency.

In an interview in Islamabad, Chief Justice Aftab Hussein said the Shariah had positive benefits over Western law: Children could not be disinherited by parents, for instance.

Among Sunni Muslims, a lone daughter must share her inheritance with nephews and other relatives. To minority Shias and their legal code (the Jaafari) a lone daughter inherits the lot.

Inheritance laws are clear and understood. At dinner in one Islamabad home, a father described the law in his case without hesitation: Since he had two sons and one daughter, an estate of 40 parts would provide 16 parts for each son and 8 for the daughter.

Still, other contradictions occur. Pakistan's Council on Islamic Ideology has just advised the government that artificial birth control is un-Islamic (and that all Muslim men should wear beards). In Indonesia, population 160 million, it is just the opposite: The government itself promotes one of the most successful family planning programs in the world. The proportion of couples between 15 and 44 using birth control on Java has reached 66 percent.

''We are proof that a Muslim country can make family planning work,'' says Dr. Haryono Suyono, chief coordinator of the program in Jakarta.

So, beneath all the movement and debate, what does it mean to individual Muslims to follow Islam?

Answers vary, of course, from country to country, city to village.

''Islam is something I belong to, something I was born with,'' says Malaysian student Nabiseh Ibrahim in Birmingham, England. ''I identify myself first as a Muslim, then as a Malaysian,'' she says.

''Islam for me is a commitment and above all a conviction,'' says Egyptian diplomat Nabil Osman. ''God for me is an invisible power I can't define except through material manifestations.''

''The key,'' says Indonesian Cabinet minister Emil Salim in Jakarta, ''is balancing the religious and material life - the life we live here is a preparation for the next, a way of gaining credit points for eternal life.''

Next: Islam and Politics

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