Yucatan cruise

As vacations go, the unassailable virtue of a Caribbean cruise is its pure relaxation. In its current incarnation as a floating hotel, the raison d'etre of the cruise ship is to assuage needs and relieve passengers of the conventional hassles of traveling, such as packing and repacking, securing accommodations, arranging transportation, and so forth. In this self-contained environment, the passenger is rarely faced with a more urgent decision than picking an activity from the ''cruise news'' and chewing or eschewing the midnight buffet.

The ship is a fanciful, luxurious playground designed to create the illusion in its passengers that they are young, idle, and rich. Serious vacationers who travel to learn about different cultures regard the cruise lover as a throwback to kindergarten or the protoplasmic state. (Let me hasten to add at this juncture that my husband and I love cruises.)

There is now a cruise, however, that combines escapism with intellectual adventure, and we found ourselves delighted with the combination. Norwegian Caribbean Lines (best known for its flagship the SS Norway) offers aboard one of its smaller vessels, the MS Skyward, a seven-day cruise to Mexico called ''Mayan Magic.'' Departing every Sunday from Miami, the Skyward sails across the Gulf of Mexico and stops at Cancun and Cozumel in the Yucatan province and on the return voyage at Key West and an uninhabited out island. The Skyward features unique shore excursions in Mexico to the Mayan ruins at Chichen Itza, Tulum, and Coba on the second and third days of the cruise. It is also the only cruise ship to anchor at Cancun, a resort that is growing in popularity despite its synthetic origins.

From the island of Cozumel, 12 miles off the coast, and from Cancun, the ship provides transportation by tender and bus to the ruin sites. Given the vagaries of Mexican transportation in the Yucatan, these excursions are a reliable means of getting to the ruins - and back. The only apparent drawbacks are the cost of the excursions ($65 to Chichen Itza, $50 to Tulum and Coba) and the length of the trip (a short tender ride and three-hour bus trip each way to Chichen Itza, about an hour on the tender and an hour and a half each way to Tulum and Coba). But in most instances the cost and duration of the trips would be greater if one were to undertake them independently from Cozumel, Cancun, or Merida, the capital of the Yucatan.

Other advantages of the shore excursions are that guides (some of Mayan descent) are provided, as well as an informative orientation tape one can listen to on the bus and a sanitary lunch box. Another plus is that all the buses are air-conditioned, and this helps compensate for the monotony of the ride - vistas of jungle and rural poverty are the most common sights.

A word of warning: These excursions are not for the impatient. Also there are precipitously steep pyramids with narrow stairs to climb and dank, tight spaces to creep into. Those who elect to remain in the sun with their feet firmly planted on the ground may feel frustrated as well as hot.

The adventurous will have their reward, especially if they prepare beforehand by attending the ship's multimedia show on the Maya, listening to the tape on the bus, and best of all, reading a book such as John S. Henderson's ''The World of the Ancient Maya'' (Cornell University Press, $29.95), which is available on board.

For those who are not familiar with the history of the Maya, their civilization spanned 3,000 years, from around 1600 BC to AD 1600, when the Spanish invaders delivered the coup de grace to a civilization that had been in a state of mysterious, irrevocable decay since around AD 900. The Maya comprised at their peak almost 3 million people; inhabited an area of 125,000 square miles in Mexico, Guatemala, Honduras, Belize, and El Salvador; and developed the most precocious of pre-Columbian civilizations. Their understanding of astronomy, mathematics, acoustics, and architecture remains a source of wonder even today.

Among the enigmas their culture poses: How were they able to predict the exact positions of the sun, the moon, and the planets and date the equinoxes, solstices, and eclipses billions of years into the past or future without a telescope? How were they able to construct their enormous limestone edifices and their roads without the use of the wheel? And how were they able to develop a system of counting - using dots, bars, and a shell shape representing zero - that is in some respects more efficient than our own?

Within their feudal society it was the peasants and slaves, of course, who performed the backbreaking labor of building the pyramids and other monumental structures that can still be viewed at Chichen Itza and other major Mayan sites. Their architecture is striking, not only for its modernity and sophistication (the Maya even invented the corbeled arch or ''false vault''), but for its articulation of their beliefs about the universe.

For example, El Castillo, the name given by the Spanish to the great pyramid at Chichen Itza, is so precisely positioned that on the days of the spring and fall equinox the shadow of the staircase railings on the north side creates the illusion of the serpent god ascending the steps. Moreover, 91 steps on each of the pyramid's four sides plus one at the top make 365, the number of days in the year.

The day after the excursion to Chichen Itza, one has the option of taking another to the Mayan sites of Tulum and Coba or to Tulum and Xel-Ha, an idyllic, limpid lagoon where the Maya once worshipped and the Americans now snorkel.At Tulum, dramatically situated on the coast, a brooding presence hovers over the water. A recurring image in the carved reliefs that decorate the buildings is that of a descending god, dubbed the diving god. Built around AD 1200 in the period of decadence, Tulum is one of the last Mayan cities, and it clearly reflects the Toltec influence. Its edifices are not remotely as impressive as those at Chichen Itza, but the juxtaposition of the two forms a poignant contrast - the zenith and nadir of a civilization.

The Tulum-Coba excursion is primarily for those who are seriously interested in Mayan culture. While the excursions to Chichen Itza were crowded, less than 20 people signed up for Tulum-Coba, the other passengers preferring to adjourn to the lagoon apres Tulum or just spend the day on Cozumel. Coba, built at the height of the classic period around AD 600, was the commercial capital of the Mayan civilization. Situated around five lakes and covering an area of 40 square kilometers, Coba was famous for its 43 roads - 20 connecting the lakes, pyramids , and other buildings and 23 leading to other cities.

Our only criticism of the Mayan excursions, which were on the whole well organized and edifying, was that there was not enough time in Chichen Itza (only about two hours) and that those choosing to take one of the Tulum tours on the second day in Mexico ended up missing modern Mexico completely, i.e. Cancun and Cozumel. Norwegian Caribbean Lines (NCL) only started its Mayan Magic itinerary last year and is still tinkering with it. It recently dropped the sleepy port of Playa del Carmen, because passengers complained it was too boring, and substituted Key West. But we think a wiser choice would have been another day in Cozumel, which boasts some of the best diving in the world, has some Mayan lore of its own, and imparts a distinctly more Mexican flavor than Cancun.

We never did get to Key West (there were tornadoes in the area at the time) and ended up in Nassau instead, which appears to be turning into the port of last resort for the cruise industry. It will be interesting to see if Key West does catch on as a port of call; the island is eager to lure cruise ships, and NCL is doing its best to promote it on the basis of its quaint architecture, its arty atmosphere (Tennessee Williams and Ernest Hemingway were among its better known denizens), its maritime flavor (a good place to stock up on sponges), and its musical night life.

The last stop on the itinerary of all NCL ships is an uninhabited out island in the Bahamas, Great Stirrup Cay, which is owned by NCL. It is featured on the last day of the Skyward's cruise and is an exhilarating but relaxing climax to what could prove, if one chooses, a busy trip. Here there is nothing to do but lie on the beach, snorkel, enjoy the natural beauty of the island, and marvel at how the cruise staff on and off the island manage to conjure up hot dogs and hamburgers with all the trimmings for 800 people. The island is more appealing from the ship than the shore, however, for what looks like a Robinson Crusoe paradise is rapidly transformed into a version of Coney Island. But it's a lot of fun.

The crew is about as international as the UN; the ship's officers and staff are mostly Norwegian and British, and the waiters and stewards are Hispanic, West Indian, and even Korean. The menu is similarly international, with Mexican, Scandinavian, and Caribbean specialties enlivening the basic continental fare. The atmosphere is definitely on the informal side, as is the dress. Those looking for an evocation of bygone European elegance won't find it here. I should add that the quality of the food is consistently above average for a cruise ship. The cruise staff are a warm and jolly lot without being overbearing , and the entertainment ranges from a Mexican fiesta to a country-western barbecue in the shadow of the fake Maya temple. What can you say but ole? Practical details

NCL is offering throughout 1983 a special Sea-Saver fare with savings of 30 percent or more on all seven-night cruises. This fare is $659 a person for an inside stateroom and $729 for an outside stateroom. (This is a fixed price for both on- and off-season so you won't save more by going in the summer; beware of the Mexican rainy season in July and August). You must make reservations at least four weeks before departure and allow NCL to select the ship and accommodations based on what is available.