But then she heard about the Allure, and how glamorous it was supposed to be as mega-ships go. And she called Malcolm, one of her luxury-cruise-ship friends, who last year went on the Oasis of the Seas (identical to the Allure but two inches shorter). He told her, “Even though there are 24 elevators and 1,700 children, you’re going to love it.”

For hard-core cruisers who go a few times a year, speed of check-in is paramount, and fetishistically discussed; it is imperative to begin the pleasure immediately. On the Allure, check-in was extraordinarily fast thanks to the huge new 5.5-acre, 240,000-square-foot terminal that Royal Caribbean built in Fort Lauderdale, Fla., in 2009 to make sure that the thousands of passengers moving on and off the Oasis and the Allure would be able to go “from curb to stateroom in 15 minutes.”

Stepping off the zigzagging gangplank into the enclosed Royal Promenade, we were hit with blinking lights, video screens and shop windows stuffed with jewels and muffins. Where had we come? On smaller ships there is a small area where a social hostess greets you with a little beverage and everyone hugs one another. This place looked like the inside of a shopping mall in Singapore or Dubai, with people from everywhere streaming by  a woman in a Muslim head covering, a tiny wrinkled man speaking Spanish with his arm around a young woman three times taller in bondage shoes, a Japanese couple in formal dress staring up at the top of the Cupcake shop. Still, we were in a crowd of only a few hundred or so; where were the other thousands?

We would feel not only the excitement of being among so many different cultures but also a certain spaciousness the whole week. Never would we be overwhelmed or crowded. One reason for this, it turns out, is that the Allure is not just very long, but hippy in the beam  215 feet wide, in fact, more than 30 feet wider than Royal Caribbean’s last big ship, Freedom of the Seas.

After a quick salad at the Park Café, one of the Allure’s 22 restaurants, where a song played about how wonderful life is, we looked at the ship’s map  nightclubs and casino on Deck 4; specialty restaurants mainly on 8, around the park; child and baby areas on 14; sunlight and sports on l6; staterooms from decks 6 to 14.

Arriving at our cabin, where the luggage appeared within seconds, my aunt said that the 182-square-foot space with a 50-square-foot balcony was “skimpy” compared with the 350-square-foot cabin that she was used to. “As you recall,” I said, “you are paying $279 a day per person as opposed to that bargain world-cruise rate of $668.15 a day in 2010.”

For our first dinner we went to Deck 16 on the ship’s bow, where a dancer in violet feathers wiggled her way through the fiery orange candles and white cloth chairs and tables at the most exciting of the ship’s specialty restaurants, the Samba Grill, a churrascaria. Eleven of the ship’s 22 restaurants charge an extra $15 to $35 a person, which includes everything that is not in a bottle. (We had made reservations for the specialty restaurants a month before, as was recommended by her travel agent.) We ate olives and fennel and oranges as waiters came through with skewers of picanha, fraldinha, costela and lombo. It is all very Rio.