Those who grow orchids call it the ''greatest show on earth.'' They are referring to the World Orchid Conference and show, which takes place somewhere in the world every three years under the aegis of the American Orchid Society, Cambridge, Mass., and the Royal Horticultural Society, London. The 11th triennial show will take place here in Miami next March 5-12.
The idea for an international meeting that would bring together people from many nations, all with one common interest, was first realized in St. Louis back in 1954. Since then it has circled the globe in both hemispheres.
Indeed, third world countries as well as industrialized nations have been hosts of the event. A love of orchids - by far the largest plant family in the world, and in many ways the most beautiful and spectacular - spans all cultures and, to a surprising degree, many economic groups as well. You don't have to be rich to grow orchids, particularly if yours is a benign climate.
Twenty-nine years ago, 250 attended the first triennial event in St. Louis; organizers of the 11th conference say from 5,000 to 7,000 are expected in Miami next March. Already 1,800 have registered.
Who attends these conferences? Mostly hobbyists, but commercial growers and horticultural research scientists as well. Others, without a single orchid in their past, attend to find out what orchid growing is all about.
''Some who now number among our most enthusiastic growers started that way,'' says Robert Scully Jr., general chairman of the conference. The point is that anyone can attend.
What registrants get for their registration fee is 65 seminars, ranging from how-to-grow-them sessions through problem solving to the state of the art in breeding. They also enjoy unlimited admission to the show itself, including the day before it opens to the public. While the official events are important, the cross-fertilization that takes place when people from distant lands meet to share experiences is often more valuable.
''There's a meeting of the minds here,'' Mr. Scully says. ''The conference opens the gate for an exchange of ideas that simply wouldn't occur any other way.''
The show itself, a breathtaking display of all that is exquisite in the orchid world, covers two acres of the Coconut Grove Exhibition Center. The general public will pay a $5 entrance fee.
Thousands of hours have gone into preparation for the event. Much as a city puts in a bid to an international body to host the Olympic Games, a city or region does the same for the World Orchid Conference. Back in 1977, the South Florida Orchid Society applied to the international committee to host next year's orchid event. Final approval came through the following year.
Miami's tourist season is also at its height during March: The weather is generally mild, rain-free, and bright. During the same week the annual Calleocho (pronounced cah-ay-oh-cho) festival and street carnival takes place. It draws contestants from every Latin American country, and is by far the largest Hispanic-culture event in the United States. In recent years it has become a major event on the Miami tourism calendar.
Registration fee for the World Orchid Conference is $125 through Oct. 31; thereafter it rises to $150. Participating hotels are offering rooms to registrants at roughly one-third off the usual rate. Eastern Airlines, too, is offering a 30 percent discount off its normal fare for registered participants from all cities it serves.
For details write to: Eleventh World Orchid Conference, PO Box 59-5150, Miami , Fla. 33159 - or phone (305) 635-6144.