Edinburgh — There's an old joke about an American rushing up to the attendant at the entrance of the Louvre Museum in Paris and asking, ''What can I see in five minutes? I'm double parked outside.''
That was a slam at what was seen as the low level of American culture. But it isn't far off the mark many times for traveling businessmen or professionals of any nationality trying to find time to see something of the sights between appointments. It is a case of look as you run, or jump when the spare moment comes.
Tourists coming to this city for the Edinburgh International Festival Aug. 12 to Sept. 1 still have time to do some planning - and should do so. Thousands of visitors jam this capital city's hotels during those weeks. According to tourist board officials, however, accommodations are still available through packaged tours, in university dormitories (which appear modern and handsome from the outside), and in small guesthouses and private homes (see details below).
In a short working trip here, I had little chance to snoop about on my own but relied on a government official to show me the tourist highlights in a hurry. Here's what we saw:
The Castle: This is the type of castle that fascinates little boys (and many older boys). Sitting on a hill some 440 feet above sea level, the old fortress dominates Edinburgh. It features, for instance, Mons Meg, a nine-foot-long, 15 th-century cannon which, when rammed with 105 pounds of powder, could project an iron ball 1,408 yards. My guide said it was used to blast a hole in the wall of a fortress, but the official guidebook says nothing of that. Unfortunately, Mons Meg burst open in firing a salute to honor the birthday of the Duke of York, later James VII.
Nearby is Lyons Den, a barred vault that kept a tame lion in King James VI's time.
There are also the Casemates, great vaulted chambers that were used to hold French and Dutch prisoners during the Napoleonic Wars at the end of the 18th century. Some men scratched their names on the stone walls or wooden doors.
Boys may also find mind-catching the small cemetery for soldiers' dogs. And, as with many ancient castles, there are a portcullis gate, gun batteries, a collection of weapons and armor, a water well, parapets, towers, and so on.
Historians can test their memories in this castle. Here is a little room where the ill-fated Queen Mary gave birth to James, who became the first king of the three kingdoms of England, Scotland, and Ireland. There's also St. Margaret's Chapel, the oldest part of the castle, dating back eight centuries. It's a small but interesting Scottish example of Norman architecture.
Another room contains the sword of state, scepter, and crown of Scotland, which my Scottish guide proudly told me is 300 years older than the British crown. To discourage Scottish nationalism, this Royal Regalia was left in a trunk and hidden away behind a wall for many decades.
Also worth seeing is the Scottish War Memorial, incorporated in the old North Barracks built in 1751. The weary, blackening regimental uniform standards are not an example of Scottish parsimony. Tradition holds they must stand until their last thread falls to the ground.
The Royal Mile: This runs from the Castle down to the Palace of Holyroodhouse , the official residence of Her Majesty the Queen when in residence at Edinburgh. The palace originated as a guesthouse of the Abbey of Holyrood, now a stone ruin. The abbey was founded by David I, King of Scots, in 1128. For many years, it was a debtors' sanctuary, a place where they were safe from their creditors at a time when debtors could be sent to jail.
The Royal Mile was the heart of Edinburgh for centuries and is lined with many historic buildings. There is, for example, the manse occupied by John Knox, the great Protestant reformer. Nearby is St. Giles's Cathedral, the High Kirk of Edinburgh. The church, with its ornately carved wooden interior, contains the chapel of the Most Ancient and Most Noble Order of the Thistles. It's here that Scots are honored by being made members of this order, the equivalent of the Order of the Garter in England.
My guide noted an interesting fact: In Scotland, the unicorn (the symbol of Scotland) is on the left, the position of prominence, in the crest of Great Britain; the lion on the right. In England, their position is reversed.
The street also contains the burial place of Adam Smith, the famous Scottish economist who wrote ''The Wealth of Nations''; the home of Sir Arthur Conan Doyle, creator of Sherlock Holmes; and many others. Guidebooks devote pages to this street.
Calton Hill: This hill gives another good outlook over the city. On its top is the Nelson Monument, shaped like an upturned telescope. It was built during the years 1806-16. There is also an unfinished monument, begun as a copy of the Parthenon in Greece and sometimes dubbed ''Edinburgh's Folly.'' The rival city of Glasgow once offered to finish it, but the city fathers would have nothing of that.
National Gallery of Scotland: This is a fine gallery, with a handsome collection of paintings by famous artists. Next door is the Royal Scottish Academy with a collection of contemporary paintings and sculptures by living artists. They are for sale and most interesting. That academy faces Princes Street, the city's main shopping street. There are good woolens available on the other side of the street, but it doesn't match similar shopping areas in London, Paris, or West German cities in the richness or variety of goods.
And that was when my double-parking meter ran out, you might say, and I had to run for an airplane.
As for the Edinburgh Festival, tickets can be ordered by telephone or mail from Edinburgh Festival Box Office, 21 Market Street, Edinburgh EH1 1BW, Scotland (tel. 031 226-4001), or in the United States from Edwards & Edwards, 226 West 47th Street, New York, N.Y. 10036 (tel. 800 223-6108, or in New York State (212) 944-0290). Except for the most popular attractions, there should be no problem getting tickets, tourist officials say.
Two companies offering packaged tours of Europe that include some days at the festival are Dailey-Thorp, 315 West 57th Street, New York, N.Y. 10019 (tel. (212 ) 307-1555); and Maupintour, which had very limited space left (as of July 19), 1515 St. Andrews Drive, Lawrence, Kan. 66044 (tel. 800 255-4266).
If a travel agent can't get you a hotel, another possibility is the university residential halls at an inexpensive $16.50 per person per night. Write or call Campus Holidays, 242 Bellevue Avenue, Upper Montclair, N.J. 07043 (tel. (201) 744-8724). A campus spokeswoman said that (as of July 19) rooms at Edinburgh University were sold out, but others were still available at Glasgow University, 45 minutes away. Another possibility is Edinburgh Accommodations Office, 1 Cockburn Street, Edinburgh EH1 1QB. It arranges for rooms in private or guesthouses at rates of, say, three nights for $90 or seven nights for $160.