Taiwan? You went to Taiwan?

That's the invariable American reaction, followed by the expected, sterotyped observations: plastic and polyester . . . cheap goods . . . junk . . . and all of it labeled with the ubiquitous "Made in Taiwain," or "Made in The Republic of China."

After this comes the next question: "C'mon, now. Is that tiny, tiny island still chasing that silly windwill of a dream of retaking the China mainland from the Chinese Communists?" (Yes, it really is, while also hoping for a revolution within the People's Republic.)

In many ways, Taiwan is quite a little giant, something like Japan 20 years ago when "Made in Japan" products flooded the United States and became the butt of jokes. Japan has long since surmounted the label problem and so surely will Taiwan. Even now the number of products made in this mini-nation with only 14,000 square miles is almost inconceivable. mOne of the most successful economies in Asia, it is among the top 20 of the world's leading exporters and the leading supplier of sewing machines, black-and-white TV sets, umbrellas and tennis rackets.

Since the United States severed diplomatic relations with the Republic of China and opened up relations with the People's Republic of China, American tourism has dropped from 150,000 in 1978 to 112,000 in 1980. But Japanese tourism has gone from 143,000 in 1969 to 600,000 last year. Total tourism in 1980 increased to 1.4 million.

The stunning beauty of this subtropical island has not changed, and newcomers will continue to be constantly awed by the variety and moods of its subtle and dramatic loveliness. It is China, too, but a free China still populated by Chinese who have been westernized in dress more than anything else. There are still side street in Taipei that will take you back to a China of 75 years ago, but no matter how disgusting and terrifying a visit to a place like "Snake Alley" can be, a Westerner can feel completely safe even if alone.

The government does not treat criminals lightly. When I was there this winter a pair of young burglars, convicted of ransacking the apartment of a young woman and tying her up at knifepoint (but not harming her) were sentenced to death. Apparently the point is made.

Taiwain, just 100 miles off the China mainland, is 250 miles long and 80 miles wide. From the air it looks like a tobacco leaf. Its winters are like our Indian Summers in autumn, but it has the fourth heaviest rainfall in the world -- although during my recent visit there was no rain at all, only sunshine. But sometimes it rains for weeks on end.

En route to Taiwan from Washington, I picked up a "China Airlines" flight at the international terminal of the Los Angeles airport. I half-expected some kind of surplus four-engine puddlejumper, but got instead an immaculate jumbo 747. The terminal was teeming with pushing and shoving travellers, as was the plane. Once aboard, the tranformation was immediate and rather exciting, from the hot face towels passed out by beautiful Chinese flight attendants to the stereo Chinese music piped in over head-set earphones.

The $870 round-trip flight, soft and gentle at 35,000 feet above the Pacific, lasted through two terrible movies and 13 1/2 hours, most of them sunny. There was a free open bar, even in coach class. An imperial quart of duty-free Johnny Walker Black Label sold for $8 (buy it on the plane to avoid lines in terminals). The meals were average airline fare. I learned one valuable lesson: Look at the seating chart and find a perch with no seats in front of it so you can stretch. And for God's sake stay away from young children.

We landed at the new, ultra-modern Chiang Kai-shek International Airport, which reminded me of Dulles. Deplaning at 7:30 p.m., we swept through customs and were soon on our way to the Grand Hotel, a 30-minute drive into the city.

First impressions? The scent of the sweet, spring-like evening and an exciting feeling of being far, far away. The totally mad rush of motorcycles and motorbikes dashing suicidally in and out of an equally mad flow of traffic; some bikes with as many as four people carefully balanced on board with no helmets on. And brightly-lit plastic cubes of white, each one with red Chinese characters, stacked one on top the other above street-level storefronts. And bikes, bikes, bikes, stacked row after row like dominoes on the wide, sheltered sidewalks and line up 10 abreast and 10 deep at traffic lights, their sputtering engines roaring as if waiting the crack of a starting gun. Off they go in a wild scramble, pedestrians leaping like frightened chickens, but never complaining.

In the Orient, one soon learns that whoever gets to a place first owns it.

I had seen photos of the 650-room Grand Hotel, said to be one of the world's greatest, but I just couldn't place it in . . . pardon me . . . Taipei, Taiwan. It is no longer lighted outside like a Chinese palace on fire because the electricity bill went from $13,500 in a summer month in 1973 to $119,000 in July 1980. So the arrival, at night, is not as spectacular as it used to be.

These days, half the lights in the place are turned off, and the lobby, as large as a football field, is actually a bit gloomy in midday. The hotel is almost always at 75 percent occupancy, and the lobby looks like a United Nations meeting with American, Europeans and Japanese mingling about. Most of them are on business, because Taiwan with its low labor cost and high productivity is a major Asian marketplace for more than 15,000 products.

Bellboys in pillbox caps and classic hotel uniforms snap to attention at the slightest hint of need in the spacious interior of this lobby -- like no other hotel lobby in the world (17,000 square feet). Even the massive bronze and glass front doors stop people in their tracks. Inside, the 42 red-lacquered redwood tree-like cerise columns soar nearly 30 feet to an ornate, hand-painted ceiling from which is suspended 34 giant place-style lanterns with red tassels. An ochre-gold carpet that took almost a year to weave rolls up a 40-foot-wide marble staircase. The entire scene cannot be taken in at a single glance until one stops, freezes, and begins turning in slow circles. Chinese grandeur, I learned, is quite grand indeed.

That first night, after almost 18 hours of continuous travel, I was in bed by 9:30 p.m. This is a government-owned hotel, so that accounts for room rates as low as $22 for a single. My bedroom, handsomely furnished, was 22-by-18 feet and even the completely pink-tiled bathroom was quite large, 10-by-12 feet. Sliding glass doors opened to a roofed veranda (13-by-19 feet) that was larger than many hotel rooms I had stayed in in the past. What a striking sight! The city of Taipei, sparkling as they say, lay before me from my hillside vantage point.

The next day, awakening at dawn, I drew open the draperies and walked out into the first of many Chinese tapestries of nature I would see every morning and every evening during my brief visit to this enchanged land. A mist came drifting in from the mountains behind the hotel, drawing moisture from the Keelung River beneath me, and, as the sun burned it off, I stoodd transfixed at this ever-changing beauty. The city emerged from the mysterious clouds and came to life with a barrage of Sunday traffic. I took a long walk late that morning, visiting the Taipei Zoo and its outdated animal accommodations, but it was like any zoo in the world on a Sunday, swarming with families, even popcorn and peanuts.

Earlier I had climbed a mountain behind the hotel where I was told I would find people practicing T'ai Chi Ch'uan (Chinese shadow boxing), a form of disciplined exercise. The trail went winding to the top, where there was an anti-aircraft gun surrounded by sandbags. But the main trail led to hundreds of other mini-trails which, in turn, stopped at hundreds of private, terraced levels, and on many of these levels were people shadow boxing in silence.

This was to be the first of two days of tramping the city streets of Taipei and wondering who buys all the goods displayed everywhere in such rampant confusion. Open-air food operations are everywhere, and everyone seems to be eating all the time. There were moments when I had to pause and look around, trying to catch as much as I could in a wide sweep of the chaotic scene. What is that, and what is this. I wanted to ask. But all I could do was shake my head in bewilderment at the frantic sidewalk life exploding all about me.

There are many international-standard hotels in Taipei, ranging in size from less than 200 rooms to the brand new 800-room Lai Lai Shangri-La, the largest hotel in Taiwan. But by far the best bargain is the Grand for opulence, service and Western and Chinese restaurants.

If you wish to be near Americans, however, and stay right in the busy heart of the city rather than the relative isolation of the Grand, the Taipei Hilton International is as American as you can get ($50 double) although the restaurants are among the best in the city. Just ordering an after-dinner Havana cigar at the Hilton's Trader's Grill is a production that goes something like this:

A brass cognac cart is wheeled over and the cigar is practically unveiled as a snifter of brandy (warmed, of course) is served. The cigar tip is properly cut by a lovely Chinese maiden, who then dips the tip into the cognac and lights it for you and even takes a few puffs. The cigar is then placed on a bronze tray set in the back of an ice-carved swan seemingly floating in a little lily pond with hot ice producing a smoky mist. Now that is how to serve a cigar!