Most people who come for the day to the Hudson Institute ride the 8:02 up from Grand Central in Manhattan. They are met at the commuter station in Croton-Harmon by a likable fellow named Gene who conveys them over to the "campus" in a brown beat-up station wagon. But Alexander Haig's arrival a week ago was clearly something different.

Into this leafy sanitarium of thought a little after 11 a.m. rolled a shiny black limo. The thing was big as a barge and looked menacing. Cameras clicked and whirred. The institute's somnolent dog Buffy was nowhere to be seen. Maybe the car and the cameras had scared her out of her wits.

Bill the chauffeur had picked up his passenger, and the passenger's aide, at the shuttle gate at La Guardia. Beside him, on the front seat, lay a copy of a recent biography of the man behind the paneled glass, but since the book is something of an unflattering biography, the driver decided not to ask the ex-secretary of state to sign it. In fact, he and Haig never spoke. "They never speak," Bill said.

Alexander Haig, 57, the Man Who Would Be Reflective, was on his way to meet the staff of the Hudson Institute. He had signed up as the institute's newest (and lone) Senior Fellow.

According to Tom Bell, institute president, a senior fellow is a kind of ambassador without portfolio. He can roam as he wishes, dip into this or that, have at his disposal the institute's immense research facilities. Haig, who will occupy his fellowship from a new Washington office, not from Croton-on-Hudson, is said to be interested in East-West relations, defense problems, tensions in the Atlantic economic community. He will make a "small" salary, says Bell. "Not anything you could get anybody to come here for." The salary may not be swell, but the new office will be.

The purpose of Haig's trip last week to the motherhouse was to meet the staff and be "brought up to speed on current projects," says Hudson president Bell.

"How do you feel about your new life, Mr. Secretary?" a TV man, up from unruly Manhattan, asked on the steps of Building Seven last week.

"Well, I'm very enthusiastic."

"Do you miss the State Department?"

"Not at all."

"What about a political career?"

"No. No politics."

"No interest whatever?"

"None."

The Hudson Institute is one of the country's venerable think tanks for policy research. It is presided over by the immense -- both corpulently and intellectually -- Herman Kahn, premier "futurologist." "Virtually the only subject that a futurologist will not talk about readily is his batting average," James Taub wrote in Saturday Review several years ago. Kahn is the man who gave us the nuclear term "thinking about the unthinkable." He is one of America's early "defense intellectuals." These days he is a Japanist.

In personality and appearance, Alexander Haig and Herman Kahn seem exact opposites. It is a case, one suspects, of opposites attracting. Kahn is loose; Haig is tight. (Everybody around the place calls Kahn "Herman.") Kahn suffers from obesity and narcolepsy and will strike up conversations with stunned people on subways. Haig, ever spit and polish, has undergone multiple bypass heart surgery, yet smokes and also drinks things with caffeine in them. His foot dances ceaselessly under conference tables.

Kahn cofounded Hudson two decades ago and today serves as its director. Some people call it Herman-on-Hudson. Kahn and Haig go back to the days when the soldier was a captain at West Point. Later, in the Nixon White House, when Kahn found himself having problems getting in to see Henry Kissinger, Al Haig--who was Kissinger's man--became the conduit for the Hudson Institute's nonstop flow of ideas. Haig and Kahn have been congenial ever since.

Last Friday, at his first Hudson briefing, Haig had on a banker's pinstripe suit and what looked like a silk tie. Kahn was in a short-sleeve dress shirt and no coat and his Amish elder's wreathing beard. The two seemed genuinely delighted to be with each other. "It's incredible to have as part of our team a man who actually ran the system--and didn't ossify from it," Kahn said, making the formal introductions. "In many ways, Al, your career is just beginning."

Haig laughed, although not with any enthusiasm.

Later, when the guests were gone, Kahn said: "I've never had any trouble explaining any of my ideas to Haig." He paused. "Being a general is very bad for you, you know."

The Hudson Institute is a child of the RAND Corp. and traces its history to the first heady years of the '60s when, as someone has said, growth was the American religion and R&D was its gospel. Hudson is a pastoral, informal, slightly-out-at-the-elbows place. In the '20s it was a sanitarium for the wealthy; now it is a retreat for the extremely brainy. About 35 young and old heads from Harvard and Oxford and other places smoke pipes and eat lunch in a woody room that looks like a prep school dining hall. After lunch these same heads go back to their slightly tattered offices and write sober monographs on things like "Coercive Tactics in Nuclear War" and the bilateral trade imbalance.

A man named Curt Guthe, still in his twenties (Harvard College, '78), is currently working up for Rockwell International a paper on the utility of long-range bombers. Someone else is worrying about Visions of the Future. An older member of the institute, Frank E. Armbruster, used to fire fast freights out of Harrisburg on the Pennsylvania and New York Central lines.

Even as Haig journeyed last week, carpenters and plastermen were readying the institute's new Washington offices for him. They are on the eighth floor of the Madison Office Building, though that has tried to be kept something of a secret. Haig and a support staff of four will take possession of the suite early next week. Transition work has been going on this week in a suite of the adjacent Madison Hotel; Haig has been in and out. He is not exactly a stranger to working out of hotel rooms.

As of yesterday, all that was visible as you stepped off the elevator at the eighth floor of the Madison Office Building was a sign for the Pharmaceutical Manufacturers Association. If you rode the elevator to the eighth floor last week, you could hear a lot of pounding behind closed doors. (There was still wallboard in the hall yesterday afternoon.) No one from the Madison has been eager to admit Haig is coming, except, that is, for the man who runs the ground floor newsstand. His name is Tony and he saw Haig and his wife slip into the building one evening about 10 days ago. Tony has seen them all come up through the Madison's parking garage. "Elizabeth Taylor has walked through that door," he says. "Charlton Heston. Jack Kemp."

Hudson, which derives much of its subsidy from government contracts, has long maintained a presence in Washington, although nothing so formal as now. Now Henry Hudson's river seems to be flowing richly into the Potomac again. Most recently the institute had been leasing space in the offices of Decision Science Applications in Rosslyn. There are those who would say the Hudson Institute has been losing out lately to other think tanks more strategically located. The Center for Strategic and International Studies, associated with Georgetown University, has both Zbigniew Brzezinski and Henry Kissinger. There is a report that Haig was offered a spot at the American Enterprise Institute and turned it down. "It didn't get to that point," says Woody Goldberg, Haig's senior adviser who served under him in Vietnam.

"We were thinking of opening our own Washington offices anyway, this just hastened us along," says Hudson president Bell.

Haig seems remarkably fit after two months out of the public eye. Eight recent days at John Gardiner's tennis ranch in Arizona has tanned him and further flattened an already flat belly. The jaw still jutted (even as he got out of the limo), though not so acutely. He didn't seem like a man contentiously straining out of his shirt collar. The sharp blue eyes of a hawk surveyed this bucolic realm (it was his first trip to Hudson) and apparently were not disappointed. But if he seemed at ease, he didn't look like a man about to retire to Great Thoughts. He looked pretty much like the man who, in 1967, was merely a lieutenant colonel in Vietnam, then suddenly began one of the fastest military catapults in history.

In July of this year Haig checked into the Texas Heart Institute in Houston. "I had to schedule that one five times," says Woody Goldberg. At the end of the physical, the doctor walked in and and said, "Congratulations, Al." There wasn't a bad blip on the screen, according to Goldberg.

Herman Kahn has an IQ topping 200. On an Army intelligence test he made a 181 -- out of a possible 182. At night he goes home and plays with computers; that is, he does when he's not watching sitcoms. He's quite fond of TV, actually.

Last week, after Haig's limo had rolled off, Kahn said: "Your image of him is that of opportunist, someone abrasive. My image is exactly opposite: a man who knocks himself out for his boss and his country. I'm not saying he isn't the former, just that I have known him another way. I ran into him once in the Bahamas. He looked at me and said, 'You're right, Herman, this is my first vacation in 15 years.' "

Several years ago, after Haig had left the NATO command, but had not yet signed on with United Technologies Corp. in Connecticut, Khan tried to lure Haig to the Hudson Institute. It almost worked. This time, after the resignation from the Reagan White House, Khan just called up his old acquaintance -- and got an almost immediate acceptance.

Much in the manner of 300-pound gorillas, ex-secretaries of state can do about anything they choose, of course. According to Woody Goldberg, there were nearly 1,000 letters of invitation since Haig's resignation in June, everything from Rotary speeches to jobs running foundations.

He could have gone solely into corporate life. (According to Goldberg, there will be a renewed association with United Technologies soon.) He could have taken over a national foundation "on the level and quality" of the Ford. (Goldberg refuses to say what foundations had tendered a job.) He could have gone solely into the academic world. (He will lecture this fall at Princeton and, though it hasn't been announced yet, will in all probability accept a Chubb fellowship to Yale. Then, too, he will attend his 35th class reunion at West Point at the end of October and do a session with cadets.)

A book will undoubtedly come. In the meantime, the William Morris agency is handling all literary and public speaking requests.

The relationship with Hudson might be called a marriage of convenience. Says Goldberg: "At the secretary's age and vigor, retirement was out of the question. The Hudson Institute came to us and said, 'We want to have a relationship with you. How can we help you?' They asked for nothing, they demanded nothing. It's an open-ended deal."

For now, says Goldberg, the ex-secretary will be occupying the Madison Office Building suite for six months. During that time he will make up his mind whether he wants to keep living in Washington.

Says Herman Kahn: "As a sheer business proposition, Haig's coming here was a wonderful coup."