The head tilts a fraction upward, as if receiving invisible beams of thought. There is a little half-smile playing on the smooth, indoor skin. An ash glows off his fingertips.

"The other day my daughter said: 'Dad, now that you're on Esquire, this means you're officially chic. It also must mean you've peaked.'"

This is Irving Kristol, 59, Brooklyn-born, blue-blazered, semianonymous synergist of ideas and counselor-friend of acolytes at the presidential altar, among them Jack Kemp and (some say) Pat Moynihan.

Jerry Brown isn't a friend -- but he is a fervid reader of the Public Interest, the lucid quarterly Kristol cofounded and still coedits, with 15,000 circulation and 10,000-word essays on graffiti, white flight, national energy policy. You can't seem to find it anywhere, though everyone quotes it. Joe Califano is a reader. So are George Will and Bill Bradley. After he got elected to the Senate, Bradley sent an aid to fetch a box of back copies.

They call Kristol "the godfather" -- but he is about as scary as oatmeal. He holds a distinguished chair at NYU -- though he has never written a book and earned only a bachelor's degree. (He tried graduate school after the army in the '40s -- and quit after five weeks.)

You'll find his name in the Manhattan telephone directory. But not in Who's Who -- it goes from Kris Kristofferson to David Kritchevsky. "I refuse to fill out the forms," he explains. He doesn't have a chalet in Gstaad. He has never been to Elaine's.

"People like Arthur Schlesinger go to 'in' restaurants, hang around with beautiful people," he says with a shrug. "I never do that. I stay home and watch TV. I like Westerns and cop shows. Nothing solemn or instructional."

A tiny gleam: Inverse snobbery?

What if People magazine calls up? "God, no," he groans. The face is a burlesque of pain. The intellect has recoiled. "I'll hide, go underground. I genuinely have no desire to be a celebrity."

A moment later, though, fidgeting back: "Esquire called me an 'unknown intellectual.' Actually, I resent that."

Irving Kristol is the centerpiece of what is either a terrific hype or a true new force in American political life: neoconservatism. Whether it is new or middle-aged or paleozoic, nobody seems quite sure. Nobody, in fact, seems quite sure what it is.

Because the world loves intrigue and because Hollywood would do it this way anyhow, it is in vogue to think of Irving Kristol as political kingmaker. Don Corleone, sitting in his magazine office on East 53rd and receiving the genuflections of his farflung "family." That is comical -- in a way.

Irving Kristol's power is in his influence, in his ability to midwife ideas, to send little microwaves of thought -- his and others' -- out into the public oven. Irving Kristol gets people together. He is the "telephone switchboard," says Robert Bartley, editorial page editor of the Wall Street Journal. He is the "intellectual catalyst," says William Baroody Sr., of the American Enterprise Institute. He is "the entrepreneur," says Rep. Jack Kemp.

He is also, you might say, the fixer.

"I don't know where this 'god-father' business got started," he is saying. Another cigarette is lit. "Do I look evil? I think my friend James Q. Wilson of Harvard may have started it. The novel had just come out, I guess. Now of course I'm fixed with it." This gets a small, evil laugh.

Irving Kristol's platforms are many: his professorship, his magazine, his professorship, his magazine, his membership on the board of contributors of the Wall Street Journal, his linkage to the cozy brainchambers of the American Enterprise Institute, where he is a senior fellow. All of it, and more, adds up to the Irving Kristol Consolidated Network, what one writer calls his "interlocking directorates." His syndicate.

Writer Jude Wanniski, one of Kristol's "horses," supposedly started the Corleone image of Kristol. He first met Kristol at a Christmas party in 1972. The New York Times had just come out with a poll naming the leading intellectuals of the age. Kristol had placed fourth. He and Wanniski spent the evening remembering the names and positions of the 1947 Brooklyn Dodgers. Kristol, says Wanniski, "is the only man over 45 I've ever met still on the hunt for new ideas."

The way the godfather's power works is like this: One day he tells Jude Wanniski to drop by Jack Kemp's office on Capitol Hill. "You'll get along," says the godfather. Wanniski goes -- and out of it eventually comes Kemp-Roth, the bill, now defeated, that would have lowered taxes by 33 percent over three years.

Nowadays, of course, Jack Kemp wants to run for president. Irving Kristol plays a paramount role in this decision, though Kemp declines to say just how much. Kemp has his "Kempians." But Kemp himself is a "Kristolian."

The Kristol wave washes on many shores. Several years ago, Kristol writes a piece in the Wall Street Journal, taking out after the "New Class" intellectual. (He doesn't think he coined the term, just popularized it.) Now, there are three books in the works on the New Class.

"Suddenly it was an idea that seemed to have explanatory power," the godfather says. "I'm not in a position myself, or do I have the temperament, to take a year and a half off to write such a book." There is immense satisfaction in his voice.

Kristol is busy, say political scientists, because liberalism is wasted. Historically, it's conservatism's time. Except for the fitful '60s, when the New Left had the national glare, America since World War II has raggedly but inescapably edged right. The evidence is everywhere: in Proposition 13, in the rage to deregulate, in the hardened faces of consumers throwing up windows and yelling down: "I'm mad as hell."

The chief voices of the new conservatism are mostly refugees from the left -- Norman Podhoretz, Daniel Bell, Moynihan. They range from Cambridge and the literary canyons of Manhattan out to the Lafferian curves of Southern California.

Some of them are old New Frontiersmen; some go back to Adlai Stevenson. Still others, like Kristol, come out of the high, heady socialist-Marxist days of New York in the '30s.

The neocon movement has roots in the 18th-century concept of Edmund Burke. It is anti-Rousseau, though not entirely, and believes that the Great Society dream is a wash. Though it is not liberal, it is not illiberal. What it is... is confusing.

Today, the godfather has come to Washington to address 300 businessmen at the University of Maryland who have convened at the invitation of Suburban Trust Co. Enough of the conferees have never heard of Irving Kristol, let alone the neocons. One company represented is Stanley Foods & Equipment Co. of Capitol Heights, Md., which, the general manager says, is "into anything you can deep-fat fry."

Edmund Burke is not to be heavily invoked.

The man on the dias with his watch face on the inside of his wrist attacks the Carter administration as soon as he gets up to talk. The folks in the White House have had to shed their "passionate egalitarianism," he says. But he also says, "The Democratic Party is a foolish party. The Republican Party tends to be a particularly stupid party."

You get the sense that Irving Kristol is above all this.

People keep calling him "Dr. Kristol." He doesn't correct them. Later, in private, he explains -- a smidge defensively. "A lot of intellectuals don't have a PhD. Like [Arthur] Schlessinger.Of course, he's a Harvard fellow, so that's a bit difference. And in England it's practically an innovation to have your doctorate. On the whole I may be better off without one."

Irving Kristol hasn't always earned his living as a thinker. Once he worked as a machinist. Another time, while his wife was at the University of Chicago reading the political philosophies of Leo Strauss, he was working as a freight handler for the Illinois Central Railroad. He was waiting to be drafted.

His roots, in fact, are lower middle class.He was born in the Williamsburg section of Brooklyn. He rode the subway to City College, full of socialist ideals. His personal odyssey to the right has been a longer journey, perhaps, than the world knows.

"I have no nostalgia for Brooklyn, not a bit. I always wanted to get out, and I did."

That closes that.

He is asked if he had a sense of the coming of the neocons. "I had a sense we were making headway. I never thought we would become chic."

Are the liberals in danger of being run out of town by midnight? He laughs, flicking away an ash. "Look, I just think the intellectual energy has run out of the left -- and drained into the right. That's all. I no longer think the left has anything much to say.

"But who knows? Maybe it'll change back. Or maybe the labels will change."

Kristol and his wife, historian author Gertrude Himmelfarb, live on Central Park South. Some say "Bea" Kristol is the greater intellect, though she doesn't say that. "My husband and I influence each other in diverse, subtle ways," she says. "In the end there is a convergence. Of course he's primarily interested in political thought and economics."

Kristol divides his days between editing the Public Interest (the magazine has one room with a lot of desks), his teaching, his writing. He doesn't use a typewriter any more for composing his crisp, rich essays. He likes yellow legal sheets with red margins. Good for marginalia. Helps to come up with nice phrases, like the "tyrannic vulgarization of the democratic idea.'

Irving Kristol used to have a friend who's name also was Irving. Irving Howe and Irving Kristol no longer speak. Howe, of course, is a preeminent American literary critic, still a democratic socialist. It was Howe who recruited Kristol for the Young People's Socialist League at City College. Kristol and Howe and their circle would sit in the alcoves in the student cafeteria and spend up their idealism on the dream of a perfect socialism. Last fall, Howe wrote a long essay in the New Republic titled "The Right Menace." One of its targets was his old pal Irving Kristol.

"That was a long time ago," Kristol says, when you bring up City College. "I look back on all the arguing we did romantically. But you move on."

Irving Kristol is moving on now. He has a plane to catch back to the city tonight.

He is thinking of writing an essay about what went wrong with liberalism, he says.

What will you call it?

"Oh, 'The Politics of Compassion,' I think." CAPTION: THE WALL STREET JOURNAL. Copyright (c) 1979, Dow Jones & Company, Inc. All Rights Reserved; The Public Interest; Pictures 1, 2, 3, 4, Irving Kristol, top center; Jack Kemp, far left; Pat Moynihan, bottom center; and Jerry Brown, above. Kristol photo by Joe Heiberger -- The Washington Post