When Arthur F. Burns was teaching economics at Columbia University and running the National Bureau of Economic Research, he found time in a terribly crowded schedule for such tasks as sitting down with a high school student who had a profile assignment to complete.

In later years, as chairman of President Eisenhower's Council of Economic Advisers, counselor to President Nixon and Chairman of the Federal Reserve Board, Burns applied his expert knowledge of business cycles to the real world, for many people a painful process.

Since the mid-1950s, he has had little time for anything but very serious work, and his record of using intellectual power to make an impact on the art of government will be properly dissected and assessed by future economic historians, as they try to write for future generations the story of what happened to America after World War II.

It is too soon to know what the judgment of history will be on the role of Burns and his thinking, but one of the glories of Washington is that individuals such as the former central bank chairman often stay on here after their formal government roles have ended. This offers an opportunity for diagnosis of current trauma by a person who has experienced the limits of government to bring about change.

And, in a leisurely afternoon seminar here last week with two dozen U.S. and Canadian newspaper business editors, Burns did just that.

"Sitting in an armchair and pontificating from the chair of irresponsibility," he said of his current role of scholar at the American Enterprise Institute, Burns expressed strong support for the Reagan administration's economic goals. But he was pessimistic about the likelihood of success for the administration's prescriptions, mainly because they imply an ability to manage growth that government may not have.

Burns called Budget Director David Stockman's federal budget overhaul an "extraordinary intellectual achievement." At the same time, he noted that the administration's economic program is not the only possible approach. Burns described the Reagan approach as gradualist, one that promises to build future economic stability from incremental reductions in the rate of inflation growth and gradual reductions of federal deficits.

Noting that he regarded himself as a gradualist while at the Federal Reserve, Burns told participants in an American Press Institute program that: "I am rethinking my mistakes. . . If we lived in a world where economic developments took place smoothly . . . perhaps you could stay with a gradualist approach and achieve results."

But plans now in effect to reduce federal deficits gradually and to cut money supply expansion by less than one percent a year "could easily be swamped by external developments," Burns stated. The precision required by the administration program, not only for Federal Reserve money managers but also government officials, is impossible to achieve in an era where money market mutual funds have soared by $100 billion in assets and other financial innovations are distorting normal measures of the economy.

As a result, the "Fed has lost its moorings" in terms of being able to monitor the availability of money in the economy.

In a broader way, Burns said, the administration is "counting very heavily" on a change in expectations, "a growing belief by the American people that the administration has a policy it will stay with." But a reduction in projected federal budget deficits from $55 billion in one year to $45 billion the next is "really standing still," once errors in estimation at that level are taken into consideration, he stated.

"The deficit is to disappear by 1984 . . . will I believe that? . . . Well, maybe gradually. But if you cut it out now, I'll believe."

Such thoughts have made Burns a supporter of what he calls "shock therapy," as the way to end inflation. He said he would go "beyond Stockman" and cut the federal budget even more than has been proposed, stop the money supply from growing at all and forget about cutting taxes now "and be unhappy a little longer."

A major problem that has beset American governments in recent years, in the view of Burns, has been carrying too far the theories of English economist John M. Keynes in trying to fine tune a huge economic machine. President Reagan "has shown courage and persistence to make good on campaign promises" by developing a program to cure inflation and reduce government's role in the economy, but the solutions propose a course of developments "outside of historical experience," Burns added.

An early test of Reagan's whole effort will be the decision, expected soon, on Japanese automobile imports. "If the President refuses to yield to the pressures from Detroit [for import restrictions] I think that would contribute enormously to the credibility of the program. . . But if he compromises, it would raise serious doubts about Reagan's willingness or ability to stay with his program" to reduce inflationary trends on a gradual basis.

"I'm glad I'm not there now," said Burns, when asked what he would do if still the nation's top central banker. "I think I would watch the performance of the economy primarily, the volume of production, employment and unemployment prices . . . the dollar on foreign exchanges and adjust the reserves of commercial banks [by Fed policy], and not be tied to specific monetary targets. . . I would concentrate on the broadest possible measure of money."

The best approach, Burns concluded, is not that of a scientist but that of a clinical physician. "Sometimes you watch the patient getting well," he said. And sometimes there is death.