Suppose it was your professional responsibility to make accurate 20-year predictions about the inflation rate, the growth of the economy, changes in the labor force and in family patterns and on the performance of the bond market.

Imagine that you had to give your clients today firm calculations of how much money pensioners will be getting in Social Security benefits in 2005, what the remarriage rate of divorced workers is likely to be and when long-term investment yields will once again exceed short-term returns.

If you would be uncomfortable at having to commit yourself on those questions in a time of economic turmoil, social evolution and mass uncertainty in the investment markets, you know how many of the nation's actuaries feel.

Actuaries, the anonymous mathematicians whose calculations are critical to every insurance and pension program, find themselves trying to know the unknowable for clients who must make promises today about payments in the next generation.

"We ask our investment department what the rate of return on investment is going to be in 20 years, and they say we must be out of our minds," said Dale R. Gustafson, vice president and chief actuary of Northwestern Mutual Life Insurance Co. "They say, 'Hell, we don't even know what it's going to be in two weeks.'"

"It's considerably harder than 10 years ago in terms of the period over which we feel our underlying assumptions have any validity," said William Whitescarver, manager of the Baltimore-Washington office of Meidinger & Associates, a major actuarial firm. "We're in rough waters in terms of the reliability of key predictions. The reliability of our assumptions diminishes rapidly."

Actuaries, who often describe themselves as "social mathematicians," represent one of the country's most exclusive and least-known professional groups. There are fewer that 10,000 in the United States, working for the federal government, for pension managers and insurance companies and, increasingly, in private practice. Compared with the nation's 550,000 lawyers, they are a miniscule presence, but their economic influence is considerable.

How much premium should an insurance company charge on a policy that won't be paid off for 50 years? How much does the corporation have to put into its workers' pension fund this year and next to make sure that guaranteed benefits will be available in 2005? How is the viability of the Social Security program affected by the "baby bust?" If pension payments are keyed to consumer prices, what happens if inflation keeps rising faster than the wages of the workers making contributions to the plan?

Ask the actuary. He (or, much less likely, she) will tell you that in times like these it's harder than ever to give firm answers -- which is what actuaries get paid to do.

"The range of certainty has dropped," said Linden Cole, director of education for the Society of Actuaries, a professional association in Chicago. "It used to be easy, but now we not only have to make a more difficult projection but also explain to the client that the uncertainty is greater." In Cole's view, the greater challenge enhances the appeal of the profession, which, he said, "is lucrative and a lot of fun. It gives you a challenge worthy of your talents."

According to Cole and Stephen G. Kellison, executive director of the American Academy of Actuaries in Washington, membership in the profession is growing rapidly -- by 10 percent a year or more -- precisely because the demands on actuaries are growing. A recruiting pamphlet prepared by the Society of Actuaries -- entitled "So you're good at math . . . then consider a career as an actuary" -- says that "the shortage of actuaries is perennial and does not seem likely to end in the foreseeable future," because of the proliferation of private corporate pension plans, new forms of life insurance, the intricacies of projecting casualty losses and the uncertainties of the economy.

Actuaries live in a world of mathematics -- calculus, probability, statistics, computer programs -- but their work, according to Kellison, is still "an inexact science for sure. When you have benefits and costs that are influenced by economic variables that are highly volatile and unpredictable, there is a degree of uncertainty and risk."

No actuary knows that better than Robert J. Myers, deputy commissioner of Social Security and former chief actuary of the Social Security system.

The Social Security system is in financial trouble, despite the heavy new taxes supporting it, partly because Social Security actuaries assumed that wages would rise faster than prices, as they historically have. With prices increasing faster than wages, payouts to Social Security recipients, which are keyed to the cost of living, have risen faster than contributions to the system by active workers.

"You just can't be sure what's going to happen to the consumer price index, inflation and wage rates," Myers said. "They have been fluctuating wildly, and interest rates have been jumping all over the place."

At the Social Security Administration, he said, "these economic fluctuations have a big effect in the short run, with prices rising faster than wages, but we assume that over the long run we won't have that condition. Wages will once again rise faster than prices."

Actuaries as a group seem to share that feeling that the economy will right itself over the long run because if it doesn't, they say, the whole economic system of the nation will collapse and no long-range projections will be valid. s

"We don't think inflation will continue at this rate for 30 years," said Steve Lewis, senior actuary at William M. Mercer Inc. of Washington. "There have been times when inflation was this high, but historically it has been much lower than this. If you went to 15 actuaries, you would get 15 different opinions, but most actuaries do not think it will continue this way for 30 years."

Kellison said that "there are a few doomsayers" among actuaries, who are finding it "very difficult" to melt projections of retirement ages, disability rates, inflation estimates, interest rates, and calculation of return on secure long-term investment into accurate predictions.

Most actuaries think, however, that "the economic problem is basically short-term, unique in the postwar period. There is a feeling that we don't have enough evidence to justify a long-term, extremely pessimistic scenario. History indicates that this is an aberration.

"If you want to forecast extended periods of negative wage gains, you are talking real problems in the country. The whole country will be in for political and social turmoil," he said.

"It's tricky," Cole said. "You either have to assume that there has been a permanent economic change or that it's temporary. Looking back on history, you would say that it's temporary, and I would go with that. Even if inflation stays up, I would say that it would not be higher than interest rates. But as an actuary, you have to choose, you can't sit on the fence."

Ferguson, whose company, Northwestern Mutual, is in the business of selling life insurance, acknowledged that current economic conditions are a threat to the industry. "It is unnatural for short-term yeilds [on fixed-income investments] to be higher than long-term," he said. "If that persists indefinitely, nobody should buy anything but money-market funds."

The job of the actuary, he said, "is to make calculations so that management can understand them, but we don't have any better a crystal ball than do the economists."