When President Reagan fired Arthur Flemming as head of the U.S. Civil Rights Commission last April it would have been understandable if Flemming had retired to his garden.

Flemming had had a long and distinguished career in public service. He had served in the Eisenhower cabinet (secretary of Health, Education and Welfare), he had been the president of three colleges or universities (Ohio Wesleyan, Oregon and Macalester) and he had served seven years, under four presidents, as an active head of the Civil Rights Commission.

At 77, Flemming might have decided that he had earned a rest. Instead, he plunged back into public life, directing his energies into three volunteer positions that end up taking more time than a full-time job.

To listen to Flemming, there is nothing remarkable about being so busy. He sees his present life as a logical extension of what he has done in the past. As he lays it all out, his age is only one factor -- and not the central one at that -- among many that define who he is.

The popular stereotype of old age as a time of sharply diminished capacities does not account for someone like Flemming, except to treat him as an exception. Gerontologists, however, are firm in their assertion that growing older does not necessarily mean growing less competent, less aware or less ambitious. Some persons can be "old" at 45 while others remain "young" at 75 or 80.

Why it is that people age the way they do is a question that scientists have only recently begun to address. As Dr. Robert Butler, former director of the National Institute on Aging, observed, "We have so little studied success." But the example of men and women like Flemming who continue to have active lives well beyond the time society classifies them as aged takes on greater significance as the proportion of the population over the age of 65 grows larger.

In 1900, only 4 percent of the population, about 3 million persons, was 65 or older. In 1980, more than 11 percent was 65 or older and by 1990 the figure will be more than 12 percent. By the year 2000, almost half of the past-65 population will be 75 or older.

The increase in the number of frail, elderly persons who are less capable or incapable of caring for themselves poses some serious questions for policy makers. But this growth in the number of elderly also means that the number of active older persons will grow, presenting society with the opportunity to use their talents, experience and energies.

The proportion of the elderly who remain active is difficult to estimate. According to a survey conducted by the National Center for Health Statistics, more than half of all persons 65 and older said there was no limitation on the kinds of activities they felt capable of performing. Roughly 60 percent of all persons 65 to 74 said there was no limitation on their activity, including work, and 44 percent of all persons 75 or older reported no limitation.

Aging, gerontologist Rose Dobrof of Hunter College said, "is a process, not a state." Generalizations, she said, ought not to obscure certain facts: "The reality is that no one wakes up one morning and is old--not even on the milestone birthday of 65 does this happen. From the day we are born to the day we die, we are growing up and growing older."

Some things can be said about the process. Good health is the sine qua non of successful aging and to the extent that good habits and proper diet promote health, we can influence our old age.

But fundamental questions remain. If good health is an essential condition, to what extent is health determined by factors beyond our control--by the inheritance of "healthy genes"? Are active older persons "younger" because of their determination to remain involved, or do they remain involved, active and younger because of some disposition not yet isolated by scientists?

"Our hunch," Butler said, "is that it seems probably likely that both are true -- that those people who have a genetic disposition to a long life may express that disposition through some activities. If you work at it, you can destroy your disposition through sloth or tobacco or whatnot. And if you're not disposed, perhaps you can make up for it."

Flemming is an example of how someone comes to terms with his own aging experience by more or less continuing to do what he has done for years. Others have found new channels for their energy, new directions and new goals.

Albert Quimby, who will be 68 in January, lives outside Easton, Md. A builder by trade, Quimby is comfortable building either houses or boats. At the moment, Quimby, with the aid of a single helper, is building a skipjack. The idea that the project is too ambitious for a man his age has not occurred to him. Quimby believes in work.

"The truth is," Quimby said, "many people would rather continue to work, but somewhere in the process of things it's fashionable to retire at 60 or 62 or 65 and the next thing you know, that individual's finished. I think there's a rhythm you get by being involved in a lifetime and I don't think there's anything constructive about getting too far away from that rhythm. Really, it's almost like the sun and the moon and the tide -- your body's adjusted to it."

Though Quimby and Flemming could not be more different in the way they spend their days, they share certain characteristics. Both are in good health; Both have wives still living, and both share the same philosophy about remaining active. "My theory is noninvolvement leads to rapid physical and mental deterioration," Flemming explained in his sunny office at the National Education Association. "If one continues to be involved, you can maintain mental and physical vigor in a way that you can't maintain it if you cease to be involved in a significant way in what's going on."

Flemming's theory has scientific underpinnings. A study of men in their late 60s and their 70s over an 11-year period found certain factors that could be isolated in determining longevity.

All those studied were extremely healthy, free of cardiovascular and chronic diseases. According to Dr. Marian Yarrow, a psychologist who worked on the study, the men who survived were carrying on more organized and complex living patterns than those who died during the course of the project. The survivors were more active, more social and "more satisfied in outlook than those who did not survive."

"Having goals and a sense of organization in one's daily life is important," Butler said. "If people are retired and no longer have the rigors of having to get up and so forth, they can deteriorate. But if they have goals, they tend to do much, much better."

James Richardson, 75, a friend and adviser of Quimby's, spends his days building a 48-foot bugeye, a working schooner on Chesapeake Bay. Richardson has concentrated on little else besides the boat for the last three years, spending 12 hours a day or more on it during the warmer months.

Asked why he is building a boat, Richardson gave two reasons. "One is that I've always wanted to build a boat the way I wanted to build it," he said. "I've always built them the way somebody else wanted them. And another thing was that I hoped that I might sail all over the Chesapeake Bay."

Richardson has done most of the work on the boat himself despite a right arm enfeebled by pulled ligaments in his elbow. Although Richardson does not speak of the boat as a labor of love, the worksmanship on it shows painful attention to detail and exquisite craftmanship. When he works on the boat, Richardson said, "I feel better."

Asked if he is too old to be building a boat, he pondered the question a moment before answering. "Certainly I would be too old to employ myself to a person," he said. "I wouldn't think of doing anything like that. But when I work with young men, we seem to get about the amount accomplished."

Not every older person is able to maintain the same energy level as Richardson. Tilford and Martha Dudley, who live in Northwest Washington, both lead active lives, pursuing separate interests. Both of them, now in their 70s, have found their considerable energy levels declining -- still relatively high, but not as high as they once were. Rather than dropping strenuous activities, both Dudleys have found ways to get satisfaction with less strain.

Tilford Dudley, 75, spent the bulk of his career working as a political activist, with Sidney Hillman of the Congress of Industrial Organizations and later with the the AFL-CIO. Dudley left the AFL-CIO at age 62 to become the Washington lobbyist for the United Church of Christ, a job he held until he was 68. He might have stayed on longer in that job, but for a variety of reasons he decided that he wanted a change.

For the last five years, Dudley has been doing as much of the management and maintenance work as he could on the seven houses he and his wife own in Washington and two others in Illinois. He has fixed leaky faucets, repaired roofs, painted and done whatever other jobs he could as problems came up. The work was physically demanding, but he did it as long as he felt up to it. Dudley is not the kind of person who likes to sit idle.

Dudley also is one of the founders of the American Committee on East-West Accord. Social issues are again taking up an increasing amount of his time. As a result, he has begun selling off his houses, finding that the effort of taking care of them is too demanding physically and consumes too much of time he wants to spend on what he considers the "top issue" facing the United States and the rest of the world: "war against peace."

Dudley's wife, Martha, lives an active life of her own, writing and helping older persons in nursing homes and adult day-care centers who are interested in writing. She describes herself as "an unsuccessful writer," but also as a person who enjoys inviting her contemporaries to go back through their memories -- feelings about things, fears that they have had, loneliness and privacy.

At 73, Martha Dudley is still physically active enough to go camping and hiking. She spends her summers in a rustic cabin on a lake in Vermont. Lately she finds that her strength is less than it once was.

"One of my greatest joys," she says, "has been climbing mountains, the White Mountains. I'm right near the trails. And I can't get up to timberline and hike the timberline any more. I can get up to timberline, but then I'm ready to rest, enjoy it and come down. Before I used to go across a ridge -- take any trail I wanted to. And this really shakes me. I've accepted that. I've learned that I can go half way up a mountain, to a ledge or something where I can see all of that, and I'm content with that. The trail has become more important to me. I see more flowers. I hear more birds. I love it more. I go more slowly because I love it rather than because I can't walk so fast. So in giving up quantity, I think I have been able to enjoy quality of beauty or presence and I'm very grateful for that. So I'm enjoying the same things, but a few more intensely."

Whether we can affect our lives in later years is a matter of some debate among aging experts. One school of thought, advanced by psychologists Paul T. Costa Jr. and Robert R. McCrae of the National Institute on Aging's Gerontology Research Center, is that people do not change much as they get older. "What we generally find," McCrae said, "is that people tend to continue into old age in the same style that they did the rest of their lives. So that the people who you find are active older people were doubtless active younger people 40 years ago. They're still active. And there are other people who were much more laid back in their 20s and 30s who will probably end up in rocking chairs and they'll be perfectly happy in rocking chairs."

Others, like Butler, believe that the evidence is not yet in to be able to know how much we can affect our lives in later years. All that can be said, without being able yet to determine causation, is that active persons seem to fare better than those who become inactive.

Arthur Flemming has elevated remaining active and involved to the level of principle. "I have this sense," he said, "that maybe people keep testing you in the sense of giving you the opportunity of continuing to be involved. And if you turn aside, they may not come back to you the second time. They'll say, 'Well, he's getting a little old and he's really not interested to the extent that he was 10 years ago or 15 years ago.' I repeat a conversation I heard in my church where an older couple was approached and asked to do something. 'No, we've done that. Let a younger person do it.' I said, 'Every time an older person responds in that way, you're contributing to the stereotype, namely that we want to be on the shelf, that we don't want to be involved. We want younger people to pick it up.'

"I think if an older person really believes in continuing involvement, you've got to work at it. You can't just sit around and expect people to come to you. If there are certain areas that you really are interested in being involved in, you've got to go out and take the initiative, just as you had to as a younger person, show you're interested, and indicate to be people that you're ready and available. There's got to be a positive approach on the part of the older person."