Sprouting at the intersection of government and medicine is a politically embarrassing, albeit congenial, puzzle for which the experts have no agreed-upon explanation: an epidemic of record longevity among the American people.

Can our growing seniority be in large part attributed to gargantuan expenditures on health care, which have doubled in this decade to a current annual total of nearly $200 billion? Or is it the case that, as is contended by the dominant school of health-policy economists both in and out of government, medical care is increasingly irrelevant to health -- that, in fact, it's sometimes detrimental to health?

What is clear as this debate goes on is that more and more of us are living to be older and older -- no matter what the alarmists are saying about deplorable diets, dirty air, hazardous medical care and many other real and imagined lethalities of modern society. And there at the center of it all, effectively fighting off government-imposed cost controls and close quality checks, is a national medical establishment that says the good results are the evidence of its good work. The results are indeed impressive, though who deserves the credit is another matter.

Statistics just released by the government's official scorekeepers of disease, health care and death show that for the average American, survival to merely three score and 10 is as obsolete as the four-minute mile. Overall, American life expectancy at birth reached a record 73.2 years in 1977, a gain of 2.3 years since 1970. And that represented a big pickup in the rate of improvement, as the Public Health Service points out in its newly published study, "Health: United States 1979" -- almost as much of an improvement as occurred between 1950 and 1970.

Average longevity variations by sex and race still persist, so that women continue to outlive men and whites continue to outlive blacks; but, on the average, Americans are living to advanced ages in extraordinary numbers. In 1950, 12.3 million, or 8.1 percent of the population, was over 65; by 1977, it was 23.5 million, or 10.9 percent. The projection for the turn of the century is 31 million over age 65, or about 12.2 percent of the population. From 1973 to 1977, the over-85 population grew by 400,000, to a total of slightly over 2 million. As a people, we are getting old, but the reasons are far from clear.

The most striking source of increased longevity is the 20-year-long, and accelerating, decline in deaths from heart disease. The age-adjusted cardiac death rate dropped by 18 percent between 1950 and 1970, and it has been going down at an average of 2.6 percent a year since then.

Why? The Public Health Service summons up an assortment of speculations about reduced cigarette smoking, better management of hypertension, improved diets, the jogging and exercise boom and swifter and more sophisticated emergency medical-care services. But though all have been subjected to careful clinical analysis and there's great eagerness to identify the origins of the good news on the heart-disease front, the health service candidly reports: "Unfortunately, there is no definitive evidence to determine which of these explanations or which combination can account for the decline" in coronary deaths.

The health-policy mandarins -- operating in a network that links up Washington, major think-tanks and the big schools of public health -- long ago satisfied themselves that health care and health are separate entities. They then moved on from there to try to persuade the American people that they should actually regard themselves as being in an adversary relationship with traditional medical enterprise. (Remember then-HEW chief Joe Califano's recommending that patients skeptically quiz their doctors about prescriptions for the drug Darvon?)

The difficulty with this effort to set patients against doctors is that it fails to recognize that longevity has replaced spiritual salvation as the mass goal of our society. The medical priesthood and its hospital edifices are looked to with hope rather than hostility. And, while the old-time clergy could offer no statistics on success, its medical counterparts can provide them by the ream.

It may be that our gold-plated medical system has very little to do with the long lives that many of our citizens are experiencing. But that's a hard one to sell to the public.