IN HIS MAGISTERIAL interpretation of the rise and fall of human cultures and societies, Harris, a noted Columbia University anthropologist, tells a tale of fascinating gloom.

Harris is in the grip of a single, powerful thesis. All societies - primitive, ancient, medieval, and modern - tend to push successful techniques of production too far. Hunters exhaust the supply of game. Farmers who pursue slash-and-burn cultivation destroy the ecological context within which the supply of arable soil is renewed. Our own energy-greedy processes threaten to use up fossils fuels in a matter of decades. Economic success allows population to grow. More mouths to feed compel this process of intensification of production which soon or late destroys social and political viability.

At least up to our own day, temporarily successful societies have unvariably confronted overpopulation. Social custom, sexual relationships, religious tenets and political organization are all, in Harris's judgement, responses to the exigencies of food shortage and population excess. Female infanticide (which, Harris reminds us, was covertly practiced in the 19th century by English factory workers) has been a favorite method of population limitation. Incessant warfare has historically been equally popular. Wars extended the winners' command over land and animals capable of enlarging food supplies. An added virtue of military solutions was the slaughter of large numbers of potent males.

Often the response to the people-resources dilemma has been even more barbarous. Some of Harris's grislier pages deal with Aztec practices of human sacrifice. Our guide cooly argues that the Aztecs, residing in an unfavorable climate, simply applied intuitive cost-benefit analysis to the solution of their economic problems. No doubt the gods enjoyed the blood drained from the bodies spread-eagled upon the ceremonial stones. But, rather more to the point, Montezuma's subjects gratified their yearning for animal protein, by eating the bodies. Cannibalism encountered religious prohibition in Europe not because Christianity enforced a higher moral code, but because the local climate encouraged the raising of meat animals as an alternative.

As a strategy of conquest, the slogan "We Shall Eat You" lacks appeal to the potential occupants of the victor's stewpots. Thus it occured that the Aztecs never achieved empire. Their neighbors to the south, the Incas of Peru, endowed with a more favorable combination of climate an resources, were able simultaneously to frown virtously upon cannibalism and accumulate an empire.

During spells of abundance, chiefs and rulers provide their subjects with ample food. They credibly act as big men who redistribute the surpluses they collect in a manner which satisfies ordinary men and women and enhances their own authority. When people multiply and food becomes saarce, rulers postpone the promise of plenty to the world to come. Harris mordantly explains the "progress" from agape, the love feasts of early Christians which featured real food, to the symbolism of the wine and the water as appropriate response to material shortage. Church fathers substituted bliss in heaven for solid meals on earth.

Male supremacy fits neatly into Harris's theoretical framework. Men make better warriors than women. Where the martial virtues are prized, their owners will naturally be highly esteemed. Hence male infants, potential heroes, are poor candidates for infanticide. Much better to dispose of female babies who eat just as much as their brothers and, into the bargain, represent future threats of population multiplication. Both sexes came to accept their appropriate roles.

Is our own era of history more enlightened? It differs from past societies two important respects. We are better at technological innovation than any of our predecessors and new technology has traditionally been the only escape from the trap of resource exhaustion. And we have available modes of population limitation less ghastly than cannibalism, infanticide, and the sort of abortion which kills or incapacitates mothers as well as their unwanted fetuses. Is ours a "better" society as a consequence? In a brief burst of nostalgia for the pleasures of the Stone Age, Harris makes this comparison between primitive and modern times.

"In most band and village societies before the evolution of the state, the average human being enjoyed economic and political freedoms which only a priviledged minority enjoy today. Men decided for themselves how long they would work on a particular day, what they would work at - or if they would work at all.Women, too, despite their subordination men, generally set up their own daily schedules and paced themselves on an individual basis . . . People did what they had to do, but the where and when of it was not laid out by someone else. No executives, foremen, or bosses stood apart, measuring and counting."

Nazi death camps, the increasing popularity of official torture, the widespread use in battle of napalm, and new devices like neutron bombs place us in an awkwards moral position vis-a-vis the Spanish Inquisition and the Aztecs. A Harris views human survival, the world has been spared nuclear war only because of mutually low estimates of each other's moral standards by the Russians and ourselves. Both parties are convinced that retaliation for an attack would make certain the slaughter of tens of millions of their own citizens.

Is there any escape from Harris's web of determinism?A little. We are, estimates Harris, near the end of a resource cycle. As resource exhaustion impends, societies have limited choices of new response, if they are alert: "In life, as in any game whose outcome depends on both luck and skill, the rational response to bad odds is to try harder."

The argument is not always easy to follow. Occasionally the text is marred by bits of anthropological jargon, as unappealing to the eye and ear as the argot of sociologists and economists. Much of the fearfully compressed exposition conveys a running argument between Harris and other scholars.

But there is no denying the timeliness of the subject. If Heilbroner's prognosis of democracy's decline depressed you last year, read Harris this year and reach for a handy bottle of tranquillizers.