THE TITLE IS from a riddle French math teachers use to illustrate exponential growth. A pond has a lily pad growing in it. If the leaves double in number every day (2, 4, 8, etc.) so that they will completely fill the pond on the thirtieth day, then how much of the pond is covered on the twenty-ninth day? Answer: Half of it. Lester Brown thinks our global lily pond has reached the twenty-ninth day. The challenge now is to accomodate human needs and numbers to earth's resources.

The book grows out of the work of the Washington-based Worldwatch Institute, which Brown heads - a Distant Early Warning System for world ecological, economic and social dangers. "Deteriorating biological systems and dwindling oil reserves are pushing the world toward a fundamental economic and social transformation," Brown says. "Rising prices for food, fuel, housing and other essentials are almost inevitable. All countries, rich and poor alike, will be affected."

The four main biological systems on which human life depends are oceanic fisheries, grasslands, forests and croplands. Each of them has a "carrying capacity" which is its maximum sustainable yield. If we exceed that capacity by placing too great a demand on the system, we destroy the base itself. We've eaten our seed corn.

Fish catches are declining because of decades of overfishing. Forests are being decimated, with resultant shortages firewood (fuel for one-third of humanity) and increases in the price of all forest products, plus erosion on a vast scale and downstream flooding.Grasslands are degraded into deserts as too manyanimals overgraze a fragile environment. Croplands are being paved over, or bown away in dust storms or washed away in unchecked erosion. Many so-called "natural disasters" are in reality man-made. "As the soil washes down from the mountains, the people - ecological refugees - are never far behind." We are even over-loading the trash bin, putting more pollution into the air and water than the earth can absorb.

The ultimate cause of these intolerable stresses is runaway population growth. On Connecticut Avenue at 18th and n Streets, the Environmental Fund has mounted a population "clock" whose green numbers tick off the arithmetic of human fertility. World population as of noon, April 9, is 4,376,762,000 and the clock shows a quarter of a million more of us sitting down to breakfast - or no breakfast - every day.

Brown says, "There is now some hope that population growth can be tamed. Sometime around 1970, the rate of world population growth reached an all-time high and then began slowly to subside." But hope notwithstanding, it is certain that the earth's population will double. Even if we could apply the fertility brakes now, the momentum is so inexorable that population will probably "skid" to the 10 to 14 billion projected by United Nations demographers. Most of the increase will occur in countries which are desperately poor. The billions yet to be born will require food, shelter and clothing - and, if their lives are to be "human" in any meaningful sense of that word, they will also require jobs, education, health care and amenities. Brown recognizes that we are not debating how many people can survive on the planet, how many can live decently.

Can a world of 10 to 14 billion feed itself? Brown's answer is guarded. The North American breadbasket may be reaching its limit, given the increasing cost of the energy required by the industrialized agriculture of our factory-farms. In any event, the shipment overseas of more millions of tons of American and Canadian grain may itself be part of the problem. This kind of aid allows weak governments to maintain cheap food for the cities while they continue to ignore rural development. The low yields in many of the poor countries can perhaps be increased. And geneticists may succeed in developing efficiency, are more resistant to pests, and more tolerant of soil, water and climatic variables.

But the core of the problem has never been agricultural, but political. Landless farmers need land, and poor farmers need credit, access to markets and technical services, as well as incentives to produce. Brown believes foreign aid donors ar going to have to promote a turnaround in priorites. "Trickle-down" has simply not worked, he says. "Quite commonly, countries with 70 percent of their population in rural areas may allocate 20 percent of their public sector investments to those same areas."

The second source of the transformation Brown predicts is the end of cheap oil. Oil production in the United States peaked in 1970 and we now import about half of what we consume. World oil production will peak as early as 1983 by one estimate, as late as 1995 by a later guess. Whatever the exact date, says Brown, "the transition to alternative sources is far behind schedule. The fading of the nuclear dream [as costs soar and environmental and proliferation questions mount] and the potential climatic constraints on the future use of coal [the increase of atmospheric carbon dioxide may trigger irreversible changes in the world's climate] further underline the urgency of developing renewable resources...Yet only a few countries - such as China with its reforestation programs, methane generators, and small-scale hydroelectric generators; and Brazil with its ethanol automotive-fuel program - are systematically developing their renewable energy sources."

The continuing rise in oil prices will most directly affect the food dilemma. New land can be cleared, and irrigation sources created by diverting rivers or pumping underground aquifers. Chemical fertilizers might be able to maintain the productivity of marginal lands. But this will require massive infusions of energy and capital - both in critically short supply. Brown says analysts should not ask, "How much food can the world produce?" "The critical question is, 'How much food can the world produce at a price people can afford?" And he reminds us that famine strikes hardest at the landless, the babies, the old, the weak.

The transition from wood to coal powered the Industrial Revolution; and the move from coal to oil characterized what Brown calls the Auto-Industrial Age. Our generation will have to make a similar transition to sustainable sources. It is inevitable, and will probably cause great dislocations. And there is little time in which to adapt.

In the final third of the book, Brown discusses the economic implications of these two transitions, and it is in this synthesis of many disciplines that he makes his most original contribution. "The accelerating deterioration of biological systems represents a deterioration in the human prospect. While the most immediate symptoms of stress are ecological - soil erosion and deforestation - they soon manifest themselves in economic terms - inflation and unemployment. Ultimately they assume a social and political character - hunger, forced migration to the cities, declining living level and political unrest . . . When offtake exceeds the regenerative capacities of biological systems . . . the real costs of production can only rise."

The new world Brown envisages will require a shift in attitude from domination to accommodation. The "cowboy economics" of smash-grab-and-run must give way to an understanding of natural forces. "One way to shake the throw-away mentality, and we surely must, is to shake the 'there's more where that came from' mentality . . . Growth as the dominant objective of economic policy will be forced to give way to sustainability . . . The basic choice will be between voluntary simplicity or enforced austerity."

"Ecologists understand that the deteriorating relationship between four billion humans and the earth's biological systems cannot continue," he concludes. "But few political leaders have yet to grasp the social significance of this unsustainable situation. Intelligence agencies are organized to alert political leaders to potential military threats, but there is no counterpart network to warn of the collapse of a biological system." This important book is just such a measured, balanced warning. One can only hope that it is read widely, translated into many languages, and helps stimulate the international dialogue which could help avert the kinds of disasters it so clearly foretells.