In the U.S. today it's hard to live on $10,000 a year. However, it's even harder to get by if over the years your annual income has swollen from $10,000 to $200,000, and is now reversing the trend and heading back toward the original figure.

This may seem to have little to do with population problems. When we look at the number of people on the planet, our worries tend to focus on uncontrolled growth rather than possible decrease. The basic figures are frightening. Two thousand years ago the world population was around two hundred million. Two centuries ago it was one billion. Two billion was reached by 1930, three billion by 1960, four billion by 1975, five billion by 1988, and more than six billion today. Projections for the year 2050 range from eight to twelve billion.

You might think, then, that any evidence of slowing population growth has to be good news. In fact, there is plenty of such evidence. Family sizes are decreasing, world wide, at a rate that no one can explain. The theory used to be that large families correlate with poverty, illiteracy, and certain religions; education was said to be the only way to lower fertility rates.

The theory seems to be wrong. Bangladesh, as poor as can be, has seen a 50 percent reduction in fertility rate in the past 25 years. Iran, for more than 20 years a bastion of militant Islam, has reduced its fertility rate to a third of what it was. Around the world, 83 countries have "sub-replacement" fertility, with less than two children per family. These countries range from Italy, with an average of only 1.22 children per family, to New Zealand at 1.85 children per family. The United States, at 2.07, is barely above the replacement level, and would be below it were it not for immigrants.

The countries with the highest fertility rates, more than six children per family, are ironically the African nations of Congo and Nigeria, where rampant AIDS is likely to make the number of children born a less relevant statistic than the number surviving to adulthood.

If the worldwide trend toward fewer children persists, the population projections quoted earlier will be too high. Before we breathe a sigh of relief, let's introduce another relevant factor. The fact that the number of children is less than two per family in a country might seem to imply that the population of that country must be going down. It doesn't, if people are also living longer. In almost all of the countries with sub-replacement fertility, populations still are increasing. What is changing is the age profile of that population. In 1810, the United States had only about 100,000 people over 65. Today it's more than 30 million, and by 2030 it will be near 60 million. Before that, China, with its strict rules limiting family size, will have 250 million people aged 65 and over. Unless these older people are well enough to work, they will be carried on the backs of a proportionately smaller young work force.

When population grows rapidly - like income rising from $10,000 a year to $200,000 - the living is easy. If population drops, it becomes harder and harder to make ends meet. A lifestyle based on $200,000 a year won't work if you make only $20,000. An infrastructure and economy designed for a quarter of a billion people won't work for a hundred million people.

Now for another complication. People are not merely living longer, but the life expectancy of the very old is refusing to follow the established model for mortality. That model is known as "Gompertz law." It was proposed by a British actuary, Benjamin Gompertz, back in 1825, and it states that mortality rates increase exponentially with age. If you make it to adulthood, then the Gompertz law says that your chance of dying doubles about every eight years. Death rates thus increase dramatically in old age, and even if the number of 65-year-olds goes way up, we would not expect many centenarians.

Gompertz had no theory behind his law. He derived it based simply on observation, and in 1825 the number of 80- or 90-year-olds alive for observation was almost vanishingly small. In the early 1990s, a group in Denmark therefore decided to see how well the Gompertz law worked when applied to very old people. They found it didn't seem to work at all. On the other hand, really old people are few enough in number that environmental and genetic factors make the statistics unreliable.

Faced with a shortage of people, scientists did what scientists so often do: they turned for experiments to the fruit fly, which can be bred rapidly in huge numbers and has a normal life expectancy of a month or less. What they found was surprising. The likelihood of death peaked at about 15 percent per day when the flies were between 40 and 60 days old, which in human terms is like an 80- or 90-year-old. Then, amazingly, the chance of death went down, until in the most ancient flies, over 100 days old, the chance of death was only about five percent. That's the same as the rate of death for flies in their prime, at 20 days old.

It's a long way from fruit flies to humans, but the possible long-term implications are enormous. All our projections of the number of old people in the next century are based upon the assumption that the Gompertz law, or something very like it, can be applied. Yes, we will have an increasingly large fraction of the population over 65; but no, the fraction over 90 or 100 will not be large, it will continue to be tiny.

Now it seems that this may not be the case. If people survive the "dangerous years" between, say, 70 and 95, perhaps they, like fruit flies, will move onto a new plateau of longer life expectancy. This century may see a great increase in the number of people living to be 110 or more. Their need for special care will be great, as will the demands that they place on an economic system already struggling to cope with a graying population in their 60s and 70s.

The failure of the Gompertz law may sound like bad news for the future, but not, I would argue, for anyone alive today and reading this. In another half century, techniques for maintaining health and fitness into old age should be far advanced. You will be a senior citizen, approaching the dangerous "middle years" - and delighted to find that the Gompertz law was long ago proved wrong.

Let's do lunch in 2050.

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