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The following pages contain the full text and figures of an article which first appeared in the journal Technological Forecasting and Social Change, published by Elsevier Science Inc., New York, NY. Posted with permission.

As Charles Darwin said, in the struggle for life number gives the best insurance to win [1]. The Bible (Genesis 22:17) records that when God wanted to boost the elected ones, he promised that they would become more numerous than the grains of sand on the sea shore (i.e., >>1012).

In fact, world population since the mid 20th century has grown by about 2% per year, a rate that doubles the population in roughly 35 years. Actual data fitted over five centuries with reasonable equations show that the secular rate of growth kept increasing until around 1970, leading, at least from a mathematical point of view, to an infinite population in a finite time (Figure 1). (See [2] for a numerical history and [3] for an infinite prediction.) Such growth worries environmentalists and many others and leads to a first question: Where is the world population moving?

So far, demographic predictions tend to diverge from the real numbers after about 20 years. To give some examples, in 1951 the Population Division of the United Nations (UN) estimated that the world population in 1980 [10] would be between 2.976 and 3.636 X 109. The use of four significant figures for a scenario is certainly worth a note. The number in 1980 was actually 4.45 x 109. In 1986 the UN predicted 6 x 109 for the year 2000. The 1995 world population is 5.7 x 109. The UN mark will probably be reached in 1997. The UN 1992 prediction for 2150 is a la carte [11]. One can choose seven different world population levels placed between 4.299 x 109 and 694.213 x 109. However, the preference is for 11.543 x 109. Unabated is the love for significant figures.

Predictions are always made with ifs. Because everybody seems scared by increasing human populations, fertility values are tamed in such a way-as to produce a maximum psychologically acceptable number of humans, usually between 1010 and 2 x 1010 by 2100. The reckoning date is well beyond the life expectancy of present politicians and demographers. These soothing predictions are obviously based on the if that current total fertility rates will fall everywhere to the conservation value of 2.1 (see Figure 6, later). As in weather forecasting, building the analysis from the bottom up becomes more and more complicated when one details to regions (and social status), and forecast results are not better.

Suffice it to say that the problem of the future size of humanity is unsolved. Whether the answer is unknown or unknowable, the problem partly lies in the methods, and no sign of breakthrough has appeared in the literature. Our response is to go back to the numbers and have a fresh look. We seek quantitative regularities to see whether it is possible to forecast with some internal logic where and when the growth will stop.

For both mortality and fertility all the mechanisms involved are regulatory and require social and cultural intervention. Because changes in culture and social behavior can be described by diffusive processes, basically captured in logistic equations (or their derivatives or sums), our fresh look will refuter the numbers along these lines. The fact that we can model with good precision over long periods several parameters usually looked at in charts in a qualitative way will show the strength of our method.

The use of the logistic model is widely established in many fields of modeling and forecasting [12, 13]. It has a controversial history in population ecology, a point to which we return near the end of this article. One of a family of density-dependent functions, the logistic law of growth assumes simply that systems grow exponentially under the constraints of an upper limit producing a typical S-shaped curve [14]. The three parameters of the logistic curve, which recur in our figures, are characteristic duration Dt, the limit K, and the midpoint tm. The characteristic duration Dtis the time needed for the curve to grow from 10% to 90% of the limit K. Appendix 1 offers a mathematical description of the logistic model.

There is obvious need for demographic statistics of reasonable quality and consistent definitions. See [2, 11, 15-28] for data sources. We also offer precise definitions of terms in the Glossary, Appendix 2. Shortcomings arise in several ways. For example, although local demographic registrations are of ancient origin and reliable, their patching up into national statistics may not be. African states may have made written records only recently. Changing cultural values affect what is recorded. Years for which detailed survey data are available are few and do not include all countries. In Appendix 3 we give some quantitative examples of the uncertainty associated, even in the present day, with fertility rates. Nevertheless, we believe that the long-run and comparative nature of our approach makes the analyses robust.

Our plan is to look first from the bottom up, using the logistic to model life expectancy and then, in much greater detail, fertility. When cases are intractable analytically, as modeling human population has been, the alternative is to look from the top down with phenomenological insights. The master case is that of thermodynamics, where a couple of well-centered axioms permitted almost two centuries ago the construction of a branch of physics unchallenged to date. Its analytical counterpart, statistical mechanics, took a full century to develop. In the case of demography, analysis of the aggregate behavior or niche started for animal populations in the mid-1800s. Before concluding, we briefly reapply the logistic model to the analysis of aggregate human populations with the help of some extra hindsight.

Life expectancy in the developed world started changing in about 1800, improving slowly. The maximum gains have been in reducing infant mortality, but octogenarians also gained a few years. Demographers and medical doctors still struggle to define the future of the process. A simple solution can be found by assuming that each of us is endowed with longevity by DNA. Dangers along the way impede reaching the final age. However, by removing the dangers through nutrition, hygiene, medicine, and various coatings and protections, finally one can reach an age corresponding to longevity.

Because the removal of the dangers is a process of social learning, the equation most apt to describe it is a logistic [29]. For a time, knowledge and experience enable people to gain years of life with increasing speed. Then the process slows as we near the limits of efficacy of our various strategies. In fact, evolution of life expectancy during the last two centuries can be precisely mapped using logistics. In Norway the gain in life expectancy at birth forms a neat logistic taking off at the 1% level in 1810 and eventually adding 39 years to the life of the new-born Norwegian child (Figure 2). The process is logistic at each age, with 20-year-olds eventually gaining 20 years, 50-year-olds 11, and 80-year-olds 3 (Figure 3). In fact, one can also map with a logistic the final gain versus age, as we have done for the Dutch population (Figure 4).

All such analyses show that in developed countries we are near a limit [30]. Barring genetically engineered defense against senescence, life expectancy for women will stay in the mid-80s and for men about 5 years less.3 Consequently, the effect of increasing life expectancy on population, which for a while has masked the decrease in fertility in some rich countries, will disappear.

For developing countries we have not attempted to analyze comparable trends because the series of credible population statistics are not long enough. We would expect similar results. The basic processes of social development are the same, though perhaps operating more rapidly than they did for the countries that industrialized early. In developing countries, increase in life expectancy will sum up quickly, boosting the size of their populations on top of the effect of fertility. 152ee80cbc

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