On the eschatology of the human condition

Conclusion

Let us summarize the conclusions we wish to draw from the preceding remarks. First, the pattern of unconstrained exponential growth of human civilization so often found in the past is similar to the pattern of exponential growth exhibited by populations of micro-organisms and insects in their earliest phases when population densities are low. Second, the con­straints imposed on the growth of the microcosmic societies by the limitations of their environment entail an absolute upper bound on their population, and similar constraints appear to apply to the various components, including population, of human societies. Both of these phases can be accurately described by simple mathematical formulae, independent of whether human or microscosmic societies are considered. Third, the microcosmic societies display an additional phase of population oscillation and ultimate decline.

We must now inquire whether this third phase may also be descriptive of the future life cycle of human population, and also whether it too can be described by mathematical formulae which lay bare its causation. If the answer to this last question is affirmative, then we will have a powerful tool with which to study the former problem.

The efforts of numerous scientific investigators have shown how this problem, at least in its gross characteristics, can be approached. One of the earliest and most distinguished of them, a truly original mind, was Vito Volterra, Professor of Mathematical Physics and Celestial Mechanics at the University of Rome, deliverer of an inaugural lecture at the founding of the Rice Institute in 1915. His theory of the "struggle for existence" prepared the foundation for all future efforts to construct a mathematical description of the interactions which determine the increase and decline of species and societies which compete with each other and amongst themselves for the limited sources of sustenance in their environment. His work, a far reaching extension of the Malthusian ideas, can be recognized in the most recent and vital computerized dynamic simulations of the world system associated with Jay Forrester, Dennis and Donella Meadows, and other contemporary scholars. The mathematical constituents of models of the Volterra and Forrester type are the formulae which describe unconstrained exponential and limited logistic growth. They are combined to reflect the structures of the various fundamental component sectors of civilization (including Population, Natural Resources, Capital Investment, and Pollution) and their intricate inter­actions. The resulting "life cycles" display the typical three stages exhibited by the life cycle of Paramecia ( [link] above), including the third oscillatory stage. [link] shows the situation for the well known World Dynamics models of Forrester [link] and Meadows et. al. [link] , based on the assumption that the interactive processes which are currently operative in our civilization will continue to follow their basic patterns subject only to the constraints which are naturally imposed by their mutual interaction. Population, Capital Investment, and Capital Investment in Agriculture Fraction (the amount of capital invested in agriculture) all exhibit: (the pattern of early exponential growth, logistic approach to a maximum, and the initiation of the subsequent oscillatory period.

The potentially catastrophic effect of the third, oscillatory, stage of development is strikingly illustrated in [link] which displays the possible consequences of the more efficient utilization of natural resources without corresponding adjustments in the other basic sectors of civilization. Without diverting our attention to argue the merits or reliability of this particular projection, let us note the beginning of the second oscillation in each of the curves describing the life cycle of Population, Pollution, Capital Investment, and Capital Investment Fraction in Agriculture (labeled CIAF in the Figure). Were the figure drawn to another scale, the similarity to the life cycle of Paramecia in [link] would be greatly enhanced.

We believe that the similarities between human and microcosmic societies which have been suggested above are more than superficial analogies. They justify, in our opinion, the most diligent and comprehensive investigation of the extent to which we can scientifically describe the condition of civilization and its variation with time. We must study the range of alter­natives, one of which may be our future; and discover the options that are open to us for directing our destiny, insofar as it is possible, to the fulfillment of the aspirations and ultimate attainments of civilization.