On the eschatology of the human condition

The second method is much more concrete and analogical, and consequently more narrow in its assertions and less certain in its implications. It consists of finding analogues, or models, of aspects of human civilization, primarily amongst the micro-organisms and insects which run through their life cycles at rates so great that the birth, development, and death of their “societies” and the eschatology of their condition can be followed and documented during an interval brief according to the standards of change of our civilizations. But a funda­mental problem always intrudes: to what extent is it permissible to generalize from the rise and fall of the fruit fly Drosophila to the rise and fall of Rome, or of humanity itself? We cannot answer this question, but we also cannot avoid the belief that one of the most pressing problems which confronts anyone concerned with the future of humanity is the determination of whether, and if so, how, human society differs from the societies of lower forms insofar as the great forces which govern growth and decay are concerned.

Logistic growth

Consider, for instance, the life cycle of a population of wild type Drosophila grown in a pint bottle, as illustrated in [link] . It is clear from that figure that the population does not increase indefinitely and exponentially, but rather approaches, after some brief time, an absolute limiting value beyond which it cannot pass. It is probable that no Drosphila savant would assert that either the historical record or common sense suggest that exponential growth is the norm for Drosphila society, as it generally seems and has seemed to be for us. Yet there is a certain lawfulness in the pattern of population growth displayed in [link] , called logistic growth, whose exact form need not concern us here. Suffice it to say that by means of a formula, not more complex than that which describes exponential growth itself, the calculations shown in the rightmost column of the Table below were obtained, which show a striking agreement with the observed population.

The logistic growth pattern is as common amongst short lived rapidly reproducing lower life forms as the exponential pattern is amongst humans, and amongst people-related phenomena such as knowledge and energy inputs. Figure 5 displays the life cycle of a society of yeast cells; once again, the presence of an absolute limit beyond which population apparently cannot press is evident, and once again, the logistic mathe­matical description is appropriate.

In order to draw the connection between these societal microcosms which pass, from our vantage point, so quickly, through all their phases, let us reconsider the data for the yeast cell population of [link] expressed with respect to the semi-logarithmic vertical scale such as used in [link] , and in terms of which exponential growth corresponds to straight lines. [link] , so drawn, shows that for the first 6 hours of growth, the yeast population does in fact increase exponentially, but thereafter a rapid decline in the rate of increase becomes apparent, leading after another 6 hours to a stagnant population whose numbers barely change until termination of the experiment. The reader can hardly help but notice the approximate correspondence between the early and middle periods of [link] with the corresponding periods of exponential growth of United States population from 1650 to 1880, and the subsequent decline in the rate of increase after 1880 displayed in [link] . Are we certain that we are different from Drosophila, or from yeast cells, insofar as the cycle of population is concerned? If we are certain, on what do we base our certainty?