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[link] shows that the population of the United States has changed in different ways at different times: in the earliest periods after European settlement, growth was exponential and extremely rapid; from 1650 to about 1880, population growth was again exponential with virtually no deviations during this 230 year interval. Since 1880 there has been a marked decline in the rate of growth with irregu­larities which obscure the general trend features. We may nevertheless conclude that any American born between 1650 and 1850 could confidently conclude from personal experience and the historical record that exponential population growth is a natural feature of life in America. The marked change evident in the manner of growth of population during the period centered about 1880 calls for an explanation) and one is readily forth­coming. Prior to that period, there remained a western frontier which was, bit by bit, continually pushed back thereby effectively increasing the land area of the settled nation, until the con­straint of fixed geographical and settled limits induced a change in the nature of population increase. Indeed, during the earlier periods, population increase in the United States did not necessarily lead to increased population density due to the effect of territorial expansion, so that, although more recent periods have seen smaller rates of growth, the local population density experienced by most Americans is probably increasing more rapidly now than before.

Alternative possibilities

The analysis to this point appears to confirm the generality of exponential growth for various important segments of civilization over periods of time significantly longer than a single generation. The feature of change in the rate of growth of United States population also suggests that there are some mechanisms which can distort or perhaps even destroy the operation of exponential increase. Let us turn our attention to the determination of what these might be and whether they and their effects are intrinsic and unavoidable, or extrinsic and removable.

We would like, of course, to be able to experiment with numerous identical copies of our world with all its inhabitants and curiosities, subjecting each replica to a distinct set of circumstances and following each along its future path to its terminus, thus we could establish the more and the less desirable modes of development which are open to us, asses their benefits and costs, and learn how to direct ourselves and our posterity, if not to the best of all possible worlds, at least away from the worst. That this option is not open to us should not act as a deterrent to serious consideration of the multiple possi­bilities the future holds, for there are still two ways left to proceed. The more refined founds itself on a deep idea of Maxwell, who in his study of the statistical properties of gases, conceived an infinite ensemble of ideal replicas of the system of actual interest which populated, in his thoughts if not in reality, the various ideally possible physical states. Maxwell then sought to identify the most probable of these states with the state which, apart from certain relatively negligible fluctuations, actually obtained. His efforts created the important and successful discipline of statistical mechanics and set a potential pattern for the study of social systems which has not yet received the attention it deserves.

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Source:  OpenStax, Dynamics of social systems. OpenStax CNX. Aug 07, 2015 Download for free at https://legacy.cnx.org/content/col10587/1.9
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