keane
Joined: 09 Jul 2007
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 Posted: Fri Nov 30, 2007 5:24 pm Post subject: Collapse: A Model |
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For those who have an interest in current events relating to sustainability of current paradigms, with particular reference to climate and energy issues, but keeping socio-political issues ever in mind, the following is a simple mechanism for framing a process of societal collapse.
The point here is not to cheer lead for collapse (I have an infant son), but to present a model for assessing conditions in order to enable the prevention of collapse, or for those that might want to prepare for collapse.
How Civilizations Fall: A Theory of Catabolic Collapse
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C(p) = W(p) + W(c) --> steady state (1)
C(p) is new capital produced, W(p) is existing capital converted to waste in the production of new capital, and W(c) is existing capital converted to waste outside of production.
W(p) + W(c) = M(p)
Equation 1 can be more simply put:
C(p) = M(p) --> steady state (2) Societies which move from a steady state into a state of expansion produce more than necessary to maintain existing capital stocks: C(p) > M(p) --> expansion (3)
[anabolic cycle] In the absence of effective limits to growth, once started, this expansion becomes a self-reinforcing process, because additional capital can be brought into the production process, where it generates yet more new capital, which can be brought into the production process in turn.
replenishment rate, r(R),
rate of use by the society, d(R),
d(R)/r(R) >1, resource depletion
Thus, unless all of a society's necessary resources have an unlimited replenishment rate, C(p) cannot increase indefinitely because d(R) will eventually exceed r(R), leading to depletion and exponential increases in capital required to maintain C(p) at any given level. Liebig's law of the minimum suggests that for any given society, the essential resource with the highest value for d(R)/r(R) may be used as a working value of d(R)/r(R) for resources as a whole.
...the relationship between capital and waste. As capital stocks increase, M(p) rises, since W(c) rises proportionally to total capital; more capital requires more maintenance and replacement. M(p) also rises as C(p) rises, since increased production requires increased use of capital and thus increased W(p), or conversion of capital to waste in the production process. All other factors being equal, the effect of W(c) is to make M(p) rise faster than C(p), since not all capital is involved in production at any given time, but all capital is constantly subject to conversion to waste. Increased C(p) relative to M(p) can be generated by decreasing capital stocks to decrease W(c); by slowing the conversion of capital to waste to decrease W(c) and/or W(p); by increasing the fraction of capital involved in production, to increase C(p); or by increasing the intake of resources for production, thus increasing C(p). If these are not done, or prove insufficient to meet the needs of the situation, M(p) will rise to equal or exceed C(p) and bring the anabolic cycle to a halt.
...a society facing the end of an anabolic cycle faces a choice between two strategies.
One strategy is to move toward a steady state in which C(p) = M(p), and d(R) = r(R) for every economically significant resource.
The alternative is to attempt to prolong the anabolic cycle through efforts to accelerate intake of resources through military conquest, new technology, or other means. Since increasing production increases W(p) and increasing capital stocks lead to increased W(c), however, such efforts drive further increases in M(p). A society that attempts to maintain an anabolic cycle indefinitely must therefore expand its use of resources at an ever-increasing rate to keep C(p) from dropping below M(p).
If the attempt to achieve a steady state fails, or if efforts at increasing resource intake fall irrevocably behind rising M(p), a society enters a state of contraction, in which production of new capital does not make up for losses due to waste: C(p) < M(p) --> contraction (4)
contraction takes two general forms
A society that uses resources at or below replenishment rate (d(R)/r(R) = 1), when production of new capital falls short of maintenance needs, enters a maintenance crisis in which capital of all kinds cannot be maintained and is converted to waste: physical capital is destroyed or spoiled, human populations decline in number, large-scale social organizations disintegrate into smaller and more economical forms, and information is lost. Because resources are not depleted, maintenance crises are generally self-limiting. As capital is lost, M(p) declines steeply, while declines in C(p) due to capital loss are cushioned to some extent by the steady supply of resources. This allows a return to a steady state or the start of a new anabolic cycle once the conversion of capital to waste brings M(p) back below C(p).
A society that uses resources beyond replenishment rate (d(R)/r(R) > 1), when production of new capital falls short of maintenance needs, risks a depletion crisis in which key features of a maintenance crisis are amplified by the impact of depletion on production.
...With demand for capital rising as the supply of capital falls, C(p) tends to decrease faster than M(p) and perpetuate the crisis. The result is a catabolic cycle, a self-reinforcing process in which C(p) stays below M(p) while both decline. Catabolic cycles may occur in maintenance crises if the gap between C(p) and M(p) is large enough, but tend to be self-limiting in such cases. In depletion crises, by contrast, catabolic cycles can proceed to catabolic collapse, in which C(p) approaches zero and most of a society's capital is converted to waste.
A society in a depletion crisis does not inevitably proceed to catabolic collapse. If depletion is limited, so that decreased demand for resources as a consequence of diminished production brings d(R) back below r(R), the accelerated fall in C(p) may not take place and the crisis may play out much like a maintenance crisis... |
NOTE: the author's discussion of the Maya is affected by the lack of recently published evidence of drought as the primary cause of collapse. |
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