HOW I STOPPED WORRYING AND LEARNED TO LOVE CONTINGENCY III: PERFECTION

The “perfect storm” metaphor describes the improbable coincidence of several different forces or factors to produce an unusual outcome. The perfect landscape refers to the result of the combined, interacting effects of multiple environmental controls and forcings to produce an outcome that is highly improbable, in the sense of the likelihood of duplication at any other place or time (Phillips, 2007a). Geomorphic and other Earth surface systems (ESS) have multiple environmental controls and forcings, and multiple degrees of freedom in responding to them. This alone allows for many possible landscapes and system states. Further, some controls are contingent, and these contingencies are specific to time and place. Dynamical instability in many ESS creates and enhances some of this contingency by causing the effects of minor initial variations and small disturbances to persist and grow over time. The joint probability of any particular set of global controls (laws or non-contingent generalizations) is low, as the individual probabilities are <1. The probability of any set of local, contingent controls is even lower.

Rabbit bioturbation in South Australia. This is an example of a perfect landscape—because they all are.

Hence, the probability of existence of any ESS state at a particular place and time is negligibly small: all landscapes are perfect. The perfect landscape perspective leads toward a worldview that landforms and landscapes are circumstantial, contingent results of deterministic laws operating in a specific environmental context, such that multiple outcomes are possible.

The laws, place, history framework (LPH) is an extension of the perfect landscape concept, mainly as a pedagogical device, but it also has some analytical utility (Phillips, 2017). The laws correspond the “global” factors in the perfect landscape framework, and are the non-contingent generalizations that apply to any ESS of a given type. The “local,” contingent factors are in the LPH split into geographically and historically contingent aspects.

Expanding the mathematic representation of the perfect landscape paper to the LPH framework, we come up with an expression for the probability of existence of any given ESS state:

 

This indicates that p(S) is a function of the product of the probabilities of n applicable laws, m geographically contingent place factors or environmental controls, and q historically contingent events or episodes. As all p(L) < 1, and p(P), p(H) < 1, and often << 1, this shows the negligibly small probabilities of any given ESS state, at least if considered in significant detail. It also illustrates the related point that the more factors (L, P, or H) considered, the more specific and idiosyncratic the representation will be.

A perfect gully & slope failure: the Tarndale Slip near Gisborne, New Zealand.

Perfection and the LPH framework are pedagogically useful for communicating ideas about contingency in ESS evolution, and provide a formal way of expressing it. The equation above does rigorously demonstrate some key points, but does not (at least thus far) provide a tool for addressing the issues raised in Part I; i.e. reconciling the historical inevitability of what did happen with the many possible evolutionary trajectories that exist.

The language of perfection (with props to Sebastian Junger, whose book launched the perfect storm metaphor) was quite deliberately chosen. This relates to the “learned to love contingency” part of the title. While perfection poses clear scientific challenges, it also leads to the magnificent, often delightful, variety of the world around us.

Previous writings on these topics:

Phillips, J.D.  2006.  Evolutionary geomorphology: thresholds and nonlinearity in landform response to environmental change. Hydrology and Earth System Sciences 10: 731-742.

Phillips, J.D.  2007a.  The perfect landscape.  Geomorphology 84: 159-169.

Phillips, J.D., 2007b.  Perfection and complexity in the lower Brazos River.  Geomorphology 91: 364-377.

Phillips, J.D., 2015. Badass geomorphology. Earth Surface Processes & Landforms 40, 22-33.

Philliips, J.D., 2017. Laws, place, history and the interpretation of landforms. Earth Surface Processes & Landforms 42: 347-354.

Next: Infinite constraints

Posted: 21 July 2017

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