For those interested in environmental modeling, Chris Freeman's and Francisco Louca's book, "As Time Goes By: From the Industrial Revolutions to the Information Revolution," is both relevant and challenging.

It discusses an important dialog in economics that has gone on for almost a century regarding models, mathematical formalisms, technique, and historical contingency. Questions arise because a number of economists, of whom perhaps Nikolai Kondratiev and Joseph Schumpeter are best known, grew fascinated with the "long waves" - patterns of change in economic, social and management systems underpinned by transitions between technology clusters of 40 or 50 years duration - that appear to characterize economic history.

Attempts to define, and explain, such waves using mathematical formalisms have generally proved ineffectual, in part because each era may be characterized in terms of a technology constellation, but the specifics of different technology systems, and associated managerial, institutional, financial, social and cultural changes, tend to be historically contingent. The system is neither recurrent, nor stochastic, but an evolving combination of both that can be understood only through historical analysis.

This piece of economic history has obvious relevance for current discussions regarding models and derivative policy formulation in environmental, sustainability, and climate change domains.

Obviously, a major factor in the complexity of all these systems, economic or environmental, arises from poorly understood processes of technological innovation. Reflecting both ignorance of how technological change occurs, and the need for tractable mathematics in complicated models, innovation is usually modeled as an exogenous factor that integrates smoothly and homogeneously into scenarios - the IPCC curves are a good example.

But, as the long waves themselves indicate, fundamental technological innovation is inherently contingent, disruptive, and chunky, and always co-evolves with equally fundamental institutional, social, financial, and cultural change.

Examples from economic history are legion. For example, the automobile mass consumption culture required the development of personal financing structures and the rise of a middle class that could afford mass consumption. The railroad required co-extensive communications networks, development of new forms of management and financial engineering, and even stabilization of time across national and international regions. The information revolution creates firms that look like networks, not hierarchies.

We can't know what future technological disruptions may look like. We do know that extension of smooth trend lines, such as in the Limits to Growth or Population Bomb treatments, is always wrong.

Moreover, differentiating between reoccurring and idiosyncratic phenomenon, the essence of generalization and thus modeling, depends on being able to differentiate between that which is stable, including those dynamics that are predictable and repetitive, and that which is unstable.

This becomes problematic, for economic or environmental modeling, when human social and cultural systems, and their reflexivity and contingency, become important components of the system.

It is here where many physical scientists and environmentalists stumble, for it is precisely the boundary between the stable and unstable, the recurrent and the stochastic, which shifts as science is extended from physical to social, cultural, and (human) historical systems.

This is even more the case as explosive and accelerating technological evolution across foundational technology systems - nanotechnology, biotechnology, robotics, information and communication technologies, and cognitive science - makes even that which we could previously assume to be stable contingent over much shorter time frames.

The stability of assumptions also reflects the time frames over which models are presumed to be valid. Over the short term, assumptions of linearity and stability of institutional and cultural structures holds.

Over the longer term, however, human history is highly contingent and unpredictable, and explanation of discontinuous changes in economic structure based on quantification and explicit models fail. Thus, econometric models that are undeniably powerful in short-term microeconomic conditions fare poorly over the decadal time frames of long wave phenomenon.

This time creep is also characteristic of environmental and climate change modeling: the general circulation models of climate change have some explanatory power regarding the physical processes behind climate change, and may be accurate so long as relatively stable technological, institutional and social bases can be assumed.

When such models are extended into social and cultural realms over periods of centuries, however, the basic assumption of institutional, technological, social and cultural stability becomes invalid. It is not that the models are "wrong," it is that they are being mistakenly applied beyond the boundary of their validity.

Another lesson from these past technological shifts is that hysteria in the face of change is not a new phenomenon. It is unfortunate, therefore, that misunderstanding the limits of important techniques should continue to contribute to such responses.

Brad Allenby is professor of civil and environmental engineering at Arizona State University, a fellow at the University of Virginia's Darden Graduate School of Business, and previously was AT&T's vice president of environment, health, and safety.