"Anyone who believes that exponential growth can go on forever in a finite world is either a madman or an economist."

Physicists understand the mathematics of exponential growth. They, along with the rest of us often ignore its consequences, including the first law of sustainability: "Neither population growth nor consumption can be sustained indefinitely."

Sustainability is a buzzword about environmental balance, recycling, energy and food production. It is a simple concept that brings a sense of environmental virtue if we feel that we are living "sustainably." We know what it is but maybe can’t quite define it.

The report "Our Common Future" — also known as the Brundtland report (1987) from the World Commission on Environment and Development of the United Nations — defined sustainability as "meeting the needs of today without compromising the ability of future generations to meet their needs." This definition of sustainability says nothing specifically about the environment, but a clean environment better meets those needs, and it is not only we humans that have needs.

Sustainability is related to carrying capacity, which is the maximum load that a given environment can support without detrimental effects. Estimating the carrying capacity of a planet is an inexact science because of the extreme complexity and nonlinearity of the components of the global ecosystem.

One cannot put Earth in a test tube, but it is possible to sew together a tapestry of observations and experiments that model how ecosystems function and then use the model to estimate the global carrying capacity.

It is a simple model but shows interactions between three variables: population, consumption and impact. The complexity of the variables, their interdependence and sparse data make precise calculations impossible.

Populations consume different amounts of food, energy, water and natural resources, while environmental impacts depend on any number of factors and are difficult to quantify.

Without knowing what the global carrying capacity is, we are stumbling in the dark with potentially dire consequences if our impact is excessive. Ecosystems at all levels can make extreme adjustments to compensate for extreme or chaotic changes.

The planet has an unknown but finite carrying capacity, to which calculations suggest we are close, and if "detrimental" is the criteria, then we have already crossed the line.

Even if we could quantify the global carrying capacity and control our human impact, what level of sustainability would we choose to maintain? All civilization creates some environmental impact in proportion to density of energy usage.

A green agricultural revolution in the 1970s postponed the predictions made a decade earlier by Paul Erlich ("The Population Bomb") of reaching carrying capacity by the millennium, but population grew exponentially to 6.8 billion with nearly 15 percent literally starving.

Evidence abounds in several areas that something is placing great stress on the planetary ecosystem. We humans are the usual suspects.

No one knows what will happen as we collectively approach the global carrying capacity, but it is almost certain that we will and equally certain that we will not like it either socially or environmentally.