"Anyone who believes that exponential growth can go on forever in a finite world is either a madman or an economist." (Kenneth E Boulding, "General Systens Theory - The skeleton of science", Management Science Vol.2 (3), 1956)
"The greatest shortcoming of the human race is our inability to understand the exponential function." (Albert A Bartlett, "
"However, and conversely, our models fall far short of representing the world fully. That is why we make mistakes and why we are regularly surprised. In our heads, we can keep track of only a few variables at one time. We often draw illogical conclusions from accurate assumptions, or logical conclusions from inaccurate assumptions. Most of us, for instance, are surprised by the amount of growth an exponential process can generate. Few of us can intuit how to damp oscillations in a complex system." (Donella H Meadows, "Limits to Growth", 1972)
"Taking no action to solve these problems is equivalent of taking strong action. Every day of continued exponential growth brings the world system closer to the ultimate limits of that growth. A decision to do nothing is a decision to increase the risk of collapse." (Donella Meadows et al, "The Limits to Growth", 1972)
"Every day of continued exponential growth brings the world system closer to the ultimate limits of that growth." (Mihajlo D Mesarovic, "Mankind at the Turning Point", 1974)
"The world's present industrial civilization is handicapped by the coexistence of two universal, overlapping, and incompatible intellectual systems: the accumulated knowledge of the last four centuries of the properties and interrelationships of matter and energy; and the associated monetary culture which has evolved from folkways of prehistoric origin. […] Despite their inherent incompatibilities, these two systems during the last two centuries have had one fundamental characteristic in common, namely exponential growth, which has made a reasonably stable coexistence possible. But, for various reasons, it is impossible for the matter-energy system to sustain exponential growth for more than a few tens of doublings, and this phase is by now almost over. The monetary system has no such constraints, and according to one of its most fundamental rules, it must continue to grow by compound interest." (Marion K Hubbert, "Two Intellectual Systems: Matter-energy and the Monetary Culture", [seminar] 1981)
"In fact, in all those cases in which the initial state is given with limited precision (if we assume that the space-time is continuous this is always the case because a generic point turns out to be completely specified only by an infinite amount of information, for example by an infinite string of numbers), we can observe a situation in which, when time becomes large, two trajectories emerge from the 'same' initial point. So, even though there is a deterministic situation from a mathematical point of view (the uniqueness theorem for ordinary differential equations is not in question), nevertheless the exponential growth of errors makes the time evolution self-independent from its past history and then nondeterministic in any practical sense." (David Ruelle, "Chaotic Evolution and Strange Attractors: The statistical analysis of time series for deterministic nonlinear systems", 1989)
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