The Fractal Structure of Exponential Growth

10 October 2010


In his Notes on the Dynamics of Human Civilization: The Growth Revolution, Part I, T. Greer of Scholar’s Stage proposed what he called a growth revolution in conscious contrast to earlier historiographical attempts to identify periods of revolutionary change in history. For example, in reference to the Industrial Revolution, Mr. Greer says that it has been, “grossly mischaracterized,” and furthermore, “The industrialization of the world economy was the result, not the cause of modernization. The nature of this radical transformation is captured better by a different title: The Growth Revolution.”

I was thinking about this today and I realized that there are several periods of exponential growth in history of which our current world can be considered a consequence, that these occur at different orders of magnitude of history, and as such we can identify a self-similarity across different orders of magnitude of history that gives to this history a fractal structure.

At the level of history where geological time meets biological time — that is to say, the longest horizon of biological time — there is what is called the Cambrian Explosion. Most of the multi-billion year history of life on earth is little more than pond scum. For billions of years the earth was essentially covered in blue green algae and stromatolites, and the development of more complex forms of life was painfully slow. Then the Cambrian explosion occurred and suddenly there were seas teaming with an astonishing variety of life. Since that time, the earth has seen increasingly complex forms of life emerge, and, with the exception of periodic mass extinctions, growing numbers of species and biodiversity. It would seem that, once having passed a certain threshold of complexity, life’s capacity of grow exponentially was actualized.

Now we move in closer to history, thinking not in terms of millions of years of tens of millions of years, but thinking of terms tens of thousands and hundreds of thousands of years. Here we find the first exponential growth spike in specifically human history, and this is the agricultural or neolithic revolution. Colin Renfrew in his Prehistory: The Making of the Human Mind, emphasizes that this cannot be connected to the evolution of the genotype or the emergence of anatomically modern human beings. It would seem that our speciation event occurred somewhere on the horizon of 150,000 years ago, more or less (give or take some tens of thousands of years), but for most of this time modern human beings lived as hunter-gatherers with no larger social structure than the tribe or the clan. Then the agricultural revolution occurs, cities emerge, social differentiation and hierarchy emerge, settled societies emerge, human beings live in much greater density and organized state societies emerge. This occurred between 10,000 and 15,000 years ago, i.e., about a tenth of the total history of our species. Once again, it looks like we idled along for a long time without much happening, and then — Bang! — suddenly things started happening with much greater rapidity. As the Cambrian explosion saw life passing a threshold of complexity, the agricultural revolution saw human societies pass a threshold of complexity.

Now we move in even closer to history, approaching to the point where we look not at hundreds of thousands or tens of thousands of years, but only at hundreds of years. We are now considering a far shorter portion of time than that between the Cambrian explosion and the agricultural revolution. History at this level of magnification reveals to us another period of exponential growth, this time the growth represented by the Industrial Revolution. Just over two hundred years ago, beginning in England, spreading to Europe, and eventually making its way even today to Asia and Africa in the twenty-first century, societies that had had a stable form for thousands of years began to change much more rapidly. The Industrial Revolution uprooted stable societies and replaced them with something radically different. But this process, rather than taking hundreds or thousands of years, tends to transform traditional, stable societies within a period of decades, turning an acculturation to absence of change into a way of thinking when individuals expect to see dramatic changes within their lifetime and we say that “change is the only constant.”

Move in closer to history once again and look only at the last few decades. The oldest societies that had experienced the industrial revolution developed a pattern of stability. It is stable growth to be sure — the populations of industrialized nation-states have grown so accustomed to increasing standards of living that they rebel when the economy does not grow several percentage points per year — but it is a kind of stability within the chaotic growth and breakneck change that is the industrial revolution. Just in the past few decades even this stable growth has been given another jolt forward. The twin developments of high speed global transportation (the passenger jet) and high speed global communication (telecommunications and the internet) mean that human lives are changing at an accelerated rate of growth — yet another growth revolution in which a threshold has been crossed that allows growth across a number of other sectors.

What more could follow in this fractal structure of exponential growth? Will we need to consider the changes that will take place in human life — and, more generally, in life on earth — at a level of months, weeks, days, hours, or seconds? While I have written several posts that were highly skeptical of the so-called technological singularity (and I retract nothing that I have said in these posts), this is about the only thing that I can imagine that could once again spike the growth chart and produce yet another exponential growth curve, this time on an even shorter time scale corresponding to an extrapolation of the fractal structure of previous growth revolutions.

Human beings, however, live at a particular level of time consciousness and historical consciousness. We cannot perceive the vast periods of time studied by cosmology, though we can come to understand them through science, and we would not be able to perceive a fractal structure of exponential growth that disappeared into ever smaller periods of time. Thus one possibility is that something like the technological singularity could occur, but it would just as rapidly disappear from our view. We would go on devoting an hour to a leisurely lunch, even while at far higher magnifications of time further revolutions of exponential growth were going on unseen by us. We might come to understand these smaller periods of time through science, but they would mean as little to us in the present as the ultimate fate of the cosmos as contemplated by cosmology.

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Grand Strategy Annex

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2 Responses to “The Fractal Structure of Exponential Growth”

  1. T. Greer said

    I have often wondered why civilization began as late as it did. I know that William James Burroughs and a few other scholars have proposed that climatic change was the catalyst for the shift to agriculture, but I have yet to read his book, so I cannot argue for against the veracity of his claim. It is telling, however, that as of 2010 there are no other (major) theories in competition with his school.

    • geopolicraticus said

      Dear Mr. Greer,

      Thanks for your comment. I’m pleased you read this as it was inspired by your piece on what you call the growth revolution.

      As for the late start that civilization got (which parallels the late start of complex life and the late start of the industrial revolution, inter alia), I have always assumed that there are small, subtle, and incremental changes always building in the background, waiting for the appropriate trigger. One recent book has suggested that the trigger for the Cambrian Explosion was the development of the eye. This is a good theory, but not the only theory.

      Much historical work in Europe has focused on the antecedents of the Industrial Revolution, which go far back into the Middle Ages. The technologies refined in thousands and wind and water mills over hundreds of years were suddenly available at any geographical location with the invention of Watt’s steam engine. If you could get coal, you didn’t need wind or water anymore, and coal could be moved anywhere.

      I assume that the emergence and development of civilization similarly has very deep roots in our hunter-gatherer past, i.e., that the long, slow, gradual development of tools and the growing sophistication of techniques of gathering were ultimately triggered to produce full-scale agricultural civilization. Brian M. Fagan in his lectures Human Prehistory and the First Civilizations discusses possibilities of gathering such as returning to the same place each year, followed by systematic efforts to derive more food from such annual efforts. (Brian Fagan has also written extensively about climate change in relation to human history.)

      The important thing about triggers for events as large as integral shifts in history is that once the trigger has occurred, the consequences that follow happen catastrophically and become separated from the smooth and continuous historical development that preceded the trigger.

      Best wishes,


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