For most of human history, technology changed very little during a person’s lifetime. Certainty, their life was not constant with the hard agricultural life being interrupted by war, disease, and famine. However, very few new technologies would come into their life. In contrast, tremendous change occurred throughout the 20th century as planes, cars, electricity, radio, and computers enter during their lives. In my life, I have also experienced rapid change, but it seems a bit different, more quantitative than the qualitative change seen by my grandparents’.

Can we make sense of this rapid change? Are there patterns to discover? One familiar pattern is the Moore’s law concerning the rapid increase in computer capability. Some, such as Ray Kurzweil, have looked at the extension of this pattern and predict that soon change will be even faster. However, the social responses to this technology are a bit slower, for example, will the internet ever be really safe for transactions and communications?

But there is another perspective that learning usually follows a general pattern, being slow as a new topic is being explored, then increases once the definitions and concepts are stable, and then slows again as some of the finer points and uncertain areas are handled. This describes an S-curve of learning – slow at the start and at the end, but fastest in the middle. This curve also applies not just to a personal learning but also learning within a community such as scientists exploring new fields and perhaps societies discovering new ways to organize.

Attempting to generalize this further, about a decade ago Theodore Modis made a list of the important events not only in human history discovery but also in human evolution, and biological evolution. The increasing rate of important events displayed a distinct mathematical pattern. However, it was unclear whether the last few points indicated a continuing trend to a singularity like Kurzweil predicted, or a logistic (learning) curve. The accelerating rate through 3 major transitions on Earth were highlighted by Carl Sagan in his 1970's book, The Dragons of Eden. The information storage and transition mechanisms in the evolution of life, humans, and civilization changed from DNA to brain to artifacts. The beginning of these periods are roughly 5 billion, 5 million, and 5 thousand years ago.  This is a reduction in the time to reach a new level  by a factor of 1,000.  (The pattern would continue with 5 years and then about 2 days which obviously will not happen.)

Are there any indications of an inflection (logistic growth)? While I discussed a logistical pattern of scientific discovery before, the science and technology do not develop in a vacuum but instead within a civilization approaching global limits in economic organization, energy resources, environmental limits, leadership, and global demographic convergence.  The limits might be replaced if a new way of organizing is discovered. This would be similar to expansion of the limits in historical transitions such as from hunter gathering to agriculture to civilization.

Some of these earlier transitions have led some like Joseph Tainter to suggest that societies do undergo learning processes from initial development growth, maturity and then grow to an extent in which the basic assumptions lead to decreasing marginal returns on investment, often leading to collapse unless another form of organization is identified. While the GDP has been a standard measure of economic health for decades, its original proponents realized its limitations and suggested the development of more realistic measures.  One such alternative indicator was the Genuine Progress Indicator which adjusted for economic activity causing environmental damage and the benefits of non-market activity such as volunteering.  This index seemed to peak in the mid-1970's and since has been flat or decreasing. Robert Costanza has recently looked at other countries also and found similar results.

This leads to questions of energy use and environmental damage.  Robert Ayres is advocating for a reinterpretation of the role of energy and entropy in economics. Energy seems to be a major contributor to the determination of economic health. Currently the technological revolution of the past couple centuries has been fueled by a gift from nature- the fossil fuels which had been stored away for millions of years to be extracted and converted into a most convenient energy source (energy density, and transportability). In a recent blog I explored the use of this fossil fuel to attain the next sustainable energy society.  This transition was compared to the launch of a rocket into orbit in that both had limited supplies of fuel to obtain an elevated level of stability. As with a launched rocket, it is unclear what the final result will be either a stable orbit or one of the many failure pathways.

During the 20th century at least three waves of environmental issues were resolved. These issues included the early problem of sanitation in urban areas; national issues of air and water pollution, and international issues such as climate change.  As larger scale problems were addressed, the time to resolve them also increased, as to be expected since the larger scales required more complex forms of cooperation.

This leads to the question of leadership.  Since the 17th century, economic leadership has been transferred about every 100 years from the Dutch to England, to the expanding United Kingdom, and then to the U.S.  One pattern in these transitions is that the population of the next leader was about twice the size of the previous leader (at the time of transition). This can be interpreted as leadership in economic growth is eventually limited by the size of the country. To continue leadership needs to be passed eventually. If the pattern were to continue, a few more transitions would head towards participation of the global population.

To more clearly relate this to global economic and demographic convergence, recently a Russian, Andrey Korotayev and an American, Jack Goldstone, collaborated to explore this potential convergence of global economic opportunities. They discovered a tight correlation between 1) the gap in first and third world countries and 2) the rate of global population growth. Again the peak, or transition point was found to be around 1970, with the population growth rate now decreasing along with the economic gap.

(Mathematical Note: A simple exponential model assumes that the increase is proportional to its current value, i.e., dy/dt= ky.  Kurzweil's accelerating growth model assumes that the exponential rate of increase is proportional to the amount already known (k=k'y) so that dy/dt=k'y².  This leads to a point in time where a singularity (infinite rate) occurs. The logistic equation assumes some limit (e.g., population size or environmental constraint) such that the exponential rate declines as the limit is reached, i.e., k=k'(1-y) leading to the equation for logistic growth , dy/dt=k'y(1-y).  A model that includes accelerating growth up to an inflection point can be constructed using a combination of these: dy/dt=k'[y(1-y)]²