Approaches to complex adaptive systems

Complex adaptive systems 16,9,26,41 displaying a range of common emergent characteristics have been found in a variety of fields such as biological evolution 25, ecosystems 52 and social systems 46. Some previous studies contribute to an interpretation that societies exhibit learning (of social organization, technologies, and energy use).

History may well form a large complex adaptive system 24,38,55,56. As systems progress, new options that arise for the systems may spontaneously bifurcate into two potential discrete states. While the simplest model of complex systems can be driven into chaos, more realistic models with limitations suggest a possible reversal of increasing complexity 57. Another approach is to take a longer view of historical trends and phases. Carl Sagan 51 presented stages of information processing, progressing exponentially from the early universe to the present day. These stages were the development of life, brains, and technology, starting with life origins about 5 billion years ago. A geometrical progression rate would suggest transitions from life evolution to brain evolution around 5 million years ago and further transition to civilization and technological development about 5,000 years ago.

Characteristic properties of complex adaptive systems include (1) a resource that drives the level of complexity, such as energy use 58,59,4,19,6,5 (2) new options at critical stages (bifurcations) along development paths; and (3) competition and learning as the options are explored (Figure 1). The difference in the dynamics of complex adaptive systems compared to a complex system is the adaptive or learning aspect. This changes the static diagram of complexity as a function of driving parameter in a complex system that might exist at one value of the parameter. The learning is logistic between bifurcations with increasing energy usage, which eventually leads to an environment that requires reorganization at a critical energy flow at the bifurcation points. Reorganization is required to control the increasing energy flow without crossing into chaos related to uncontrolled energy release such as fires, wars, and environmental degradation. The increasing energy flow drives environmental changes and challenges that might lead to a self-organized criticality at the bifurcation point. If the changes between bifurcation points are too large, the logistic learning phase might become nested (i.e., a single long logistic transition may be realized as several smaller logistic transitions). This has been observed in the development of fundamental physics discoveries that seem to be flowing within one large logistic growth pattern that could possibly be realized as seven sequential smaller logistic transitions 32. The logarithmic time scale of Big History may be related to the substitution of the energy driving parameter with time, where each phase has a similar integrated energy flow. The energy flow rate ratio is about 4 times greater than in the previous phase. This ratio is similar to a reduction by considering energy flow in fractal systems by Bejan 1. Korotayev 27 has articulated that an integrated large-scale world-systems model may be easier to understand and model similar to the way that aggregate macroscopic gas laws are simpler than the underlying microscopic molecular dynamics.

This evolution of increasing complexity goes against the natural flow toward randomness from the second law of thermodynamics. This is possible only because the Earth is not a closed system; it experiences a net flow of energy from the Sun. The process of this more general evolution is not continuous; instead, it is separated into sequential phases of logistic adaptation followed by discrete bifurcations. This behavior has been seen in the development of leading capitalist countries 30. In physics, one way to go against the flow is to use energy for controlled oscillations. For example, the natural tendency would be for a sailboat to go with the wind, just as the natural tendency for an inverted pendulum would be to fall under the force of gravity. In both cases, a strategy of oscillation—tacking for the sailboat and tip vibration for the inverted pendulum—can be used to stabilize the dynamic system out of equilibrium. In tacking, the boat alternates between traveling at angles to the left and right of the wind direction 36.

Fig 1. Characteristics of a complex adaptive system

This paper reviews previous studies that indicate elements of the above system. These studies include recent and longer-term energy flow rates, logistic trends of major historical events, nested logistic transitions in physics, and trends in important length scales. This complex adaptive system hypothesis of Big History is compared with two recent hypotheses concerning the rate of technological change of Kurzweil 28 and Modis 40. Possible implications are then explored, including a possible slowing-down in progress due to going beyond the inflection point of the overall logistic curve; interpreting the Big History logistic curve as a spiral along a double cone; and possible connection with a self-consistent interpretation in quantum mechanics.

Historical energy flows

How have energy flows changed in the past? 53,43 Since the hunting-gathering stage, human societies have undergone transitions toward more complex forms (e.g., from agricultural villages to civilized states, to trading networks, to industrialization, to the current evolution of a services- and knowledge-based economy). Human beings have used various sources to derive energy to support various levels of societies. These energy sources include our own muscle and that of animals, as well as wood, wind, water, coal, oil, and nuclear power. The increase in energy usage over this period is illuminating: a human’s intake of 2,500 calories per day corresponds or averages to about 100 watts (W) (i.e., about as much energy as a large incandescent light bulb uses). The average current per capita rate of energy use in the United States stands at 15 kilowatts (kW) of energy (including commercial, industrial, and residential use), or about 150 times a person’s food energy intake/use per day. This measure corresponds to about 3.5 factors of Feigenbaum’s number and suggests there might be three or more transitions, or bifurcations, where the energy flow increases by a factor of about 5 (assuming that the ordering parameter is inversely related to the energy flow). Additional transitions might be the result of a concentration of energy use by parts of a civilization. For example, the agricultural transition from hunting/gathering occurred over a long period but saw a concentration of effort (as measured by time spent on food production). In addition, the development of civilizations then organized rural work efforts to support urban development and classes. The details of specific developments or energy sources and uses have been studied; 53 however, to test the relationship between leadership and an aggregate measure such as energy consumption it is necessary to estimate the energy use quantitatively for various leading societies in human history.

Fig 2. Temporal relationship of the energy fuel source, energy intensity, and leadership. The energy fuel source and leadership exhibit pulses. The ratio of the energy intensity (energy per person in the leading nation) between pulses is about four 35.

Once freed from depending on slave labor as in the ancient civilizations, there was more motivation to explore mechanical and energy extraction to help reduce physical efforts, leading the West to utilize water, wind, and wood along with mechanical machines. Artifacts such as cathedrals, ships, and castles attest to their ability to apply these technologies and energies in creative ways. This activity led to a shortage of wood in Western Europe (especially in England and the Netherlands) after the recovery from the Black Plague, which created the need to import vast amounts of wood and timber from further north and east as was traded by the Hanseatic traders 3. An estimate of annual wood use in the middle of the Northern Renaissance (in 1670) is 4 cubic meters (m3) per person. Water, wind, and animal-derived power were also utilized. The sum of the usage conversion rates of these energy sources suggests that there could have been approximately 500 W of energy consumed per person in the late Renaissance, or about a factor of 5 times greater than the 100-W consumption rate of one person.

The energy use per person then increased again as fossil fuels became extensively used 42,47. The use of coal enabled the Industrial Revolution. By 1860, energy use in the United States was up to about 3.5 kW per capita. Over the course of the 20th century, oil and natural gas, along with nuclear power and hydroelectricity, were added to use. The oil crises in the 1970s prompted a more efficient use of energy resources, with the result that the productivity of energy resources increased by about a factor of 1.6 12. This increase in raw energy resources use, combined with more efficient use, led to an increase of a factor of about 5 in energy use per person in the United States (Figure 2).

Energy changes in extended evolution suggest a geometrically decreasing timescale for subsequent transition periods, along with increasing energy flows. If evolution occurs in three phases 8, there are 3 factors of approximately 1,000 in this timescale from the beginning of life approximately 5 billion years ago, to the beginning of human brain development 5 million years ago, to the beginning of Ancient civilizations 5,000 years ago.

Within each of the three phases, the evolution might also occur in a geometric pattern. If the shortest duration of the most current sub-phase is 50 years, chosen because it is similar to the current Kondratiev period 13 and similar to a generational time, then there were 20 of these periods during the civilization phase. Spread out over 6 sub-phases would give the geometric factor in time of 20 to the 1/6 power which is a factor of just greater than 3. This time contraction factor was used in describing the changes in energy intensity 18,11,43 as summarized in Table 1. Note that just one time contraction factor was realized from the big bang to the beginning of life on Earth. This factor is also similar to time and energy contraction factors found by Snooks 54 and Bejan 1.

Table 1. Changes in energy flows through extended evolution

Transition (years ago) Description Energy Change
15 Billion Gravitational Gravitational energy causes clumping and nuclear energy causes energy to be release and element formation
5 Billion Planet/Life Life first gathers energy through chemicals or thermal gradients. Later the light from the sun is captured and turned into chemical energy
1.5 Billion Complex Cells Simple prokaryotes form symbiotic relationships to form a larger and more organized eukaryote cell
500 Million Cambrian Oxygen levels reach a concentration so that multicellular organisms can be supported. The many body types and survival strategies lead to rapid evolution
150 Million Mammals Animals move to land after plants. The larger temperature variations lead to a way to regulate temperature to ensure ability to be active throughout the day and seasons.
50 Million Primates A generalist strategy using various food sources including fruits leads to greater energy to the brain
15 Million Hominids Further generalist strategies and social organization again leads to greater energy use by the brain
5 Million Humans Humans adapt to a changing climate by leaving the forest for the savannah along with the capability for walking to expand the range of natural resources
1.5 Million Speech Further social organization leads to an expanded food sources including scavenging.
500,000 Fire Fire improves the energy availability from food
150,000 Ecoadaptation Humans move out into other ecosystems expanding the range of energy resources
50,000 Modern Humans The benefits of specialization and social organization are realized during the ice age
15,000 Agriculture Domestication of plants and animals leads to a more intense and reliable use of the land
5,000 Civilization Organization at a city level allows risk reduction and order with increasing population
1,500 Commercial Revolution Financial and mechanical technological techniques are applied and improved in a sustaining growth organization
500 Science/Exploration Exploration of lands and ideas leads to expanded energy resources
150 Industrial Fossil fuel allows large amounts of resources to be used along with increasing specialization
50 Information Control through systems and computers allows greater efficiency in the use of energy and handling of pollution.

Trends in addressing environmental issues

The issues of energy use and environmental sustainability are deeply entwined. Analysis identified the marginal return on investment of resources, such as energy, as societies grow larger and more complex as a major cause of the collapse of complex agricultural societies 58. Tainter suggested that many agricultural societies collapsed by overextending their reach into nonsustainable systems. The impact of environmental degradation has been an important factor in the development and decline of civilizations 7,15,48. Most of Tainter’s analyses focused on agricultural societies because of their simplicity relative to industrialized societies.

In the 20th century, three key phases, or waves, of environmental issues arose at different times and different political scopes: (1) the sanitary phase of rapidly growing urban centers in the early 20th century; (2) national concern with clean air and water, with action peaking in the early 1970s; and (3) international concern over transboundary issues (e.g., wildlife) and atmospheric release (e.g., chlorofluorocarbons, sulfur dioxide, and carbon dioxide), with treaties peaking in the mid-1990s 39,44,33 (Figure 3). However, throughout the 20th century these issues arose faster but took longer to resolve than they did in the past, which is an unsustainable pattern.

This leads to questions concerning ways of understanding waves, their connections, and their directions. Specifically, what is the next environmental phase and how will it be organized? A prediction based on logistic learning trends is that new issues, such as global climate change, trade, inequality, and environmental degradation, need to be addressed at a quicker pace as the world population and energy demand increases. If the interval between the last two phases, in 1970 and 1996, is repeated, then the next environmental phase will peak in just over another decade

Fig 3. Environmental phases since the early 20th century

The three identified periods of environmental interest had different spatial scales: local, national, and international. It would be interesting to look at the trends in both the duration of elevated interest and the time between the peaks of the periods. The data in Figure 7 suggest a complete logistic growth period, with a midpoint in 1972 and a 22-year duration. Including this, the time between the periods drastically diminished, about halving, from about 57 years (1915 to 1972) to 23 years (1972 to 1995) 33.

What might be next? There are many dimensions to be considered, including new technologies, better understanding, new governance models, and new levels of environmental complexity. New technologies, including combinations of genomics, robotics, artificial intelligence, and nanotechnology, offer potential environmental benefits and risks.

The environmental interest and activities in the previous century seem to indicate a pattern of periodic interest as technologies are developed, environmental problems arise, and social responses are formulated. A critical factor for determining the continuation of this pattern is the relative rate of technology development compared to the social response. Possible leading indicators of the next period of environmental interest include new social mechanisms such as the incorporation of environmental impacts in economic accounting and the responsible development of new technologies.

Modern leadership transitions

The trend of simple characteristics of population and relative productivity are examined within the nations that formed the sequence of leading capitalist countries 30. The population influences both the scale and complexity of the state organization. For example, a larger population produces more only if it is efficiently organized. Therefore, the historical sequence of leading nations does not start with the most populous nation but instead with a limited population where new organizational structures could be explored. The diffusion of technological and social ideas from these leading countries might be demonstrated by their relative productivity and resource use. The trends are then analyzed with regard to how they might indicate potential future directions and factors.


Fig 4. Relative productivity of large regions. The x-axis is the annual gross domestic product in millions of dollars. Some time markers indicate the year in which these markers were achieved 30 .

To test the relative speed of intensification and diffusion, the relative productivity (defined as the ratio of gross domestic product [GDP] per capita of a region to the global average) is explored in Figure 4. Relative productivity is plotted as a function of GDP (with a log-scale) instead of as a function of time. If the GDP grew exponentially at a constant rate, the x-scale would be proportional to the time difference. Since the GDP grew slower at earlier times, this graph emphasizes the more recent, quicker, and more dynamic global economy. As expected, before the modern era, relative productivity was initially quite uniform. (In 1500, the global GDP was about $250 billion.) Then it diverged, with Western Europe’s productivity increasing, followed by that of its Western colonial offspring (United States, Canada, and Australia), and then by that of Japan (in the 1970s). The relative productivity of Asia (except for Japan) and Africa decreased. The productivity of the two remaining areas (Latin America and Eastern Europe) hovered around the average relative productivity. Recent dynamics reveal a sharp rise in non-Japanese Asian productivity, although it is still below the average. If innovations were to diffuse around the world faster than the rate at which current leaders could generate any additional competitive advantage, the expectation would be that relative productivity would converge again. However, current data show that the increasing competitive advantage is still growing. It is possible that with rapid change and growth in China, India, Russia, and Brazil, this trend might soon reverse.

The three state trends investigated—population, relative productivity, and energy use—suggest that a global transition is near the inflection point. The estimates are based on population limits, limits on the progress rate and diffusion rate of technological innovations, and environmental limits on energy use. This conclusion is not surprising since the global system seems to be nearing its furthest extent from equilibrium.

Historical events and logistic growth

Similar to the analysis of the history of fundamental physics discoveries32 , a list of important events during various development phases might be constructed and analyzed corresponding to a logistic (or learning) pattern. Modis saw a hint of this in his paper and made some suggestions as what the various sub-phases might be 40. For example, Diamond lists some important events in the transition from agriculture to city life which can be treated with equal weight to form a logistic curve 14. What one expects is a slow rate of discoveries early in the process, followed by a quicker discovery rate, with the quickest rate at the inflection point in the middle, followed by another slower phases of discoveries. Figure 5 shows events in the transition to agriculture. Other transitions in human history from modern human hunter-gatherers, to agriculturalist., to a civilization, to a modern commercial system, to industrialism, to the information age are currently being explored with a similar method. Early indications are that the duration of a phase is roughly a third of the previous phase.

Fig 5. Logistic trend of major events in the transition to primitive agricultural societies


As mentioned earlier, one interpretation of events from the Big Bang to the present is a logistic transition in complexity 40. If this transition is realized, the rate of technology progress is peaking and will eventually slow down. It might be symmetrical about its midpoint; in other words, if the transition point was around 2000, then the first half of the 21st century might be similar to the second half of the 20th century, and the second half of the 21st century would see slower progress, as happened during the first half of the 20th century.

Are there other trends that might connect these transitions? Some patterns in history concern the scale at which evolution occurs and the scope of its influence (Figure 6) 31. In the very early universe, fundamental Planck-scale effects, such as hypothesized inflation, would have caused fundamental changes throughout the universe. One interpretation of the events that followed entails a sequence of better-understood processes involving larger particles occurring over decreasing scales—for example, recombination of electrons and protons to form hydrogen atoms in clouds; fusion into larger nuclei in stars; crystal formation involving rocks condensing into planets; and simple molecules transformed into complex organic molecules in the early atmosphere and seas. Biological evolution occurred on various ecosystem scales through complex cells, multicellular organisms, and finally humans. One interpretation of human evolution includes a transition in a relatively small ecosystem of part of the Great Rift Valley from forests to grasslands. Cultural evolution continued in ever increasingly larger communities (bands, tribes, villages, cities, states, alliances) with ever decreasing sizes (or, more specifically, increasing precision) of tools (fire, stones, sharp metal, clock parts, machine tool-made parts, microelectronics). If this pattern continues, the current scales might include a global community investigating tools at the nanotechnology scale.

Fig 6. Highly schematic drawing of the changes in evolutionary length scales through time. At early times, larger particles formed through processes in large structures (e.g., larger nuclei forming in stars). At later times in cultural evolution, technology tools with higher precision were developed as human organizations grew in size (e.g., machining mills with high precision enabled interchangeable parts leading to industrialization on a national scale) 31.

Interpretations of recent rapid technological and social change

Forecasts of the near future vary widely in scope and outlook, predicting situations from near utopia to near dystopia. Issues of great concern during this period include (1) the energy transition problem of moving from an unsustainable fossil fuel—based economy to something else; (2) the widespread nature of the problems currently being discussed in terms of global warming, global trade, global terrorism, and global knowledge transfer; and (3) the possible opportunities and risks of new technologies such as genetics, nanotechnology, and artificially intelligent computers and robots 50.

Recently, various interpretations of trends in technological progress have led to widely differing predictions. Specifically, Ray Kurzweil 28,29 hypothesized an ever-increasing rate of technological change, based on his analysis of over a century of progress in computation technologies. Theodore Modis 40 hypothesized a very different future, one having a decreasing rate of technological change, based on analyses of events from the Big Bang to the present. However, Kurzweil investigated the computing and electronics sector by looking at cost per computation to formulate a possible extension of Moore’s Law. The inclusion of early electronic technologies, such as relays and vacuum tubes, led Kurzweil to propose that the rate of technological change is increasing with time; in other words, that Moore’s Law of the doubling of electronic device densities every 18 months will be surmounted by new technologies that double in performance in less time. An ever increasing rate of technological change could soon lead to a technological “singularity.”

Another model of technology progression and diffusion that has been studied is based on the logistic equation. This progression assumes that the rate of progress is proportional to both the current level of complexity and the fraction of complexity yet to be discovered. Theodore Modis 40 suggests that the history of the universe might also be viewed as a logistic development of complexity. He arranged important events in the history of the universe from a variety of sources, assumed that each event was equally important, and then made the assumption that the complexity of an event is its importance divided by the transition time to the next event. The dependence of the cumulative fraction of complexity on milestone number (not the event’s time) could be interpreted either as (1) the first half of a logistic curve or (2) a sequence of events that will culminate in a singularity. Modis favored the logistic development interpretation 40.

These two scenarios can be related to different simple models: Kurzweil’s singularity scenario, with continual increasing exponential progress, might derive from a simple complex model, whereas Modis’s long-term logistic growth, with a tipping point determined by limitations in the learning rate and energy extraction rate, might be related to the more complex but realistic model . If this latter transition is accurate, the rate of technological progress might peak and eventually slow, with impacts for economics and leadership 37.

The overall logistic of the Big History might be viewed as consisting of three spirals on one side of a double cone representing the evolution of life, mind, and human civilization (Figure 7). Each spiral would consist of six to seven nested smaller logistic growth phases with time durations decreasing by about a third. The astronomical period before life began (i.e., 13.8 billion to 5 billion years ago) is a factor of three times the duration represented in the cone. This period was driven by gravitation and expansion as the universe’s temperature dropped, at first quickly but then slowing down. This can be represented by a cone pointed in the opposite direction. After the inflection point, a reflection in the duration of phases might occur. For example, the next hundred years after the inflection would have a technological development rate about the same as preceding century. However, after that the rate of change would slow.

Fig 7. Hypothesis of the Big History logistic growth pattern

The possible implications that history follows a complex adaptive system path informs other avenues of pursuit such as the anthropic principle 2,21,49, the Fermi question, 61 and the big questions 60. The anthropic principle raises the question of why the six fundamental physical constants seem to be set to support the development of life (and of black holes). For example, Fred Hoyle (Davies 2007)was able to predict the energy of a nuclear state in carbon, based on the need for its existence to support life. If life has a more fundamental role in the universe, as many have suggested 62, this might help explain the possible developmental patterns seen in this large complex adaptive system. The Fermi question was asked by Enrico Fermi, the nuclear scientist who first demonstrated the capability of a sustained nuclear fission. After the atomic bomb had been developed, the rapid pace of technology led him to think about life on other planets and ask the question “Where are they?” This arose because if the rate of progress is so quick, an extraterrestrial civilization would only require a bit of a head start to develop seemingly magical technologies to explore the galaxy. While there are many potential answers proposed to resolve this mystery, the logistic interpretation of development suggests that the rate of technology development might slow down, although it has a long way to go. It might take longer to develop sophisticated technologies for exploration, thus reducing the advantage of a short head start by one civilization.

Others are exploring basic questions of the relationship between physics and consciousness and exploring the possible relationships of current and future intelligence to the evolution of the universe. For example, if the Copenhagen interpretation of quantum physics is taken, that consciousness is necessary to collapse the wave function, then it is possible to interpret the development of the universe as a vast parallel quantum computer to search for intelligence 20. The path that generates such intelligence first collapses the wave function, and all possible quantum paths that had existed in entanglement before would disappear, leaving the historical record of the universe and earth as we know it. A different approach is concerned with the possibility of closed time loops such that the universe is self-consistent and self-explanatory with a necessary condition that it generates intelligence that would be able to get it started. Potential deep connections between the mind and quantum physics have been proposed and are being investigated 17,45,22,23.

As a result, we are left with many more questions, sparse partially subjective data, and multiple conflicting hypotheses. However, the exploration of these questions is interesting in itself. As Paul Davies recently expressed 10 :

If life follows from [primordial] soup with causal dependability, the laws of nature encode a hidden subtext, a cosmic imperative, which tells them: “Make Life!” And, through life, its by-products: mind, knowledge, understanding. It means that the laws of the universe have engineered their own comprehension. This is a breathtaking vision of nature, magnificent and uplifting in its majestic sweep. I hope it is correct. It would be wonderful if it were correct. […] if it is, it represents a shift in the scientific world-view as profound as that initiated by Copernicus and Darwin put together.