In his 1972 article for Science, Phillip Anderson makes the claim that while all scientific disciplines are reductionist — meaning, they seek to understand a system by breaking it up into smaller parts — they are not constructivist because the symmetry of one stable state is not always applicable to a higher state. The lessons learned at each level, however, can provide valid insights into the workings at other levels, even if the same symmetries do not apply. Anderson argues for interdisciplinary communication to find qualitative relevance wherever the quantitative breaks down.
According to Anderson, intensive research seeks to discover new fundamental laws, and extensive research seeks to the application of these laws. Problems arise when fundamental laws do not scale upward as the number of objects in the system increases. Symmetry is not evident (or necessary) as the levels of interest change. The agents comprising a symmetrical object do not need to be symmetrical themselves. This description by Anderson turns the traditional notion of the universe as a continuous constructionist spectrum into a discrete collection of related contexts building off of behaviors not necessarily present in the levels below.
Why is this important? “More is Different” is considered to be the article that planted the seeds of complexity by describing this notion that the rules at one level don’t necessarily apply to higher levels. It would be another decade before Per Bak helped usher in complex systems as a focus of study by describing piles of sand.
Bak, with his second wife Maya Paczuski, wrote a seminal work (PDF) in 1995 for the National Academy of Sciences describing phase transitions through their sand pile model. It preceded his best-known publication, How Nature Works, by a year. In the paper, Bak offers simulation as a means of examining complex phase transition phenomena through experimentation rather than narrative.
In a narrative approach, typical of traditional “soft” sciences, attention is paid to the points of criticality in phase transitions as the catalyst to the inevitable flow of events over time. As it focuses on these isolated events in time, narrative is good at becoming aware of short-term phenomena but offers no understanding of their mechanisms. Simulation uses computation to provide a rough model of reality based on simple rules. It reveals the critical systemic state rather identifying a single catalytic event. This self-organizing criticality describes large dynamic systems as ones that evolve naturally into a highly interactive state.
In the sand pile simulation, the grain of sand which causes an avalanche can easily be skipped during a repetition of the same sequence. When that intervention occurs, that particular avalanche may be avoided, but only temporarily. Another grain will cause another avalanche — often of greater impact — to surface later. The probability of an avalanche increases if the naturally occuring catalyst is removed.
In an equilibrium state, the assumption is that the collective assembly of parts will be intelligently aware of and respond to catastrophe. However, in nature equilibrium is only a period of “relative tranquility between the bursts of activity.” The outcome, then, is not contingent on any specific minor detail. It is an inevitable response of a system in a non-equilibrium state.