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Bak's paradigm for self-organized criticality is the formation of a sand pile where the sand pile represents a complex system. Initially as sand grains are trickled down, they remain within a close proximity to their position of landing causing the sand pile to appear flat. As time progresses the sand pile becomes steeper, leading individual sand grains to experience minor slides around the sand pile. When the sand pile reaches its maximal steepness, further trickling of sand grains leads to avalanches or the sliding of sand grains down most or all of the length of the sand pile. At this point, the sand pile system has reached a state of unbalance and its behavior cannot be explained in terms of the actions of individual sand grains. The avalanches are also dynamic and this behavior can only be explained by examining the properties of the overall sand pile.
Bak also points out that sand piles display their own punctuated equilibria, an idea that evolution occurs in spurts instead of gradually. As sand is being trickled down, there are long periods of time where there is little or no activity. These states of apparent equilibrium are interrupted by sudden bursts of sand slides that affect the whole system. Bak says that the avalanches observed in a sand pile are very similar to the punctuations in evolution. According to Bak, avalanches or punctuations are the trademark of self-organized criticality. Furthermore, Bak claims that since complexity is seen everywhere, nature functions at the self-organized critical state and complexity observed across the sciences can be explained in a manner analogous to the sand pile system.
Bak defines complexity as variability and says that a theory of complex systems has to be abstract where all possible scenarios are considered and there are no references to individual components of the system. Bak believes that the theory also has to be statistical and probabilistic where specific details about the system cannot be obtained. Lastly, Bak believes that a theory of complexity must be able to explain general observations across individual sciences that cannot be understood within the realms of the particular sciences. The examples of general observations used by Bak are the occurrences of catastrophic events, fractals, one-over-f noise (1/f noise), and Zipf's law.
Catastrophic events are encountered since complex systems are composite where components of the system can affect each other through a domino effect. Earthquakes are caused by the proliferation of cracks on the earth's crust in this manner. It has been observed that nature is fractal where fractal is described to be geometrical structures with features with varying length scales. Specific examples in nature include the geometry of mountains, coastlines and trees. 1/f noise can be thought of as fractals over time and it has been observed in diverse systems such as the flow of the Nile, light from quasars, and highway traffic. Zipf's law says that the magnitude of a system's element is related to the element's rank in the system. Zipf's law has been applied to various systems such as the population of a city as a relation to the city's rank and the frequency of a word as a relation its rank. An observed trend in all of the phenomena described is that they are emergent and can be described in terms of power laws. Mathematically, when a straight line is obtained on a double logarithmic plot, the straight line represents a power law.
Since all of these phenomena can be expressed as power laws, Bak argues that they are expressions of a single underlying theory: self-organized criticality. Next, Bak guides the reader through the process that led to his discovery of self-organized criticality as well as the ways in which the theory has been tested on "real sand piles" and landscapes. For the rest of the book, Bak discusses earthquakes, evolution, economics and traffic jams as being applications of self-organized criticality. Using earthquakes as a model for self-organized criticality, Bak says that the Earth's crust has self-organized to a critical state through platetectonics, earthquake and volcanic activities. The Gutenberg-Richter law is used as evidence that the earth's crust has gone through this organizational process. Furthermore, Bak finally allows for the fact that earthquakes, volcanic eruptions, river network formation and avalanches are all interlinked. In this way, the Earth's crust is thought to be a complex system at a critical state where the criticality is caused by different phenomena. Bak also shows that pulsar glitches, the changes in a pulsar's rotational velocity, black holes and solar flares are also phenomena that operate at the critical state.
Bak says that one can think of the Gaia hypothesis, an idea that all life on earth can be thought of as a single organism, having self-organized criticality as the underlying principle. Based on this belief, in the critical state all species can be represented as one organism following a single evolutionary path. In this system, an event can lead to the collapse of a large fraction of the ecological network and its replacement by a new stable ecological network. The replacement represents the "mutated" global organism. When the ecological system is at the critical state, all species affect each other yet act jointly as a single organism sharing the same fate. As evidence, Bak uses mass extinctions where a small portion of the overall organism is affected by a meteorite but a large portion of the overall organism becomes extinct.
Bak then talks about the significance of power laws in connecting earthquakes and evolution. He says that according to the power law, the longer a place has gone without an earthquake, the longer it has before it will experience an earthquake. Similarly, the longer a species has existed, the longer it will exist. Bak also mentions that John Conway's Game of Life displays criticality, but once the rules set by Conway are changed, the Game of Life is not critical. He goes on to say that complexity is only observed in the Game of Life when it is in the critical state since non-critical rules result in simple structures. He uses this to stress the point that complexity only results from criticality.
There seems to be a similarity between Bak's How Nature Works and Wolfram's A New Kind of Science in that both authors declare that they have come upon a new and original idea that explains all complex systems. Although Bak gives credit to work contributed by his colleagues, the reader is left with the impression that Bak is the one with that connects all the pieces. The book itself is an interesting read as Bak includes his insights into the scientific community. One can also argue that the models presented in How Nature Works are very vague and general since they overlook important biological and physical factors. Regardless, as Bak points out in the preface of the book, the theory of self-organized criticality must carry some weight since more than 2,000 papers had been written on self-organized criticality from the time the idea had been proposed to when this book was published, making the original paper the most cited paper during that period in physics. [an error occurred while processing this directive]