Per Bak Archives – The Rabbit Hole

Key Takeaways

Manifestations of SOC - regularity of catastrophic events, fractals, 1/f noise, Zipf's laws
1. So similar that they can be expressed as straight lines on a double logarithmic plot - are they all manifestations of a single principle? Can there be a Newton's law of complex behavior? Maybe SOC is that single underlying principle.
2. Catastrophism - majority of changes take place mostly from catastrophic events, also known as punctuated equilibrium
3. Fractal - nature is generally fractal, scale free
4. 1/f noise - features at all time scales, found all over nature
5. Zipf's Law - straight line plot between rank and frequency
Complex systems - systems with large variability
1. Brain may be the most complex system of all as it is able to model the complex outer world
2. Biggest puzzle of all may be how does complexity arise out of simple laws
3. Because of the large sensitivity of the critical state, small perturbations will eventually affect the behavior everywhere (butterfly/Lorenz effect)
4. Complexity is a consequence of criticality
5. Complexity deals with common phenomena in different sciences so the study of complexity benefits from an interdisciplinary approach
Chaos theory - shows that simple, mechanical systems show unpredictable behavior
1. Chaos is not complexity - gas in a chamber is chaotic but not complex (no emergent properties where non-obvious consequences occur based on underlying dynamical rules. Small changes in initial value does not cause huge differences in the end)
SOC systems evolve to the complex critical state without interference from any outside agent, an external organizing force. Criticality, and therefore complexity, can and will emerge "for free" without any watchmaker tuning the world
The process of self-organization takes place over a very long transient period. Complex behavior, whether in geophysics or biology, is always created by a long process of evolution. It cannot be understood by studying the systems within a time frame that is short compared with this evolutionary process
Once the poised state, the critical state, is reached, it is similar to that of a nuclear chain reaction
Catastrophes can occur for no reason whatsoever
Nature is SOC, the only known mechanism to generate complexity (sand pile metaphor and "avalanches" - punctuated equilibria)
1. Punctuated equilibrium - rate of evolution occurs periodically in spurts. This idea is at the heart of the dynamics of complex systems (expect Black Swans!)
  1. This idea is contrary to Darwin's original theory which proposed that evolution happens gradually, uniformly and steadily
  2. These fluctuations are unavoidable and cannot be repressed over the long-term and the most efficient systems show fluctuations of all sizes!
Perhaps our ultimate understanding of scientific topics is measured in terms of our ability to generate metaphoric pictures of what is going on. Maybe understanding is coming up with metaphoric pictures
1. All thinking is a type of analogy
Laws of physics are simple but nature is complex - the philosophy of physics has always been reductionist
Quality, in same way, emerges from quantity. But how? Maybe through the ever pressing laws of nature and scarcity. The fittest (most able to rapidly adapt) will survive and this becomes deemed as "quality"
An unlikely event is likely to happen because there are so many unlikely events
Must learn to free ourselves from biases and herd mentality in order to see things as they truly are
The problem with understanding our world is that we have nothing to compare it with (Galilean relativity!)
Systems in balance are not complex and generally have no emergent properties
Earthquakes may be the cleanest and most direct examples of SOC in nature
1. Faults form fractals; earthquakes follow power laws
2. Crust of earth has self-organized to the critical state, as evidenced by the Gutenberg-Richter law (simple power law)
  1. The importance of this law cannot be exaggerated. It is precisely the observation of such simple empirical laws in nature that motivates us to search for a theory of complexity
3. Pulsar glitches, black holes and solar flares also exhibit elements of SOC
Real life operates at the point between order and chaos, the critical state. Punctuations, avalanches, are the hallmarks of SOC
1. May be living in a highly nonlinear world where emergent events are very difficult, if not impossible, to predict.
Nothing prevents further progress more than the belief that everything is already understood
Science is often driven by sheer inertia. Science progresses "death by death"
Adaptation at individual or species-level is the source of complexity in biology
Fitness - we are "fit" only as long as the network/ecosystem exists in its current form. Fitness is not absolute and evolution cannot be seen as a drive towards a a more fit species
Life only in cold places with little chemical activity, not a hot sizzling primordial soup with a lot of activity since this does not allow for large periods of stasis for complexity to emerge
Gaia hypothesis - all Earth should be viewed as a single system as all organisms interact and co-evolve
1. Red Queen effect - if all other species adapt and become more fit, you have to become more fit just to stay in the same place
Regularity does not mean periodic. Just because a massive earthquake hasn't happened in 5,000 years, does not mean we should expect one soon
Acquiring insight is itself a worthwhile effort
Insight seldom arises from complicated messy modeling, but more often from gross oversimplification. Once the essential mechanism has been identified, it is easy to check for robustness by tagging on more and more details
Complex behavior can arise from a simple model through the SOC process
Thought can be viewed as a punctuated equilibrium event as it occurs only once enough signal hits the brain
1. Seek out challenges and important questions to focus on!
Brain operates at the critical state where ideas are just barely able to propagate. Too little and nothing happens, too much and the brain would overload
1. It appears that the human brain has not developed a language to deal with complex phenomena. We see patterns where there are none, like the man in the moon and the inkblots in a Rorschach test. We tend to experience phenomena as periodic even if they are not, gambling casinos and earthquakes. When there is an obvious deviation from the periodicity, like the absence of an event for a long time, we say that the volcano has become dormant. We try to compensate for our lack of ability to perceive the pattern properly by using words, but we use them poorly
Economics shows many signs of being critical but has made the mistake of trying to be "scientific" where everything needs to be predictable - it cannot be predicted
1. Shows periods of avalanches (financial crashes)
Traffic jams also at critical state
1. No cataclysm necessary to cause a jam
2. Perfect 1/f noise - stop and go behavior
SOC is a law of nature for which there is no dispensation - cannot suppress the fluctuations forever
1. Critical state is the most efficient state that can happen dynamically
  1. Why does it occur all over nature? Because it is robust and efficient!!
  2. Fluctuations are not perfect but they are healthy for dynamic systems. An over-engineered system may be more efficient for some time but catastrophically unstable

What I got out of it

Self-organized criticality stems from simple rules with no "blind watchmaker" and can lead to very complex outcomes. Exhibits criticality through occasional punctuated equilibria and emergent, non-linear properties (such as earthquakes). Fluctuations should be expected and are healthy! They are the most efficient way to run a dynamic system. Complexity can arise out of simple laws with no outside help and is seen all over nature. Chaos is not complexity.