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1996 | Buch

How Nature Works

the science of self-organized criticality

verfasst von: Per Bak

Verlag: Springer New York

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SUCHEN

Über dieses Buch

and acknowledgments Self-organized criticality is a new way of viewing nature. The basic picture is one where nature is perpetually out of balance, but organized in a poised state-the critical state-where anything can happen within well-defined statistical laws. The aim of the science of self-organized criticality is to yield insight into the fundamental question of why nature is complex, not simple, as the laws of physics imply. Self-organized criticality explains some ubiquitous patterns existing in nature that we view as complex. Fractal structure and catastrophic events are among those regularities. Applications range from the study of pulsars and black holes to earthquakes and the evolution of life. One intriguing conse­ quence of the theory is that catastrophes can occur for no reason whatsoever. Mass extinctions may take place without any external triggering mechanism such as a volcanic eruption or a meteorite hitting the earth (although the the­ ory of course cannot rule out that this has in fact occurred). xu How Nature Works Since we first proposed the idea in 1987, more than 2,ooo papers have been written on self-organized criticality, making ours the most cited paper in physics during that period. How Nature Works is the first book to deal with the subject. The basic idea is simple, and most of the mathematical models that have been used in the implementation of the theory are not complicated.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Complexity and Criticality
Abstract
How can the universe start with a few types of elementary particles at the big bang, and end up with life, history, economics, and literature? The question is screaming out to be answered but it is seldom even asked. Why did the big bang not form a simple gas of particles, or condense into one big crystal? We see complex phenomena around us so often that we take them for granted without looking for further explanation. In fact, until recently very little scientific effort was devoted to understanding why nature is complex.
Per Bak
Chapter 2. The Discovery of Self-Organized Criticality
Abstract
In 1987 Chao Tang, Kurt Wiesenfeld, and I constructed the simple, prototypical model of self-organized criticality, the sandpile model. Our calculations on the model showed how a system that obeys simple, benign local rules can organize itself into a poised state that evolves in terms of flashing, intermittent bursts rather than following a smooth path. We did not set out with the intention of studying sandpiles. As with many other discoveries in science, the discovery of sandpile dynamics was accidental. This chapter describes the events leading to the discovery. In hindsight, things could have been much simpler; our thinking went through some quite convoluted paths.
Per Bak
Chapter 3. The Sandpile Paradigm
Abstract
The importance of our discovery of the coupled-pendulums case of self-organized criticality was immediately obvious to us. An open dissipative system had naturally organized itself into a critical scale-free state with avalanches of all sizes and all durations. The statistics of the avalanches follow the Gutenberg-Richter power law. There were small events and large events following the same laws. We had discovered a simple model for complexity in nature.
Per Bak
Chapter 4. Real Sandpiles and Landscape Formation
Abstract
Our ambitions extend beyond understanding the dynamics of real sandpiles. Nevertheless, experiments on sandpiles can be viewed as the first test of self-organized criticality. If the theory that large dynamic systems organize themselves to a critical state cannot even explain sandpiles, then what can it explain? Our abstract model grossly oversimplifies real sand, but we still hope that our experiments live up to our predictions. However, nature has no obligation to obey our ideas; our intuition could be entirely wrong. Theory has to be confronted eventually with real-world observations, so we study sandpiles and we ask, Do they or don’t they self-organize to the critical state?
Per Bak
Chapter 5. Earthquakes, Starquakes, and Solar Flares
Abstract
Earthquakes may be the cleanest and most direct example of a self-organized critical phenomenon in nature. Most of the time the crust of the earth is at rest, in periods ofstasis. Every now and then the apparent tranquillity is interrupted by bursts of intermittent, sometimes violent, activity. There are a few very large earthquakes and many more smaller earthquakes. The small earthquakes do not affect us at all, so scientific efforts have been directed toward trying to predict the few large catastrophic ones. Scientists have taken a very direct approach, formulating individual theories, or explanations, for individual earthquakes or earthquake zones; there has not been much effort directed toward a general understanding of the earthquake phenomenon.
Per Bak
Chapter 6. The “Game of Life”: Complexity is Criticality
Abstract
So far we have visited many phenomena on Earth and in the universe. However, one geophysical phenomenon was left out, the most complex of all, namely biological life. In the early days ofself-organized criticality, we did not think about biology at all; we had only inert dead matter in mind. However, this situation has radically changed. The story is one in three acts, to be told in the next three chapters, with more to follow. We have constructed some simple mathematical models for evolution of an ecology of interacting species. However, to appreciate the content of the theory that came out at the end, a historical account of the activities seems most suitable.
Per Bak
Chapter 7. Is Life a Self-Organized Critical Phenomenon?
Abstract
The step from describing inert matter to describing biological life seems enormous, but maybe it isn’t. Perhaps the same principles that govern the organization of complexity in geophysics also govern the evolution of life on earth. Then nature would not suddenly have to invent a new organizational principle to allow live matter to emerge. It might well be that an observer who was around when life originated would see nothing noteworthy—only a continuous transition (which could be an “avalanche”) from simple chemical reactions to more and more complicated interactions with no sharp transition point indicating the exact moment when life began. Life cannot have started with a chemical substance as complicated as DNA, composed of four different, complicated molecules called nucleotides, connected into a string, and wound up in a double helix. DNA must itself represent a very advanced state of evolution, formed by massively contingent events, in a process usually referred to as pre-biotic evolution. Perhaps the processes in that early period were based on the same principles as biology is today, so the splitting into biotic and prebiotic stages represents just another arbitrary division in a hierarchical chain of processes.
Per Bak
Chapter 8. Mass Extinctions and Punctuated Equilibria in a Simple Model of Evolution
Abstract
Darwin’s theory is a concise formulation of some general observations for the evolution of life on earth. In contrast to the laws of physics, which are expressed as mathematical equations relating to physical observable quantities, there are no Darwin’s equations describing biological evolution in the language of rigorous mathematics, as my colleague and friend Henrik Flyvbjerg once eloquently pointed out. Therefore, it is a highly important matter to determine if Darwin’s theory gives an essentially complete description of life on earth, or if some other principles have to be included. Darwin’s theory concerns evolution at the smallest scale, microevolution. We do not know the consequences of his theory for evolution on the largest scale, macroevolution, so it is difficult to confront, and possibly falsify, the theory by observations on the fossil record.
Per Bak
Chapter 9. Theory of the Punctuated Equilibrium Model
Abstract
The reader who is not mathematically and analytically inclined may skip most of this chapter, in which we take a brief look into the mathematical analytical theory of the punctuated equilibrium model, except for the final section, which points out an insightful analogy between evolution and earthquakes. It is important not to skip this section because the main point of this book is to prepare the ground for, and to develop, relevant analytical insight into the behavior of the model, and hence into the underlying physical processes. The main reason for dealing with grossly oversimplified toy models is that we can study them not only with computer simulations but also with mathematical methods. This puts our results on a firmer ground, so that we are not confined to general grandiose, philosophical claims.
Per Bak
Chapter 10. The Brain
Abstract
The human brain is able to form images of the complex world surrounding us, so it might seem obvious that the brain itself has to be a complex object. However, it is not necessarily so. We have seen that complex behavior can arise from models with a simple architecture through a process of self-organization. Perhaps the brain is also a fairly simple organ.
Per Bak
Chapter 11. On Economics and Traffic Jams
Abstract
So far we have proceeded from astrophysics to geophysics, and from geophysics to biology and the brain. We now take yet another step in the hierarchy of complete phenomena, into the boundary between the natural world and the social sciences. Humans interact with one another. Is it possible that the dynamics of human societies are self-organized critical? After all, human behavior is a branch of biology, so why should different laws and mechanisms be introduced at this point? Here two specific human activities will be considered, namely economics and traffic. Perhaps these phenomena are simpler than other human activities. At least, the activities can be quantified and measured, in terms of prices, volumes, and velocities. That might be the reason that economics exists as a discipline independent of other social sciences.
Per Bak
Backmatter
Metadaten
Titel
How Nature Works
verfasst von
Per Bak
Copyright-Jahr
1996
Verlag
Springer New York
Electronic ISBN
978-1-4757-5426-1
Print ISBN
978-0-387-98738-5
DOI
https://doi.org/10.1007/978-1-4757-5426-1