Charles Darwin :: Origin of Species :: 1872
Inspired by John Maudlin’s Thoughts from the Frontline Weekly Newsletter, here are some excerpts from the book Ubiquity, Why Catastrophes Happen by Mark Buchanan.
Think about the below in the context of society, structure, centralization/decentralization, financial markets, ecosystem, and black swan events.
Imagine, Buchanan says, dropping just one grain of sand after another onto a table. A pile soon develops. Eventually, just one grain starts an avalanche. Per Bak, Chao Tang, and Kurt Weisenfeld, played the sandpile game in their lab at Brookhaven National Laboratory in New York. They wrote a computer program to do create virtual sandpiles, dropping one grain of sand at a time on top. What is the typical size of an avalanche? Well it turns out there is none; however, they did find as you double the number of grains of sand involved in an avalanche, the likelihood of an avalanche is 2.14 times as unlikely. We find something similar in earthquakes. In terms of energy, the data indicate that earthquakes simply become four times less likely each time you double the energy they release (power law)
Some involved a single grain; others, ten, a hundred or a thousand. Still others were pile-wide cataclysms involving millions that brought nearly the whole mountain down. At any time, literally anything, it seemed, might be just about to occur.
In this simplified setting of the sandpile, the power law also points to something else: the surprising conclusion that even the greatest of events have no special or exceptional causes. After all, every avalanche large or small starts out the same way, when a single grain falls and makes the pile just slightly too steep at one point. What makes one avalanche much larger than another has nothing to do with its original cause, and nothing to do with some special situation in the pile just before it starts. Rather, it has to do with the perpetually unstable organization of the critical state, which makes it always possible for the next grain to trigger an avalanche of any size.
To find out why [such unpredictability] should show up in their sandpile game, Bak and colleagues next played a trick with their computer. Imagine peering down on the pile from above, and coloring it in according to its steepness. Where it is relatively flat and stable, color it green; where steep and, in avalanche terms, ‘ready to go,’ color it red.
What do you see? They found that at the outset the pile looked mostly green, but that, as the pile grew, the green became infiltrated with ever more red. With more grains, the scattering of red danger spots grew until a dense skeleton of instability ran through the pile. Here then was a clue to its peculiar behavior: a grain falling on a red spot can, by domino-like action, cause sliding at other nearby red spots. If the red network was sparse, and all trouble spots were well isolated one from the other, then a single grain could have only limited repercussions.
But when the red spots come to riddle the pile, the consequences of the next grain become fiendishly unpredictable. It might trigger only a few tumblings, or it might instead set off a cataclysmic chain reaction involving millions. The sandpile seemed to have configured itself into a hypersensitive and peculiarly unstable condition in which the next falling grain could trigger a response of any size whatsoever.
Buchanan concludes in his opening chapter -
There are many subtleties and twists in the story … but the basic message, roughly speaking, is simple: The peculiar and exceptionally unstable organization of the critical state does indeed seem to be ubiquitous in our world. Researchers in the past few years have found its mathematical fingerprints in the workings of all the upheavals I’ve mentioned so far [earthquakes, eco-disasters, market crashes], as well as in the spreading of epidemics, the flaring of traffic jams, the patterns by which instructions trickle down from managers to workers in the office, and in many other things.
At the heart of our story, then, lies the discovery that networks of things of all kinds – atoms, molecules, species, people, and even ideas – have a marked tendency to organize themselves along similar lines. On the basis of this insight, scientists are finally beginning to fathom what lies behind tumultuous events of all sorts, and to see patterns at work where they have never seen them before.
Related concepts -
self-organization
A process of attraction and repulsion in which the internal organization of a system, normally an open system, increases in complexitywithout being guided or managed by an outside source. Self-organizing systems typically (but not always) display emergent properties.
self-organized criticality
A property of (classes of) dynamical systems which have a critical point as an attractor. Their macroscopic behaviour thus displays the spatial and/or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to precise values.
scale-free network
The most notable characteristic in a scale-free network is the relative commonness of vertices with a degree that greatly exceeds the average. The average distance between two vertices in the network is very small relative to a highly ordered network such as a lattice
Catallaxy
The term Hayek used to describe a “self-organizing system of voluntary co-operation,” in regard to capitalism
Relational order theories
A number of independent lines of research depict the universe, including the social organization of living creatures which is of particular interest to humans, as systems, or networks, of relationships.
Complexity economics
Complexity economics rejects many aspects of traditional economic theory. The mathematical models used by traditional economics were formulated in an analogy with early models of thermodynamics. These mathematical models of economics were substantially based on the first law of thermodynamics,equilibrium. Later, the second law of thermodynamics, concerning the growing amount of entropy in any spontaneous physical process, was formulated by Rudolf Clausius. Proponents of complexity economics claim that traditional economic models never adapted to the latter discovery and thus remain incomplete models of reality, and that mainstream economists are yet to introduce information entropy to their models. Information entropy was developed in 1949 by C. Shannon and W. Weaver, based on Boltzmann’s statistical thermodynamics, as “information uncertainty”, associated with any probability distribution. Entropy has been used at least since 1988 to formulate the important concepts of organization and disorder, viewed as basic state parameters, in describing/simulating the evolution of complex systems (including economic systems).
I’m particularly interested in the concept of scale-free networks because they exhibit fault tolerant behaviour in the face of random failures.
