May 01 2010

Space: The Fractal Frontier — How Complexity Drives Exploration

Like a breath of fresh air, the science of self organized criticality has illuminated many disciplines, including astrophysics, biology, climate, economics, geopolitics, and others (see Turcotte & Rundle (2002) PNAS, “Self-organized criticality in the physical, biological, and social sciences.”)

What do Apollo and the new international Space Age have in common?
…Self organized criticality?

Click .

The brainchild of Danish physicist Per Bak (1948-2002) — “one of the most original people in science” — SOC is an emergent property of complex systems whereby they organize themselves into a critical state such that rapid changes, including catastrophes, can occur. You can see the famous “Bak sandpile” conceptual model of SOC in Aschwanden (2010) as well as in Bak (1996), How Nature Works.

The captivating assertion of social scientist and SOC enthusiast Gregory Brunk (2002) that,

Virtually all aggregate-level, monumental events are somehow ’caused’ by the process of self-organized criticality,

suggests that SOC may have played a major role in the Apollo program and other major MEPs over the last 200 years. This post is a brief sketch how that might work.

Apollo Was the Most Recent of the Great Explorations
Cordell (1996) described the extraordinary pulses of great human explorations (e.g., Lewis and Clark), macro-engineering projects (e.g., Panama Canal), and major wars (e.g., WW I) that cluster together exclusively every 55 to 60 years, over the last 200 years. I speculated that the decade from 2015 to 2025 would have economic, technology, and geopolitical parallels with the spectacular Apollo 1960s, including a JFK/Camelot-style zeitgeist.

Cordell (2006) introduced the concept of a “Maslow Window,” triggered by rhythmic, twice-per-century economic booms. Affluence-induced ebullience propels many to higher states in the Maslow hierarchy, where their momentarily expanded worldviews make great explorations and MEPs seem not only intriguing, but almost irresistible. As ebullience decays — due to widespread perceptions of budget stresses, a war, etc. — the Maslow Window closes.

The Bottomline is: The realization that Apollo is the most recent in a rhythmic, 200-year long string of great human explorations starting with Lewis and Clark, potentially opens the door to Bak-style SOC.

Wars and the Evidence for Complexity
According to Bak, a complex system exhibits SOC only if it has some form of power-law scaling, called “fractal” by Mandelbrot (1963). Based on their size-frequency plots for wars, Roberts and Turcotte (1998) conclude that,

The results we have shown indicate that world order behaves as a self-organized critical system independent of the efforts made to control and stabilize interactions between people and countries; and wars, like forest fires, are SOC processes.

Although Roberts and Turcotte (1998) only had data up to 150,000 deaths per war, the fact that “medium-size” wars are almost pure SOC indicates that the major wars of Maslow Windows are also fractal, as suggested recently for World War I by Harvard historian Niall Ferguson.

Punctuated Equilibria and Exploration
In 1994, the National Academy of Sciences held a major colloquium in Irvine, CA on “Physics: The Opening to Complexity.”

In Bak’s conference paper, he considers SOC in the contexts of geology, biological evolution, and macroeconomics. For example, in economics each system consists of many “agents” that interact together,

such as producers, governments, thieves, and economists. These agents each make decisions optimizing their own idiosyncratic goals. The actions of one agent affect other agents. In biology, individual organisms … (or individual species) interact with one another. The actions of one organism affect the survivability, or fitness, of others. If one species changes by mutation to improve its own fitness, other species in the ecology are also affected.

Bak generalizes Stephen Jay Gould’s biological theory of “punctuated equilibrium” to all complex systems:

The system exhibits punctuated equilibrium behavior, where periods of stasis are interrupted by intermittant bursts of activity … They are intrinsic to the dynamics of biology, history, and economics … Large, catastrophic events occur as a consequence of the same dynamics that produces small, ordinary events … We believe that this punctuated equilibrium behavior, first noted by Gould and Eldredge (1977, 1993), is common to all complex dynamical systems.

The Bottomline is: The Apollo program — seen in the context of 200 years of great explorations — exhibits punctuated equilibrium behavior, an important step toward identifying it and the other MEPs as a SOC process.

Dynamics of SOC — The Gap Equation
Bak’s Gap Equation governs the system’s evolution from weak SOC to the fractal, self organized critical state.

The model is so general that it can also be thought of as a model for macroeconomics. The individual sites represent economic agents, and the random numbers f1 represent their “utility functions.” Agents modify their behavior to increase their wealth. The agents with lowest utility functions disappear and are replaced by others. This, in turn, affects other agents and changes their utility functions.

Bak’s quote above could apply just as well to agents of particular space projects modifying their behavior and vying for funding at NASA (or elsewhere) and/or Macro-Engineering Projects likewise seeking support of all types. Agents and projects with the “lowest utility functions” soon disappear (a Darwinian principle), no matter how big they are – just ask Constellation advocates!

The Bottomline is: This compatibility with Bak’s law indicates that space projects and MEPs are most likely governed by SOC. The Space Project/MEP System is most fractal just before and during a Maslow Window. As in Bak’s computer simulations, transitions into and out of the strong SOC state are abrupt just before (e.g., in 1901; in 1958) or just after the Maslow Windows (e.g., in 1914 and in 1970). While in the critical state, large changes (i.e., great explorations, MEPs, major wars) can occur in response to even a minor stimulus.

Predictability and SOC
The fractal nature of SOC inhibits long-term predictability of specific events during the critical state (i.e., during a Maslow Window). However, the last 200+ years show that, especially during the non-fractal decades between Maslow Windows, the long wave has been a reliable guide to the rhythmic, twice-per-century timing of Maslow Windows from Lewis and Clark through 1960s Apollo to the present. And other intriguing regularities are also observable.

For example, according to former UCLA geophysics professor Didier Sornette — who more recently founded the Financial Crisis Observatory in Zurich — in reference to the U.S. stock market, “It is possible to identify clear signatures of near-critical behavior many years before the crashes and use them to ‘‘predict’’ the date where the system will go critical …”

Bak also hints at predictability (by analogy with his sandpile model, he refers to major changes during the critical SOC state as “avalanches”):

During an avalanche, a great deal of rapid activity occurs in which species come and go at a fast pace. Nature “experiments” until it finds another “stable” ecology with high fitnesses. The Cambrian explosion 500 million years ago can be thought of as the grandmother of all such avalanches.

So what should we expect prior to a Maslow Window? What’s the analog for Nature looking for a more “stable” ecology while “species come and go” in a Darwinian sense? What signal should we see of “near-critical behavior many years before” the critical Maslow Window?

Two potential candidates have been identified that appear regularly over the last 200+ years:
1) Major financial panic/great recession combinations (e.g., Panic of 1893) that usually begin 6-8 years before a Maslow Window (including the Panic of 2008 and current great recession),
2) Moderate wars and/or dangerous confrontations (e.g., Cuban Missile Crisis) that are rapidly resolved and occur early in or just before Maslow Windows (including the current Iran crisis).

These precursors are consistent with both long wave patterns and self organized criticality, when our complex international economic system self-organizes into a critical state — characterized by Great Explorations, Macro-Engineering Projects, and major wars — that we call a Maslow Window.

One response so far

One Response to “Space: The Fractal Frontier — How Complexity Drives Exploration”

  1. dirk alanon 07 May 2010 at 4:30 am

    was not the trans continental railroad and apollo 11 – 100 years apart ?

Trackback URI | Comments RSS

Leave a Reply