Fractal collapse: How the dominant societies and economies may fail.

Six images showing the stages of formation of a Sierpinski triangle
The stages of formation of a Sierpinski triangle illustrating fractal collapse

Fractal collapse is an important, useful idea.  It helps us understand that a society, economy, political system, or civilization may not “fall,” but rather become pock-marked and weakened—shot through with micro-collapses.

The United States may be in an advanced state of collapse.  There are many indicators that this is the case.  The national debt, nearly $20 trillion, about a quarter-million dollars per family of four (see my “US national debt per family”), seems unrepayable.  America’s former industrial heartland is now mostly rustbelt, and parts of Detroit look like sets for “Walking Dead” or “The Road.”  Climate change is bearing down from one side and resource depletion from another.  Its democratic system—rotted by dark money, voter suppression, gerrymandering, the distortions of the Electoral College, and messianic populist politics—has delivered gridlock, ideologues, cartoon-level analyses of complex issues, and, now, Trump.  Many of the manufacturing jobs that have not moved to Asia may soon be taken by robots.  Inequality and incarceration-rates are at record highs.  One could extend this list to fill pages.

Despite the preceding, I’m not predicting that America (or Greece or Australia or England) will “fall”—pitch into rapid and irreversible economic contraction and social disintegration.  Instead, fractal collapse is more likely.  In fractal collapse, parts of a system fail, at various scales, but the system, in diminished form, carries on.  We’re seeing this in America.  We see the collapse of a household here (perhaps a result of the opioid crisis), and a neighbourhood, there; a city declines rapidly (think Detroit or Scranton) and a county declares bankruptcy.  Collapse occurs in various places and at various scales but the aggregate entity moves forward.  And such collapses are not predictable—they do not just happen to poor people or in the “poor” places.  Suddenly and unexpectedly, the investment banks collapse, then General Motors becomes insolvent.  The Senate and House of Representatives cease to function properly.  Collapse is not a single event.  As we are seeing it play out now—amid the hyper-energized and dominant “industrial” economies—collapse is multiple, iterative, and repeated across scales: it is fractal.

And collapse is not monolithic or pervasive.  Indeed, some parts of the system expand and prosper.  The US is manufacturing billionaires at a record pace, the stock market continues to climb, output of everything from corn to natural gas is up, and Google and Apple are world-leading corporations.  A hallmark of collapse is that societies become dis-integrated, allowing some parts to fall as other parts rise.

The image above is a Sierpinski triangle or “gasket.”  It helps visualize this idea of fractal collapse.  Step by step, the original triangle shape develops more holes and loses area, but it does not disappear.  its outlines remain apparent.

To make a Sierpinski gasket, we start with an equilateral triangle.  Then we identify the mid-points of each side and use these as the vertices of a new triangle, which we remove from the original.  (See the top-middle triangle, above.)  This leaves us with three equilateral triangles.  We repeat this process over and over; we iterate.  From each remaining triangle we remove the middle, leaving three smaller triangles.  The Sierpinski gasket and its repeated holing can serve as a visual metaphor for the fractal collapse that may now be hollowing out many of the world’s nations.

The future is not binary, not rise or fall.  Increasingly, nations may become less homogeneous.  Some parts may expand and prosper while other parts may wither or fail.  The overall trendline may not be upward, however, but rather downward.  Our future may not be a train wreck, but rather a slow dilapidation.  Not with a bang but a wimper.  We can change this outcome.  But currently very few are trying.

The intellectual history of the idea of fractal collapse is not wholly clear.  The concept came out of the physical sciences and has been popularized as a description of social and economic collapse by author and analyst John Michael Greer.

Unimaginable output: Global production of transistors

Approximate global production of transistors, per capita, selected years, 1955 to 2015
Approximate global production of transistors, per capita, selected years, 1955 to 2015

Global production of transistors has surpassed 20 trillion per second—hundreds of quintillions per year.  Transistors are the primary building blocks of modern electronic devices: computers, smartphones, TVs, radios, and other devices.  Transistors use semiconductor materials to amplify (think transistor radios) or switch (think digital computers) electronic signals and electrical power.  Transistors can be individual components, but are found in far greater numbers embedded in integrated circuits—in computer “chips.”

The graph above shows global production of transistors per year per person.  Per capita values are used here to make the size of the numbers more manageable.  In 1955, production was one transistor per 1,000 people—essentially zero.  Radios and TVs in the mid-’50s used vacuum tubes rather than transistors and integrated circuits.

Just ten years later, in 1965, production had increased 1,000-fold, to one transistor per person per year.  Transistor radios were gaining popularity in the 1960s.  Each radio contained several transistors—often 5 to 10.

While production in 1965 was one transistor per person per year, by 1975 it was nearly 1,500 per person.  Individual transistor components had been replaced by semiconductor computer chips, each containing thousands or millions of individual transistors.

The 1980s saw the proliferation of computers and home electronics.  By 1985 global production of transistors had surpassed 40 thousand per person per year.  By 2000 it was 65 million.  Today it is 56 billion per person.

The world now produces more transistors in one second that it did in one year in 1980.

The global population could not afford to purchase, on average, 56 billion transistors per person per year if prices had remained at 1965 or 1985 levels.  In the latter-1950s, a transistor radio with 5 transistors cost nearly $500 in today’s dollars.   Now, for not much more money, you can buy an iPhone that contains hundreds of billions of transistors.

A pound of rice sells for approximately one dollar and contains about 25,000 grains.  For that same dollar you can buy—as part of a memory stick or a phone—not 25,000 transistors, but billions.  A transistor today is thousands of times cheaper than a grain of rice.

Much of the news about the world is negative: famine, genocide, fisheries collapse, climate change, extinctions, resource depletion.  But we also need to acknowledge that our global hyper-civilization is truly wondrous.  We have built human systems of nearly incomprehensible power and productivity.  This is both their great strength and their great peril.  Nonetheless, if we are to safeguard some version of this civilization into the future we must appreciate and value it, despite its profound flaws.  We must take the time to understand it.  And we must work together to reform it.

Graph sources: VLSI Research.   Note that values are approximate and were derived, not directly from data, but from an existing graph.  Thus, while overall trends and conclusions are robust, individual values for specific years are approximate.