Guest Post: Scale Invariant Behaviour In Avalanches, Forest Fires, And Default Cascades: Lessons For Public Policy

Tyler Durden's picture

Submitted by The World Complex

Scale Invariant Behaviour In Avalanches, Forest Fires, And Default Cascades: Lessons For Public Policy

We show that certain extended dissipative dynamical systems naturally evolve into a critical state, with no characteristic time of length scales. The temporal "fingerprint" of the self-organized critical state is the presence of flicker noise or 1/f noise; its spatial signature is the emergence of scale-invariant (fractal) structure.  - Bak et al., 1988 (one of the greatest abstracts ever written!)

1987 saw the publication of an extraordinary paper--one which led to a dramatic change in our understanding of the dynamics of certain kinds of dynamic systems. Most importantly  . . . introduced the concept of self-organized criticality, or self-organization to the critical state--which is a condition neither fully stable nor fully unstable, with a characteristic size-distribution of events (or failures). In the kinds of systems that interest geologists, earthquakes and avalanches were quickly recognized as being SOC systems, and SOC was recognized as the most efficient means of transmitting energy through a system.

Avalanches and SOC

An early computational experiment went like this:  imagine a pile of sand, on which single grains of sand are dropped one by one until an avalanche occurs.  An avalanche occurs when the slope at some local point is greater than a defined value.

If your sandpile is two-dimensional (length and height--imagine a cross-section of a real sandpile), you would have to visualize it as a string of numbers, where each value represented the number of grains of sand stacked at that point. In the figure below, we are only looking at half of the pile, from the midpoint to the edge.

In our simple sandpile consisting of four stacks, a grain of sand of thickness dx falls onto the middle stack. If the difference in heights between this stack and its neighbour x1 in the figure above) exceeds some threshold value n, then one grain of sand would drop from the higher stack onto the lower stack. You would then have to check whether the height of the next stack was now more than  n higher than its neighbouring stack. If so, then another grain of sand would drop down one more stack and so on to the end of the pile.

What happens in a two-dimensional sandpile is that eventually the height of the sandpile is such that each stack is exactly n higher than its neighbouring stack. As a new grain of sand is dropped onto the pile, it migrates along all of the stacks and drops off the edge of the pile.

The behaviour of the sandpile is very simple; but what happens when you move to a 3-dimensional model (I'm counting the height of the pile as a dimension--not all authors describing this problem do so!)? You might expect similar behaviour--that the slope of the pile will increase until a single grain of sand causes a rippling cascade through the entire pile. This doesn't happen, for it would imply that the natural behaviour of the system is to evolve towards a point of maximum instability. In the experiment, the behaviour of the sandpile was much more interesting. The pile built up until it reached a form of stability characterized by frequent avalanches of no characteristic size.

Bak et al. (1987) called this condition of minimal stability the "critical state", and pointed out that as it developed independent of modelling assumptions and external parameters, it arose by self organization--the term "self organized criticality" (SOC) was introduced to describe the process. The characteristics of systems displaying SOC are fractal geometry, and flicker noise (also called 1/f noise).

There are many systems in nature--and increasingly in the human environment--which are similar to the avalanche model described above. Real avalanches, and similar mass sliding events (debris flows in the deep sea, for instance) have been recognized as SOC processes; along with earthquakes, volcanic eruptions, and economic events.

Forest fires were quickly recognized to be characterized by SOC--at least in environments without a lot of active management. Curiously, it quickly turned out that the effects of fire management, at least as practiced in the United States, might have had an effect opposite to that which was desired.

Fire suppression in the United States

“Strange to say, that, obvious as the evils of fire are, and beyond all question to any one acquainted with even the elements vegetable physiology, persons have not been found wanting in India, and some even with a show of scientific argument(!), who have written in favor of fires.  It is needless to remark that such papers are mostly founded on the fact that forests do exist in spite of the fires, and make up the rest by erroneous statements in regard to facts.”   B.H. Baden-Powell

As European settlers spread through what became the United States, they were confronted by an unusual world. Wilderness was something that had to be eliminated so that "civilization" could spread. Forests were to be cut and the land put to the plow. This was more than an economic imperative--it was a moral imperative as well. 

The rapid westward expansion in the 19th century brought railroads, and railroads brought further development and fire. While clearance of the forest was necessary for development, the desire to create a forestry industry based on sustainable harvesting rather than a short-sighted liquidation of old forests was driven by European examples. And thus the American ideas of forestry were transformed by the turn of the 20th century. Forests were resources that had to be tended. And as resources, any fires within them resulted in economic losses.

Fire had been used as a method of maintaining the forest by the native populations--but such a method was far too messy and unpredictable for a modern people--particularly those who looked to the forestry programs of western Europe, where fires were uncommon. The European model worked tolerably well in the eastern forests in North America, where water was plentiful year-round; but this model turned out to be unsuitable for the western forests, the life cycles of which required fire as a controlling element.

Major Powell launched into a long dissertation to show that the claim of the favorable influence of forest cover on water flow or climate was untenable, that the best thing to do for the Rocky Mountains was to burn them down, and he related with great gusto how he himself had started a fire that swept over a thousand square miles. - Bernard Fernow

The forests of the southwestern United States were subjected to a lengthy dry season, quite unlike the forests of the northeast. The northeastern forests were humid enough that decomposition of dead material would replenish the soils; but in the southwest, the climate was too dry in the summer and too cool in the winter for decomposition to be effective. Fire was needed to ensure healthy forests. Apart from replenishing the soils, fire was needed to reduce flammable litter, and the heat or smoke was required to germinate seeds.

In the late 19th century, light burning--setting small surface fires episodically to clear underbrush and keep the forests open--was a common practice in the western United States. So long as the fires remained small they tended to burn out undergrowth while leaving the older growth of the forests unscathed. The settlers who followed this practice recognized its native heritage; just as its opponents called it "Paiute forestry" as an expression of scorn (Pyne, 1982).

Supporters of burning did so for both philosophical and practical reasons--burning being the "Indian way" as well as expanding pasture and reducing fuels for forest fires. The detractors argued that small fires destroyed young trees, depleted soils, made the forest more susceptible to insects and disease, and were economically damaging. But the critical argument put forth by the opponents of burning was that it was inimical to the Progressive Spirit of Conservation. As a modern people, Americans should use the superior, scientific approaches of forest management that were now available to them, and which had not been available to the natives. Worse than being wrong, accepting native forest management methods would be primitive.

Bernhard Fernow, a Prussian-trained forester, thought fires were the ‘bane of American forests’ and dismissed their causes as a case of ‘bad habits and loose morals’. - Pyne (1995).

Through the early 20th century, the idea that fire was bad under all circumstances, and fire control must be based on suppression of all fires came became the dominant conservation ideology. After WWII the idea became stronger still, partially because of the availability of military equipment; but also due to the Cold War mentality. Just like Communism, the spread of fires simply couldn't be tolerated--and it was the duty of America to contain both "red" menaces (Pyne, 1982).

In the latter part of the 20th century, the ideas behind fire suppression once again began to change. The emphasis on "modern" methodologies began to fade, with a preference appearing for restoration of the "old forest" from pre-settler times. Research into the forest had begun to reveal the importance of fire in the natural setting, and that humans had used fire to manage the forest throughout history. Costs of fire suppression had risen dramatically, and the damage done to the forest by the equipment and the methods of fire suppression often exceeded that done by the fires.

Gradually the idea of fire suppression faded, to be replaced by a determination to allow fire to return to its natural role. Major fires in Yellowstone Park in 1988 brought about something of a reversal again in policy, but it was recognized that a century of fire suppression efforts had left the western forests in a dangerous state. Even though fire was to return to that natural cycle, the huge growth of underbrush has created a substantial risk of massive, out-of-control fires. This risk is an indicator of just how unhealthy fire suppression has made American forests.

By comparison, forests in Mexico, where there have been no fire-suppression efforts are far healthier. Fires are more common, but tend to be smaller, due to lack of fuel.

Fire, water, and government know nothing of mercy. - Latin proverb

Default cascades as avalanches

Economic fluctuations have long been recognized as SOC phenomena. One type of fluctuation that has been recently posited is the "cascading cross default" in which the failure of one entity to repay its debts drives one (or more) of its creditors into bankruptcy, which in turn drives one or more of its creditors into bankruptcy, and so on.

Clearly these default cascades can be of nearly any size. A default may only affect the defaulting institution--or it may take down all institutions in a global collapse. As a conceptual model, the sandpile automaton of Bak et al. (1987) is a pretty good representation--the key difference being that each individual stack in the economic sandpile is actually connected to a large number of other stacks, some of which are (geographically) quite distant. For instance, the failure of Deutsche Bank would likely put stress on Citigroup. Would it cause it to fail? Perhaps. We would model this by assigning a probability of failure for Citigroup in the event of a default by DB. And we would have to do this for all relationships between the different banks.

But we need conditional probabilities--because it may be that DB's failure alone wouldn't topple Citigroup. But suppose it topples ING, and Credit Suisse, and Joe's Bank in Tacoma, and Fred's Bank in Springfield, and Tim's Bank in Akron, . . . and many others, all of whom owe money to Citigroup. Then it might fall. So apart from having tremendous interconnectivity, with each bank connected to many others, there is also tremendous density of those connections, all of which would appear to make the pile very unsteady. 

Instead of dropping grains of sand one at a time on the same spot, multitudes of debt bombs are dropped randomly on the pile of financial institutions, provoking episodic failures. What might we expect of their size distribution?

The experiment as I've described is too difficult to set up on my computer, mainly because I don't know how to establish the probabilities of failure for all of the various default chains that may exist. Furthermore, the political will to prevent financial contagion, although finite, is unmeasurable. Luckily we don't have to run the model, as it is playing out in real life.

Paper now primed to burn

We have lived through a long period of financial management, in which failing financial institutions have been propped up by emergency intervention (applied somewhat selectively). Defaults have not been permitted. The result has been a tremendous build-up of paper ripe for burning. Had the fires of default been allowed to burn freely in the past we may well have healthier financial institutions. Instead we find our banks loaded up with all kinds of flammable paper products; their basements stuffed with barrels of black powder. Trails of black powder run from bank to bank, and it's raining matches.


Bak, P., Tang, C., and Wiesenfield, K., 1987. Self-organized criticality: An explanation of 1/f noise. Physical Review Letters, 59: 381-384.

Pyne, S. J., 1982. Fire in America: A cultural history of wildland and rural fire (cycle of fire).

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BaBaBouy's picture

"" SocGen Sees $600 Billion QE3 Starting In March 2012 Sending Gold Up Between $1900 And $8500/Oz ""


Laymens Terms: GOLD-To-The-Moon ... $10K, and then it starts going up...


Buy GOLD ...

trav7777's picture

there was no real injun forest management.  Lightning and nature managed forests here, not injuns.  Injuns used fire predominantly to clear agricultural area, not manage forest health.

The dude who wrote the article seems to fail to understand that indian forest management using fire is from INDIANS, aka from INDIA, idiot.

YesWeKahn's picture

ultimate fix to this mess is to shut down the FED.

The Big Ching-aso's picture



Shit.   Just understanding the article title requires an I.Q. of 160.

kaiserhoff's picture

Great article, but it's heavy going.  This is (I think)  a special application of chaos theory that is helpful, not in understanding markets, but in showing that they can't be predicted, and trying to do so is dangerous.

Two points -

prediction is impossible because describing even the simplest cases quickly outstrips the calculation capacity of the known universe

"most efficient path of energy" means sudden and catastrophic failures, which appear to feed on themselves..., because they do

On the other hand, this might just be a warning to snowboarders;)

trav7777's picture

pour water out of a big jug.

Repeat except giving the water a spin.

You will now understand why tornados form.

Avalanches can be predicted; you misstate chaos theory.  It is impossible to predict even with infinite computation power as a function of Uncertainty.

metastar's picture

Article summary: Let the fv(k1ng banks burn!

Acet's picture

The example of the virtual sand pile given in the article is quite deceitful with regards to this kind of systems. The computer simulation they show is made up of a very small number of "sand grains" which are all equal, standardized "grains" which interact with their neighbours in a simple, exact way. Also the sand seems to be added at regular intervals in a small area and all new grains that are added have the same amount of energy and always hit in the center of a cell in the simulated space. Not at all like reality, more like simulating a pile of micron-perfect small metal cubes in a lab environment.

What you see there and what is computationaly feasible is a simulator, not a model that can be used to predict outcomes: for example you can make pretty realistic looking simulations of the weather (which is a chaotic system) splitting your simulation space into "cells" and having specific rules for properties and iteractions between cells, but no matter how much detail you added to it and how small you made the cells, said simulation would be worthless to predict how real weather develops over a long period of time (in fact this is the method used for weather forecasting).

So one can do a really good looking simulation of a sand pile, but in order to do a model that predicts the future behaviour of a real sand pile, one would need to know about the size, shape, exact composition and weight of each and every sand grain (since they're all different), and of each grain falling into the sand-pile and the precise time, speed angle of approach and location of each falling sand grain (a sand grain that would cause an avalanche might, falling slightly slower or slightly to the side or being slightly heavier or lighter cause a different result). This quickly becomes computationally intractable for any real life sand pile with more than a tiny number of grains and, like weather prediction models, would slide further and further away from reality because miniscule changes in inputs over time can result in huge changes in results (the butterfly effect).

Real sand piles are chaotic systems


By the way, avalanches are not predictable: you can make a good estimate of the time and area when and where they are likelly, but not predict the exact time (not even down to the hour) and location (not even down to the meter) of the avalanche (unless you trigger it yourself and even then it might be much smaller, or bigger, than you expected).


LowProfile's picture

Mine's only ~120, I had no problem.  Familiartiy with the background material is likely more an issue.

Just remember:  "Don't fuck with Mother Nature", and that Creative Destruction is a force of nature.

Big fires coming.

The Big Ching-aso's picture



Hey we might be related.   I think we have similar eyes.


Vampyroteuthis infernalis's picture

The take home message of the article is natural systems behave according to certain laws. Western forests (which I spent many a day in) require fire for revitalization to burn away the unnecessary excess. The author is relating this to economic systems. Our economic system has be tampered with preventing fires from clearing away the waste and excessive growth. In the near future, the big fire will come and devour everything, banks and the Fed included.

Xanadu_doo's picture

Big fires coming indeed. My analagy the last couple weeks has been the weather. Here in the upper Midwest, we barely had any winter to speak of. Last year was 90+ inches of snow; this year I suspect less than 20 total. I've been saying that we need rain and lots of it, fast, or this is going to be one long, hot, brutal summer full of fire.

All this bad paper needs to go away, or it will feed these fires. Not pretty.

Timmay's picture

I'll summarize. "BALANCE" requires Growth and Destruction.


Italics, underline and quotations added for extra effect.

JW n FL's picture



Bak et al. (1987) called this condition of minimal stability the "critical state", and pointed out that as it developed independent of modelling assumptions and external parameters, it arose by self organization--the term "self organized criticality" (SOC) was introduced to describe the process. The characteristics of systems displaying SOC are fractal geometry, and flicker noise (also called 1/f noise).

There are many systems in nature--and increasingly in the human environment--which are similar to the avalanche model described above. Real avalanches, and similar mass sliding events (debris flows in the deep sea, for instance) have been recognized as SOC processes; along with earthquakes, volcanic eruptions, and economic events.

Forest fires were quickly recognized to be characterized by SOC--at least in environments without a lot of active management. Curiously, it quickly turned out that the effects of fire management, at least as practiced in the United States, might have had an effect opposite to that which was desired.

I Love! what you have shared.. but more and more new comers to Zerohedge means this may not go over well with everyone.. But I assure you! that there are more than a few here who will appreciate your contribution(s).

Thank You!

Please Share Again and / or More Often if you have the ability to do so!

to the giy above me that said buy Gold! I say Buy Silver and then Buy Gold!

Bastiat's picture

Drawing a comparison betweeno natural systems and financial systems implies that central bankers and their economists may be somehow constrained in their power.  Outrageous!

GeneMarchbanks's picture

Perceived power. We are dealing with shamanism here. What you mean to say is: how can it be valid to compare the Physical World with a faith based Financial System?

Answer: You can't. The answers don't matter if you're asking the wrong questions.

MrPalladium's picture


Let us assume that central bankers are not constrained, and more to the point, are determined to do whatever is necessary to keep the present financial system players solvent and in business by printing however much is necessary.

The problem is that the financial players will collectively and in a herd overestimate the speed at which the central bankers are willing to print, piling up leveraged positions that cannot be sustained by that speed thereby starting a cascading collapse, albeit from much higher nominal dollar levels.

The central banks are analogous to an agent that can dramatically increase soil nutrients in a forest and thus cause the trees to multiply and grow much faster than normal.

All that such an agent would do is produce a bigger and more dangerous fireball.

ebworthen's picture

$7 Trillion thrown at the markets by central banks in the past four years is a lot of snow.

The Big Ching-aso's picture



And yellow snow at that.

TheFourthStooge-ing's picture

The Big Ching-aso said:

And yellow snow at that.

...and his mama cried,

and his mama cried,

"Bernank, no no,

Bernank no no,

don't do no naughty POMO-ow-ow!"


Imminent Collapse's picture

The normalcy bias continues until the avalanche begins.  Then it is too late.  Most people have no idea what could happen and just assume that nothing will happen.  So far they have been mostly right, but I can't help but think that will soon change.

twotraps's picture

very well said.  Although I don't agree with all the manipulation of the Fed...gotta admit they have bought themselves the most expensive thing in the world, Time.  In that time, people see that the sky has not fallen and most likely will not.   Something tells me that others are using the precious time for other things, preparations, positioning or whatever, for what I wish I knew.    I do think that adjustments can be rapid and unforgiving and given their proven ability to change rules to suit themselves who knows what sort of crap they will do once it starts working lower.

Convolved Man's picture

All the FED's economic models include elements of risk and reward -- bad luck and good luck respectively.

-The Bernank Papers (60 Minutes Edition)

OutLookingIn's picture

Time. Just a matter of time.

The slope remains stable as long as its at the optimum angle of repose.

Then ~ BAM! Something like tossing a ping pong ball, into a room full of mouse traps, that are armed.


trav7777's picture

Rogue wave formation is another interesting scientific study.  These things self-organize then dissipate naturally.  The waves apparently borrow energy from adjacent waves then give it back.  No consolation when one sinks your ship mid-ocean.

skipjack's picture

...but are the matches lit ?

mickeyman's picture

It's like in this video (after about the 5:30 mark)

GeneMarchbanks's picture

'After WWII the idea became stronger still, partially because of the availability of military equipment; but also due to the Cold War mentality. Just like Communism, the spread of fires simply couldn't be tolerated--and it was the duty of America to contain both "red" menaces (Pyne, 1982).'

For the most part I agree but somewhere around the above the analogy starts to break down. For one thing, only one of these 'red' menaces pertains to the world of natural phenomena, the other is a man-made socio-economic construct that 'exists' conceptually and perhaps works practically -- that is to say is adhered to by society at large. Now, it gets tricky. If we are going to impose our will on nature, that is one thing but it is an entirely another thing to impose our ideals on a society that is adhering to a minds construct or idea. This terrible confusion is leading to an unimaginable schizophrenia for modern Western man who is already living in a fear based culture.


trav7777's picture

man has been imposing his will on nature since there've been men.  It's not a bad thing.

Zeitgeist evolves just like anything else.  I mean look around you...people unabashedly believe things which are utterly silly and demonstrably stupid.  They are unembarrassed by the things they DO NOT know and the fact that there are a lot of them.

Vampyroteuthis infernalis's picture

Allowing the fires to burn in a selective, controlled manner is still Man enforcing his will on nature. The fires are the correct action. Fire prevention is the incorrect action.

Controlled defaults are correct fires. Bailing out banks is incorrect.

GeneMarchbanks's picture

'man has been imposing his will on nature since there've been men.  It's not a bad thing.'

Nothing moral was implied. It is, however, temporary as nature inevitably slips from the grips of man. Man is left wondering as he remains a step behind.

Nobody For President's picture

As a 25 year volunteer fire fighter, mostly concerned with wildland fire danger to our rural community (I was the founder-chief of our local vfd), I gotta say the biggest drivers of the 'put all fires out all the time' mentality did not involve the cold-war red menace bs - it was that god-damned Bambi and Smokey the Bear. 

No shit.

Those two very public memes screwed up the message of locals and fire ecologists for YEARS, and control burns during appropriate times of the year when fuel moisture and weather variables are conducive to safe, undergrowth clearing burns were verboten. Now, thanks to some high-profile fires (the Oakland fire for one) involving populated rurban and urban areas, the idea of control burns is seeping through some of the public's thick skull.

Just in time for gubermint austerity... Control burns, especially in areas that really need them due to high fuel loads (tons of underbrush/acre) - are expensive. Lots of prep work is labor intensive, fair number of fire crew on hand for burn day - the upshot is 'we can't afford' control burns, but CAN afford the millions to control wildfires in the middle of the hot summer with Foehn winds pushing them.

So forest fires, for people living in the woods like myself, are similar to the economy = you gots to take care of your own shit: lots of clearance, lots of water storage and delivery mechanisms, fire-safe construction of your buildings - proper safety equipment to stand and fight without help of any fire equipment from outside - stuff like that - to go with the beans and bullets and bullion and broads and booze.


I guess Keynes is the equivalent to Bambi...


rant off...



SgtShaftoe's picture

Both are natural systems. Read Taleb's "Black Swan of Cairo" at his website or google it.

Societies are also complex natural systems and work the same way, only with different operational and failure modes.

GeneMarchbanks's picture

I have read it. Indeed they are not both 'natural systems'. The Black Swan of Cairo speaks of US foreign policy and cognitive biases unlike this article. Society is made of individuals making decisions day-to-day and does NOT have constants.

Piranhanoia's picture

Nothing better than an ignorant ego in charge.  Major idiot starts fire because he is right and watches thousands of acres burn.

Spot on analogy.  Allowing moneyists to have a say, who thought that was a good idea?   No one.   It had to be paid for.

upWising's picture

Being a firefighter can be interesting. You get to run into peoples' houses when they didn't know you were "coming over" and haven't had a chance to "straighten up the house." One house fire is particularly memorable in that the owner had dogs....LOTS of dogs who lived inside.  She dealt with the "problem" by simply put old newspaper on top of the problem.  LOTS of newspaper...everywhere. In some places the newspaper was nearly a foot thick!  Talk about fuel for the fire!  We stayed around for hours trying to keep that fire from re-igniting.

I imagine that is how forensic auditors at MF GLobal and other "suddenly collapsed" enterprises feel when they "come over" unexpectedly and the Fine Folks in the Accounting Department haven't had a chance to "straighten up" or at least throw nice rugs over the piles of stinking financial "records".

Ain't no Fire Dpeartment that is going to be able to put this fire out and keep it out once it takes off.  There are times when Fire Departments have to stand back and "let the structure burn" trying to prevent exposures from igniting as well.  


Nobody For President's picture

Don't forget the house where the homeowner was storing a *shitpot* bunch of ammo, that started popping off mid-fire...

(And some smart guy who knows guns is gonna say "Yeah, but it wasn't too dangerous because the rounds were loose, and not chambered, and the force was disapated...yah da da da da"  Right - "Perfectly safe, here's the hose - you go in first.")

Swain's picture

Absolutely relevant!!


Schmuck Raker's picture

GREAT article.

TY World Complex, and ZH.

oldman's picture

This is the basis of 'do-nothing' philosophy.

All systems have always self-organized whether it is proven by words or mathamatical language makes no difference.

Does anyone here imagine that that we humans arrived at this point in our history because of our brilliance or emotional stability?  No, we have arrived at this point despite our brilliance and emotional stability. We are a very tiny part of a very big puzzle----once we leave the very narrow and limited human context.

If we could only accept this as our reality(which it is) and pretend for a few years that we want to survive as a part of a universal order, we might make that 'happy and healthy community that includes all species'. I'm OK with whatever comes until someone has a better idea---better ideas are not self-organizing.

OK, now let's focus on the problems of Angolandia---what fun we will have as it self-organizes trying to second guess it.

The universe doesn't even know we are here                       om



blu's picture

The universe doesn't even know we are here

Well let's hope it doesn't. Otherwise we're in for worse times that we'd feared.