Ubiquity: Why Catastrophes Happen

I review this book with a specific message (and specific audience) in mind: The driving insight behind "Ubiquity" is of potential great worth to active traders and investors.The book is excellently written -- an easy and engaging read. I first read it many years ago, found it effortless to pick up and read again with fresh eyes a year or two on, and am only now returning to review it (in May 2009) having stumbled across an interesting market-related connection. (The book touches on out-of-the blue market crashes, but I suppose it took the awe-inspiring volatility of Q408 and Q109 to really open my eyes to the point in question.)To briefly summarize the key idea, no one knows how big an earthquake will be before it starts. This is so because the earthquake itself does not know how big it will be until events actually play out.Earthquake energy feeds off a series of feedback loops, which are in turn driven by a chain of complex interlinked events (plate tectonics, geothermal pressures and whatnot) beneath the earth's surface. If any event in the chain fails to sustain the feedback loop, the earthquake fizzles out.The same idea applies to wildfires, flu pandemics, and other complex "catastrophic events" of unknown size and duration fueled by myriad complex inputs.One can perhaps think of an earthquake or a wildfire, then, as the combined result of thousands of hidden domino chains. The ultimate size and destructive power of the event is determined by the combined manner in which all the domino chains fall, and there are far too many inputs (most of them hidden from the human eye) to track.So the only thing that really governs the ultimate size of earthquakes, wildfires, pandemics, and other complex catastrophic events is something called a "power law"... a sort of linear inverse correlation between the size of an event and the probability of its occurrence.The power law, in other words, cannot tell you how big the earthquake will be either. But it CAN tell you that the starting conditions for big and small earthquakes often look exactly the same... that big earthquakes occur relatively less often than small ones over time... and that this established relationship between size and frequency remains stable up and down the line.The market insight that brought "Ubiqity" back to the forefront of my mind is as follows: Major market rallies and declines behave a lot like the phenomena discussed in the book. And thus we can hypothesize that:1) No one knows in advance how big a rally or decline will be, because the market itself does not know beforehand...and2) Major market rallies and declines are ultimately governed by power laws.This is why it's so hard (if not impossible) to know how far a market will travel -- in either direction, up or down -- if conditions are suitably conducive to a wide range of possible outcomes.In other words, there's no effective way to predetermine the magnitude of a major market move, without first having a VERY clear sense of all the myriad inputs and all the ways they can combine.In the case of the monster bear market rally that has been unfolding for nine weeks or so as I write this review, an improbably long chain of positive economic data points fed into a number of other supportive conditions... and thus the stock market equivalent of a giant bullish "earthquake" resulted.This concept is valuable to traders and investors because it offers a tangible intellectual anchor for a critical market insight. Again, if rallies and declines follow power laws, it doesn't make sense to try and anticipate magnitude ahead of time without a VERY clear sense of what could stop the movement in its tracks.At the same time, power law governance is instructive in that, while traders and investors cannot reliably predict deeply complex outcomes, they CAN analyze the general conditions necessary for producing a significant outlier event, in the same manner that one can examine conditions conducive to "extreme" outcomes on the natural disaster front.Just for fun, take the relatively recent (as of this writing) earthquake in Italy for example. There was a scientist who predicted a major earthquake around L'Aquila weeks before it happened. He was reported to the authorities for "spreading alarm" and forced to take his findings off the internet.Afterwards the authorities (in deep damage control mode) said the scientist's method of earthquake prediction (involving radon gas) was hopelessly unreliable, mainly because "earthquakes cannot be predicted." And yet they were using the baseline belief that "earthquakes cannot be predicted" as a tautological first principle! Not unlike the way some say that significant market movements can't be predicted... even though clear evidence shows that general conditions can most certainly serve as a "heads up" guide for those with eyes to see and ears to hear.All that to say is, in some ways smart traders and investors are like geologists or forest rangers on the lookout for earthquake-prone / wildfire-prone conditions... persistent tremors, dry underbrush, extreme low humidity, and so on. And then as active market participants, they get involved with the phenomena as it gets underway... but with a healthy respect for catalyst points and potential / probable ranges of outcome, as opposed to an overly anxious fixation on pegging the size of the move.If you've read this far, I hope I've inspired you to read the book.

In the book Ubiquity by Mark Buchanan, processes as diverse as forest fire size, stacking rice grains, market fluctuation, scientific paper citations, species extinction history, epidemiology, sizes of wars and earthquake severity are said to generate occasional catastrophic behavior following similar statistical behavior. Buchanan presents these arguments in a very readable style at a level that can be grasped by the layman. I found the physical descriptions of the processes fascinating. The phenomena is, indeed, ubiquitous. Repeatedly, we find that, if X measures severity and f is the frequency histogram of occurrence, then numerous processes containing a catastrophic component adhere to a linear log-log plot with negative slope. Although unsaid in the book, probably to allow access to a wider audience, the underlying probability density function of the ubiquitous process is a Pareto random variable with probability density function f(x)=(a/b)*(b/x)^(a+1) for x>b and zero otherwise. The enormously fat tails of this distribution allow the outlier-like catastrophic events described in the book. Taking the log of both sides of the density function gives log[f(x)] = -(a+1)*log(x) + constant which is a line of negative slope on a log-log plot. If U is a uniform random variable on (0,1), then X=b*U^(-1/a) is a Pareto RV. Using this, plots similar to the time series and log-log plots in Ubiquity can be straightforwardly simulated. Googling "Pareto distribution" gives a plurality of interesting web accounts, many mathematically deeper, of this remarkable phenomena made wonderfully accessible by Buchanan.

Are there general rules in situations where scientists have so far failed to find predictable patterns (for instance, the timing of the next big earthquake, the form a snowflake might take, the next big move in the stock market, etc.)?The author explores examples of natural or social systems that are out of balance (in a “critical state”) – as these systems are stressed, they are in a constant battle between stability and instability. For instance, dropping grains of sand on a sand pile creates a critical state. Over time, with every new piece of sand dropping on a sand pile, whatever happens next becomes unpredictable.In a critical state, the individual system parts may act in accordance to “simple” and predictable rules, but because there are so many parts and they may each interact and influence each other, the emerging behavior of the system as a whole becomes complex and unpredictable.When you look back in time, however, the system's behavior is not random and a pattern emerges: the power law - every time a certain defining feature (earthquake strength, % change in stock market) is double (or halved), the number of times such a feature occurred in history increases or decreases by a fixed factor.The power law produces scale invariant or self-similar systems: systems that look fundamentally the same at a bigger or smaller scale (think of fractals in computer land).Because the system looks the same at every level, there is no fundamental difference between a very large event or a very small event (a massive or small earthquake, a huge or small stock market move, a large or small slide in a sand dune).The key implications are that there is no such thing as a typical fluctuation (patterns of change are neither regular nor random), there is no reason to think that a very large swing is unusual or needs further explaining, and it is fundamentally impossible to predict the magnitude of the upcoming change.Because of this, any attempt to look for a singular cause to explain complex behavior is doomed to fail – there are no simple, deterministic laws for complex chains of events.The only thing that can be said about critical states is that under certain conditions, systems of interacting objects show universal features in their behavior (the power law). These ubiquitous properties arise again and again in things driven away from equilibrium and in things in which history matters.There are many critical states in nature (forest fires, earthquakes, snowflakes, gas phase transitions) and it is somewhat awesome to think that while unpredictable, there is a universal pattern that governs their behavior.The book becomes more speculative in the exploration of critical states in social settings, such as the stock market, spread of diseases, and more broad societal patterns (wars, city size and structure, evolution of scientific paradigms).I’m still trying to figure out the takeaways. At some level, if you can only understand these systems in hindsight through statistic analysis and if you can’t predict what happens next and specific individual causes don’t really matter, then so what? Still chewing on that.An interesting part of the book is that the science behind critical states takes the form of designing and running simulation games. Simulating natural or social critical states in (computer) games with (surprisingly) basic parameters produces statistical results that very closely match what is observed in real life. It will be interesting to see how these games will develop further.I would have perhaps liked the book to have a bit more structure, such as in terms of specific definitions of critical states and their components. Also, there are very clear links with topics such as entropy, network / information theory, biology / brain / intelligence, and emergent behavior and exploring those links in more detail would have been interesting as well.Having said all this, love reading about this stuff: exploring and trying to understand complex systems.

Excellent book.

Worth analysing

A very accessible and interesting read. Very well researched and a good technical contrast to Taleb's Black Swan. Highly recommended if this is your subject of interest. My only negative comment would be that the second half of the book was essentially lots of interesting examples of the principle, but didn't really make any new points.

Ubiquity est un livre étrange et fascinant, à la frontière de plusieurs disciplines. Il s'agit d'une suite d'exemples concrets (par exemple les feux de forêts), racontés à l'aune de l'analyse systémique, actions/réactions, etc... En fil conducteur du livre, la conclusion omniprésente que le hasard mène le monde et qu'il n'est pas utile de mettre en place des modèles prédictifs qui ne peuvent rien prédire. Un seul bémol, le livre n'a pas une chute à la hauteur des autres chapitres, il s'arrête juste, c'est un peu dommage.

Great book, I found it very interesting and good introduction to critical state and complex systems. Well worth a read.