The Econophysics Blog

This blog is dedicated to exploring the application of quantiative tools from mathematics, physics, and other natural sciences to issues in finance, economics, and the social sciences. The focus of this blog will be on tools, methodology, and logic. This blog will also occasionally delve into philosophical issues surrounding quantitative finance and quantitative social science.

Monday, May 28, 2007

Greenspan chimes in on Chinese stockmarkets

I've written a couple of posts lately about the possibilities of a stockmarket bubble in China (More signs of a Chinese stockmarket bubble, 5/13/07, and Makings of a Chinese Stockmarket Bubble?, 4/29/07) . According to the New York Times (5/25/07), former Fed Chairman Alan Greenspan has chimed in as well. According to the Time article:
Mr. Greenspan, now 81, struggled to contain the tech stock boom, issuing his famous “irrational exuberance” warning in December 1996 only to watch the American market keep rising and finally collapse in early 2000. He tried his hand at forecasting Chinese stocks on Wednesday, telling an audience in Madrid by satellite that the Chinese market was “clearly unsustainable” and could undergo a “dramatic contraction.”

After setting records on Monday, Tuesday and Wednesday, the A shares, those traded in yuan, fell 0.47 percent in Shanghai and 0.6 percent in Shenzhen on Thursday as investors responded to the warning.

But the warning was not news to Mr. Zhou and other Chinese officials. The central bank, securities regulators and prominent business executives have all been cautioning investors that buying stocks is not a guaranteed path to riches — all with less apparent effect than Mr. Greenspan.
To reiterate my earlier warnings, developments in China can (and has) effects on an increasingly inter-linked, globalized financial markets.

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Tuesday, May 22, 2007

Book Review: Chaos Theory Tamed

I'm presuming that most of you have either read my musings (The Black Swan ... "Well That's Life!") on Nassim Nicholas Taleb's new book, The Black Swan, and/or read the book on your own accord. It occurred to me that a large segment of the reading public may have difficulty following the mathematics presented in Part Three and in the Notes of Nassim Taleb's book. If your mathematical skills or training is limited or rusty, then you will certainly have a hard time following the logic of the Black Swan, fractal randomness, power law, etc. Even if you have had a fair amount of technical education, many of the topics covered in The Black Swan aren't things that are normally covered in the standard curriculum.

Fortunately, there is a (partial) solution to this problem. Chaos Theory Tamed, by Garnett P. Williams, clearly explains much (but not all) of the mathematics invoked in The Black Swan: the mathematics of complexity theory. (Note: There are epistemological distinctions between complexity theory, chaos theory, fractals, etc. However, for the purposes of this book review, I will mostly ignore those distinctions. At any rate, Garnett Williams' book covers math that are cross-disciplinary and would be useful for any of those aforementioned categories.) Uniquely, Garnett Williams' book manages to explain the mathematics of complexity, chaos, and (to some extent) fractals in a way that is both accessible yet sophisticated.

Most books on chaos theory, complexity theory, fractals, etc., fall into two categories. The first category are books that are of a 'pop science' / 'pop math' variety; relatively easy to understand but whatever knowledge one can glean from these books are given with a lot of hand-waving and not a lot of ways for more sophisticated readers to get beyond generalities and the 'gee whiz' factor. The second category of books are for the more technically minded. The more technical books are (hopefully) good for the initiated but are over the heads of the uninitiated. Frankly, even for those comfortable with the mathematics and scientific jargon invoked by these technical works, the more formal papers and books are usually unpleasant to read and may deny people the sense of epiphany that one should get from good science.

There are a handful of books that attempt to bridge this gap between pop sci/math and more formal literature, but most of these books, frankly, fail. Garnett William's book is the one bright exception ... a positive Black Swan.

The mathematical prerequisites for reading Chaos Theory Tamed are light. The reader only needs to have the equivalent of a good American high school math education (basic algebra, and hopefully, some exposure to pre-calculus), and the patience to go through the logic (and equations) presented throughout the book. Unlike the few other gap bridging books that are in the marketplace, Chaos Theory Tamed's mathematical prerequisites are very minimal.

This low level of mathematical pre-knowledge should not be mistaken with a low level of mathematical sophistication. On the contrary, Garnett Williams' book does a great job of covering math that is actually invoked and used by professional researchers in the fields of chaos and complexity theories (as opposed to hand-waving toy models presented in other pop sci/math books and, even, in the gap bridging books on chaos theory). Without assuming an active knolwedge of calculus, Garnett Williams explains the workings of difference equations and differential equations of the type that Edward Lorenz and Mitchell Feigenbaum used to 'discover' chaos theory. Like other books on chaos theory, Chaos Theory Tamed discusses topics like 'strange attractors','bifurcation,' etc.; unlike those other books, Garnett Williams actually explains what those terms mean and the logic (math) behind them.

More relevant to Nassim Taleb's The Black Swan, Chaos Theory Tamed does an excellent job of explaining probability theory and the mathematics of the power law.

Garnett Williams does an excellent job of explaining the nuts and bolts of probability theory and mathematical statistics to the uninitiated. In fact, if that is all he did in his book (and he did much more than that), it would be a worthy book in it of itself since he provides the sort of explanations that would be useful to anyone wanting to learn probability and statistics beyond an elementary level. He also explains information theory along with the idea of entropy (in both the thermodynamics and Shannon information theory senses) and ties those ideas in with probability theory. Again, Garnett Williams' explanation of these complex topics -- topics that are so riddled with difficulties that more technical books try to avoid it -- are both so ambitious and helpful to the uninitiated that I could recommend the book on these grounds alone.

But Chaos Theory Tamed doesn't stop with explanations of 'strange attractors,' 'entropy,' and 'autocorrelation in time series.' Garnett Williams' book gives the best accessible explanation of power laws that I've encountered. Chaos Theory Tamed explains power law and scalability (scale free, scale invariant, etc.) in terms of 'dimensions.' Dimensions are essentially the kind of dimensions that we are all familiar with ... three dimensions of space (four dimensions if you include time), two dimensions of a sheet of paper or a fictional 'flatland,' and the single dimension of a Platonic straight line. With power laws, the dimension of what is being measured is the exponent and is relatively invariant (within some range). When graphed on log-log axes, a power law is a straight line and the power law exponent (represented as 'alpha' in The Black Swan) is the slope (usually, negative) of this line.

Garnett Williams uses the concepts of dimensions and scales in order to give a very clear-headed explanation of fractals. Chaos Theory Tamed doesn't dwell on fractals as much as other books that are more specifically focused on fractals, but, when the book does deal with fractals, the explanations of what fractals are and how they relate to chaos theory are brilliant for its clarity. Basically, fractals are defined in this book as being "fractional dimensions" -- i.e., instead of 1, 2, or 3 dimensions (integer dimensions), fractals are fractional (non-integer) dimensions (1.2, 1.4, 2.8, etc.). I actually find this sort of definition to be much more useful and interesting then the thousands of pretty pictures of fractals I have seen in other books, magazines, and on the web.

One can tie this fractal dimension idea in with power laws in the following way: The power law exponent (the dimension) is usually not a whole number. For example, 1.1 is the exponent (as provided by Nassim Taleb in The Black Swan, p. 264) for the net worth of Americans; that power law exponent translates to the top 20% of the wealthiest Americans having 86% of the wealth (from p. 265 of The Black Swan). Again, this way of thinking about fractals is at least as valuable as seeing a pretty picture of fractals.

Another distinguishing feature of Chaos Theory Tamed is that, unlike other books on chaos theory, it goes into how one might empirically detect and measure chaos and/or complexity; i.e., it goes beyond mere scientific speculation or even theorizing. The concept of dimensions (i.e., the power law exponent; the 'alpha' in The Black Swan) is important to the empirical study of chaos and complexity. There are different standards/measures of dimensionality including Hausdorff dimension, information dimension, and correlation dimension; they are distinct but similar ways of measuring dimensions. Information theory, in the form of Kolmogorov-Sinai entropy and mutual information, is also important to the quantitative study of chaos, and Garnett Williams does a commendable job of explicating these topics.

Garnett Williams is also quite frank about the limitations and difficulties inherent in trying to empirically detect and measure complexity. This note of caution fits in well with Nassim Taleb's warnings about not placing too much weight on 'precise' (frankly, there aren't any) measures of 'alpha' when thinking about randomness from a Mandelbrotian perspective.

One final point to praise in Chaos Theory Tamed is its glossary. Its glossary -- clearly defining terms in chaos theory, probability, mathematical statistics, information theory, etc. -- alone is worth the price of the book!

Garnett Williams' professional background is worth noting. He was a geologist for the U.S. Geological Survey. A geologist might not be the first person to come to mind in writing a book about the mathematical backbone of chaos theory, but in many ways he is the ideal person to write the book. The distribution of earthquakes and other natural geological phenomena follow power laws and have been studied by complexity theorists as being examples of complexity in nature. In fact, many natural -- as opposed to social -- phenomena seem to be consistent with Black Swan theory. Thus, Nassim Taleb's ideas should not be thought of as being confined to social sciences only but as being applicable to natural sciences as well.

Bottom-line: If you're looking for a clear-headed explanation, that is both accessible and sophisticated, of the mathematics behind The Black Swan (and complexity/chaos/fractal theory, in general), then Chaos Theory Tamed is a great place to start ... in fact, it's the best place to start. Frankly, I wish there were more books like Chaos Theory Tamed and more authors like Garnett Williams; books that aren't afraid to cater to the intellectually ambitious and science/math writers who aren't afraid to lay bear the equations that tend to mystify science and math to the uninitiated.

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Wednesday, May 16, 2007

The Foresight Saga Revisited (or How Much Money Can You Make If You Had Perfect Foresight?)

So what is the 'Foresight Saga'? The Foresight Saga was a gedanken (i.e., thought experiment) conducted by The Economist magazine in its fin de siecle (1999) Christmas issue. The Economist magazine created an imaginary character named 'Felicity Foresight' who was able to perfectly predict the performance of financial markets -- across different asset classes and across borders -- for each and every upcoming year from January 1st 1900 onwards.

Starting with an initial investment of $1 in January 1st 1900 (and by reinvesting any dividends and/or interest income in the coming years), Felicity Foresight would decide at the beginning of each year which investment would bring the highest return (capital gain plus income) for that year and put all her wealth into that single asset. She would repeat this process year after year, shifting her funds to match her new forecast for each and every year starting from the year 1900.

How did Felicity do? By January 1st 2000, she managed to turn $1 into $1.3 quadrillion even after deducting transaction costs and taxes. Compared to the $9,000 she would have earned had the $1 been invested in a broad collection of American stocks, Felicity Foresight's performance is truly staggering! The last time The Economist checked in on Ms. Foresight (January 2, 2003), her investment acumen more than doubled her portfolio (to $2.7 quadrillion). [Note: All figures in this paragraph are the revised figures from the 2003 article, and not from the original 1999 article.]

In addition to Felicity Foresight, the Foresight Saga also included two ancillary characters (and potential suitors) -- Henry Hindsight and Charlie Contrarian -- that added zest to this tale of predictive perfection. Unlike Felicity, neither Henry nor Charlie were able to perfectly foretell the future direction of financial markets.

Henry Hindsight follows the same investment process that Felicity does with one major exception: Henry invests in the previous year's best performing asset. In other words, Henry Hindsight is like most investors, following 'fashions' and 'trends.' Henry's initial $1 invested at the beginning of 1900 would have only grown to $783 -- much less than either Felicity's portfolio or investing in a broad index of American shares.

Charlie Contrarian, on the other hand, invested in the previous year's worst performing asset (apparently believing in a sort of 'mean reversion'). Charlie did somewhat better than Henry -- turning his $1 into $1,730 in a century of investing -- but not as well as either Felicity or a broad index of U.S. equity.

The following chart lists the investment choices that Felicity Foresight made over the last century (you can click on the image to enlarge it).

Needless to say, no one has perfect foresight. So inventing 'Felicity Foresight' may, at first blush, seem a rather pointless exercise. However, I believe that we can learn a great deal from gedankens / empirical studies like the Foresight Saga.

One of the things we can learn from this thought experiment is that financial experts often underestimate the effects of taxes and transaction costs. If Felicity's porfolio had been constructed without those costs, it would have grown to $27.5 quintillion; i.e., 99.99% of potential investment wealth was eliminated by transaction costs and taxes (along with effects of compounding). Many experts tend to think of these kinds of costs to be negligible and readily dismiss them, but this extreme example demonstrates that investment costs can add up -- or, more precisely, compound -- to a sizable amount in the long run.

Another valuable lesson that can be learned from this seemingly fanciful tale is that there has been a fundamental change in the ability to achieve investment performance over the last decade and a half. Until the early 1990s, both Henry Hindsight's and Charlie Contrarian's strategies -- which are the typical strategies used by most investors -- would have led to respectable gains. Since then (or at least until the early 2000s), these strategies would have been less successful and, up until the year 2000 or so, would have led to substantial losses.

What is the nature of this 'fundamental change' over the last decade and a half or so? Could it be a more globalized financial market where poor performance in one part of the globe or in one asset class can reverberate much more readily than prior to the 1990s? Could it be that a more dynamic marketplace has shortened the time frame and/or reduced the opportunities where either of the two traditional investing strategies can profit?

One final lesson that can be learned from the Foresight Saga is that the creator(s) of the story have shown that they -- unlike Felicity, but like the rest of us -- lack perfect foresight. None of the installments of the Foresight Saga (the last one was in January 2003) foresaw with any detail what has happened since then and no one could have profited at the rate that Felicity did by what they could glean from her tale of investment success.

Despite the lack of useful predictions for the future, I do hope that The Economist revives the Foresight Sage in the near future because of the insight that this gedanken gives us about the past's future. What do I mean by the 'past's future'? What I mean by that is that we can use the Foresight Saga -- not as a way to give us perfect foresight (which it doesn't) -- but as a way to put ourselves in the proverbial shoes of those who in the past had been trying to make decisions based on uncertain projections of the future. In other words, we can evaluate the past's predictions about the future ... and see the frustrating nature of such attempts at prediction. For example, anyone who had predicted in 1939 (the eve of World War II) that, by the early 1940s (well into World War II), the French stockmarket would have over a 200% annualized return would have been dismissed as a lunatic ... yet it happened!

The Foresight Saga is more about hindsight than foresight ... gendankens and empirical studies like this one can place us back in time to see how those who came before us (or even ourselves in the distant past, if we are old enought) viewed their future ... and usually got it wrong! The most important lesson to learn from Felicity Foresight's amazing track record as an investor is how all of us, in reality, lack such consistently perfect foresight about our future.

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Sunday, May 13, 2007

More signs of a Chinese stockmarket bubble

According to the Financial Times [in Bourses in China eclipse all of Asia (May 9, 2007)]: "The value of shares traded on China’s stock markets on Wednesday was greater than the rest of Asia combined – including Japan – helping the benchmark index to breach the 4,000 mark for the first time. Analysts said this was almost certainly the first time that turnover at the Chinese bourses had exceeded that of the rest of Asia." (Although, it should be noted, that the Chinese stockmarkets in Shanghai and Shenzhen are still substantially smaller than the markets in Japan, the UK, and the US, in terms of market capitalisation.)

This is more evidence for some of the comments I made in previous posts on China's financial sector ... the latest post being Makings of a Chinese Stockmarket Bubble? (April 29, 2007). A financial bubble (that bursts ... as they invariably do) in China could have devastating consequences for markets (and economies) of other countries (including the US, the UK, and Europe). It's definitely worth keeping an eye on developments in China.

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Thursday, May 10, 2007

Switching Costs

In his weekly Financial Times column, 'The Undercover Economist,' Tim Hartford wrote about research into the costs of switching goods and services (April 27, 2007). One might expect (especially with the 'rational man' presumption of most economists) that people would make the switch away from goods and services they have been accustomed to unfamiliar goods and services in order to save money. The research and examples Tim Hartford cites, however, contradicts this: People often lose money by making switches.

Why? There are many possible reasons for this. One possible reason is that searching for alternatives is itself costly. But this rationale doesn't seem to apply here since the article talks about scenarios where people searched for alternatives, made the conscious decision to switch, and, yet, it still costs them more than if they had stayed with their prior commitments.

The better explanation for higher switching costs (under these circumstances) is a combination of information asymmetry and just plain confusion about the true costs of making the switch. One of the examples the article cites is switching electricity suppliers. Consumers get confused about the different tariffs and pricing schemes involved in switching utilities suppliers. Another example the article cites is hedge funds. Investors have a hard time figuring out whether a particular group of hedge fund managers are good or not. The information asymmetry can come in because suppliers -- whether they supply electricity or hedge fund investment management -- can 'exploit' this confusion or lack of information/knowledge on the part of consumers.

All of this turns on its head the usual presumption in economics that prices efficiently reflect all available (and, in the most strongest forms, even all or most private) information. So, even assuming that consumers are acting rationally, prices don't seem to serve as an efficient means of delivering information and making 'rational' economic decisions. This suggest a sort of 'shadow' or 'undercover' prices; perhaps, it takes an Undercover Economist to point that out.

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Friday, May 04, 2007

The Black Swan ... "Well, That's Life!"

The late, great Polish journalist, Ryszard Kapuscinski, wrote -- in his book on the last days of the Soviet Union, Imperium -- that the genius of the Russian people can be summed up in their oft-repeated phrase, "Well, that's life!"

A young boy finds that his hometown is no longer a part of Poland but is, instead, a part of the Soviet Union due to the extremely improbable (and brief) courtship between Hitler and Stalin. Well, that's life! Shortly thereafter, that same boy finds many of his friends and neighbors being carted off on trains to Siberia by the NKVD (the forerunner to the KGB) for no apparent reason. Well, that's life!

On some perverse whim, Stalin decides to (literally) starve ten million Ukrainian peasants -- almost a third of the population -- to death. Well, that's life! At the death/work colony of Kolyma -- a place that gave birth to another phrase of relativist consolation, "Don't despair, it was worse in Kolyma!" -- Beria's henchmen gave their victims the 'choice' between dying of hunger, hard labor, sleep deprivation, disease, sadism, hopeless despair, (literal) freezing, and, for the fortunate few, being shot. Well, that's life!

All of a sudden, the mighty Soviet Union -- which had terrorized, humiliated, enslaved, and froze people to death -- collapses and disappears from the maps ... its red tzars going the way of the tzars of old. Well, that's life! Just as unexpectedly, there are new nations and quasi-nations that arise out of the Imperium that virtually no one -- including the people who are part of these would-be nations -- had known had existed. Well, that's life!

The genius of Nassim Nicholas Taleb -- on masterful display in his new book, The Black Swan: The Impact of the Highly Improbable -- is that he has managed to capture what Kapuscinski calls the "essence of truth," as represented by the aphorism "Well, that's life!", in an even more succinct (but no less scientific) concept/turn-of-phrase: "The Black Swan."

This being (in part) a book review, I feel compelled to offer up some sort of recommendation for the book buying public. So here it is: Buy this book. Read this book. Read it carefully. Read it again.

The Black Swan, the book, is the most important book in social science since Adam Smith's The Wealth of Nations. Nassim Taleb's book also happens to be the most significant contribution to the science and philosophy of uncertainty since Andrey Kolmogorov axiomitized probability theory (which along with Bayes, gave us the solid foundation necessary to think clearly about chance) and made progress (with contributions by Chaitin and Solomonoff) towards a more mathematically precise definition of randomness. In terms of epistemology, reading The Black Swan gave me a sense of intellectual kinship that I have not felt since reading Isaiah Berlin's "The Hedgehog and the Fox."

The rest of this essay will be dedicated to explaining, at least in part, why I am heartily endorsing Nassim Taleb's latest book. As a bonus, I will explain why I started The Econophysics Blog.

"Amen," Platonicity, and 'The Little Prince'

I am slightly embarrassed, but not too embarrassed, to admit that reading The Black Swan was an almost quasi-religious experience, full of sublime epiphanies. There were parts of this book where I found myself muttering "amen" -- in the fashion of many in the plebeian parts of Protestantism -- in delighted agreement with the sentiments of its author. (I don't know whether the Reverend Thomas Bayes ever generated an amen from his congregation, but I'm sure he would have given a hearty amen to Nassim Nicholas Taleb.)

All of this genuine enthusiasm is despite the fact that I was expecting to be slightly disappointed by the latest book. After reading his previous book, Fooled By Randomness, I had the impression that Taleb's next book, which became The Black Swan, would be a book that would be geared toward a more technical audience and would be something akin to an anthology of NNT's more formal writings with a sprinkling of more accessible material. Instead, The Black Swan, the book, that we have before us is targeted toward more-or-less the same audience as Fooled By Randomness had, and follows a similar format and tone. But this superficial similarity is (unintentionally) deceptive.

The Black Swan goes into intellectual territory that Fooled By Randomness almost but did not ultimately tread. The best way to distinguish the two books (and contrary to some book reviews out there, there definitely is a distinction) is via the following: Fooled By Randomness raised important and discomforting (which is precisely why it is important) questions about our understanding of, and decision making under, uncertainty; that book inspired the creation of The Econophysics Blog (more on this in the next section). The Black Swan either answers many of the questions raised by the previous book and/or it provides a solid road map to arriving at whatever solutions (and there may ultimately be no solutions) that may exist to the fundamental problem of living in a world where changes in time and chance profoundly affect us all.

In other words, The Black Swan, the book, is one of the best maps available to help us navigate through a world of uncertainty. The idea of distinguishing between useful versus misleading maps is one of the themes that stood out in my mind as I read the book.

Nassim Taleb mentions the analogy to maps in relation to his disdain for what he calls "Platonicity." Taleb defines Platonicity (named after the philosopher Plato) as "our tendency to mistake the map for the territory, to focus on pure and well-defined 'forms,' whether objects, like triangles, or social notions .... we privilege them over other less elegant objects, those with messier and less tractable structures ..." The cardinal sin of Platonicity is that it "makes us think that we understand more than we actually do."

As he makes clear throughout the book, Taleb is not absolutely against the use of intellectual 'maps' (i.e., idealized forms, concepts, methodologies, etc.); what he is opposed to is the uncritical acceptance and use of such Platonic maps and to the use of wrong or misleading maps for inappropriate situations.

Taleb's idea about the foolishness and dangers of Platonicity reminded me of the observations Kapuscinski made about the map used by Antoine de Saint-Exupery as recounted in Saint-Exupery's book, Terre Des Hommes (the English translation: Wind, Sand and Stars). Saint-Exupery was an aviator, adventurer, and writer, who is best known for writing a book that is considered by some to be a classic in children's literature and by others to be a fascinating work of philosophical fiction, Le Petit Prince (The Little Prince).

In 1926, Saint-Exupery was to make a flight from Toulouse (in France), across Spain, to Dakar (in north Africa). Kapuscinski sums up Saint-Exupery's predicament in the following manner (from Imperium):
Saint-Exupery studies the map of his route, but it tells him nothing; it is abstract, general, "vapid." He decides to consult his older colleague, Henry Guillaumet, who knows this route by heart. "But what a strange lesson in geography I was given!" the author recalled. ". . . Instead of telling me about Guadix [Cadiz], he spoke of three orange-trees on the edge of town. 'Beware of those trees. Better mark them on the map.' " And those three orange-trees seemed to me thenceforth higher than the Sierra Nevada." .... "I also assumed a defensive posture vis-a-vis the thirty sheep scattered as in a loose battle formation on the slope of a hill. . . . 'You think the meadow empty, and suddenly bang! there are thirty sheep in your wheels. . . .'"
When Taleb is warning us against the Platonic confusion between maps and territories, what he is suggesting is that we are all in the same predicament that Saint-Exupery found himself in. Just as Saint-Exupery needed a good map to help him navigate in the highly dangerous and risky world of early aviation, we need good maps to help us navigate through a world full of high impact but difficult to predict risks (i.e., Black Swans, the concept). Yet, like that French aviator/writer, we are given useless and/or misleading maps by the so-called experts.

Platonic 'maps' based on (Gaussian) bell-curve probability/statistical distributions (what Taleb calls the "Great Intellectual Fraud (GIF)") are like Guillaumet's map; they are (as Kapuscinski would have put it) 'map-mementos.' Platonic maps are too devoid of detail, too vapid, to serve as a useful guide when navigating a world shaped by extreme, catastrophic risk; those maps exaggerate non-dangers (like Guillaumet's 'giant' orange trees and the platoon of 'fearsome' sheep) while totally ignoring (or severely discounting) very serious dangers (like the actual mountains and platoons of hostile natives that Saint-Exupery was really worried about).

One of many examples that Taleb dissects of a psuedo-expert promoting Platonic/Guillaumet maps of risk is the book on catastrophic risk written by Judge Richard Posner, a highly controversial U.S. federal appeals court judge, law school lecturer, and public 'intellectual' (I use the term loosely here). I can't think of someone who is less qualified by temperament, education, training, skill set, life experience, etc., to claim to be an expert on catastrophic risk. So what does he do? He writes a book about it! (Presumably, it sold well enough.) At least Henri Guillaumet had the decency to be qualified to make his map.

Posner, along with a rogue's gallery of pseudo-experts (and, to be fair, real experts), advocate the use of Platonic Gaussian models of probability and risk despite the fact that one doesn't need to be Ramanujan or Karl Friedrich Gauss to figure out that events like 9/11 and many financial market crashes are double-digit sigma events, i.e., essentially impossible in the bell-curve, GIF world. Frankly, even from a textbook Gaussian perspective, many of these would-be Platonic 'mapmakers' are creating more confusion than clarity by their attempts to over-simplify the risky world we live in. Platonizers, like Posner, are essentially dismissing the possibilities of Black Swans, the concept; because they have seen thousands of white swans, they severely discount or completely dismiss the possibility that 'all swans aren't white.'

What Nassim Nicholas Taleb does so well in this book is to offer up an intellectual map of our risk-filled world (an a-Platonic map) that is more accurate and realistic than the pedantic view of chance that routinely misses the black swans. In The Black Swan, Taleb embraces the emerging scientific field of complexity theory -- especially the fractal mathematics of Benoit Mandelbrot. Power law-Zipf-Mandelbrot-Pareto-Levy-whatever one wants to call it probability distributions, self-similarity / self-affinity, scale-free structures, undefined (or infinite) statistical moments, and 'wild,' fractal randomness, are what Taleb calls "Grey Swans of Extremistan," and they serve as viable alternatives to the Platonic models when it comes to understanding the high impact, almost unpredictable nature of extreme and catastrophic Black Swan events.

I was GIF'ed (and Why Crowds Can Never Be Wise)

When I took my first class in statistics (this was before Nassim Taleb started writing books), I faced an intellectual crises of confidence. I felt I was reasonably good at mathematics (at least the marks I received in math courses and exams said so), but some of what I was being told in my statistics class sounded daft to me.

My biggest dilemma was over the concept of 'outliers.' In a nutshell, outliers are observations or data points that are considered to be so far outside the range of the expected (or hoped for?) bell-curve Gaussian density distribution that they could be ... ney, they should be! ... dismissed. I had a very serious problem with this cavalier dismissal of outliers. Why? It wasn't because I was too dull (or perhaps I was) to understand what the lecturer was saying or what was written in my introductory statistics textbook. I could deal with dogma as well as anybody. No, the problem went much deeper than that.

I'm from a rough working class background. The 'outliers' -- what NNT calls Black Swans, the concept -- that my statistics class so easily waved away are what shaped my life and what shaped the lives of the people I was familiar with. The outliers ... the Black Swans ... are what we -- for better or worse (usually the latter) -- lived by. Most of the Black Swans people like myself faced were ugly: the spectre of poverty, humiliation at the hands of 'betters,' crappy hand-me-down clothes, illness and injury with no time or money to fix it, abusive families, alcoholism, tyrannical bosses, dead-end jobs, hopeless despair, fear. What kept us going was the possibility of a good outlier for a change: winning the lottery, hearing our favorite song on the radio, dreaming of a better life, and a down-on-his-luck kid somehow getting a fancy education.

So I'm sitting in my statistics class trying to get a fancy education, and I'm in the grips of an intellectual (and, almost, moral) dilemma. On the one hand, every fiber of my blue-collar common sense being wanted to point out that it is ridiculous to dismiss some infrequent or improbable event when it is precisely such events that may have the biggest impact in the real world (keep in mind, this was well before NNT started writing books and I had heard of Sextus Empiricus, et al.). From where I came in life, you'd have to be a dummy to think that some out-of-the-blue thing wouldn't change (usually, mess up ... I'm trying to avoid profanity) your life. On the other hand, I knew I would be considered an idiot or a worm by those 'better' than me if I seriously challenged the pedantic notion of outliers.

So I kept my mouth shut (for once in my life). I was a good boy and accepted the 'wisdom' of the bell-curve, along with the idea of outliers. But this always bothered me.

So a few years ago, I bought and read a book by some guy named Nassim Nicholas Taleb titled, Fooled by Randomness (the second edition). This book was usually shelved in the business section in most bookstores, which automatically made me suspicious and reluctant to buy the book since I find most business books by business 'gurus' to be too vapid to be worth my time (I'd rather read a book by Kafka or a book on neuroscience, particle physics, or poker). I was pleasantly surprised to read Dr. Taleb's book. Here was someone who was my social 'better' giving me permission to think the way I always wanted to think. To me it was a proclamation of intellectual freedom.

That is why I started blogging about a year ago and started The Econophysics Blog, which you are reading if you got this far. My original intent was to promote the spirit of Nassim Taleb's ideas ... basically, because the way he thought is basically the way I thought. On the masthead for this blog I could have put, instead of the nerdy stuff I have up there, the motto "I'm an intellectual explorer searching for truth in a world of uncertainty inspired by Taleb, Popper, et al.," but that sounded a bit too soft-in-the-head.

That is also why I am writing this ringing endorsement of Dr. Taleb's latest book, The Black Swan. As I wrote in the previous section, The Black Swan picks up where Fooled By Randomness left off. Any would-be intellectual explorer searching for truth in a world of uncertainty must buy and read this book.

There is one book out there that I will never give a positive review to. I agree with the idea that a book should not be judged by its cover, but some things on the cover, in this case the title, are so odious to me that I can't possibly like it. There is a book out there called The Wisdom of Crowds; the title is daft. Crowds can't be wise. They can never be wise.

Yes, crowds can often have more information and, even, knowledge, but they may also be more ignorant than even the most marginalized individual. Crowds, or 'swarms,' can be more correct than individual judgments, but they can also be terrifically and terrifyingly wrong. But even if crowds were almost always better informed and almost always right, they can still never be wise.

Wisdom is an outlier; wisdom is a Black Swan. By its very nature, wisdom goes against the grain. Wisdom cannot be manufactured by groupthink, or by a swam of bildungsphilisters, or a bildungsphilister(s) that happens to get a publishing deal.

The Black Swan is full of that extremely rare and improbable quality, wisdom. As the book jacket states, The Black Swan, the book, is itself a Black Swan ... the good kind, the kind that is wisdom itself.

Black Swan Virgins (or Did They Really Get It?)

Needless to say, I have no serious criticism of The Black Swan, the book and the concept, or its author. But, since this is a (sort of) book review, I suppose I am expected to say something critical. In that case, the only criticism I can have is directed toward the potential readership of the book.

Most of the book reviews of The Black Swan (with one unfortunate exception) have been positive. As of the time of writing, the book is number five on the New York Times Bestsellers' List. Someone not having read, or not understanding, the book might conclude that all of this good news is confirmatory evidence that the public gets it ... they really understand the Black Swan, the concept and the main point of the book. Unfortunately, as much as I love the book, I am skeptical about whether the reading public really gets it or will get it.

The problem is not with the book, its author, or its editors. The book is well-written and well-thought out. There aren't any major errors or typos in it ... certainly, nothing that would cloud someone's understanding of the main points of the book. No, the problem lies with the readers themselves.

As I wrote in the last section, reading Dr. Taleb's previous book opened up intellectual vistas for me. But this made me wonder, "How can this guy with a fancy pedigree understand things that cab drivers, auto mechanics, factory workers, janitors, truck drivers, et al., understand but those socially 'better' than them not understand?" I eventually got the answers when I read Malcolm Gladwell's excellent profile of NNT in The New Yorker (you can get a similar biography by reading The Black Swan book). Taleb got it 'because' he had experienced Black Swans -- homeland and culture torn apart due to an out-of-the-blue event, and health problems that the GIF-prone mind couldn't have foreseen.

I want to take a slight digression here. I want to make it clear that I do not want to make the same logical mistake the southern Italian professor makes in chapter six of the book. This mistake is something that the book constantly challenges. The mistake -- which Taleb calls "the round trip fallacy" -- is really the idea of the sufficient condition being confused with the necessary condition in formal logic (e.g., "all poodles are dogs" does not make all dogs poodles). The mistake that the Italian professor makes in chapter six is a variant of this fallacy -- with the twist that the notion of assigning causality is involved along with the problem of sufficient vs. necessary.

(By the way, I strongly object to the Italian professor's characterization of Protestants as being incapable of appreciating Black Swans. As Rev. Thomas Bayes and Sir Dr. Karl Popper could have attested to, being Protestant is no impediment to believing in Black Swans.)

Clearly not all Lebanese Orthodox Christians who experienced the civil war and wound up becoming financial traders are Black Swan believing skeptical empiricists. What I am saying is that -- while it is not sufficient to have experienced (suffered) Black Swans to become a Black Swan believing skeptical empricist -- it is absolutely necessary.

It is interesting to note that the two people that Nassim Nicholas Taleb expresses the highest respect towards -- Benoit Mandelbrot and George Soros -- are men who experienced Black Swans in their lives (escaping the Nazis during World War II). It is also interesting to note that my hero and the father of modern probability theory, the mathematician, Andrey Kolmogorov, experienced Black Swans in his life (lost both of his parents at an early age and was raised by his maternal aunts).

One of my other heroes, Ryszard Kapuscinski, would have loved Nassim Taleb's book. Kapuscinski would have really gotten it. It's not because of any quantitative ability; Kapuscinski wasn't Stanislaw Ulam. I doubt Kapuscinski could have solved a stochastic differential equation to save his life, or had the foggiest notion of what a power law or a fractal was.

But, time and time again, Kapuscinski experienced Black Swans. In fact, he made his career out of Black Swans by telling the stories of Black Swans that took the form of armed revolutions, ethnic conflict, deposed Middle Eastern shahs and African emperors, fearful and fleeing colonists, disintegerating empires, and wars fought over football (soccer).

This leads me to another set of fallacies that are directed toward NNT. Many people claim that Taleb and those who are like minded are advocating taking no risks whatsoever. Nothing could be further from the truth!

Obviously, Nassim Taleb, as a financial trader, has had to take a tremendous amount of risks in his professional life. Ditto for George Soros.

Benoit Mandelbrot has taken on a tremendous amount of risk intellectually. Instead of taking the safe and intellectually deadening route of most academics, he has worked at the margins to make the idea of fractals a viable academic discipline. A similar sort of thing could be said about Andrey Kolmogorov.

As for Ryszard Kapuscinski? He once asked the rhetorical question of why he did what he did, "Why do I risk my life time and time again?" Why did he risk his life time and time again when faced with murderous rebels, soldiers, and policemen? The answer: He was on a "mission" ... the mission was to get the story behind the story ... to get to the "essence of the truth."

So those who believe in the Black Swan often take incredible risks ... they've stared the Black Swan in its face and they often want to do it again and again. As Nassim Taleb has so eloquently answered his critics, it's not that he wants people to take no risks, it's that he doesn't want us to take risks in ignorance or blind to the reality of 'wild,' discontinuous randomness.

Other criticisms directed towards NNT -- that he is denying all casuality (no, he is not; he believes that assigning causal links should be based on skeptical empiricism -- which can include applying Einsteinian 'thought experiments'), or that he is opposed to all reductionism (i.e., Platonicity) in science (again, no; he -- as Einstein would have put it -- wants 'science' to be as simple as possible but no simpler) -- can be addressed in a similar fashion. But I must end this essay.

In closing, why am I so skeptical that potential readers (recognizing the fact that buying a book is not the same thing as reading it) won't really get it? Because many readers of this book -- especially the MBA totting types (or want-to-be's), and, I suspect, even people with solid scientific backgrounds -- are Black Swan virgins. They've won't really get it 'because' they have never really experienced Black Swans. I'm not saying these people have never experienced problems or challenges, it's just that the problems they have faced belong in Mediocristan while Black Swans are creatures of Extremistan (read the book and you will know what I mean).

I think Nassim Taleb makes the point about the importance of distinguishing between those who are experienced with Black Swans versus the Black Swan virgins eloquently in the Prologue of The Black Swan (p. xxiv):
I don't particularly care about the usual. If you want to get an idea of a friend's temperament, ethics, and personal elegance, you need to look at him under the tests of severe circumstances, not under the regular rosy glow of daily life. ... the normal is often irrelevant.
There used to be a time when -- even in the swankiest professions and socio-intellectual circles -- there were some old-hands and young 'Horatio Algers' that had experienced Black Swans ... i.e., those who had been tested under severe circumstances. It might be a financial trader who had been affected by the Great Depression or had to flee their homeland with only a suitcase or two. It might be a scientist (natural or social) who survived a war, revolution, genocide, or a famine. It might be a student whose parents didn't know the lingua franca (usually English) and really knew what hardscrabble meant without ever having heard that word because he or she lived it.

But those times have passed. It is ironic that -- as I wrote in my previous blog post, Tyranny of the Power Law -- that the very thing that brought the 'elite' success in life, the power law -- a symptom of the Black Swan, makes people blind to Black Swans by allowing the Black Swan blind to 'protect' themselves by entrenching their privilege.

Anyone who reads and understands The Black Swan, the book, will realize, however, that this can't last. Black Swan virgins -- especially those who are responsible for billions of dollars (or pounds, or Euros, etc.), or those responsible for the lives of millions (or even billions) of innocent people -- will eventually experience the Black Swan. Sadly, for innocent pension holders or even more innocent peace-loving, law-abiding citizens the world over, these Black Swan virgins won't know what to do. They'll fumble at the moment of destiny because they were blind to the fact that life is punctuated by extreme risks and they were blinded to that reality by the Platonized idea that risk can be 'managed' or controlled ... "risk leaps not glides."

Even a book of rare genius like Nassim Nicholas Taleb's book -- unless read carefully and with humility -- can do much to prepare these Black Swan virgins. When they face their Black Swan -- what the truly great historians and thinkers used to call 'destiny' -- it will be too late. Well, that's life!

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