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.

Saturday, July 22, 2006

Book Review: Puzzles of Finance

Puzzles of Finance: Six Practical Problems and Their Remarkable Solutions
by Mark P. Kritzman

I've decided to occasionally post reviews of books that might be interesting to the readers of this blog. Some of these books will have been recently published while other books reviewed here will have been around for a while. Mark Kritzman's fascinating book will be the first book review in what I hope will be a regular feature of this blog.

The title of this book accurately summarizes the contents of the book (which doesn't always happen). Mark Kritzman, a respected investment professional, researcher, and intellectual, wrote this book with a rather original and ingenious purpose: Writing a mathematical / logic puzzle book (a la Martin Gardner or Dennis Shasha) but using six thematic problems from finance. The six 'puzzles' considered are:

(1) 'Siegel's Paradox' (having to do with an anomaly in exchange rate calculations)
(2) likelihood of loss (it turns out that you can obtain a bewilderingly wide range of answers depending on how one approaches the problem)
(3) time diversification
(4) "why the expected return is not to be expected"
(5) Fischer Black's question "all stocks half the time or half stocks all the time?"
(6) irrelevance of expected return to option valuation (basically going through the derivation of the Black-Scholes & Merton's option pricing model)

It's worth noting that the book doesn't attempt to address so-called puzzles like the equity risk premium puzzle. The reason for this is consistent with the author's intention to write a book that focuses mainly on purely mathematical and logical puzzles in finance rather than more psychological or philosophical problems from finance.

The best features of this book -- a 'bonus' that is worth the price of the entire book itself -- is the last chapter which goes through the basics of quantitative finance in an succinct but accessible way, and the glossary which does a great job of defining some rather sophisticated terms from finance (in fact, the glossary is a lot better than a lot of finance & investing dictionaries I've seen). The last chapter and the glossary makes this book both accessible to a wide audience and useful even to people-in-the-know.

The relatively minor drawback of this book is that -- while the intention to write a Martin Gardner-esque book is a noble one -- the reader should not wind up being convinced that most problems in finance are purely mechanically mathematical or formally logical in nature. The biggest problems in finance usually come from philosophical and psychological issues -- e.g., overly rigid assumptions about human rationality -- that are buried underneath the math. In fact, focusing on the 'math' -- especially if 'math' is incorrectly thought of as just a bunch of equations and numbers instead of what it really is, a logical way of thinking -- may distract us from more puzzling puzzles of finance.

A more serious drawback, in my opinion, is that the book uses a purely efficient markets / lognormal approach to finance. I, and others, are increasingly disillusioned by this type of approach. In fairness to the book and the author, this book gets a lot of mileage -- especially in the likelihood of loss puzzle chapter -- out of the traditional approach and the author can't be faulted for writing an accessible book for a wide audience using textbook finance rather than concepts that even the experienced trip over.

I only found one typo in this book (which is an impresively low number of errata for a techincal book). On page 119 (of the hardback edition), in chapter 6, where it says "4,050 estimates of correlation" is incorrect. Doing a very simple pairwise combination calculation the answer I came up with is 4,950. When you add my figure to the "100 estimates of volatitilty" one gets the "5,050 risk estimates" for the portfolio selection problem discussed in the book.

Overall, this is a great book that both novices and experts can get interesting knowledge out of. It's worth buying the book just for the last chapter, the introductory overview of finance, and the thoughtful glossary of quantitative finance terms. Although I doubt that the solutions the book offers for the six puzzles of finance will be entirely satisfactory, I enthusiastically endorse Mark Krtizman's goal of getting his readers to approach problems in finance and economics using the type of logical problem solving mindset that Martin Garnder has advocated in his writings.

Friday, July 21, 2006

NY Times Op-Ed on Economics of War

Austan Goolsbee, an economist at the University of Chicago, wrote about the economics of war (both the international and the intranational varieties) in today's (July 20, 2006) New York Times: Count Ethnic Divisions, Not Bombs, to Tell if a Nation Will Recover From War. The following paragraph from the 'Economic Scene' column neatly summarizes the op-ed:
The good news is that history suggests that the destruction of war has no lasting impact on economic prospects. The bad news is that most of these countries, especially Iraq, are filled with ethnic divisions and civil discord. The evidence shows that these problems, unlike bombs, cause lasting damage to the prospects for a nation’s economy, even if they do not boil over into civil war.
Evidence for the "good news" comes from research done by Edward Miguel and Gerard Roland -- both of University of California, Berkeley -- The Long Run Impact of Bombing Vietnam. Evidence for the "bad news" comes from research done Alberto Alesina and Janina Matuszeski -- both of Harvard University -- and William Easterly -- of New York University -- Artificial States. The Artificial States paper is particularly interesting. The following is from the abstract of that paper:
Artificial states are those in which political borders do not coincide with a division of nationalities desired by the people on the ground. We propose and compute for all countries in the world two new measures how artificial states are. One is based on measuring how borders split ethnic groups into two separate adjacent countries. The other one measures how straight land borders are, under the assumption the straight land borders are more likely to be artificial. We then show that these two measures seem to be highly correlated with several measures of political and economic success.
This economics research is, sadly, very relevant to what we are seeing on the news everyday.

Tuesday, July 18, 2006

Tyranny of the Power Law (and Why We Should Become Eclectic)

The -- sometimes referred to as the , , or the -- has drawn a great deal of attention lately as an alternative to the 'normal' (Gaussian) distribution (i.e, the bell curve). The power law has gained in popularity among more numerate intellectuals, policy makers, and business people because it seems to fit better with common sense than what we were told in Statistics 101: Extreme and rare events have a greater than expected impact; a few products, people, and websites seem to have the bulk of market share, wealth, and mindshare; etc.

As a descriptive model of the way many things work, I have and will extol the virtues of the power law. As a purely descriptive framework, I will even go so far as to say that the power law is so ubiquitous that the so-called 'normal' distribution may not deserve that moniker.

However, as a normative or prescriptive approach to how things should work, I believe that the gaining popularity of the power law holds some dangers as well as benefits. After all, should we find it acceptable -- even if it is an accurate description of how things really are -- that the top 20% of people control 80% of the wealth in a society? Is it really a good idea that a few 'hits' (often ginned up to be that way rather than by popular demand) swamp out more meritorious 'misses'? Is it really ultimately beneficial, efficient, or rational for a society to have a few people at the top of the power law -- at least those who got there by inherited privilege and/or genetic accident -- hold sway over the lives of the many who live down along the 'long tail' of the power law?

In this blog essay -- which was originally intended to be a follow up to Netflix and the Sandpile -- I will argue that the power law, if misapplied so that it becomes a model of the way things 'ought to be,' is fraught with dangers. This sort of misapplication of the power law could lead to what I call the "tyranny of the power law." On the other hand, properly applying the power law, by using it as a mostly descriptive model rather than as a platonic ideal, can help in guarding against catastrophic risks as well as assisting those who are striving for a more democratic and meritocratic society.

An Intuitive Introduction to the Power Law

In the bell curve view of the world, the most likely -- i.e., the 'expectation' in mathematical statistics speak -- place you will find something is close to the average. With the power law, however, the concept of an 'average' (or 'expected value') is essentially irrelevant because substantially more (relative to the Gaussian) of the distribution of observations or events is located at the extremes.

Think of it as Shaquille O'Neal versus Bill Gates. Shaq, in our example, represents the distribution of human heights -- which follows the normal distribution; Bill Gates represents the distribution of human wealth -- which follows the power law.

Everyone can agree that Shaq is at the extreme (both in terms of magnitude and probability) of the distribution of human heights. Yet, Shaq is only about a foot (and a bit more) taller than the average American male. It is almost prohibitively unlikely for an eight foot tall human being to exist and impossible to have a ten foot tall human. Since even the 'extremes' of human heights are within a relatively tight range of the average (or mathematical expectation), the concept of an average is important in describing the distribution of human heights and most heights will tend to be bunched around more-or-less symmetrically around the average (hence, the bell curve shape).

The distribution of human wealth, however, behaves differently. The 'average' American makes somewhere around $45,000 to $50,000 a year. Bill Gates makes several thousands times that a year. Bill Gates' wealth, in terms of his Microsoft shareholdings alone, is in the mid $50 billion range. The 'extremeness' (in terms of magnitude) of Bill Gates' extreme wealth essentially makes the notion of an 'average' wealth or income much less useful in describing the distributions. Having a Bill Gates in the wealth distribution is like having a ten foot tall human being; it just can't happen if the distribution of wealth was Gaussian.

Wealth is among the many phenomena -- social and natural -- that seem to obey the power law. In nature, the number of earthquakes, the behavior of granular piles, population dynamics in some ecological models, the number and magnitude of solar flares, the x-ray signature of black holes, the observed distribution of digits from 1 to 9 (i.e., ), and the impact of forest fires, are a few examples of the many natural phenomena that conform to the power law distribution.

Even more examples of power laws are being found in the social sciences. As I have already mentioned, the 80-20 rule (first formulated by the Italian economist, Vilfredo Pareto) applies to the distribution of wealth -- the top 20% of the population holds 80% of the wealth in a society. According to economist, Arthur De Vany, the 80-20 rule also applies to major motion pictures -- about 20% of the films will grab about 80% of the market share (the research is contained in his book Hollywood Economics). The same principle can be applied to many other products and services.

When it comes to admissions at Ivy League and quasi-Ivy League universities, the principle can be called the 75-25 rule: nearly three quarters of the undergraduate students at Harvard and other so-called "most selective" universities and colleges come from the top income quartile (see next section for references).

The power law, where the extreme and the rare have a disproportionate impact, also applies to financial markets. As repeatedly pointed out by Benoit Mandelbrot and Nassim Nicholas Taleb, "just ten trading days represent 63 percent of the returns of the past 50 years" (emphasis added) (from A Focus on the Exceptions that Prove the Rule, Financial Times supplement on Mastering Uncertainty, 2006). The power law also applies to concentration of market capitalization to the shares of a small number of publicly traded companies (e.g., the 80-20 rule approximately applies to the market value of the FTSE 100 compared to all shares traded in London), the size of hedge funds, and a number of other areas in finance.

Can Power Laws Corrupt?: The Power Law versus Meritocracy

Lord Acton has been credited with coining the phrase "power corrupts, and absolute power corrupts absolutely." In light of the fact that the existence of the power law across so many social phenomena often means that social, commercial, and political power (as opposed to mathematical 'power,' which is where the power law gets its name) is concentrated among a small segment of people, institutions, etc., can the misapplication of the power law -- as a platonic ideal rather than as a tool of empirical science -- lead to a corrupt and less meritocratic society? Unfortunately, the answer seems to be yes.

Take culture for example. Because of the 80-20 power law principle, movie studios, tv networks, record companies, and even book publishers tend to promote what they hope will be hits at the expense of other products and services. Although hits can be created because of popular demand, these media companies often try to artificially create hits whether the public truly wants them or not.

This type of hit-based culture would not be so bad if it did not hurt higher quality fare. Unfortunately, however, the hit-driven marketing and business models used by media companies often crowd out or even prevent more meritocratic movies, tv shows, music, and books from reaching potential audiences. For example, in the music industry, instances of 'Payola' have surfaced from time to time. Even without overt bribery, the hit-driven mentality of major music labels and the various outlets for music (major radio networks, etc.) often prevent higher quality 'indie' offerings from getting heard and noticed.

Another egregious example is the movie industry. It is quite routine for many Oscar nominated films to have never been shown in many markets. Even in markets, like Los Angeles and New York, that have outlets for art house films, many higher quality movies are relegated to a few screens located at relatively obscure locations. Documentaries, until very recently, have rarely been available to the majority of movie audiences due in part to theater owners needing to cater to major studios and their hit fictional films. Needless to say, most of the top 20% of films are often of poor quality.

A much more troubling aspect of the potential misuse of the power law is in the unhealthy concentration of political and social power. Not only is it the case that the wealthiest quartile of Americans tend to make up the vast majority of the student population at so-called 'elite' universities, at these universities "only three percent of students come from the bottom income quartile and only 10 percent come from the bottom half of the income scale" (the quote comes from the Harvard Gazette, which is the official newsletter of the university's administration, and is based on various research studies studying the makeup of various Ivy League and quasi-Ivy League universities). Anyone who is seriously and sincerely interested in a fair and meritocratic society should be appalled by these statistics.

This type of concentration of wealth at institutions that people hope would be meritocratic -- along with the 80-20 rule of wealth in society -- bodes ill for socio-economic mobility (aka, 'the American Dream'). Nobel laureate and University of Chicago econometrician, James Heckman, has warned that "the big finding in recent years is that the notion of America being a highly mobile society isn't as true as it used to be" (from Aaron Bernstein, Waking Up From the American Dream, Business Week, December 1, 2003). This combined with programs to help the already privileged -- see, e.g., Lexington: The curse of nepotism -- A helping hand for those who least need it (The Economist, January 10, 2004) -- add weight to Princeton economist, Paul Krugman's, comment that "the underlying economic, social, and political trends will give the children of today's wealthy a huge advantage over those who choose the wrong parents" (emphasis added) (New York Times, The Sons Also Rise, November 22, 2002).

Education has traditionally been seen as a vehicle for socio-economic mobility. If the most highly esteemed universities -- schools that are often seen (rightly or wrongly) as the breeding ground for the 'power elite' -- have in place anti-meritocratic barriers (see, e.g., Malcom Gladwell's excellent article in The New Yorker on Ivy League admissions, Getting In: The social logic of Ivy League admissions) that unfairly reinforce the current power law dynamics, then social, political, and economic power that is already concentrated in the hands of a privileged few will be further concentrated based -- not on the democratic ideas of the Founding Fathers (the so-called "natural aristocracy") -- but on the plutocratic idea that those who inherited privilege by paternal accident should be 'protected' from having to fairly compete with those from more humble backgrounds.

If the power law is misapplied in this way -- so as to reinforce unmeritocratic privilege -- then society could suffer dire consequences. We will have leaders -- in what are suppose to be democratic societies -- that will be out of touch with their people. Rather than being public servants, politicians and policy makers will become callous and self-serving. Entrepreneurs that are from the 'long tail' rather than at the top of the power law may find themselves unable to find suitable business opportunities regardless of the merit and objective worth of their ideas. Otherwise intelligent and deserving people may be shut out of educational opportunities largely because they 'chose' the wrong parents.

More insidious than even those worrisome scenarios is the possibility that those who have the most power and influence in society will have too much in common with each other and too little in common with the masses down the long tail. This sort of cookie-cutter conformity will lead to a tacit lack of diversity and may even create an atmosphere of thinly disguised discrimination and bigotry.

The elites will suffer from 'groupthink' -- locked into a feedback loop where they will mostly look out for their own interests and reject counsel from 'outsiders' (e.g., good people of modest means, those with unorthodox but interesting perspectives, etc.). Our political, economic, and societal 'leaders' will be devoid of creativity and a sense of fairness and justice. Rather than solving problems -- whether they be in matters of war & peace, domestic policy, the economy, business management, or academia -- the 'power elite' will simply force us to accept mediocre to terrible ideas and throw up barriers to those who could offer up more creative and fair solutions. Just as the hit-driven popular culture leads to bland or even awful entertainment, a system of giving or denying socio-economic and educational opportunities based on plutocratic criteria will lead to unimaginative and foolish approaches to making policies, running businesses, and advancing knowledge.

Returning to our original question, can misapplying the power law corrupt? Absolutely.

The Right Way to Apply the Power Law -- Becoming Eclectic

So how can an awareness of the power law further rather than hinder progress in society? To find the answer, I have to return to the original inspiration for this series of posts: Netflix.

According to David Leonhardt's New York Times article on Netflix -- instead of having a power law for on-line DVD rentals that is similar to the power law at work with theatrical releases -- the distribution of DVD rentals on Netflix is actually closer to the relatively tight bell curve of the normal distribution:
Out of the 60,000 titles in Netflix's inventory, I ask, how many do you think are rented at least once on a typical day?

The most common answers have been around 1,000, which sounds reasonable enough. Americans tend to flock to the same small group of movies, just as they flock to the same candy bars and cars, right?

Well, the actual answer is 35,000 to 40,000. That's right: every day, almost two of every three movies ever put onto DVD are rented by a Netflix customer.
(Having about 66%, "two of every three," of the movies being rented, rather than 10, 20, or 25%, would be consistent with the familiar bell curve of the Gaussian distribution.)

This is a paradox. Why would only 20% of movies find a commercially meaningful audience when they are released in theatres, but 66% of movies find an audience when distributed via Netflix? David Leonhardt's article offers up an important clue to resolving this paradox:
"Americans' tastes are really broad," says Reed Hastings, Netflix's chief executive. So, while the studios spend their energy promoting bland blockbusters aimed at everyone, Netflix has been catering to what people really want and helping to keep Hollywood profitable in the process.
The solution to this paradox is simple: becoming eclectic. As it turns out, people have broad tastes and interests that extend far beyond the manipulative strictures imposed by media giants. People value diversity; they're eclectic.

On a profound level, Netflix -- in contrast to pre-existing distribution channels (including other DVD rental outlets like Blockbuster) -- became as eclectic as the audience. Either by serendipity or by epiphany, Netflix has found a way to offer people what they really, sincerely want. Netflix is one business model where an eclectic supply is meeting eclectic demand.

Reflecting on what we've discussed thus far, I would argue that the correct lessons to learn from the power law are the following:

(1) The power law is often an empirical fact (the way things are) but not necessarily the platonic idea (the way things ought to be); and

(2) We can tame or mitigate at least some of the negative aspects of the power law by encouraging eclectic and diverse strategies.

Chris Anderson -- in his new book The Long Tail, his blog, and his original Wired magazine article -- seems to favor this correct application of the power law. Chris Anderson's conception of "the " turns the logic of the power law (mis-applied) on its head: Rather than catering solely to the concentrated extremes of the power law (the biggest hits, the wealthiest people, etc.), the logic of the long tail calls on companies and institutions to address needs and desires all along the long tail of the power law. To draw on a baseball analogy (reminiscent of Michael Lewis' Moneyball), rather than just focusing in on home runs, a wise manager will also try to get his players on base via doubles, singles, and, even, drawing walks.

Another example of the long tail that comes to mind is in the world of pop music. Most music radio stations are owned by major media companies. They tend to preprogram their music and give little or no control to DJs (that is if they even employ them in some markets) in the selection of music. Not surprisingly, most (if not all) of the airplay is devoted to hits. It's as if these radio networks, and the record companies that influence decision making, are trying to only go for home runs.

Fortunately, there are some wonderful exceptions to this general trend. For example, KCRW -- a National Public Radio station in the Los Angeles area -- has championed reaching out to the varied tastes of music-loving audiences by playing music by independent and lesser known artists. The flagship music program on KCRW, Morning Becomes Eclectic (as well as its weekly syndicated program, Sounds Eclectic), has even helped to launch the careers of once fledgling musicians -- but now bona fide stars -- like Coldplay.

Can this eclecticism be applied to other arenas as well? I believe it can.

For instance, we can achieve a fairer and more meritocratic society by opening up legitimate opportunities for socio-economic advancement all along the long tail. Rather than "only 10 percent" of the students at so-called 'elite' universities coming "from the bottom half of the income scale" (i.e., where only 10% of the student body at prestigious universities reflect the working class and the poor in America), a larger proportion of the places at these schools should be opened to the talented but disadvantaged. Not only will this lead to a truly democratic society, it will also give us a more eclectic and imaginative set of leaders in policy making, business, and in academia. Having people in positions of power and influence from a more diverse set of circumstances than what we currently have will benefit all of us by opening up the possibility of more optimal decision making compared to what we can get from plutocratic groupthink or plutocratic autocracy.

Diversity and eclecticism -- the right lessons to learn from the power law -- can also be applied to finance and investing. It is widely recognized that diversification in an investment portfolio is important to managing and controlling risk. This type of risk management strategy is usually based on Gaussian thinking where only linear and static correlations between the valuation of assets are taken into account with the hope that there will be offsettinging set of simultaneous gains and losses. In other words, risk management is often done with the tools of "mild randomness" (in the terminology of Benoit Mandelbrot and Nassim Nicholas Taleb).

As it turns out, this kind of diversification is not nearly diverse enough. Because markets reflect the power law -- a world of "wild randomness" -- non-linear and dynamic co-movements between the prices of assets have to be taken into account. In this wilder power law world, what we think will offset losses using the mindset of the normal distribution may actually exacerbate losses. Therefore, a much more eclectic risk management strategy -- e.g., investing in as great a number of offbeat asset classes as possible -- will be a better hedge against catastrophic risk than can be achieved by ignoring the correct lessons of the power law.

For example, a recent Buttonwood column, Sting in the Tail (July 11, 2006), on the website of The Economist magazine, has argued that contrarian investment strategies focusing in on small and mid cap stocks is a manifestation of long tail logic being applied to equity investing. Applying this long tail investment strategy allowed some investors to weather, and even profit from, recent stormy periods in the market like the 2000-2003 bear market.

Another way in which the correct lessons from the power law -- such as a long tail strategy -- might be fruitfully applied is in the timing of investments and trades. As I discussed extensively in my blog post, , the different ways in which traders and investors perceive and react to time can have a large impact on market returns and risk as well as contribute to the power law characteristics of market returns. Perhaps, by acting more calmly in times of market turbulence and being more active in times of relative tranquility (thus evening out, somewhat, the disjointed behavior of investors and traders across time), some of the wild randomness brought on by the 'mind time' phenomenon can be reduced.

The lesson to take away from the long tail and the power law for investors is that they -- like the movie and music businesses -- would be wise to become eclectic.

Overcoming the Tyranny of the Power Law

To reiterate, I strongly believe that the power law is a useful paradigm and tool for studying the many natural and social phenomenon that are consistent with that model. As a descriptive ('positive' in philosophy of science speak) framework, the power law is often superior to the 'normal' distribution and should be adopted and utilized more widely.

From a normative, prescriptive perspective, however, the logic of the power law could easily be abused (just as the 'bell curve' has been). To any person of both intelligence and conscience, it is not a laudable nor a desirable thing to have 20%, 25%, or some other percentage of small concentrated elites or 'hits' crowd out higher quality competition and, even, endanger meritocracy and democracy. The catastrophic financial, economic, and other risks implied in a power law world of "wild randomness" -- as discussed elsewhere by this blog and by others -- is also less than desirable. (Reflecting on the Netflix example, one is tempted to go so far as to say that -- from a purely normative standpoint -- a world of the normal, Gaussian distribution -- a framework that underlies the utopic world of efficient markets -- may be more desirable than the reality of a world with power laws.)

We can reduce some of the harmful effects of the power law by using a long tail strategy of encouraging eclecticism and accommodating niches. The power law can then become a useful and desirable normative framework to tackle problems in business, finance, policy making, and culture. We can overcome the tyranny of the power law by what 'indie' music radio station, KCRW, has encouraged its listeners to do ... become eclectic.

Monday, July 10, 2006

Quantitative Mutual Funds

The New York Times had an interesting article today on so-called quant funds -- mutual funds using proprietary quantitative models to make investment decisions: How a Computer Knows What Many Managers Don't.

Many mutual funds that make their trades based on the recommendations of a proprietary computer model, known as quantitative or quant funds, have outperformed their benchmarks in the last three years. And investors have noticed.

At the Vanguard Group, which created its first such fund in 1985, the amount of money managed by its quantitative group has quintupled in the last three years, to $20 billion at the end of 2005 from $4 billion in 2002.

While no organization keeps track of flows into quantitative funds, they are probably still a very small part of the $9.5 trillion mutual fund industry. Many quant managers, however, say the funds' recent performance has received a lot of attention.

Quant funds can come in different flavors. Those like the Vanguard Strategic Equity fund, which is closed to new investors and was up 5.9 percent this year through June, let the computer model make practically all the decisions, from which stocks to buy and sell to when to trade them. Other funds, like the Quant Foreign Value fund, up 11.1 percent, use quantitative analysis as a screen to narrow down a basket of stocks. The final investment decisions in this type of fund are then made by carbon-based life forms.

Thursday, July 06, 2006

Netflix and the Sandpile, Part 1 of 2: The Power of Inertia

Recently, I had the (belated) chance to read a fascinating article in the New York Times -- What Netflix Could Teach Hollywood -- by David Leonhardt, who writes on quantitative and economics related issues for the Times. While I was reading the article, there were two sets of profound insights (although I don't know whether Mr. Leonhardt intended to inspire these particular insights) that I felt drawn to write about. I will write about the second epiphany I had -- the power law versus 'normal' / bell curve distribution -- as part 2 of this series in the near future.

Today, however, I will tackle the first epiphany I had after reading David Leonhardt's column: the power of inertia.

Inertia is a relatively simple concept from physics. Inertia can be best described as the embodiment of Sir Isaac Newton's First Law of Motion: A body tends to persist in its state of rest or uniform linear motion unless it is compelled to change by forces acting on it. In other words, things tend to stay as they are -- either standing still or moving in a straight line -- unless something strong enough moves it off its state of rest or moves it off course.

Mr. Leonhardt invokes the concept of inertia to defend Netflix's business model -- renting DVDs via a physical delivery system (i.e., the postal service) -- against naysayers who quite reasonably claim that movies sent over broadband internet connections will make Netflix's current approach as obsolete as the horse and buggy:

But it could be years - 5? 20? - before downloading approaches the size of the DVD business. Sometimes, inertia can outlast technology long enough for somebody to build a very big business. And once a business gets big, it doesn't easily go away.

In other words -- drawing an analogy to Newtonian physics -- sometimes a business with a good, but not great, business model can survive and evesucceeded because it is simply easier to maintain the status quo -- ordering movies on the web but waiting a couple of days for it to arrive by mail -- until some 'force' is strong enough to knock it off its position. In the meantime, as the article points out, Netflix may have enough time and capital to develop a downloadable delivery system for films. Thus, in the business world, inertia can become a powerful 'force' (I realize I'm taking poetic license here with the scientific concept of force) that sustains business models that seem vulnerable to technological improvements.

The power of inertia, as applied to Netflix and the possibility of downloading films off the internet, is reinforced by Hollywood's attempts to use intellectual property law and licensing in order to hinder progress in the distribution of films over the internet. As Mr. Leonhardt points out, it is Hollywood's "fading business model" that seems more vulnerable than Netflix.

What can tip the balance in favor of technology over inertia so that downloading full length films over broadband connections is as appealing as renting DVDs from Netflix? This brings us to the 'sandpile.'

According to the of , as developed by a trio of physicists (Per Bak, Chao Tang, and Kurt Wisenfeld) at Brookhaven National Laboratory, carefully dropping grains of sand onto a specific area will create and build up a sandpile. Most of the time, each grain of sand will tend to 'stick' to other grains of sand due to friction, thus building up the sandpile. However, at various points throughout the evolution of the growing sandpile, a grain of sand will trigger a catastrophic avalanche that will topple large portions of the sandpile, thus displacing and re-shaping the pile.

(Bak, et al.'s, original model was a computer based simulation based on idealized mathematical algorithms. In real life, rice grains and rice-piles tend to behave more like the 'sandpile model' than real life sand grains do.)

The sandpile model of SOC has also been found to apply to earthquakes, forest fires, ecological population models, and financial markets. All of these examples of self-organized criticality exhibit the empirical signature of the power law (more on this in part 2 of this series of blog posts).

Returning to the question posed earlier, what can tip the scales in favor of new technology versus existing business models like Netflix or Hollywood studios? This is analogous to asking what are the conditions in which a particular grain of sand will cause a catastrophic change in the sandpile.

My interpretation of the sandpile model of self-organized criticality is that a grain of sand has to hit a point along a sufficiently pervasive network of criticality -- what science journalist Mark Buchanan refers to as "fingers of instability" -- to trigger catastrophic avalanches. Similarly, I believe based on my understanding of SOC, that the technology to make movies more readily downloadable will have to hit a collective social 'nerve' in order to bring about the kind of revolutionary change that can displace the business models that are currently protected by what David Leonhardt calls "inertia."

Perhaps something like the video iPod or YouTube will get people used to the idea of downloading video content off the web and, thus, be the kind of triggering event or technology that takes advantage of network effects -- i.e., hits a collective social nerve. I tend to think that the inertia-displacing technology will be something else that may only be a glimmer in the eye of some entrepreneur somewhere. I'm willing to bet that we will here about it sooner rather than later. In the meantime, Netflix is probably safe (although I wouldn't say that for Hollywood movie studios). Who knows ... perhaps the inertia that protects Netflix will give it enough time to develop or adopt the 'avalanche' trigger that will make downloading movies as ubiquitous as downloading music.

Stay tuned for part 2 of this series -- power law versus the bell curve -- sometime in the near future.