This year marks that 50th anniversary of the branch of mathematics known as chaos theory. Appropriately enough for a field of study premised on the idea that seemingly insignificant events can have large and unpredictable consequences, the eureka moment of chaos is generally considered to be a short dense paper titled "Deterministic Nonperiodic Flow" published on page 130 of volume 20 of the Journal of the Atmospheric Sciences in 1963.

As James Gleick writes in his very entertaining history, Chaos: Making of a New Science, "In the thousands of articles that made up the technical literature of chaos, few were cited more often than "Deterministic Nonperiodic Flow." For years, no single object would inspire more illustrations, even motion pictures, than the mysterious curve depicted at the end, the double spiral that became known as the Lorenz attractor."

The paper's author, Edward Lorenz, was an MIT mathematician working on an early computer weather modeling simulation. One day in 1961, in an effort to save time waiting for his vacuum tube-powered Royal McBee computer to run the program, Lorenz started his simulation from the middle, manually entering in data from an earlier simulation, but crucially, rounding a six decimal point number to three decimal points in order to save space. What Lorenz found after returning from a coffee break was that these tiny, seemingly arbitrary changes in his initial inputs had led to vastly different outcomes in the weather models he created.

As Gleick writes, "Lorenz saw more than randomness embedded in his weather model. He saw a fine geometrical structure, order masquerading as randomness." Lorenz, who died in 2008, would later become best known for coining the metaphor of the "butterfly effect" to describe systems that are extremely sensitive to their initial conditions.

Most casual readers can't understand much of the mathematics of chaos theory, but the basic principles were popularized thanks in part to Gleick's bestselling book,  not to mention the trippy Mandelbrot Set images that have graced countless screensavers and dorm room posters and, of course, Jeff Goldblum's character in Jurassic Park.

Chaos doesn't have quite the pop culture cachet that it used to, but the study of what Lorenz called nonlinear systems - those in which outputs are not necessarily proportional to inputs --  has been highly influential in fields ranging from physics, to engineering, to astronomy, agriculture to economics. (One of the main themes of Gleick's books is that researchers in different fields were often working along very similar lines without being aware of each other. Some of this work was actually going on years before Lorenz's "discovery.")

The late mathematician Benoit Mandelbrot's ideas about turbulence in financial markets have enjoyed something of a renaissance in recent years thanks the global financial crisis. I was lucky enough to get the chance to interview Mandelbrot for FP a year before his death.

But chaos has also had applications in some less obvious areas, such as politics and international relations. In fact, there's an argument to be made that the ideas behind chaos are far more intuitive in the study of politics and armed conflict than in the natural sciences where it originated. Take, for example, the old English proverb that's second only to the Butterfly Effect as a commonly used layman's explanation for chaos:

For want of a nail the shoe was lost.
For want of a shoe the horse was lost.
For want of a horse the rider was lost.
For want of a rider the message was lost.
For want of a message the battle was lost.
For want of a battle the kingdom was lost.
And all for the want of a horseshoe nail.

What, after all, is a better example of chaos theory than the harassment of a street vendor in Tunisia leading to a civil war in Syria?

As Ohio State political scientist Alan Beyerchen has argued, Carl von Clausewitz seemed to have an intuitive grasp of the idea of nonlinear systems and chaos more than a century before anyone used those terms. Take, for example, this passage from On War:

[I]n war, as in life generally, all parts of the whole are interconnected and thus the effects produced, however small their cause, must influence all subsequent military operations and modify their final outcome to some degree, however slight. In the same way, every means must influence even the ultimate purpose.

In more recent times, ideas from chaos and its related subfield complexity theory influenced the writing of Columbia International Relations theorist Robert Jervis, who in his book System Effects¸ argues that many social scientists don't adequately grapple with the fact that interconnected actors in a complex system can produce results that seem like vastly more or vastly less than the sum of the system's parts. Our own Stephen Walt summarized the argument in a review for the Atlantic back in 1998:

Because system effects are everywhere, Jervis emphasizes, "we can never do merely one thing." Any step we take will have an infinite number of consequences, some that we intend and others that we neither intend nor foresee. A military buildup may deter a threatening adversary and help to preserve peace, for example, but it may also divert funds from other social needs, encourage one's allies to free-ride, and cause formerly neutral states to become friendlier with one's rivals. The more complex the system and the denser the interactions between the parts, the more difficult it is to anticipate the full effects of any action.

More recently, some political scientists have tried to apply chaos to international relations even more explicitly. The Dutch military analyst Ingo Piepers, for instance, sees relations between great powers over the last five centuries as a complex system moving toward "attractors" like those described by Lorenz in his weather model.

Political scientists Joan Pere Plaza i Font and Dandoy Regis put together a very good and readable overview of chaos theory's applicability to political science in 2006. They write:

Chaos theory is particularly useful in the field of peace research. First, the more diverse possibilities are actualized in a given situation, in terms of both actors' roles and interactions between actors, the greater the likelihood of peace. Peace will therefore occur in states with high entropy, meaning that increasing disorder, messiness, randomness and unpredictability will bring more peace than it could occur in predictable or excessive ordered countries. Second, chaos theory aims to model whole systems, looking at overall patterns rather than isolating the cause-and-effect relations of specific parts of a system. Through this approach, chaos theory has discovered that many social systems are not simply orderly or disorderly. Some are orderly at times and disorderly at other times. Others are in constant chaotic motion, yet display an overall stability.

In an ambitiously titled 2007 paper, "A Chaotic Theory of International Relations? The Possibility for Theoretical Revolution in International Politics" the French IR theorist Dylan Kissane argues that a view of international relations derived from chaos theory provides an alternative to both the realist view of an international system defined by anarchy and the liberal view that highlights interdependence. Kissane writes that "chaos better reflects the reality of an international system where individuals and non-state actors can have a significant effect at the international or system level."

Much of Kissane's analysis is concerned with the distrution of power between actors in a chaotic system. "Unlike the anarchy of neorealist theory, chaos does not favour one distribution of power or security to another in terms of bringing stability to the system," he writes. 

Kissane also discusses one of the primary limitations of the "chaotic theory" by quoting the late Kenneth Waltz's argument that "success in explaining, not in predicting, is the ultimate criterion for a good theory." Chaos may not fully pass this test:

"A theoretical approach to international relations that expects that anything can occur within the system and which simultaneously cannot fully explain why such an event occurred - outside some basic notions arising from the nature of the system - may not be much of a theory at all."

This may be where "Big Data" - a concept as trendy today as chaos was 20 years ago - comes into play. Back in the late 1950s and early 1960s - around the same time Lorenz was doing his research on weather - many believed that the power of computers would eventually allow social movements and political trends to be predicted with a great degree of accuracy.

Today, most theorists have more modest goals. Chaotic systems are extremely difficult to predict in the long run, but they're also not entirely random - as Lorenz observed - and with enough detailed information, patterns emerge allowing short-term predictions to be made, though always with a degree of uncertainty. As Kalev Leetaru told me recently discussing the GDELT events database, "Most datasets that measure human society, when you plot them out, don't follow these nice beautiful curves," he says. They're very noisy because they reflect reality. So mathematical techniques now let us peer through that to say, what are the underlying patterns we see in all this."

In other words, we're hopefully getting better at analyzing patterns in war, peace, and social movements the same way Lorenz did in the months and years following his fateful coffee break.    

The OECD is out with its latest data on income inequality in member countries and it's a pretty grim picture. "In the first three years of the crisis, the inequality in income from work and capital increased as much as in the previous twelve, the report notes: 

The increase in inequality between 2007 and 2010 was been felt more in some countries than in others. As the following chart shows, the increase in Ireland and Spain was shocking, while inequality actually narrowed in Poland, the Netherlands, the Czehch Republic, and Germany:

At the same time that incomes have become more unequal, overall they've also been falling. The Iceland bar in the following graph is pretty astonishing -- the drop in employment income is larger than every other country's drop in total income. Poland, again, comes out looking pretty good:

Poverty rates increased overall -- about 11 percent in the OECD as of 2010 --  affecting households with children particularly hard. Poverty actually decreased among the elderly. 

In other words, inequality is increasing even in measures of inequality.

Last Friday, a member of Greece's neo-Nazi Golden Dawn party was expelled from parliament for mocking members of the leftist Syriza party as someone in the parliament chamber shouted "Heil Hitler." The Greek government's Golden Dawn problem continues to worsen as the U.S. State Department highlighted the group in its annual religious freedom report for causing an uptick in anti-Semitism. Criminal prosecutors recently launched a hate-speech investigation on the party after one of its members was filmed for a television documentary, saying, of immigrants: "We are ready to open the ovens. We will turn them into soap ... to wash cars and pavements. We will make lamps from their skin."

Odious as these statements are, the experience of other countries in Europe suggests that prosecuting extremist parties for hate speech may be counterproductive. In a study published in the journal Party Politics, Dutch political scientists Joost van Spanje and Claes de Vreese looked at the effect of the 2009 prosecution of controversial Dutch politician Geert Wilders on his Party of Freedom's political support. Wilders was charged with defaming Islam with various statements including describing the Quran as a "fascist" book and calling for it to be banned:

Our results suggest that the court decision caused an across-the-board increase in probabilities to vote for the PVV. In addition, we have found that this increase in vote probabilities translated into a 1 to 5-percentage points surge in PVV vote intentions among moderate assimilationists -those  who would like to see ethnic minorities adapt to Dutch culture and society. Both among those who are more radically assimilationist and among those who feel that minorities should be allowed to preserve their own customs and traditions, the court decision slightly increased PVV vote probabilities without resulting in more PVV vote intentions. This is because many radicals already supported the party, and because many multiculturalists have other parties that they still prefer to the PVV. More generally, the shift in vote probabilities largely occurred among those who would not normally vote for the PVV and would still not vote for it after the prosecution.

These findings imply that the decision to prosecute Wilders helped him in the electoral arena, both in the short run and in the long run.

This increase in support may have been critical in the 2010 parliamentary election, in which Wilders' PVV party earned enough votes to support a right-wing minority government. 

Admittedly, the statements that got Wilders prosecuted were mild compared to the sort of things that Golden Dawn members say on a regular basis. But the authors believe what's critical about these prosecutions is the way that far-right parties are typically structured:

Leadership, arguably key to electoral success of any party, is particularly important for anti-immigration parties. This is because these parties are generally strictly heirarchically structured. 

Prosecutions can help bolster an anti-immigrant leader's legitimacy. The parties can also benefit from the increased media exposure that a trial will bring for their issues of choice, a variation on the Internet's "Streisand Effect".

In any event, Wilders fared much worse in the 2012 elections, the year after he was acquitted.

My colleague Ty McCormick links to an article over at Quartz by Christopher Mims on the development of new technologies for the 3-D printing of food.  The technology's developers have some pretty bold claims for its potential:

He sees a day when every kitchen has a 3D printer, and the earth’s 12 billion people feed themselves customized, nutritionally-appropriate meals synthesized one layer at a time, from cartridges of powder and oils they buy at the corner grocery store. Contractor’s vision would mean the end of food waste, because the powder his system will use is shelf-stable for up to 30 years, so that each cartridge, whether it contains sugars, complex carbohydrates, protein or some other basic building block, would be fully exhausted before being returned to the store.

Ubiquitous food synthesizers would also create new ways of producing the basic calories on which we all rely. Since a powder is a powder, the inputs could be anything that contain the right organic molecules. We already know that eating meat is environmentally unsustainable, so why not get all our protein from insects?

If eating something spat out by the same kind of 3D printers that are currently being used to make everything from jet engine parts to fine art doesn’t sound too appetizing, that’s only because you can currently afford the good stuff, says Contractor. That might not be the case once the world’s population reaches its peak size, probably sometime near the end of this century.

“I think, and many economists think, that current food systems can’t supply 12 billion people sufficiently,” says Contractor. “So we eventually have to change our perception of what we see as food.”

That last sentence may very well be true, but I'm not really sure what problem the printer is solving. 3-D printing of other objects is exciting and potentially transformative because it takes all the difficulty out of manufacturing -- you won't need any skill or specialized equipment other than the printer itself to turn raw materials into useful household goods. 

But using chemical reactions to turn plant matter into food isn't a revolutionary idea -- homo erectus may have had it figured out. By this standard, the oven in my kitchen is a 3-D printer: If I put in special powders called flour and yeast, it will print me out a loaf of bread.

The powder in these cartridges still has to be made of stuff that someone has to grow. The Quartz article identifies some possible sources:

• algae

• duckweed

• grass

• lupine seeds

• beet leafs

• insects

Great! Algae-as-food has its advocates. So do insects. People in many countries already eat insects. Why don't we just make these things into food instead of making them into raw materials for food printing?

I find a certain level of arrogance in the idea that global hunger is just a technology problem.   There's already enough food in the world for everyone to eat enough to survive, yet poor people still starve. How will this change if we're buying food cartridges at the store instead of just food? 

Somalia's famine didn't happen because Somalis can't make food, it happened because it was too dry to grow it, they were too poor to buy it, and other people were stealing it. If they had shiny new 3-D food printers, they would still have been too poor to buy it. If anything, it would only make the global poor more dependent on the companies producing the food. 

Maybe -- in the name of sustainability -- we could all get used to eating synthesized glop squirted onto our plates by a machine. Or maybe we could all just try eating less meat and more vegetables first and see how that works out.

Uber-nerdy sidenote: Mims' article compares 3-D food printers to the replicators on Star Trek, an obvious comparison since the first (and more logical) application of this may be for long spaceflights. As Matt Yglesias points out, replicator technology seems to have been essential in creating the post-scarcity, post-monetary, quasi-socialist utopia in which the various Star Trek shows and movies take place. 

But as far as we know, the replicators worked by "rearranging subatomic particles, which are abundant everywhere in the universe," using technology similar to the transporter beam. There's no indication that the Enterprise had to restock on powders and food goops for the replicators every time it docked at a starbase.  

If that were the case, rather than asking the replicator for "Tea, Earl Grey, Hot," Captain Picard might just as easily have brought a big box of Lipton on board with him.

1. The man who killed himself in dramatic fashion on the alter of Notre Dame cathedral today turns out to have been a prolific right-wing historian and author who was protesting both gay marriage and sharia law

2. Ken Opalo argues that Tanzania's efforts to promote Swahili as a national language have hampered the country's education system 

3. Are the BRICS signs of a new "revolt against the west"?

4. Bruce Schneier says the "internet of things" means a world of ubiquitous surveillance 

5. You probably shouldn't be getting your information on population trends from Dan Brown novels

A new paper by Michael Clemens of the Center for Global Development looks at just how much it's worth for an Indian computer programmer to come to the United States. Clemens analyzed the personnel records of an unnamed Indian-based IT firm,whose employees participated in the H-1B vista lottery in 2007 and 2008. The firm has employees working at both its Indian office and onsite with foreign clients, so the winners of the lotteries were sent to the United States while the losers did offsite work. 

Clemens found that "for 2008 lottery entrants observed in 2007, the effect of working outside India is about 55,000 dollars per year in exchange-rate dollars. For 2007 lottery entrants observed in 2009, the effect is about 58,000 dollras per year."

So what does this tell us?

The results suggest that in this setting, the large majority of workers' value arises from location alone. Most of these differences in wage and MRP cannot be attrributed to differences in the workers themselves or the technology they use.

Or perhaps these computer whizzes should be working on their catwalk strut. According to Bloomberg, fashion models -- the only category of workers who can get H1-B visas without a college degree -- "are almost twice as likely to get their visas as computer programmers."

Since Amy Chua's Battle Hymn of the Tiger Mother ignited a firestorm of controvery in 2011, a number of studies have questioned the wisdom and effectiveness of the strict style of parenting she advocates. But a study published in the Asian American Journal of Psychology by a team of psychologists from NYU and several other insitutions, takes a different approach, looking into whether there's anything actually "Chinese" about Tiger Mom parenting. (The authors grant that much of Chua's book is tongue-and-cheek and she doesn't claim to be describing all Chinese families, but there are also frequent contrasts between "Chinese" and "Western"-style parenting in the book.)

The authors conducted interviews with over 700 families in Nanjing, "chosen for research because it is considered a modal urban city, neither a "first-tier" city that has experienced dramatically rapid economic reform and growth (e.g., Beijing,Shanghai) nor a rural city that has been slow to embrace social andeconomic development."

What they found is that the attitudes of a typical Nanjing mom aren't that different from what you might hear from your prototypical, touchy-feely American parent:

Mothers wanted their children to be socially skilled, happy, healthy, autonomous, and to attain good grades. Yet there was variation in theextent to which mothers valued these goals, with most mothersplacing equal or more emphasis on social and emotional goals thanon academic ones. Only two mothers in our study emphasized academic achievement above all other goals. Some mothers be-lieved that their children had achieved these social and emotionalgoals, whereas others worried about their children's introversion orlack of friendships, their bad moods, their children's dependence and lack of assertiveness. With few exceptions, mothers believed that if their children were not socially and emotionally adjusted, they would not thrive in school. Mothers also repeatedly underscored the importance of fostering the autonomy of their child and not forcing their children to do anything, as they believed that such actions would backfire and make their children unhappy.

Granted this is just one study and one location, but there is more evidence that if the authoritarian style of parenting described by Chua was ever prototypically "Chinese," it's not necessarily the case in a rapidly changing China. The authors note that "between 1998 and 2002, Shanghai parents' scores on parenting measures evidenced a notable shift toward higher warmth and autonomy support and toward lower power assertion" and that "the emerging literature on Chinese parenting in contemporary China is a far cry from the unwavering ideology that Chua (2011) described in her book onparenting her 3rd generation Chinese American daughters the"Chinese way."

Whether the style of parenting Chua describes as "Chinese" actually the function of older family attitudes or of the immigrant experience in America, or some other factor entirely is another question. But it does seem significant that the Chinese-language version of Chua's book was titled, Being a Mom in America.

The Journal of Peace Research has a great new special issue on the topic of  "Understanding Nonviolent Resistance" which is, for the moment, ungated online. Several of the papers in the issue take advantage of the new Nonviolent and Violent Campaigns and Outcomes (NAVCO) project created by Korbel Professor Erica Chenoweth and Orion Lewis of Middlebury College -- a coded database of violent and non-violent resistance movements around the world between 1900 and 2006. (Also see Chenoweth's Think Again: Nonviolent Resistance from FP in 2011.)

One paper by Kathleen Gallagher Cunningham of the University of Maryland -- co-editor of the issue with Chenoweth -- uses the NAVCO data to test a number of hypotheses about why some groups seeking self-determiniation choose violence, non-violent resistance, or traditional political methods to advance their goals. 

Examining 146 groups making claims for self-determination in 77 different states since 1960 Cunningham finds that:

...civil war is more likely, as compared to conventional politics, when self-determination groups are larger, have kin in adjoining states, are excluded from political power, face economic discrimination, are internally fragmented, demand independence, and operate in states at lower levels of economic development. I find that nonviolent campaign is more likely, as compared to conventional politics, when groups are smaller, are less geographically concentrated, are excluded from political power, face economic discrimination, make independence demands, and operate in non-democracies.

The finding on group size ran counter to Gallagher's expectations. The hypothesis was that large groups seeking self-determination would be more likely touse nonviolent campaigns given their strength in numbers.

Another paper examine the correction between a political organization's attitudes toward, and inclusion of women on the form of resistance it chooses. Another finds data to support the claim that nonviolent protests -- as opposed to violent action -- substantially increase the likelihood of transition to democracy. 

There's a lot more to read and it's great to see nonviolent movements getting the type of attention and data-driven analysis usually devoted to armed conflict.