Discord in the Quantum World
An alternative quantum resource to entanglement could help physicists in the quest to construct a quantum computer.
A View From the Top
Thinking of causation as a "two-way street"—along which the passage of information can be inverted—could have implications for the origin of life.
Classic Article: Black Holes, Paradox Regained
In 2004, Stephen Hawking famously conceded that black holes do not devour all information when they swallow matter—seemingly resolving the "black hole information paradox" that had perplexed physicists for decades. But some argue that the paradox remains open, and we must abandon our simple picture of spacetime to unravel it.
Ideas inspired by microscopic physics and magnetism could one day help predict the spread of disease, financial markets, and the fates of Facebook friendships.
by Graeme Stemp Morlock
November 6, 2012
Raissa DíSouza University of California, Davis.
Your grade ten math teacher probably wrote this several times on your tests: SIMPLIFY. And, for much of science, thatís part of the work: SIMPLIFY. The universe can be broken down into smaller and smaller chunks in an attempt to find its most basic level and functions. But what do you do when that doesnít work? Complex systems that defy reduction are all around us, from the elaborate workings of an ant colony—which could never be predicted from the physiology of a single ant—to fluctuations in the financial system that can send ripples around the globe. When broken into their constituent pieces, examined and put back together, such systems do not behave as expected. The sum of the parts does not equal the whole.
Surprisingly, the best way to analyze these decidedly large-scale systems may be by exploiting techniques first developed not in biology or economics, but in microscopic physics. Raissa DíSouza, a complexity scientist at UC Davis and an external professor at the Santa Fe Institute, is applying lessons learned from studying how physical systems go through phase transitions—becoming magnetized, for instance—to try to predict when everyday networks will go through potentially catastrophic changes. Her work has implications for the spread of disease, sustaining the energy infrastructure, the financial health of countries, and for the way we connect with our friends in online communities.
While completing her PhD in statistical physics at MIT in the 1990s, DíSouza became fascinated with complex systems and the behavior patterns that emerge from them. Since she did not know of anyone who specialized in the subject, she went to the library and searched the entire Boston area for someone who did, before finding Norm Margolus, who it turned out was handily also at MIT and with whom she studied pattern formation and computing in natural systems. DíSouzaís background in statistical physics introduced her to the prototypical phase transition. It considers a collection of atoms, each with a magnetic moment, that could either line-up with each other—so that the overall system becomes magnetized—or remain in a disordered mess. There is a tension in this case: on the one hand, the atoms want to line-up, lowering the systemís energy; on the other hand, the laws of thermodynamics tell us that systems prefer to move to a state of increasing disorder, mathematically expressed as having a higher entropy. It was first discovered experimentally that the outcome depends on temperature. At high temperatures entropy rules, the atoms remain disordered and the system does not become magnetized. But below some critical temperature, the system undergoes a phase transition and the atoms align.
That sounds simple enough, but the phase transitions that change a systemís behaviour so profoundly are often unpredictable, especially if you only study the system in its smallest components. How for instance, could you predict what the critical temperature would be, in theory, if you only focus your attention down onto one isolated atom? Instead, youíve got to see the big picture. And sometimes that picture is very big.
The Power of Networking
Taking a step back, DíSouza sees everything as being interconnected. Her job is to work out when linked objects or entities will go through profound phase transitions, which could lead to a negative (or sometimes positive) outcome. For instance, the United States power grid was once a collection of small isolated grids, made of a few powerplants run by some municipality or corporation. Then, local grids were connected to create state-wide and regional grids that remained largely independent. Distinct regions were then interconnected to allow power transfer in emergency situations. But, with deregulation, those interconnections now transfer massive amounts of power bought and sold on power auction markets each day. As DíSouza points out, this interdependence has changed networks in ways that were originally never intended, leading to unforeseen bad consequences. The U.S. power grid has grown to a point where it has seemingly encountered a phase transition and now occasionally suffers from large cascading blackouts, where a problem in one area can drag many areas down. Worse, a failure in one network can actually drag down many different networks. So a failure in the power grid can cause a failure in the telecommunications grid which causes a failure in the transportation grid and the impact keeps rippling through time and space.
Speaking at FQXiís Setting Time Aright meeting, DíSouza discussed the conception of time that emerges from considering examples of interconnected networks in terms of complexity theory:
"In the last 3-4 years, Iíve been working to take the ideas from single networks, such as the structure of the network and the dynamics happening on top of the network substrate, and extending it to this bigger context where we have networks of networks," says DíSouza. "Iíve been trying to understand what it does to emergent properties like phase transitions and what it means for the vulnerability of these systems. So, if there is a small ripple in one layer can it go into other layers and how long does it take?"
Understanding how networks interconnect and evolve has huge implications for public health, for instance. DíSouza cites the example of pandemics, where infection rates have changed drastically over time based on advancements in our transportation networks. In the Middle Ages, the bubonic plague took years to spread across Europe, for example; by contrast the Spanish flu pandemic of 1918 killed over 20 million people across the globe, taking only a matter of weeks or months to spread. But now, with the arrival of mass air travel, it only takes hours for SARS, swine flu or bird flu to reach new countries.
Pinpointing the critical point of a phase transition is not easy in the world of networked networks, but part of DíSouzaís work has been to find a generalised model, or set of equations that will apply to many different examples, not just the power grid or the transportation network. In February 2012, DíSouza and colleagues published a paper in the Proceedings of the National Academies of Sciences (PNAS) in which they analysed such a universal model and predicted where the optimal level of connection and interdependence would be—and that, ultimately, too much connectivity would be detrimental.
There are drawbacks to basing your mathematical analyses on equations inspired by mathematical physics that are usually used to analyse the collective behavior of atoms and molecules, however. Such statistical equations usually work by considering a collection of around 1026 atoms (thatís 10 followed by 26 zeros, Avogradroís number). By contrast, even the biggest real-world networks today only get up to about a billion (109), which makes it difficult to take theoretical predictions from the equations and apply them directly to real-world networks. Nonetheless, independent network scientists aiming to forecast financial crises have found intriguing evidence that backs DíSouzaís theoretical predictions about interdependence and phase transitions.
Soon after DíSouzaís PNAS paper appeared, Stefano Battiston, at ETH Zurich, and colleagues published an independent study in the Journal of Economic Dynamics and Control that investigated the dominant view in finance that diversification is good. The idea is that it is better to spread your money around, so that even if one investment goes bad, you will still win overall. However, Battistonís group found that diversification may not be the best strategy. In fact, they calculated that it could actually spread "financial contagion."
Dangerous Liaisons? Networks of networks share the good and the bad. Credit: aleksandarvelasevic
What Battistonís group realized was that a naturally occurring financial mechanism known as trend reinforcement was enough to push a single failure through the entire system. Trend reinforcement works through a rating body that evaluates an entityís performance. In the financial case that Battistonís group evaluated, when the market was disappointed by a companyís returns, they downgraded that company, which resulted in additional selling, which caused the company to underperform and disappoint the rating body again. This negative cycle and penalization altered the probability of the company doing well and magnified the initial shock. Furthermore, they found that if the shock became big enough, then a phase transition would occur, as DíSouza hypothesizes, allowing the shock to travel through the entire system.
"There are some benefits in diversification and connections of course," says Battiston, "but there are serious threats that come from connecting everything in a single system that behaves in synchrony because recovering from a complete collapse is obviously very costly, not just economically but socially as well."
Extending their tentacles beyond the financial world, networks can also help expose the way politicians and nation-states act. Zeev Maoz, a political scientist at UC Davis and a distinguished fellow at the Interdisciplinary Center in Herzliya, Israel, has found that geopolitical networks have significant spillover to other networks, for instance security and trade. Importantly, Maoz has also shown that nations are not connected equally; often smaller states are connected through more central players. So, you get a situation where there are a few major players each with a large cadre of states connected on their periphery, and this can be destabilizing.
"The uneven structure is a cause of potential instability because if everyone is connected to a few major partners and the major powers experience a shock then everyone suffers," says Maoz. Unfortunately, there arenít any levers that can help mitigate a shock like that because of the nature of connectivity, he explains. Take for instance Greece, which is dependent on Germany and France and the United States. If a shock because of the recession hits the big players, then Greece suffers more than Germany, France, or the USA, because Greece is dependent on them and does not have trading partners of its own.
Complex Conceptions of Time
All these studies converge on one conclusion: complex systems are, fittingly, even more complex than first thought. Complexity theorists have long accepted that you cannot just look at components and understand the whole system—their discipline is based on that assumption, after all. But now complexity scientists have learned that you cannot even look at a single system and understand it without the context of all the other systems it interacts with. "So weíre at the point where we can begin to analyze systems of systems," says DíSouza, each evolving on its own timescale, with feedbacks between these systems. Take, for instance, online social networks that evolve much faster than say social norms or transportation networks. Users of Facebook or Twitter typically develop a web of "friends" or "followers" that extends well beyond the number of people they would have time to physically meet up with and interact with face-to-face, says DíSouza: "How do we characterize time in these disparate systems?"
Social networks could breakdown if they got so dense you couldnít distinguish meaningful information from noise anymore.
- Raissa DíSouza
At first sight, the ability of online social networks to bring people around the world closer together and shrink the time that it takes to interact may seem like an unambiguously positive thing. But even social networks are vulnerable to phase transitions, so DíSouza urges caution: At some point that connectivity might backfire and potentially cause the network to collapse. "Maybe we will find that Facebook becomes a great big mush and isn’t interesting anymore because there is no way to differentiate who is a true friend and who is someone that you used to know 20 years ago and youíre just overwhelmed with information," DíSouza says. "That could be one way that a network like Facebook could fail. It could break down if it got so dense that you couldnít distinguish meaningful information from noise anymore."
And your number of Facebook friends is only going to increase, according to DíSouza. In fact, she believes that to be almost a rule in thinking about networks of networks. "I firmly believe networks become more interdependent in time," says DíSouza. "We see the global economy becoming more interdependent. We see Facebook making everyone more interconnected. Weíre relying increasingly on technologies like the Internet and communications networks, for instance, the smart-grid, a cyber-physical system. All these networks that used to operate more independently are now becoming more interconnected, and to me that is really a signature of time."
Comment on this Article
Please read the important Introduction that governs your
participation in this community. Inappropriate language will not be tolerated and posts containing such language will be deleted. Otherwise, this is a free speech Forum and all are welcome! Recent Comments
GEORGINA PARRY wrote on November 26, 2012 Cambridge University is to launch a centre for the study of existential risks to the human race Quote: "But new hazards are emerging that could be so catastrophic that even a tiny probability is disquieting. For instance, global society depends on elaborate networks - electricity grids, air traffic control, international finance, just-in-time delivery and so forth. Unless these systems are highly resilient, their manifest benefits could be outweighed by catastrophic (albeit rare) breakdowns...
GEORGINA PARRY wrote on November 23, 2012 I like the association of time with the growth of the complexity of the systems.
It seems to me there is that kind of time associated with any kind or growth or senescence and decay, or dismantling. It is a very different kind of time to the time dimension of space-time though. As it does not have the same association with space that forms the 'fabric of space-time'. It could be imagined as a time line where the structures (or systems) are arranged in increasing or decreasing complexity,...
THOMAS HOWARD RAY wrote on November 19, 2012 "So we're at the point where we can begin to analyze systems of systems," says D'Souza, each evolving on its own timescale, with feedbacks between these systems."
Exactly so. And I think we're finding further -- as Raissa's research suggests -- that assuring the independence of systems within systems is becoming increasingly important to avoid the kind of out of control degradation of an interdependent system that Battiston's group identified.