Can There Be a Mathematics of War?

People do many things without knowing why: buy stuff they didn't think they wanted, vote differently when they're in one setting than they would in another, order a different lunch because of what the person next to them just ordered. As scientists learn more about all this, they should be able to predict, more often and more accurately, what people will do--regardless of what those people think they'll do.

Those predictions will be a scientifically rigorous version of our usual methods for interpreting behavior: explaining people's actions as the result of their feelings, perceptions and thoughts. When Josh Aronson and his colleagues showed they could get women to score better on a math test by telling them gender doesn't affect math scores, they're showing what psychologists can do with better knowledge of that familiar subject, the individual person. It's impressive, but not eerie.


There are other methods of predicting people's behavior, though, that aren't intuitively easy to grasp. They're based on patterns in the actions of very large numbers of people—stock markets, highway systems, cell-phone calls by the billions, and the like. That kind of prediction is harder to grasp, because it contradicts our intuitions about free will. How could my decision next Friday depend on what millions of other people do? The prospect is a little freaky.

Case in point: Today's issue of Nature features a paper by Juan Camilo Bohorquez, Sean Gourley, Alexander R. Dixon, Michael Spagat and Neil F. Johnson, which argues that all insurgencies--wars in which guerrilla-type units are fighting a standing military--share a single, predictable pattern in their violent attacks. In other words, according to their model, the decisions of insurgents--about whether to attack on a Wednesday or a Saturday, about whether to try for an average success or go for a spectacularly bloody result--don't take place in a wildly unpredictable "fog of war.'' Instead, they'll always tend to follow the same rhythm. Regardless of their beliefs, ideologies and motives. Regardless of their immediate tactical concerns. Regardless of what they may think they are doing.

Johnson, Spagat and their colleagues analyzed 54,679 violent events in nine separate insurgencies -- Colombia, Peru, Senegal, Sierra Leone, Northern Ireland, Israel-Palestine, Iraq, Afghanistan and Indonesia -- and plotted the frequency of insurgent attacks against the number of people killed in each one. They found the same relationship between the two in every conflict.

Let's back up to see what that means. (If you prefer video, check out one of the authors describing the work here.) All over nature and in human affairs as well, that kind of a plot (size of a measurement against frequency of occurrence) often reveals a relationship between the two. For human height, for example, the most typical measurements are the most frequent (a lot more human beings measure five foot ten than reach eight feet), so height measurements fall on the familiar "bell curve": small at the extremes, fat in the middle.

The bell curve teaches you to expect that what's typical is frequent, which makes extreme and rare events look unpredictable. But the bell curve isn't the only possible relationship between size and frequency. For any given earthquake zone, for example, there will be a hundred quakes that score 2.0 in the Richter scale for every 4.0 quake. The Richter scale is logarithmic--3 is ten times stronger than 2, and 4 is ten times stronger than 3--so this relationship between strength and frequency isn't anything like a bell-curve plot. It's looks more like Chris Anderson's "long tail,'' where a few rare giants reach the top of the graph and most of the measurements trail after.

Because of the way they're represented mathematically, these kinds of relationship between size and frequency are called "power law'' distributions. And such distributions are extremely common. Power-law plots fit, for example, the relationship between a meteorite's kinetic energy and the size of the crater it creates on the moon; sales of books, the frequency of different openings in chess games, the participation of editors on Wikipedia, and the frequency of words in any given language.

Power-law graphs are significant, first, because they give a different perspective on extreme events. Bell-curve expectations make those rarities--the mega-best-selling book, the magnitude 7 earthquake, the terrorist strike that kills 3,000 people--appear impossible to predict. On a power-law distribution, rarity doesn't mean "unforeseeable.'' Secondly, power-law patterns suggest that physical facts might govern behavior that looks to us as if it must be caused by psychological, economic or historical factors.

The rap against this approach is that it's just numerology. Not every pattern in data describes real-world causes and effects, after all. For instance, from 1860 until 1980, every President elected in a year ending with "0" died in office. It seems unlikely that this numerical coincidence could tell anything about physical or social reality.

The Nature authors have an answer to that. If there is a common signature to all insurgencies, they argue, it must because all insurgent fighters converge on the only viable strategy. (The pattern they found in insurgent attacks does not apply to non-insurgent conflicts, they write.) The authors believe guerrilla movements are bound by a mix of physical and social constraints. Physically, insurgent groups maintain a particular size and organization to persist; socially, they have to strike in such a way that they get the maximum media attention and political impact. A terrorist group doesn't want to strike on a day when three other units also attack, because then their assault will be lost in the general coverage. In other words, guerrillas, like stock brokers, are making decisions based on what they think other people will do.

So, does this mean power-law analysis can predict future terrorist attacks? Not to a very fine grain--though one of the pioneers of this analysis, Aaron Clauset, has said the power-law pattern of global terrorist attacks suggests a strike on the scale of 9/11 will occur before the end of 2012. The Nature authors say they're more interested in using the model to understand insurgencies. In an email, Johnson and Spagat wrote: "We are now looking at where events occur, and when, to see if we can understand the spreading. We are also looking at intervention strategies etc. Also we are addressing 'what if' questions such as: What would happen if we added a third population of 'peacekeepers'? How should they be deployed in order to minimize casualties?''

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Yale scientists restore brain function to 32 clinically dead pigs

Researchers hope the technology will further our understanding of the brain, but lawmakers may not be ready for the ethical challenges.

Still from John Stephenson's 1999 rendition of Animal Farm.
Surprising Science
  • Researchers at the Yale School of Medicine successfully restored some functions to pig brains that had been dead for hours.
  • They hope the technology will advance our understanding of the brain, potentially developing new treatments for debilitating diseases and disorders.
  • The research raises many ethical questions and puts to the test our current understanding of death.

The image of an undead brain coming back to live again is the stuff of science fiction. Not just any science fiction, specifically B-grade sci fi. What instantly springs to mind is the black-and-white horrors of films like Fiend Without a Face. Bad acting. Plastic monstrosities. Visible strings. And a spinal cord that, for some reason, is also a tentacle?

But like any good science fiction, it's only a matter of time before some manner of it seeps into our reality. This week's Nature published the findings of researchers who managed to restore function to pigs' brains that were clinically dead. At least, what we once thought of as dead.

What's dead may never die, it seems

The researchers did not hail from House Greyjoy — "What is dead may never die" — but came largely from the Yale School of Medicine. They connected 32 pig brains to a system called BrainEx. BrainEx is an artificial perfusion system — that is, a system that takes over the functions normally regulated by the organ. The pigs had been killed four hours earlier at a U.S. Department of Agriculture slaughterhouse; their brains completely removed from the skulls.

BrainEx pumped an experiment solution into the brain that essentially mimic blood flow. It brought oxygen and nutrients to the tissues, giving brain cells the resources to begin many normal functions. The cells began consuming and metabolizing sugars. The brains' immune systems kicked in. Neuron samples could carry an electrical signal. Some brain cells even responded to drugs.

The researchers have managed to keep some brains alive for up to 36 hours, and currently do not know if BrainEx can have sustained the brains longer. "It is conceivable we are just preventing the inevitable, and the brain won't be able to recover," said Nenad Sestan, Yale neuroscientist and the lead researcher.

As a control, other brains received either a fake solution or no solution at all. None revived brain activity and deteriorated as normal.

The researchers hope the technology can enhance our ability to study the brain and its cellular functions. One of the main avenues of such studies would be brain disorders and diseases. This could point the way to developing new of treatments for the likes of brain injuries, Alzheimer's, Huntington's, and neurodegenerative conditions.

"This is an extraordinary and very promising breakthrough for neuroscience. It immediately offers a much better model for studying the human brain, which is extraordinarily important, given the vast amount of human suffering from diseases of the mind [and] brain," Nita Farahany, the bioethicists at the Duke University School of Law who wrote the study's commentary, told National Geographic.

An ethical gray matter

Before anyone gets an Island of Dr. Moreau vibe, it's worth noting that the brains did not approach neural activity anywhere near consciousness.

The BrainEx solution contained chemicals that prevented neurons from firing. To be extra cautious, the researchers also monitored the brains for any such activity and were prepared to administer an anesthetic should they have seen signs of consciousness.

Even so, the research signals a massive debate to come regarding medical ethics and our definition of death.

Most countries define death, clinically speaking, as the irreversible loss of brain or circulatory function. This definition was already at odds with some folk- and value-centric understandings, but where do we go if it becomes possible to reverse clinical death with artificial perfusion?

"This is wild," Jonathan Moreno, a bioethicist at the University of Pennsylvania, told the New York Times. "If ever there was an issue that merited big public deliberation on the ethics of science and medicine, this is one."

One possible consequence involves organ donations. Some European countries require emergency responders to use a process that preserves organs when they cannot resuscitate a person. They continue to pump blood throughout the body, but use a "thoracic aortic occlusion balloon" to prevent that blood from reaching the brain.

The system is already controversial because it raises concerns about what caused the patient's death. But what happens when brain death becomes readily reversible? Stuart Younger, a bioethicist at Case Western Reserve University, told Nature that if BrainEx were to become widely available, it could shrink the pool of eligible donors.

"There's a potential conflict here between the interests of potential donors — who might not even be donors — and people who are waiting for organs," he said.

It will be a while before such experiments go anywhere near human subjects. A more immediate ethical question relates to how such experiments harm animal subjects.

Ethical review boards evaluate research protocols and can reject any that causes undue pain, suffering, or distress. Since dead animals feel no pain, suffer no trauma, they are typically approved as subjects. But how do such boards make a judgement regarding the suffering of a "cellularly active" brain? The distress of a partially alive brain?

The dilemma is unprecedented.

Setting new boundaries

Another science fiction story that comes to mind when discussing this story is, of course, Frankenstein. As Farahany told National Geographic: "It is definitely has [sic] a good science-fiction element to it, and it is restoring cellular function where we previously thought impossible. But to have Frankenstein, you need some degree of consciousness, some 'there' there. [The researchers] did not recover any form of consciousness in this study, and it is still unclear if we ever could. But we are one step closer to that possibility."

She's right. The researchers undertook their research for the betterment of humanity, and we may one day reap some unimaginable medical benefits from it. The ethical questions, however, remain as unsettling as the stories they remind us of.

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