Mathematical analysis and intelligence and counterintelligence
Mathematical analysis plays a crucial role in the fields of intelligence and counterintelligence, particularly in military contexts. Historically, during World War II, mathematicians like Alan Turing significantly advanced cryptography, which was instrumental in breaking enemy codes and contributing to military victories. In the Cold War and subsequent conflicts, including the "War on Terror," mathematical theories such as game theory and statistical analysis became vital for developing strategies against adversaries employing rational tactics.
Organizations like the National Security Agency (NSA) leverage data mining and social network analysis (SNA) to identify potential threats by mapping relationships between individuals. Techniques from lattice theory aid in understanding the structure and hierarchy within terrorist networks, helping agencies determine the most effective targets for disruption. Additionally, mathematical models have been utilized to predict the dynamics of terrorist recruitment and public sentiment, providing insights into the evolution of insurgencies. Overall, mathematics serves as a powerful tool for enhancing national security efforts through better analysis and prediction of complex social behaviors.
Mathematical analysis and intelligence and counterintelligence
Summary: Quantitative data, mathematical models, cryptography, data analysis, and social network analysis have proved powerful tools in intelligence.
“Mathematicians Won the War”
During World War II, the mathematics underlying cryptography played an important role in military planning. Winston Churchill admired Alan Turing, the Cambridge University mathematician who had mastered the Nazi codes, recognizing him as the man who had perhaps made the single greatest individual contribution to defeating Germany. After the first frosts of the Cold War descended in the Soviet East, approximately $2 billion was spent in the development of game theory.
After the Cold War came the “war on terror.” The adversary uses rational strategies to attack, so rational strategies are needed for defense.
The “War on Terror”
The National Security Agency (NSA) is a riddle wrapped in a mystery inside a code—a black palace of glass located in Fort Meade, Maryland. It dwarfs the location of the Central Intelligence Agency (CIA). Its budget is unknown, and it is the world’s largest employer of mathematicians, primarily number theorists, whose work depends integrally on the presumed complexity of factoring large numbers.
In May 2006, one of the NSA’s secrets escaped. USA Today reported that the phone companies AT&T, Verizon, and Bell South had handed customer records over to the agency—not transcripts of calls, they said, just who was calling whom. Technically, only telephone numbers were being recorded, but one could easily obtain a name from a phone number. This information was being used to determine who might be a terrorist. With the NSA data, one can draw a picture or a graph with “nodes” (or dots) representing individuals and lines between nodes if one person has called another. The field of social network analysis (SNA) deals with trying to determine information about a group from such graphs, such as who the key players are or who the cell leaders might be.
Even if everyone in the graph is a known terrorist, graphs do not directly portray information about the order or hierarchy of the cell. SNA researchers look instead for graph features like centrality—they try to identify nodes that are connected to many other nodes, like spokes around the hub of a bicycle wheel. Indeed, Monterey Naval Postgraduate School researcher Ted Lewis, in his textbook Critical Infrastructure Protection, defines a critical node to be such a central hub.
There are two problems in creating such a graph. First, the “central player” might not be as important as the hub metaphor suggests. For example, Jafar Adibi of the University of Southern California looked at e-mail traffic between employees of the company Enron before its famous collapse and drew a graph. He found that if you naively analyzed the graph, you could mistakenly conclude that one of the “central players” was CEO Kenneth Lay’s secretary. Second, as the journal Studies in Conflict and Terrorism reported in 2003, one can capture all the central players in a terrorist cell and leave the cell with a complete chain of command still capable of carrying out a devastating terrorist attack.
Lattice Theory Applied to the “War on Terror”
While it is true that NSA expert Kathleen Carley of Carnegie Mellon University was twice able to correctly predict who would take over Hamas when its leaders were assassinated (Hamas, the Palestinian Islamic Resistance Movement, is considered a terrorist organization by the U.S. government), her analysis uses detailed information about the individuals in the organization, not just which anonymous nodes were linked with which. Since terrorist cells are composed of leaders and followers, it is important to utilize lattice theory, which takes into account order and hierarchy.
Formal concept analysis (FCA), a branch of applied lattice theory, helps identify persons of interest. Individuals who share many of the same characteristics are grouped together as one node, and links between nodes in this picture, called a “concept lattice,” indicate that all the members of a certain subgroup with certain attributes must also have other attributes. For instance, one might group together people based on what cafés, bookstores, and houses of worship they attend and then find out that all the people who go to a certain café also attend the same church, but maybe not vice versa. At Los Alamos National Laboratory, the laboratory that helped build the first atomic bomb, formal concept analysis has been used to mine data drawn from hundreds of reports of terrorist-related activity and to discover patterns and relationships that were previously in shadow—connections that human analysts could not have easily found without something like FCA.
Tools from lattice theory can be applied to help intelligence agencies determine whether they have disrupted a terrorist cell. In early June 2005, the Pentagon announced plans to revise its strategy in the “war on terror.” While then U.S. president George W. Bush repeatedly cited that 75 percent of Al Qaeda’s leadership had been killed or captured, Al Qaeda remained active. The Pentagon shifted its target to mid-level captains and foot soldiers. Lattice theory, along with some extramathematical analysis, will help law enforcement agencies determine which individuals in a terrorist cell should be captured first, in order to maximize the chances of disrupting a cell by expending as few resources as possible. Lattice theoretical methods tell us the probability that a terrorist cell has been disabled based on how many terrorists have been captured and what rank they held in the organization.
Social choice theory has been applied to the hierarchical relationships within terrorist cells, determined from the direction of communications traffic, to model network formation. Researchers at New York University have identified two types of coalitions. They have found that the detection of one type of cell is more effective in disrupting networks, whereas the detection of the other type of cell is more effective in identifying all the members of the cell. They have also used the lattice theory to try to determine the leaders from the graph of a terrorist network. Lattice theory and graph theory can even account for gaps in one’s knowledge of the structure of a terrorist cell by making assumptions about how the “perfect” terrorist cell must be organized. The knowledge of the structure of the perfect terrorist cell could also be used by terrorists to counter intelligence efforts.
Winning the Battle for Hearts and Minds
Former U.S. defense secretary Donald Rumsfeld stated in a USA Today article on October 22, 2003, “Today, we lack metrics to know if we are winning or losing the global war on terror. Are we capturing, killing, or deterring and dissuading more terrorists every day than the madrassas and the radical clerics are recruiting, training, and deploying against us?” To model the growth of a terrorist network, one could use the same differential equations that govern the spread of an infection, like severe acute respiratory syndrome (SARS). Such models could be used to help the government understand, and eventually contain, the spread of a terrorist insurgency.
On March 16, 2003, then U.S. vice president Dick Cheney predicted on Meet the Press that Americans would be “greeted as liberators” in Iraq. Ideas from statistical physics have been used to model the battle for the hearts and minds of the people of Iraq. Just as a magnetic pole may be north or south, a person could be either for the occupation or against it. The model shows that there can be a tipping point in the evolution of public opinion. It may seem as if much of the population is with one side (for example, the United States) but then, dramatically, a wave of hostility sweeps down, and one witnesses the birth of an insurgency.
Terrorism of the Futures Market
When bombs explode, the stock market drops. Mathematician Stefan Schmidt of the Technical University in Dresden, Germany, has attempted to quantify the impact on the market of a terrorist incident. The only people who know when a bomb will explode are, of course, the terrorists. By playing the market, they may already have obtained as much money as they need, thus stifling U.S. Treasury Department efforts to cut off their funding. The terrorism of the futures market may be the terrorism of the future.
Bibliography
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