Skip to comments.Homeland security studying fractal mathematics vs. decentralized groups (BAD title)
Posted on 10/11/2004 6:42:09 AM PDT by Calpernia
PISCATAWAY, N.J. - A small group of thinking men and women convened at Rutgers University last month to consider how order theory a branch of abstract mathematics that deals with hierarchical relationships could be applied to the war on terror.
It almost seems ridiculous for people who inhabit a world of concept lattices and partially ordered sets to think they can affect a war that is being fought on the streets of Baghdad and in the remote mountains of northern Pakistan. But the war on terror is also fought in cyberspace, and in the minds of people from Lahore to Los Angeles. Mathematicians are right at home in such abstract realms.
"It's not just theoretical," said Fred Roberts, director of the Center for Discrete Mathematics and Theoretical Computer Science, the Rutgers research institute where the conference was held.
Terrorism takes brains. You don't need political influence, military might or economic resources to plant bombs or take hostages; but without brains, terrorism is nothing more than random violence.
Consider al-Qaida's attack on New York City and Washington, D.C., three years ago. It required a force of only 20 men armed with box cutters, yet it was so brilliantly conceived, meticulously planned and keenly attuned to global politics that it changed the world.
"Terrorism is a thinking man's game," said terror expert Gordon Woo.
Mathematician Jonathan Farley of the Massachusetts Institute of Technology (news - web sites) said he was inspired to organize the meeting by the movie "A Beautiful Mind." The film tells the story of mathematician John Forbes Nash, whose work in game theory found application in Cold War military strategy, international trade and the auctioning of broadcast frequencies by the Federal Communications Commission (news - web sites).
"I'm a pure mathematician, so I'm completely useless for the most part," Farley said. "But it would be nice to take some of what we do and make it useful for some people maybe even lifesaving."
The new Homeland Security Institute has a mandate from Congress to do just that, said Gary G. Nelson. A senior researcher at the quasi-governmental institute, he attended the conference in hopes of finding research projects for the institute to support.
Some ideas sounded promising, Nelson said. The most intriguing were those that could help intelligence agencies boil down the vast amounts of data they contend with.
Other proposals were "a pretty long logical distance" from the real world. And not everything was easy to understand, he said, even for a systems engineer.
Theoretically, Farley said, abstract math could help intelligence officers figure out the most efficient way to disable a terrorist network.
Say it's cheaper or more practical to go after a terrorist cell's "middle management" rather than its leadership. How many of those lieutenants would you have to remove in order to disrupt communication between the top dogs and the field operatives? Are there one or two key individuals whose capture would completely cut off the chain of command?
Order theory is all about such questions.
"This helps them decide where to spend the money," Farley said.
Of course, many times the organizational structures of terrorist groups are unknown. Mathematical techniques could also be applied to that problem, by using computer programs that comb through giant databases looking for connections between individuals, locations or events. For example, a program might discover that everybody involved in a given attack attended the same London mosque. Or it might find large numbers of e-mail messages between members of one terrorist cell in Germany and another in the United States, suggesting that they may be working together.
Such data mining techniques are nothing new. But the explosion in computing power over the past few years has spurred innovation in the field.
Jafar Adibi, a computer scientist at the University of Southern California, is developing ways to find hidden links between known terrorists and their as-yet-unknown confederates.
"You're trying to detect major groups of these bad guys," Adibi said.
The technique relies on having an initial group of known terrorists. Then it analyzes things those known terrorists have in common with other people in the database, such as phone calls, places of worship, political affiliations or blood relation.
The program concludes that anybody who has enough connections of the right kind with a known terrorist probably is one also.
Adibi has tested his program using a database built from newspaper accounts and other publicly available information. He labels 20 percent of a terrorist group's members as "known" and challenges the program to find the rest. Right now, the system misses 20 percent of the remaining members, and three of the 10 people it does identify as "bad guys" aren't actually terrorists.
Adibi said he hopes to improve those numbers a bit. But even so, programs like his could help focus anti-terror efforts on the most likely suspects. Mass detentions by law enforcement authorities have often snared too many innocent people, Woo said. Britain has arrested more than 600 people on suspicion of terrorism since the Sept. 11 attacks, and convicted only 15 of them. By some counts, the United States has detained more than 5,000 foreign nationals under the provisions of the Patriot Act, alienating them and their families.
"Part of the war on terrorism is winning hearts and minds," said Woo, an analyst in the London office of Risk Management Solutions. The Newark, Calif.-based consulting firm assesses catastrophe risks for the banking and insurance industries.
Minds are the specialty of Vladimir Lefebvre, a cognitive scientist at the University of California in Irvine. The Russian-born researcher has spent his career developing ways of reducing human decision-making to mathematical equations. The work stems from a top-secret Soviet research project that Lefebvre worked on during the 1970s.
"I can compute feelings," he said with a grin.
Lefebvre's ideas are so obvious that you wonder if he might be kidding. Every person, he argues, has a view of the self that he or she uses as a tool for making decisions. That view can be influenced by the outside environment.
So in principle, there ought to be things we can do to make terrorists feel less sure about themselves or less ardent in their beliefs. The right strategy might even make them think of themselves as something other than terrorists.
Lefebvre believes human decision-making is so straightforward that simple equations can describe how an individual's behavior arises from his or her self-image as it is shaped by other people and the environment.
Stefan Schmidt, a New Mexico State University researcher who has worked with Lefebvre, offered a hypothetical example. Suppose, he said, terrorists were considering three points of entry into the United States one in the Pacific Northwest, one in the Southwest and one in the Northeast. Looking at the level of security on the various borders, and considering other factors such as remoteness, terrorists might decide on the Southwest as the best place to cross.
Assume that border agents, on the other hand, are heavily guarding the Northeast border. They would benefit by making the Southwest seem more heavily patrolled than it really is, and the Northeast appear relatively unprotected. If they did a credible job, the terrorists would incorrectly choose the most secure border as their best bet and run a much higher chance of being caught.
Conceptually, this kind of reasoning is no different from military strategy. If you can plant an inaccurate idea in your opponent's head, you will have an advantage on the battlefield.
But actually doing that at least for the time being requires a combination of brilliance, instinct and luck that few people possess. Lefebvre would reduce the process of outwitting your opponent to a computer program.
In some ways, researchers at Carnegie Mellon University have done just that. Computer scientist Kathleen M. Carley heads a lab that tries to simulate all kinds of social groups, including terrorist organizations.
The lab has built simulations of Hamas and al-Qaida by dumping newspaper articles and other publicly available information about the organizations into a computer database. A program then takes that information and looks for patterns and relationships between individuals. It finds weak and strong figures, power brokers, hidden relationships and people with crucial skills.
Then another program can predict what would happen if a specific individual were removed from the organization. After Israel's assassination of Hamas founder Sheikh Ahmed Yassin in March, the program correctly predicted he would be succeeded by hard-liner Abdel Azziz Rantisi.
Three weeks later Israel assassinated Rantisi as well. Carley's lab predicted that Hamas political director Khaled Mashaal would succeed him, and posted its pick on the Internet.
This time, Hamas declined to reveal who had taken power for fear he too would be assassinated. But eventually it became known that Mashaal was indeed the one.
At that point, Carley said, "we were told to quit putting such predictions on the Web" by federal officials.
Bullshit. It was a sucker punch.
Breaking the german and japanese codes allowed the allies to sink hundreds of ships and subs, and probably cut the war 1.5 to 2 years shorter by some estimates, ultimately saving lives on both sides.
Developing the Atom bomb was largely a work of mathmatical genius. Although the war was already winding down, the A-bomb made it unnecessary to wage a costly land war on the island of japan, and ultimately saved civilian lives in Japan, which would have been wiped out by the millions in such an invasion.
Math is the deadliest weapon we have.
Yep, first time I saw Arafat I thought to myself, "Now THERE'S a thinking man for 'ya! " </sarcasm>
Arafat was trained as an Engineer.
I liked the article. Very interesting, and has merit.
Look up Turing. Look up Enigma. Britain would have been sunk without RADAR and breaking the German Code. Outside of the bomb, Mathematics made all the difference.
Brilliantly conceived? Not so. Any suicidal passenger mad at the world could have crashed a plane into a building.
Keenly attuned to global politics? Not so. Quite the opposite. It mobilized the world against the religion of terror.
Neat concept. I understand the intelligence agencies are
identifying how swarms of insects or animals communicate
so well, in order to understand how the terrorists can
Part of this might be good strategy for disrupting their
communication. If you know how they communicate you can
always send false messages, and confuse them. Then you can
wipe out their intents.
At least one downside, the enemy can learn the techniques we use,
and "spoof" them. So our real understanding of them
should be kept secret until well after the conflict ends
(if it ever does).
Finally, there is no way to account for the depravity of
mankind. If they want to do evil they will try with all
the deception, arrogance and cruelty they can muster.
This article was posted a couple days ago under a different title.
A most enjoyable read about math and warfare is contained in Korner's "Pleasures of Counting. http://www.dpmms.cam.ac.uk/~twk/my-book.html
Better use of the money could be made by arming the population. We're dealing with a multitude of autonomous crazies programmed with a death wish who don't require leaders.
Thanks for cross linking!
This war will be won not just by force, but by brains.
Thus an exercise not unlike playing with a rubiks cube.......when I finally solve it no one will be around to share my success.....
But the point is that he thinks. Bad mojo to underestimate our enemies.
I might have agreed with Woo if Arafat, bin Laden, etc., had ever had a single tactical or strategic victory against us. But they haven't. Sucker punches don't count, nor does sneaking a bomb onto a bus full of children. The cold, hard fact for these cowardly murderers is that wherever they've dared to meet us on the battlefield, we've out thought them, out fought them and overpowered them. Saddam and his supporters thought he was a great military genius, too. But they were completely delusional.
So, we're not underestimating them; We're accurately estimating them. They are not game theorists. They're not even chess players. They're not thinkers at all, imo, just cold-blooded, vicious animals.
If a few INS employees and Boston security guards had decided to do their jobs, it never would have happened.
If a smart security guard had noticed that two Arabs had tried to get on the same flight carrying boxcutters and told someone about it, those people would be alive today.
Yes, it is. Interesting screen name, btw
That's just the problem...no it didn't. All it did was line up liberals to preach the glory of that worthless religion and defend it as ardently as their own. It brought it to the world's attention but other than a handful of ppl like us, all it did unfortunately was make it more "liked" as it became more "understood"...read crammed down stupid, gullible ppl's throats. Every hate-America-first liberal was given the ultimate way to stab us in the back.
Well, I'm not sure that we are only a 'handful,' but I understand what you are saying. And 'more liked' is another way of saying that the 'gullible' are stricken with fear. There will always be the cowards and appeasers amongst us. That will only make our task longer, not harder.
Defeating Terrorists on the Waterfront
Article by U.S. Navy's Commander James Pelkofski
(This article by Commander James Pelkofski, U.S. Navy, commanding
officer of the USS Deyo (DD-980), was published in the June 2004
Proceedings, a U.S. Naval Institute magazine, and is in the public
domain. No republication restrictions.)
Defeat al Qaeda on the Waterfront
By Commander James Pelkofski, U.S. Navy
(Fighting terrorism involves efforts on many fronts. One of the most
vital for the Navy is guaranteeing the safety of harbors, piers, and
ships pier side. Anticipating how terrorists will attempt to exploit the
Navy's vulnerabilities on the waterfront is key to defeating them.)
Stealing a page from Sun Tzu, al Qaeda preaches to its disciples the
value of knowing your enemy. Terrorists instruct that "winning the
battle is dependent on knowing the enemy's secrets, movements, and
plans."(1) Sun Tzu's timeless edict of knowing the enemy applies
equally well for developing successful Navy antiterrorism/force
Knowing al Qaeda
A review of the al Qaeda attacks against U.S. embassies in Africa in
1998 and against housing complexes in Saudi Arabia in 2003 reveals
operations that unfold in discernible sequential and complementary
phases within a compact operational timetable. The operational
objective in each attack was the successful delivery of a primary
In the attack on the U.S. embassy in Nairobi, Kenya, a truck carrying
explosives approached the main embassy gate, possibly posing as a
delivery vehicle. It was redirected by guards to a back gate. There, a
gun and grenade attack on security personnel by as many as three
assailants preceded the explosion that destroyed the embassy.(3) The
preliminary gun and grenade assault ensured the primary weapon, the
truck bomb, was delivered into the compound with devastating effect.
The 12 May 2003 midnight attacks on three housing complexes in
Saudi Arabia displayed greater sophistication. In these synchronized
operations, al Qaeda operatives dressed as Saudi National Guardsmen
and driving vehicles typically used by Guardsmen approached security
personnel manning the entrances at the compounds. When asked for
identification, the terrorists engaged the security personnel with
automatic rifles, opened the gates and drove explosives-laden
vehicles through, detonating their bombs well inside the
The al Qaeda attack on a gated housing community in Riyadh, Saudi
Arabia, on 9 November 2003 combined diversion and deception. The
diversion was an initial assault by gunmen who advanced and fired on
Saudi guards. Then, terrorists dressed as police officers, driving in
what resembled a police vehicle, approached the gates and claimed to
be reinforcements sent to combat the attack. Once inside the
compound, the terrorists detonated their car bomb.(5)
According to terrorist documents, "special operations" such as these
are divided into three "integrated and inseparable" stages: research,
planning, and execution.(6) A closer review, however, reveals four
phases in al Qaeda operations:
Operational Surveillance. During this phase, which can take weeks or
months, al Qaeda seeks "precise information" on a target's patterns,
behaviors, routines, and defenses.(7) Using this information, al Qaeda
plans and prepares for the attack. For example, the October 2000
attack on the USS Cole (DDG-67) in Yemen was preceded by months
of operational surveillance from an apartment overlooking Aden
Target Approach. The attacks on the Saudi housing complexes
demonstrated how al Qaeda could use deception to advance on a
target and cause security personnel to relax their defensive posture.
Alternatively, as demonstrated at the Nairobi embassy in 1998,
operatives might attempt rapid entry past a target's defenses with
speed and force. The November 2003 attack on Saudi housing
complexes combined deception with rapid entry to approach and clear
defenses quickly. Common to the deceptive techniques are the use of
uniforms and vehicles that either are or look official.
Initial Assault. The initial assault occurs during or on completion of the
approach and is designed to soften, if not defeat, the target's
defenses and open the way for delivery of the primary attack. In
addition, this assault might serve to divert security forces and
reinforcements from combating the primary attack.
Primary Attack. The primary attack, usually some type of
vehicle-borne explosive, might be delivered in the same vehicle
carrying the initial assault team or in a separate vehicle. The attack
typically occurs along the same vector as the target approach and
initial assault, although attacks from alternate or even multiple
vectors cannot be discounted.
Beware the Head Fake
The attack on the Cole during a fuel stop in Aden reinforced for the
U.S. Navy the painful lesson of controlling the water space around its
ships, even in an ostensibly friendly or benign environment. Although
al Qaeda succeeded against the Cole, it is now unlikely that a hostile
boat will again get so close to a large U.S. Navy ship simply by
appearing innocent, friendly, or official amid traffic in a busy port. No
doubt, al Qaeda will explore new methods.
Possible future attack scenarios are limited only by the nefarious
imaginations of terrorists. In the basic situations outlined below, a key
point is the distinction between the initial assault and the primary
attack phases. Like the head fake familiar to football and basketball
players -- feigning movement in one direction so the opponent is
enticed to commit toward the feint and then moving quickly in the
other direction -- the terrorist head fake could be a diversionary
assault on a pier gate or pier guards while the primary attack is
delivered from a seaside vector by small boat or a swimmer.
Alternatively, no head fake would be necessary in a direct assault that
forcibly opens access to the pier for a primary attack by a truck or car
bomb that detonates its payload near a ship.
A seaborne approach to a ship at pier side could completely bypass
the base entry gates and pier gate by conducting a more sophisticated
deception during the target-approach phase, similar to what was first
suspected in the Cole attack. Early reports suggested the small boat
that attacked the Cole gained access by operating among and possibly
posing as one of the harbor workboats assisting with mooring and
Though apparently not the case in the Cole attack, a well-disguised or
even hijacked harbor tug or workboat could cause enough uncertainty
to delay a ship's force-protection response and allow a boat to
approach close enough to detonate a potent payload. Terrorist
teachings cite historical examples of commercial ships used as decoys
to get close to enemy warships before opening fire with hidden
A ship under way, though less vulnerable, is not invulnerable. In the
midst of heavy or even moderate traffic in a harbor, channel, or strait,
a terrorist boat sufficiently disguised or at least inconspicuous could
attempt an approach through a slow, nonthreatening closing
movement. By appearing innocent and engaging in amiable
communications and discussions regarding intentions, terrorists could
defer requests to alter course and remain clear -- essentially
approaching in plain view close enough to conduct a successful attack.
Alternatively, the same stratagem of a disguised or inconspicuous
boat movement toward a Navy ship could be exercised in a much
shorter operational timeline through a high-speed approach.
The approach to a ship under way could involve, at any time, an initial
assault with an assortment of small arms and shoulder-launched
weapons to facilitate closing with the ship and conducting the primary
attack. Moreover, a target approach and initial assault that serve as a
head fake to divert attention from a primary attack conducted from a
different axis (or even multiple axes) would only further complicate
defending against and defeating an attack while under way.
Do Not Assume Friendly Intent
More imaginative and dangerous scenarios are conceivable, though,
fortunately, not so simple to plan or execute. There are two important
points. First, regardless of whether a ship is in port or under way, the
threat sector is 360° and involves surface, subsurface, and air
dimensions. Second, it is imperative when detecting and defeating
terrorists not to assume friendly intent. In more traditional wars, the
U.S. military shapes a battle space extended out as far as possible to
allow for early detection of hostile intent. Against al Qaeda, however,
the U.S. Navy operates in a much more limited -- and vulnerable --
In this confined space, establishing hostile intent requires avoiding
assuming friendly or innocent intent. The Israel Navy is aware of
terrorist tactics that use emergency calls to lure a navy ship close to a
vessel ostensibly in need of assistance but rigged for a lethal
explosion -- a stratagem often augmented by the distressed voice of a
female caller. Terrorists teach the value of authentic disguises, a
masquerade enhanced by terrorists trained to an intimate
understanding of the role being played.(11)
Though not a "false emergency" lure, a friendly or at least open
invitation to come alongside for a compliant boarding might have been
the lure tactic employed in the 24 April 2004 suicide boat attack during
a boarding operation by the USS Firebolt (PC-10) in the Arabian Gulf.
From what is known at present about the attack that killed two Navy
sailors and one Coast Guardsman, the Firebolt's rigid inflatable boat
was permitted to come alongside the suicide boat -- an otherwise
In today's threat environment, facing a foe unconstrained by rules of
engagement or the laws of war and versed in the use of stratagem,
Navy force protection requires heavily armed defenses imbued with a
healthy skepticism regarding everything not positively and definitively
identified as friendly.
"Know the Enemy and Know Yourself"
A study of al Qaeda tactics reveals a meticulous, careful, and
educated foe capable of designing multidimensional attacks within a
limited attack space. Disrupting, deterring, and defeating an al Qaeda
attack requires Navy force-protection measures that address each
phase of an al Qaeda operation.
Fleetwide countersurveillance. In today's threat environment,
countersurveillance cannot be left solely to skilled but widely tasked
intelligence operatives. By operating under a cautious assumption that
al Qaeda surveillance is occurring at all times, watch standers can
disrupt terrorist operational surveillance simply by remaining alert to
what is happening not just around their posts, but beyond the obvious
perimeter, lifeline, gate, or fence, and by detecting and taking action
on any activity that appears unusual or even too normal. It is
important to note that al Qaeda surveillance techniques involve
establishing regular patterns of behavior that attempt to mask the
surveillance and condition an observer to accept those behaviors as
routine and unsuspicious. Therefore, countersurveillance requires
healthy skepticism, if not a light dose of paranoia, to avert wrongly
assuming friendly or innocent intent for activities that are, in fact,
Show-of-force random antiterrorism measures. These measures
delay, complicate, and, if completely effective, confound operational
surveillance and planning by presenting a constantly changing,
complex defense for which no pattern is distinguishable and no
weaknesses are evident. Terrorists are taught to continue
reconnaissance until shortly before conducting an operation "to
confirm that nothing new has occurred."(12) Random antiterrorism
measures can complicate and disrupt the detailed planning inherent in
such frequent reconnaissance. Furthermore, a side effect is the ability
to combat the potentially deadly complacency that can easily infect
watch standers who become too familiar with routine and too
unaccustomed to change. Although random antiterrorism measures
can take many forms, those involving just unusual activity and
movement will give observers only brief cause to pause.
Formidable, visible, layered force-protection posture. Show-of-force
measures reinforce the objective for any Navy ship, base, or
installation to appear too hard to approach and attack. By practicing
counters countersurveillance, conducting an aggressive random
antiterrorist measures program, adhering strictly to security
procedures, and deploying an obvious, layered, and imposing defense,
we reduce the likelihood of being targeted, or, if we are targeted, the
attack space is extended in our favor.
Training on the head fake. In a violent, chaotic situation, maintaining
complete situational awareness, recognizing a suspicious approach,
repelling an initial assault, and reserving forces to defeat a primary
attack are unlikely unless force-protection personnel are organized
and trained on all four phases of an al Qaeda attack. The tendency on
the athletic playing field is to go all out for the head fake; do so, and
the opponent sprints by. That tendency is only magnified in deadly and
confusing attacks where the military and human instinct is to
concentrate attention and assets toward defeating the immediate and
As a commanding officer, I used the analogy of the head fake to
inculcate in my crew the fact that the threat sector is all around them,
even when an attack is occurring from one direction. That initial
assault, though lethal, may be a misdirection and a precursor. As
compelling as repelling the initial assault may be (and it must be
repelled), maintaining complete situational awareness and reserving
forces to repel the primary attack might prevent the destruction or
crippling of a Navy ship. Only through training that aspires to capture
the chaotic characteristics of a terrorist attack can forces be
conditioned and prepared to extend the attack space, avoid falling for
the head fake, and establish hostile intent in the face of what
otherwise appears benign.
Shoot to Kill
Although posing a challenge both to normal peacetime procedures and
the imperative to limit collateral damage, the greatest deterrent to an
al Qaeda operation is a defense poised to shoot early -- and shoot to
kill -- in the event of any attack. Fundamental to this ability is
unquestioned proficiency with the weapons manned by
force-protection watch standers. In the 1993 battle in Mogadishu,
Somalia, several hundred U.S. servicemen were able to hold off
thousands of Somalis because of the U.S. forces' knowledge of their
own weapons, specifically in rapidly loading and skillfully shooting
those weapons.(13) Al Qaeda needs to know we are fluent in the
"dialogue of bullets."(14)
Terrorists who are willing to die for their cause are deterred only by
certain failure in the execution of their operation. If force-protection
measures meant to disrupt and deter a threat fail, Navy forces must
recognize the deceptive and diversionary features of an attack and
defeat it through adroit employment of firepower, ensuring the
terrorists who attempt an attack die in vain.