Over five years have passed since the 9/11 attacks, and we still cannot agree on how to handle the problem of terrorism. In order to have a strategy, you have to decide what kind of enemy you face, and thus far we don’t have a clear idea of the opponent.

To focus this issue, it is useful to draw on an analogy from the animal kingdom. Admittedly, using analogies is a rough way to elucidate reality, but considering where sober and official theories of terrorism have led us, perhaps we can profit from an unorthodox perspective.

Traditionally, foreign enemies have resembled lions: large beasts with a definite home base, capable of destroying us and capable of being destroyed by us. Hitler was lion-like. So was Stalin. So was Mao. These enemies had huge, multi-million-man armies that could invade and occupy other countries. They were centralized actors with one brain, so to speak. They could focus their military power on making political demands, such as a change in our leadership. Conflicts with them were life or death struggles.

These enemies were lion-like in another way: they were prudent actors, concerned with the survival of their regimes. Thus they adjusted their aggression according to the probability of a strong reaction. Because these lion-like enemies were watching us for signs of strength or weakness, we learned that appeasement is dangerous, and security lies in strength.

Does this traditional perspective on foreign policy serve us in the battle against terrorism? A close look shows that terrorism—that is, the terrorism of Islamic radicals—is an un-lion-like enemy in almost every respect. To begin with, terrorism does not have a home country. Terrorists can be recruited anywhere in the world from the pool of a billion Muslims. Although you can kill or capture individual terrorists, there is no way to win a war against terrorism.

Just as we cannot destroy terrorism, terrorism cannot destroy us. Islamic radicals specialize in shocking people and—with the aid of the media—they do this very well. But they do not have the capacity to invade and govern any Western country. Osama bin Laden has no army that could march into Cleveland and impose Sharia.

The Islamic radicals are not a single, unified organization capable of making demands and keeping bargains. They include scores of groups with no common platform of political objectives. Nor are they prudent planners like the lion-like enemies of the past. They are emotional and easily give in to hatred. They can be provoked by trivial, symbolic incidents—cartoons in a distant newspaper, a few enigmatic lines in a pope’s speech. Their ready use of suicide reflects their mentality. Radical leaders do not view suicide attacks as the tragic destruction of one of their own true-believing comrades, to be undertaken only after grave and careful deliberation. Violence is seen as an intoxicating tactic, attractive even if it brings a trivial result.

The radicals overlook that their acts of gratuitous violence alienate moderate Muslims and increase the resistance of their enemies. And they seem unconcerned with consolidating their victories. In Afghanistan, Osama bin Laden had a chance to build the kind of Muslim fundamentalist state he is supposed to cherish, yet he threw it away by provoking the U.S. with the 9/11 attacks.

The radicals’ proclivity for dispute and violence leads them to divide into factions ready to fight and kill each other for almost no discernable reason, as we see in the recent battles between Hamas and Fatah in Palestine. The idea that these temperamental rabble-rousers could carry out a sustained program of world domination is beyond plausibility.

In no important respect, then, does Islamic terrorism resemble a lion. We need to look about the forest for another kind of animal in order to make sense of this disjointed, irascible enemy. In my opinion, it’s ants.

Ants specialize in shocking people; indeed, they seem to be programmed to attack even when it does them no good at all. You can’t deter ants, you can’t reason with them, you can’t bargain with them. And no matter how many individual ants you kill, you can never defeat them because the forest has an infinite supply.

Though you can’t win a war against ants, neither can they defeat you. They can sting and cause injury, but their bites are not fatal, at least not directly. Indirectly, ants can cause death if the victim reacts irrationally—for example, if the stinging goads him to jump off a cliff.

Does the analogy still hold if the ants can employ nuclear weapons? That certainly would make the ant bites more painful, but it doesn’t change the character of the threat. A nuclear explosion may—or may not—do greater damage than a conventional attack, but it would not translate into a military victory for the terrorists. They could not occupy territory or transform U.S. institutions any more than they could after 9/11.

It might help steady our thinking if we realized that terrorism is not a functional military campaign designed to take objectives and impose outcomes. It is more akin to a natural disaster like an earthquake or an influenza epidemic. Natural disasters are painful, but they do not change values or leadership. In Indonesia, the December 2004 tsunami left a toll of 236,000 dead and missing. After that disaster, Indonesia went on with the same rulers and the same institutions.

Employing nuclear weapons, the radicals might cause a similar disaster in the United States, but it would not change our culture, traditions, or ideals. We would pick ourselves up, rebuild, and carry on as before. The more lasting injury stemming from such a tragedy would be self-inflicted if we gave into a hysterical overreaction. We might, for example, be impelled to invade and occupy half a dozen countries in an attempt to exact revenge.

The ant analogy for terrorism suggests that the first principle for dealing with this diffuse, emotional enemy is not to overreact, not to do more harm to yourself than the ants can do to you. Patience is the watchword in grappling with terrorism.

The ant analogy also points us in a useful direction for limiting the incidence of terrorism. The principle here is that stomping on or near an anthill is the surest way to stir up trouble.

As just noted, Islamic radicals have a shallow, emotional perspective. They are not sophisticated about political philosophy or foreign affairs, but they respond in defense of their territory when it is threatened. When they see the United States attempting to direct the destiny of Muslim countries, it excites them. Never mind that this U.S. intervention is well intentioned; never mind that most of it is futile. Just the act of trying to throw our weight around in that area stimulates radicals to a frenzy of opposition.

Hence, the most important move the United States can make to diminish Islamic terrorism is to step back from its involvement in the Middle East. Those who think that all foreign enemies are lions will call this a policy of appeasement and say that the best way forward is to show resolve by increasing our political and military involvement in the region. So you see, it makes a difference which kind of animal you think terrorism is.

James L. Payne has taught political science at Yale, Wesleyan, and the Johns Hopkins School of Advanced International Studies. His latest book is A History of Force: Exploring the Worldwide Movement Against Habits of Coercion, Bloodshed, and Mayhem.