In the past few decades, scientists have developed a rich understanding of how living systems organize and function. They describe life's capacity to self-organize as networks of interdependent relationships, to learn and adapt, and to grow more capable and orderly over time. These dynamics and descriptions stand in stark contrast to how we humans organize as hierarchies and chains of commands. Although many reject living systems theory as inapplicable to the "real world"of organizations, the real world that appears in the daily news reveals the dynamics of living systems in human affairs quite clearly. Our inability to perceive that insurgent groups are self-organized networks puts us at risk in the War on Terror, because we evaluate the wrong things. Using the lens of living systems, rather than our traditional hierarchical one, we develop a very different sense of who's winning. This lens allows us to accurately assess the strength of terrorist groups, and to see the role of leadership in any self-organized network. We observe that networks are fueled by passion and meaning, not by traditional commanding leadership. They are "webs without a spider," becoming more innovative at the local levels as leadership at the top recedes. Using measures appropriate to assessing the growth and strength of networks, we see that the only way to diffuse self-organized networks of insurgents is to change the fundamental conditions of economics and culture that fuel their rage.