Trying to decipher this complex enemy - a hybrid terrorist organization and a conventional army - is such a conundrum that Nagata assembled an unofficial brain trust outside the traditional realms of expertise within the Pentagon, State Department and intelligence agencies, in search of fresh ideas and inspiration. Business professors, for example, are examining the Islamic State's marketing and branding strategies.
"We do not understand the movement and until we do, we are not going to defeat it," he said, according to the confidential minutes of a conference call he held with the experts. "We have not defeated the idea. We do not even understand the idea."
Nagata's frustration is shared by other U.S. officials. Even as President Barack Obama and his top civilian and military aides express growing confidence that Iraqi troops backed by allied airstrikes have blunted the Islamic State's momentum on the ground in Iraq and undermined its base of support in Syria, other officials acknowledge they have barely made a dent in the larger, longer-term campaign to kill the ideology that animates the terrorist movement.
Four months after his initial session with the outside advisers, Nagata, one of the military's rising stars and the man Obama has tapped to train a Pentagon-backed army of Syrian rebels to fight the Islamic State, is still searching for answers.
"Those questions and observations are my way of probing and questioning," Nagata said in a brief email this month, declining on orders from his superiors to say any more.
The minutes of internal conference calls between Nagata and more than three dozen experts he convened through Pentagon channels in August and October offer an unusual insight into the struggle to understand the Islamic State as a movement, and where the U.S. military's top leaders are most focused.
One of the panel's initial observations that has intrigued Nagata is the Islamic State's "capacity to control" a population, according to the minutes.
It is not so much the number of troops or types of weapons the militants use, the experts said. Rather, it is the intangible means by which the Islamic State, also called ISIS or ISIL, wrests and maintains control over territory and its people.
This ability, they discussed, centers on "psychological tactics such as terrorizing populations, religious and sectarian narratives, economic controls."
The minutes, which are confidential but not classified, reveal disagreements among the experts over whether Islamic State's main objective is ideological or territorial - Nagata encourages competing views, urging the group to have "one hell of a debate" over his questions.
But the panel raised doubts whether Islamic State "has the bureaucratic sophistication necessary to govern."
"The fact that someone as experienced in counterterrorism as Mike Nagata is asking these kind of questions shows what a really tough problem this is," said Michael T. Flynn, a retired three-star Army general and former director of the Defense Intelligence Agency who has publicly raised similar concerns.
A final report by the group, which draws from industry, academia, and policy research organizations, is due next month.
How to defang the Islamic State's enticing narrative weighs heavily on many other senior administration officials, as well as top leaders in the Middle East and Europe.
This month, Lisa Monaco, Obama's counterterrorism and homeland security adviser, said the increasing effort by the Islamic State to branch out to countries like Saudi Arabia, Jordan, Lebanon and Libya "is a huge area of concern." About 1,000 foreign fighters flock to Iraq and Syria every month, U.S. intelligence officials say, most to join arms with the Islamic State.
"We have to, I think, as an international community, come to terms with how we're going to deal with these ideologies and movements that are exploiting the weaknesses of various countries," John O. Brennan, the CIA director, said this fall. "We have to find a way to address some of these factors and conditions that are abetting and allowing these movements to grow."
Enter Nagata. He has fought in the shadows most of his 32-year Army career, serving in Special Operations forces and classified military units in hot zones such as Somalia, the Balkans and Iraq. Colleagues say he has displayed bureaucratic acumen in counterterrorism jobs at the CIA and the Pentagon, and diplomatic savvy as a senior U.S. military liaison officer in Pakistan during the turbulent period there from 2009 to 2011.
"He's the rare warrior who is most comfortable in complexity," said Stanley A. McChrystal, a retired four-star general and former commander of allied forces in Afghanistan.
Complexity is precisely what Nagata, by then head of U.S. commandos in the Middle East, wanted in July when he asked a tiny think tank within the military's Joint Staff, known as Strategic Multilayer Assessment, for help in defeating the Islamic State.
In the past year, the group has produced studies on the security implications of megacities around the world and how to apply neuroscience to the concept of deterrence.
When Nagata first convened the specialists on a conference call Aug. 20, he described his priorities and the challenges the Islamic State posed.
"What makes I.S. so magnetic, inspirational?" he said. He expressed specific concern that the militant organization is "deeply resonant with a specific but large portion of the Islamic population, particularly young men looking for a banner to flock to."
"There is a magnetic attraction to I.S. that is bringing in resources, talent, weapons, etc., to thicken, harden, embolden I.S. in ways that are very alarming," Nagata said.
During the call, Nagata alluded to the Islamic State's sophisticated use of social media to project and amplify its propaganda, and insisted the United States needed "people born and raised in the region" to help combat the problem.
"I want to engage in a long-term conversation to understand a commonly held view of the psychological, emotional and cultural power of I.S. in terms of a diversity of audiences," the general said. "They are drawing people to them in droves. There are I.S. T-shirts and mugs."
"When I watch Americans use words like cowardly, barbaric, murder, outrageous, shocking, etc., to describe a violent extremist organization's actions, we are playing right into the enemy's hands," Nagata added. "They want us to become emotional. They revel in being called murderers when the words are coming from an apostate."
He continued: "We have to remember that most of their messaging is not for us. We are not the target. They are happy to see us outraged, but they are really communicating to people, 'We are being drawn to their banner.'"
Six weeks later, in a second conference call on Oct. 3, Nagata praised the group's initial efforts, but again noted, "I do not understand the intangible power of ISIL."
Nagata scoffed at those who he said had questioned his decision to focus so much on understanding the intangibles of the Islamic State.
"What we have been asked to do will take every ounce of creativity that we have," he said. "This may sound like a bizarre excursion into the surreal, but for me it is about avoiding failure."