April 17, 2013 — -- A man in a cowboy hat jumps the fence in the VIP stands and runs toward the chaos at the Boston Marathon to apply homemade tourniquets on severed limbs.
A Vietnam vet from the Bronx jumps into the New York City subway tracks to shield a man he has never met from an oncoming train.
A third-grade teacher at Sandy Hook Elementary School in Newtown, Conn., calms 14 frightened students in a locked bathroom, keeping them alive as gunfire erupts and kills 20 children.
WATCH: Heroes Emerge from Boston Marathon Bombing
Are heroes born or made? Even experts can't answer that question.
"We really don't know for sure why people put their lives on the line for other people," said Frank Farley, a professor of psychology at Philadelphia's Temple University.
"It is the most mysterious act, in my view. How does someone get close to giving up their life for someone else they may not even know?" he asked. "It's so profound."
After two explosions erupted near Boston's Copley Square Monday, killing three people and injuring 175, ordinary citizens performed extraordinary deeds.
"It was like 911 all over again -- with front row seat," said John Mixon, a 60-year-old builder from Ogunquit, Maine, who jumped into action in the VIP stands at the finish line to tear down a fence and lift bleeding victims into wheelchairs.
"All the bodies were there and people were struggling, like, to climb over it -- they were kind of trapped with nowhere to go," Mixon said.
FULL COVERAGE of the Boston Marathon bombings.
His friend, Carlos Arredondo, sporting a cowboy hat in some of the tragedy's most iconic photos, had already jumped the fence to apply pressure to the hemorrhaging artery of a limbless man.
Those who risk their lives to help others fall into a category of heroism that Farley calls "big H," or big heroism.
"Small H," or small heroism, he added, are everyday good deeds -- "helping someone across the street."
"My favorite example [of small H] is Mr. Rogers," Farley said, referencing the late children's television show host.
In what could be called small H deeds at the marathon, runners sprinted across the finish line and on to Massachusetts General Hospital to give blood. Homeowners gave shelter to those who were separated from their families.
"The big H I am talking about is where the risks are high," he said. "But there are two particular ingredients in the recipe. ... The second one is the generosity factor."
A patient being treated for a leg injury at Tufts Medical Center told her doctors she was grateful to the Marine she knew as "Sgt. Tyler," who carried her to waiting ambulances.
"If you are risk averse, you are not going to run toward the explosion," said Farley. "You might be willing to dial 911, but the likelihood of you going into the maelstrom is extremely low."
Some studies show that the stress hormone cortisol makes the difference between being a coward or a hero. Yale scientists measured those levels and concluded those who remained calm had lower levels of the hormone.
The hormones adrenaline and dopamine seemed to flood pleasurably into the veins of risk-takers, according to Farley. But that does not explain heroic actions.
"You can get all that from great sex," he said. "You can get a rush climbing Mount Everest or on a supercoaster. There are high biological sensations."
"For the big H, you have got to have risk-taking and the generosity piece," he said.
Bruce Shapiro, executive director of the Dart Center for Journalism and Trauma, said there are two faces to courage: those who respond and those who cope.
"The first are the people who, in the moment of the bombing, run toward danger -- the first responders, the photographers and the reporters and others who simply keep a calm head," he said. "Equally important, in the aftermath, are those who seem to stay resilient in times of crisis."
Doctors at Massachusetts General Hospital, where 12 marathon victims were treated, showed a "calm and collected response."
Most victims were admitted with metal pieces from the bomb -- pellets and nails -- inside of them and required surgery.
"The ones that could talk when they were arrived, they were amazingly responsive and resilient," said Dr. George Velmahos, division chief of trauma, emergency surgery and surgical critical care. "We were able to provide better care because of it."
Melanie Greenberg, a psychologist who specializing in stress and overcoming trauma, said cultural and personal ethics play a role in courage.
"One of the key things about heroism is that it's not the absence of fear, but feeling fear and choosing to act anyway," she said. "Something is more important than fear and survival. It's certain values you have that drive your life and make it meaningful."
She was hesitant to describe cowardice: "Sometimes, you freeze like a deer in the headlights. That's the primitive lizard in us, when the social compassion switches off."
Greenberg, who blogged about the qualities of courage for Psychology Today, cited "empathy, kindness and compassion" as the motivators for heroism.
Training for emergencies gives responders courage, according to Greenberg.
Others draw it from "a sense community and compassion," she said. "The culture of being together, that you are brothers and doing it for your buddy -- that inspires heroism. The support group means more than the individual life."
Standing up for what is right, "following your heart, doing what the situation calls for," is another motivator for heroism.
"It brings out the best in people to stand up to terrorism and not let the bad guys win," said Greenberg. "You are part of something larger than yourself."