I rode the peace train from Washington to Philadelphia last Saturday night. When my CNN program ended on Capitol Hill at 7 p.m., I ran to make the Northeast Regional, Amtrak train No. 182, which left Union Station on time at 7:20 bound for Boston. On board with me were 600 women who had just marched against President Trump.

There were no empty seats on the festive train. Many women wore hand-knitted, pink pussy hats and homemade signs dotted the overhead luggage compartment. An animated welcome on the PA from a conductor was greeted with applause, a first in my many trips aboard Amtrak.

Rachel Barany was my seatmate for two hours. She was headed home to New York City, having spent the day marching with her daughter, a junior at Johns Hopkins. Meanwhile, her older daughter was doing likewise with her husband in New York City. Barany told me she teaches history to fifth and sixth graders at Friends Seminary, a Quaker school near Union Square. She was tired from an exhilarating day spent with five mothers and daughters, one father and a son, and a "wonderful ragtag group of Hopkins friends."

"Our numbers continued to grow as more and more kids found each other at the march. . . . There were a good number of us on the mall, after the rally - that we couldn't hear, but no matter," she said.

"Two big gifts," she told me, were "getting to know the kids in this setting and hearing so much from passersby about their concerns and hopes for the country."

While I was en route to the café care on a beer run, it occurred to me that if there were 600 exuberant guys aboard, many having a drink after an emotion-filled day, it would have been a much different train. There would probably have been arguments and fights, even if they were united in purpose. After all, common desire for Eagles victories didn't eliminate the need for Judge Seamus McCaffery to preside for years at the Eagles Court in the basement at Veterans Stadium. And there is this statistic: According to the federal Bureau of Prisons, as of Dec. 24, the U.S. prison population was 93.3 percent male and 6.7 percent female.

The following day, my observation was reinforced by countless news reports about the attendance at the more than 600 marches around the world and the absence of arrests. In Washington, there were 500,000 marchers and none were locked up. (That number is not subjective. More than 470,000 people had taken the Metro, the Washington subway system, by 1 p.m., a weekend ridership record. By comparison, on Friday, Inauguration Day, there were 193,000 trips by 11 a.m., according to Metro. The swearing-in was at noon.) In Philadelphia, city officials estimate that 50,000 people participated, and the Police Department told me that none were arrested. The crowds were huge all over - 20,000 in Houston, 60,000 in Oakland, 60,000 in Atlanta, 100,000 in L.A., and 120,000 in Boston. But according to CNN, police reported only four arrests in 21 American cities.

So I decided to share my wonderment with Steven Pinker, the Harvard psychologist who has published extensively on crime. He told me that the difference in violence is one of the most robust sex differences, and that on average (across societies) men are 11 times more likely to kill other men than women are to kill other women. In his book The Better Angels of Our Nature: Why Violence Has Decline, he wrote:

"Though in many primate species, including humans, both sexes jockey for preeminence, usually against members of their own sex, it seems to loom larger in the minds of men than in the minds of women, taking on a mystical status as a priceless commodity worth almost any sacrifice. . . .

"And men are, of course, by far the more violent sex. Though the exact ratios vary, in every society it is the males more than the females who play-fight, bully, fight for real, carry weapons, enjoy violent entertainment, fantasize about killing, kill for real, rape, start wars, and fight in wars. Not only is the direction of the sex difference universal, but the first domino is almost certainly biological. The difference is found in most other primates, emerges in toddlerhood, and may be seen in boys who (because of anomalous genitalia) are secretly raised as girls."

Fifteen minutes past Wilmington came the announcement: "Next stop, Philadelphia's 30th Street Station." Around me women gathered their belongings, many retrieving signs, including my favorite: "March Like a Girl."

When the doors opened the platform quickly became a sea of pink. At the top of the escalator there were hugs and handshakes and people headed their separate ways. The station was busy for a Saturday night, but like the march, without incident. I headed for my car without looking over my shoulder.

"This doesn't mean that a train full of drunken post-demonstration men would inevitably fight, but the odds would certainly be higher than in the train you rode on," Pinker told me.

But chances are, if I'd been with 600 guys, the theme song wouldn't have been "Peace Train." It would have been "Saturday Night's Alright for Fighting."

Michael Smerconish can be heard 9 a.m. to noon on SiriusXM's POTUS Channel 124. He hosts "Smerconish" at 9 a.m. Saturdays on CNN.