I have found the nomination of a woman for president this week to be an emotional experience in ways I did not expect.

And it’s not just me — I heard from lots of people who didn’t expect to cry during a roll call vote but all of a sudden found tears coming down their faces. I started asking people to tell me about it. Where were they? What happened?

"I wasn't sure how I'd feel this week as I've been lukewarm on Hillary in the past," Andrea Coleman told me. She’s 35 and lives in Colorado. "However, as I was watching the roll call, I started getting oddly emotional. Each announcement I found my lip quivering and my eyes welling up. Then when she crossed over the 1,382, I immediately burst into tears."

"I wasn’t expecting to burst into tears listening to a roll call vote"

"I consider myself to be a pretty rational and collected person, but I've found myself tearing up at random times — at work, on the train, etc. — thinking about how many women before me never thought they would see this day, including my own mother and grandmother," says Suzy Dolan, who is 23 and lives in Boston.

And then there was this response, on Twitter:

@sarahkliff easy. Wasn't expecting to burst into tears while listening to roll call vote on phone while food shopping. — melissa (@melissalvla) July 28, 2016

Why has this week been such a powerful, emotional experience — in such an unexpected way?

Because we are watching a woman tell voters, "I would be the right person to fill the most powerful position in this country."

And we’re watching millions of voters say back, "Yes. That sounds right."

Why role models mattered to me

The first time I recognized I had something close to a role model, I was an impossibly dorky 15-year-old who wanted nothing more than to win a speech and debate tournament.

I was the quiet new kid on the team — but then Katie showed up. She was a redheaded senior who did win awards. She drove me to Sears to buy my first "power suit," a flimsy gray skirt and jacket. She made the thing I really, really wanted seem possible because she was doing it.

I wore the power suit. I won awards. I got good at public speaking. I wouldn’t, of course, tell Katie I thought she was a role model, because I was a 15-year-old striving to be less dorky. But she was important in my life because she was doing the thing I wanted to do. She showed me I could do it too.

Having these role models is important. This one email I received, from Marisa Bartolotta, who is 22, just put it so well.

"People talk about the glass ceiling so much that it feels like a cliche, but the presidency really is the ultimate symbol of power in our country," she wrote. "I’ve been watching the convention and tearing up several times per night. It feels like it really might happen and it fills me with pride."

This is exactly right: It’s emotional to so many because this is the first time it really might happen.

Seeing women in positions of power changes our reality

One of the best studies on precisely how much this matters to young women was published in the journal Science in 2012.

The research happened in West Bengal, India, which mandated a certain number of positions of "pradhan" (essentially city council chief) be given to women. Each election cycle, a certain number of villages would be chosen, at random, to fill this quota.

This created a perfect natural experiment in which economists could compare cities where girls grew up with female leaders to those where they didn’t.

The results were stunning — and suggest that when women took leadership positions, the community started to view other women in fundamentally different ways. In villages assigned female pradhans, parents became more aspirational in what they expected of their daughters.

The fraction of parents who believed that a daughter’s occupation (but not a son’s) should be determined by her in-laws declined from 76 percent to 65 percent.

Adolescent girls in those areas became less likely to want to be housewives, too. The number of minutes young girls spent on housework declined 18 minutes in the areas with female representatives — and the gap in educational attainment of young boys and girls completely closed. That didn’t happen in the areas that weren’t assigned female pradhans.

When more women are in government, a community's fundamental view of women changes

There wasn’t any evidence that these pradhans legislated differently; they didn’t pass new educational programs for girls, for example.

Instead, the most powerful thing about women rising to power was just the act of doing it.

Or, as the researchers put it, "It is their presence as positive role models for the younger generation that seems to underlie observed changes in aspirations and educational outcomes of adolescent girls."

Or, as Hillary Clinton put it in her acceptance speech tonight, "When any barrier falls in America it clears the way for everyone."

Women have made remarkable advancements — but we haven’t gotten nearly far enough

I don’t have kids right now. But I’d like to someday. And I bet you can guess which of the scenarios above I would want them to grow up in.

Women have made huge advances in recent decades. There was a 102-year-old delegate at the Democratic National Convention, Jerry Emmett, who represented Arizona. When she was born, women didn’t have the right to vote. Now she’s helping nominate a woman for president.

That’s a remarkable amount of change in just one lifetime.

It’s also far from enough. Even in 2016, the top spots in most fields remain dominated by men. Women make up just 4.6 percent of Fortune 500 chief executives. Women are 14.6 percent of health care’s executive officers. In law firms, women are 15 percent of equity partners. And there has never, of course, been a woman president of the United States.

The role models at the bottom of the career ladder are plentiful. I have been so lucky to work with incredible women as a journalist. And I’ve had great role models who have consistently shown me: Your career could look like this in five, 10, or 20 years. It matters that these role models are women because that says: You belong here. You are the type of person who can do this type of thing.

Exactly what Katie did for me 15 years ago.

"I never actually thought I'd see it in my lifetime. I did my best to explain to my daughter why I was crying."

The role models at the top, however, are sparse. And this is something I’ve only fully understood as I’ve gotten older myself, a topic I’ve written about previously. The trajectory of a woman’s career still differs very much from that of men.

Women still do the majority of the housework and child care in families with two working parents. Women's salaries go down when they have children — but men's salaries go up. And women are still penalized for speaking "too loudly" or "too frequently" in professional settings.

There are fewer women at the very top who can say, "You belong here." And at the top of our country, the very top leadership position in America? A female role model doesn’t exist.

As someone who was told as a kid that a woman shouldn't be President "because emotions," this election is pretty damn powerful. — Adrianna McIntyre (@onceuponA) July 27, 2016

As the results of the India study suggests, this matters an incredible amount. It matters when we think of who looks like a president — who could be a president.

Tracy Clementi was watching the roll call vote Tuesday night. She was preparing dinner for her 5-year-old daughter, making her ravioli.

"As it got closer to the end, I realized I was crying," says Clementi, who is 40 and lives in Wisconsin. "I suppose I never actually thought I’d see it in my lifetime. I did my best to explain to my daughter why I was crying and why it meant so much to me."

What makes the experience of watching a woman win a major political party’s nomination emotional is partly thinking of what other women didn’t have: the right to vote and certainly not the right to imagine that they, one day, could lead the country.

It’s emotional thinking about what young girls could have, too: a role model whose gender says: This belongs to you. This is yours too. You belong here.