(By Flickr user Thy)

In the wake of a horrific event like this weekend's killings near the University of California at Santa Barbara, there's an instinct to reach for statistics, to wrap our arms around objective numbers that might put the incomprehensible in perspective.

And so we round up data points like these: Women are more than five times more likely than men to be killed by an intimate partner. Nearly one in five American women say they have been raped or experienced an attempted rape in their lifetime. One in six have been stalked. About half say they've experienced physical violence at some point.

These numbers, though, feel frustratingly insufficient, because they capture only part of the problem. Violence is an outcome. The input is cultural. And that culture touches many, many more people, as is evident by the vein that's opened on Twitter since Friday night. Problems of culture, however, are by definition data-resistant.

There is little data that says "X percent of all women have felt threatened in public after dark by a stranger." Or "Y percent of women plan their lives and routes home according to where they believe they'll feel safest." Or "Z percent of women select their clothing in the morning based on how they believe men will interpret those choices."

Likewise, there's little data on the share of teenage boys who grow up believing in the "friendzone," or the ratio of men who feel that a short skirt is somehow "asking for it." We know one in five women in college have been sexually assaulted, but we don't know how many men have heard of such an assault and then shrugged.

In often subtler ways than outright violence, these ideas permeate our culture. But it's so hard to see how tightly they're held by men, or how tight a grip they hold on women. That's part of the reason why #YesAllWomen has turned into such a startling deluge. The hashtag has tapped into something that is even more deep-rooted and universally experienced than assault itself:

Every single woman you know has been harassed. And just as importantly, every single woman you don't know has been harassed. #YesAllWomen

— Sarah W. (@toasterposey) May 25, 2014

Statistics are good at describing discrete actions. They're not quite as good at describing cultural problems. And they particularly fail us on subjects that regularly go unspoken, about which we don't ask enough questions.

Meanwhile, the very thing that makes problems of culture hard to quantify -- whether the culture surrounds gender or race or sexual orientation -- is also what makes policy solutions here so elusive. We could stiffen penalties for domestic violence or tighten gun laws to help prevent such violence (guns, however, are encased in their own hard-to-penetrate culture). But how do we design correctives to the underlying ideas that women are somehow second class, that they alone don't control their bodies, that harming them is a lesser crime?

Public policy doesn't deal well with questions like that, which ask us not just to change statutes and initiatives and budgets, but culture.