The day of the Boston bombings was the world’s saddest in five years—at least according to the “Hedonometer,” a tool designed by mathematicians at the University of Vermont that acts like a mood ring for the Internet.

The tool is simple, in theory. It’s powered by Twitter, pulling in 50 million tweets each day. It matches those tweets against a database of the 5,000 most frequently used words in four different bodies of digital work. Each word is assigned a happiness value on a scale of one to nine. Some days the scale skews up— Saturdays, for instance—and other times it drops—like on, say, Tuesdays.

Granted, you probably didn’t need science to tell you that.

But days like May 2, 2011, the day Osama bin Laden was killed, or Apr. 15, the day of the bombing in Boston—those days slump way down.

Sometimes these slumps may seem counterintuitive, such as on the day President Obama announced the killing of Osama bin Laden. “Many people presume this day will be one of clear positivity,” the researchers explain on their Web site. “While we do see positive words such as ‘celebration’ appearing, the overall language of the day on Twitter reflected that a very negatively viewed character met a very negative end.”

That apparent contradiction hints at some of the complexities of the happiness machine. Since it measures language sentiment, and not sentiment itself, some populations get lost—like the millions of people who tweet in other languages (currently the Hedonometer only analyzes English) and, obviously, the billions who don’t tweet at all.

It also misses out on context: there’s a big emotive difference between the tweets “I believe in brutal honesty and unconditional love” and “force-feeding at Guantanamo is just brutal” —but the Hedonometer would give both “brutals” the sad-face score of 2.6.

But despite its drawbacks, the tool also offers some stunning insight into the way we—the collective, en masse, Internet “we”—live, feel and communicate now. The researchers recently found, for instance, that Twitter users’ happiness increases the further they move from home. And their blog, One Happy Bird, is full of small-scale, striking insights. For example, populations in college cities use the word “cafe” far more than others. People swear more frequently as the day wears on. They use “haha” more than “ha,” and “hahaha” least of all.

In those tiny insights, the project almost verges on the digital performance art of people like Jonathan Harris, whose interactive “We Feel Fine,” described on the site as “an exploration of human emotion, in six movements,” harvested emotive phrases from 15,000 to 20,000 blogs each day.

“It will grow and change as we grow and change, reflecting what’s on our blogs, what’s in our hearts, what’s in our minds,” Harris and his collaborator, Sep Kamvar, wrote in an introduction to the project. “We hope it makes the world seem a little smaller, and we hope it helps people see beauty in the everyday ups and downs of life.”