Updated at 3 p.m. ET on Jan. 27
There has been a lot of arguing about the size of crowds in the past few days. Estimates for President Trump's inauguration and the Women's March a day later vary widely.
And for crowd scientists, that's pretty normal. "I think this is expected," says Mubarak Shah, director of the Center for Research in Computer Vision at the University of Central Florida. Shah says he encountered something similar during mass protests in Barcelona, Spain a couple of years ago.
"The government was claiming smaller number than the opposition was claiming," he says.
Counting quarrels have popped up during previous events in the U.S. as well. During the Million Man March in 1995, the National Park Service estimated the crowd to be far smaller than the organizers claimed. The controversy led Congress to bar the Park Service from doing head counts on the National Mall.
The reason that disagreements frequently arise is that there's no foolproof way to get an accurate head count of a large crowd.
Decades ago, crowd estimates were done by people who simply looked at photographs of an event. They would count the number of people in one small area of a photo, then extrapolate that number to estimate the entire field of view.
This method was inaccurate, though, in part because some areas might have lots people packed together, while others would have just a few people with large spaces between them.
Computers have improved counting somewhat. They don't suffer fatigue the way humans do, and a computer doesn't have any political bias, Shah says.
But even computers have limits, says Dinesh Manocha of the University of North Carolina at Chapel Hill. They have no problem sorting a few people who aren't packed together. But when you have big crowds, like those seen across the country in the past few days, it gets tricky.
"When it's more than 100,000, we just can't estimate right. We don't have an answer today," he says.
It often comes down to image resolution. Manocha says even professional cameras only capture about 40 million pixels. So if there are one million people, each person will appear as a 40-dot smudge.
A company called Digital Design & Imaging Service, is actually trying to make an estimate of attendance at the Womens' March.
They used high-resolution cameras attached to a tethered balloon to take photos of the marchers. Even with his high-tech surveillance system, Curt Westergard, the company's president, says he doesn't expect to get a precise figure. Clouds meant the company couldn't supplement their own photos with satellite images. And the number of people changed constantly throughout the day.
"Our main goal really on this just to ascertain a rough order of magnitude," he says. "So if somebody says a million vs. 100,000 we can easily prove one or the other."
On Friday, Westergard said his company estimated some 440,000 people were on the National Mall and surrounding streets for the Women's March. The firm will also share its raw data so that others can try to make their own estimates.
"We can and do make all of our data transparent. We put it online," he says. "If you don't like what we said, count it yourself, and here's the data."