Mind, Blown.
July 23, 2014

Graham's Number is an upper bound on a mathematical proof that I don't grasp very well, but what it's famous for is being really big. How big? You almost certainly can't imagine it. Watch the video below, but here's a motivating idea: if you tried to write the number as a "tower of powers" (3^3^3^3...) there wouldn't be enough atoms in the universe to write it all out.

Check out Graham himself explain how his number works. --Ryan Cooper

#Hashtags
7:20 a.m. ET

Jimmy Fallon normally reads out his own Hashtag selections — tweets using a hashtag he suggested — but on Thursday night's Tonight Show he handed that responsibility over to Tariq Trotter in his house band, The Roots. Most of the #SpringBreakRaps tweets are about what you'd expect — drinking, hooking up, regret — but there are a few pleasant surprises thrown in. My favorite: "Gonna trash the hotel / We won't clean up the mess / Leave your town black and blue / Like a white and gold dress." So, nice work, @edillades. Watch that and the other tweet raps artfully performed by Tariq and the band below. —Peter Weber

Clintonemails
7:01 a.m. ET
Lisa Lake/Getty Images for Massachusetts Conference for Women

Hillary Clinton has requested that the State Department make public the stash of emails from her private account that her aides vetted and turned over to the department last fall, but an unidentified senior State Department official told Reuters that "the review is likely to take several months given the sheer volume of the document set."

Separately, a department official told The Washington Post that Clinton's use of a private email account didn't necessarily violate State Department rules, as long as the emails were preserved, but that the review would determine if she broke security policies by transmitting sensitive or classified information over an email system that didn't meet security standards. A Clinton aide told The Post that 90 percent of Clinton's correspondence was with department employees at their state.gov account — presumably meaning it is already archived — but the remaining 10 percent was with government officials in other departments or email accounts "not on a government server."

The red planet was blue
5:47 a.m. ET

About 4.3 billion years ago, up to 20 percent of Mars was covered by an ocean that reached about a mile in depth, according to scientists from NASA's Goddard Space Flight Center. The polar ice caps today contain the 13 percent of that ocean that didn't evaporate into space when Mars' atmosphere largely disappeared.

Geronimo Villanueva and his colleagues at Goddard reached this surprising conclusion by using infrared beams to make a map of water molecules in what's left of the Martian atmosphere, they report in Thursday's issue of the journal Science. "Our study provides a solid estimate of how much water Mars once had, by determining how much water was lost to space," Villanueva said in a statement.

Scientists already knew that Mars once had water, but this extends the red planet's wet period for much longer. "With Mars losing that much water, the planet was very likely wet for a longer period of time than was previously thought, suggesting it might have been habitable for longer," said Goddard's Michael Mumma, another author of the report. Mumma and Villanueva explain their research and its implications in greater detail in the NASA video below. —Peter Weber

The Daily Showdown
4:27 a.m. ET

The murder of Russian opposition figure Boris Nemtsov, right outside the Kremlin in the heart of Moscow, has prompted a lot of speculation about what role, if any, Vladimir Putin played in the killing. Jon Stewart didn't directly point the finger at Putin on Thursday night's Daily Show, but he did laugh at the Russian president's insistence that he will personally lead the investigation into Nemtsov's murder.

"Oh good, he's vowing to find the real killer," Stewart laughed, showing a photo of OJ Simpson. "That's a promise that always inspires confidence. The only thing that could be more OJ is if Putin started stealing sports memorabilia...." which, of course, he allegedly has. Not that Stewart was done with the comparisons: Putin started out as a fairly normal guy, like Draco Malfoy in the first Harry Potter novel, he said, but after spending too many nights "in the dungeon-y parts of Hogwarts" with the bad kids, Putin has become "Lord Vladimort." Hopefully there isn't a sequel. —Peter Weber

The Daily Showdown
3:39 a.m. ET
The Daily Show

When Michael Brown, a black teenager, was shot by white police officer Darren Wilson in Ferguson, Missouri, last August, everyone was outraged — just not for the same reason, Jon Stewart said on Thursday night's Daily Show. Now, a new set of Justice Department reports suggests, "everybody was right!" The DOJ declined to press charges against Wilson and also found a troubling history of racism and de facto extortion by the Ferguson police. "According to our Justice Department," Stewart summarized, "everybody's anger was separate but equally justified."

Stewart largely left the "self-vindicating gloating" about Wilson to Fox News, while he and correspondent Jessica Williams tackled the Ferguson PD's habit of stopping black residents for things like "manner of walking along roadway," then funneling the resulting selective fines to city coffers — to the tune of $2.6 million in 2013. "What? $2.6 million?" Stewart said. "Maybe they don't hate blacks, they just love green." Williams played up the shake-down angle, but watch for Jason Jones' cameo at the end. —Peter Weber

ISIS
3:15 a.m. ET

About 20,000 Iraqi army troops, Shiite militia members, and Iranian advisers are advancing on Tikrit, in Iraq's largest effort to retake a city from Islamic State control. ISIS is staging counter-attacks and, sources tells Reuters, setting fire to oil fields about 20 miles northeast of Tikrit to slow the assault. Torching the Ajil oil field, ISIS apparently believes, will protect them from Iraq military helicopters.

Before ISIS conquered Tikrit last August, the Ajil field produced about 25,000 barrels of oil and 150 million cubic feet of gas a day. Under ISIS control, that amount has gone down significantly, but ISIS partly relies on its oil sales to fund its self-proclaimed caliphate.

panda-monium
2:24 a.m. ET

Here's something you don't see every day (or night): A giant panda walking through the deserted streets of a town in southwest China. Closed-circuit television captured the bear as it ambled down the road late one night, seemingly enjoying having the streets all to herself. Experts who viewed the footage believe the animal is about 2 years old, and say that pandas are commonly found in this area. —Catherine Garcia

Ay caramba!
2:08 a.m. ET

A long-term substitute Spanish teacher in Columbus, Ohio, was sentenced to 90 days in jail after showing students the explicit film The ABCs of Death, featuring graphic violence and sex.

Sheila Kearns, 58, was found guilty of four counts of disseminating matter harmful to juveniles. Kearns — who doesn't even speak Spanish — showed The ABCs of Death to students on April 11, 2013, and two classmates testified that they found it extremely disturbing. "This is what happens when you put a teacher in a class that she cannot teach," Judge Charles A. Schneider said, according to The Columbus Dispatch.

The excuse Kearns came up with further infuriated Schneider: Kearns claimed that she didn't watch the movie before putting it on, and had no idea what it was about. (The title didn't give her a clue?) She said that the entire day, her back was turned to the television, and she never once turned around to see what was on the screen. Schneider didn't fall for it, calling her claim "unconscionable. There's no way you'll persuade me that's what happened."

last night on late night
1:53 a.m. ET

On Thursday night's Late Night, Jada Pinkett Smith talked about working with hot topless men on Magic Mike XXL, and told Seth Meyers that the film finally made her understand that thing about men having two separate, competing command centers. "For the first time in my life, that other head below started talking to me: Procreate, procreate, procreate, procreate," she said. "My top head was, like, 'Jada, there is not a Will Smith on this set, you can't procreate with nobody!'" That whole day of filming, she added, "I felt really bad for guys."

That led to Pinkett Smith talking about how she enjoys watching her husband's on-screen sex scenes. As with her use of "procreate," she got the message across using family-safe language. "When I'm with Will, I get to experience him physically," Pinkett Smith explained, "but very rarely do I get to see what he looks like when he's in the game." Meyers kept his head, but at the end he conceded that "this is the hottest interview I've ever done." And yet, somehow, it's safe for work. —Peter Weber

equal rights
1:33 a.m. ET
Facebook.com/UNWomen

It's been 20 years since the U.N. women's conference in Beijing, where 189 countries adopted a platform for action to achieve equality for women, but Phumzile Mlambo-Ngcuka says that no country on earth has reached gender equality.

The executive director of UN Women said that while there has been some progress — mostly in women’s health and girls’ education — violence against women and a lack of women in decision-making roles are "global phenomena" that make equality difficult. "The sheer scale of the use of rape that we've seen post-Beijing, I think that tells us that the women's bodies are viewed not as something to respect, but as something that men have the right to control and to abuse," she told The Associated Press. Leaders across the world need to start speaking out "very strongly and very openly" against sexual violence and the denial of women's rights, she added.

The platform for action from the Beijing conference called for the end of discrimination against women and the closing of the gender gap in health, human rights, employment, education, and other areas. Today, there are less than 20 female heads of state and government and the percentage of women lawmakers has only increased by 11 percent over the past two decades. "We just don't have critical mass to say that post-Beijing women have reached a tipping point in their representation," Mlambo-Ngcuka told AP. Next week, the Commission on the Status of Women will meet to revisit the Beijing platform.

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