This article originally appeared on 07.10.21
Dr. Daniel Mansfield and his team at the University of New South Wales in Australia have just made an incredible discovery. While studying a 3,700-year-old tablet from the ancient civilization of Babylon, they found evidence that the Babylonians were doing something astounding: trigonometry!
Most historians have credited the Greeks with creating the study of triangles' sides and angles, but this tablet presents indisputable evidence that the Babylonians were using the technique 1,500 years before the Greeks ever were.
Mansfield and his team are, understandably, incredibly proud. What they discovered is that the tablet is actually an ancient trigonometry table.
"The huge mystery, until now, was its purpose – why the ancient scribes carried out the complex task of generating and sorting the numbers on the tablet. Our research reveals that Plimpton 322 describes the shapes of right-angle triangles using a novel kind of trigonometry based on ratios, not angles and circles. It is a fascinating mathematical work that demonstrates undoubted genius."
"The tablet not only contains the world's oldest trigonometric table; it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry. This means it has great relevance for our modern world. Babylonian mathematics may have been out of fashion for more than 3,000 years, but it has possible practical applications in surveying, computer graphics and education. This is a rare example of the ancient world teaching us something new."
The tablet predates Greek astronomer Hipparchus, who has long been regarded as the father of trigonometry. Mansfield's colleague, Norman Widberger, added:
"Plimpton 322 predates Hipparchus by more than 1,000 years. It opens up new possibilities not just for modern mathematics research, but also for mathematics education. With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own."
"A treasure trove of Babylonian tablets exists, but only a fraction of them have been studied yet. The mathematical world is only waking up to the fact that this ancient but very sophisticated mathematical culture has much to teach us."
People were understandably excited by the news.
Some mathematicians actually think studying the Babylonians back then could help us improve the way we do trigonometry today.
Babylonian tablet Plimpton 322 will make studying maths easier, mathematician says http://ab.co/2vuEzuL\u00a0 | @abcnewspic.twitter.com/U10wQ7ZA42— ABC Australia (@ABC Australia) 1503644411
"With Plimpton 322 we see a simpler, more accurate trig. (with) clear advantages over our own."\n@n_wildberger: https://www.theguardian.com/science/2017/aug/24/mathematical-secrets-of-ancient-tablet-unlocked-after-nearly-a-century-of-study\u00a0\u2026\n#TOK— Roo Stenning (@Roo Stenning) 1503658186
Of course, there were the haters...
Find someone who loves you as much as this guy dislikes a hypothesis about Babylonian math: http://www.sciencemag.org/news/2017/08/ancient-babylonian-tablet-may-contain-first-evidence-trigonometry\u00a0\u2026pic.twitter.com/c5yO8LmjhE— Miles Brundage (@Miles Brundage) 1503605001
But all in all, Twitter users were pretty impressed with the Babylonians' skills.
And we're over here trying to figure out how to do trig with our TI-83s... man I love it when the ancients show what real intelligence is.— Kenny Hayse (@Kenny Hayse) 1503633184
Congratulations to Dr. Mansfield and his team on their incredible discovery... and for making trigonometry exciting!
'It feels like the sacred circle is completing itself before I go in this life.'
A little more than two weeks after receiving a formal apology from the Academy of Motion Picture Arts and Sciences for the abuse she suffered at the 1973 Academy Awards, Native American rights activist Sacheen Littlefeather has died at age 75.
Littlefeather is a Native American civil rights activist born to an Apache and Yaqui father and a European American mother. Littlefeather made history at the 1973 Academy Awards by forcing Hollywood and America to confront its mistreatment of Native Americans by rejecting Brando's award on his behalf.
Dressed in traditional clothing, she explained that Brando "very regretfully cannot accept this generous award, the reasons for this being … the treatment of American Indians today by the film industry and on television in movie reruns, and also with recent happenings at Wounded Knee."
Littlefeather was courteous and nonconfrontational in her brief speech, but still wound up the target of jokes that night. “I don’t know if I should present this award on behalf of all the cowboys shot in all the John Ford westerns over the years,” Clint Eastwood said later in the evening while presenting the award for best picture. Presenting best actress, Raquel Welch cracked: “I hope they haven’t got a cause.”
Littlefeather later said that John Wayne attempted to assault her backstage.
"A lot of people were making money off of that racism of the Hollywood Indian," Littlefeather told KQED. "Of course, they’re going to boo. They don't want their evening interrupted."
Three months later, Brando explained his reasoning for rejecting the award on "The Dick Cavett Show."
"I felt there was an opportunity," Brando told Cavett. "Since the American Indian hasn't been able to have his voice heard anywhere in the history of the United States, I thought it was a marvelous opportunity to voice his opinion to 85 million people. I felt that he had a right to, in view of what Hollywood has done to him."
Nearly 50 years after the incident, the Academy issued a formal apology this past August.
"The abuse you endured because of this statement was unwarranted and unjustified," former Academy President David Rubin wrote in a letter to Littlefeather, CNN reported. "The emotional burden you have lived through and the cost to your own career in our industry are irreparable. For too long the courage you showed has been unacknowledged. For this, we offer both our deepest apologies and our sincere admiration."
On September 17, the Academy hosted an event honoring Littlefeather at the David Geffen Theater for more than 800 people, nearly half of which are Native American. Littlefeather asked them to stand before she formally accepted the apology.
“I am here accepting this apology, not only for me alone but as acknowledgment, knowing that it was not only for me, but for all of our nations that also need to hear and deserve this apology tonight,” she addressed the crowd. “Look at our people. Look at each other and be proud that we stand as survivors, all of us. Please, when I’m gone, always be reminded that whenever you stand for your truth, you will be keeping my voice, and the voices of our nations, and our people, alive.”
Littlefeather was also part of the Native American occupation of Alcatraz Island in 1969 and began acting with San Francisco’s American Conservatory Theater in the early ’70s. Her career in show business was derailed after the Oscars controversy and she claims she was “red-listed” from the business.
But that didn’t stop her from being a vocal activist for Native American rights throughout the rest of her life. She also worked with Greenpeace and served on the board of directors for the American Indian AIDS Institute of San Francisco.
Littlefeather’s niece confirmed that she died peacefully from breast cancer with her loved ones at her home in Marin County, California, on Sunday, October 2. The Academy’s apology in the final months of her life brought a sense of closure.
“It feels like the sacred circle is completing itself before I go in this life,” Littlefeather told the Academy. “It feels like a big cleanse, if you will, of mind, body, and spirit, and of heart. It feels that the truth will be known. And it feels like the creator is being good to me.”
This article originally appeared on 08.05.21
Six years ago, a high school student named Christopher Justice eloquently explained the multiple problems with flying the Confederate flag. A video clip of Justice's truth bomb has made the viral rounds a few times since then, and here it is once again getting the attention it deserves.
Justice doesn't just explain why the flag is seen as a symbol of racism. He also explains the history of when the flag originated and why flying a Confederate flag makes no sense for people who claim to be loyal Americans.
This high school student, Christopher Justice, does a great job at explaining the Confederate flag and its problems.pic.twitter.com/CcOXHCB8GQ— \ud835\udc0b\ud835\udc1a\ud835\udc27\ud835\udc1c\ud835\udc1e \ud83c\udff3\ufe0f\u200d\ud83c\udf08 (@\ud835\udc0b\ud835\udc1a\ud835\udc27\ud835\udc1c\ud835\udc1e \ud83c\udff3\ufe0f\u200d\ud83c\udf08) 1628088843
But that clip, as great as it is, is a small part of the whole story. Knowing how the discussion came about and seeing the full debate in context is even more impressive.
In 2015, a student at Shawnee Mission East High School outside of Kansas City came up with the idea to have student journalists document students engaging in open discussions about various topics. In support of this idea, history teacher David Muhammad helped arrange a debate about the use of the Confederate flag in American society in his classroom.
According to the Shawnee Mission Post, Muhammad had prepared a basic outline and some basic guiding questions for the discussion, but mainly let the students debate freely. And the result was one of the most interesting debates about the Confederate flag you'll ever see—one that both reflects the perspectives in American society at large and serves as an example of how to hold a respectful conversation on a controversial topic.
The full discussion is definitely worth a watch. Justice had quite a few Confederacy defenders to contend with, and he skillfully responded to each point with facts and logic. Other students also chimed in, and the discussion is wildly familiar to anyone who has engaged in debate on this topic. For his part, Mr. Muhammad did an excellent job of guiding the students through the debate.
"I had Chris in class, so I knew he was super intelligent and that he read a lot," Muhammad told the Shawnee Mission Post in 2018. "But that really came out of left-field. He was never out there very much socially, so I didn't expect for him to want to speak in front of a crowd like that."
(In case you're wondering, according to LinkedIn, Christopher Justice is now studying political science at Wichita State University after switching his major from sports management. David Muhammad is now Dean of Students at Pembroke Middle School and also serves as a Diversity Consultant.)
Thanks, SM East, for documenting and sharing such a great discussion.