NEW YORK – Edith Windsor, a widow who brought a Supreme Court case that that struck down parts of a federal law that banned same-sex marriage and led to federal recognition for gay spouses, died Tuesday. She was 88.
Windsor died in New York, said her lawyer, Roberta Kaplan. The cause of death wasn’t given, but Windsor had struggled with heart issues for years. In 2009, she had an attack of stress cardiomyopathy, also known as broken heart syndrome, that was so bad that her heart stopped.
“The world lost a tiny but tough-as-nails fighter for freedom, justice and equality,” said her current spouse, Judith Kasen-Windsor.
Windsor’s first spouse, Thea Spyer, died in 2009. The women had married legally in Canada in 2007 after spending more than 40 years together.
Windsor sued the federal government after Spyer’s death, saying its definition of marriage as a relationship between a man and a woman prevented her from getting a marital deduction on Spyer’s estate. That meant she faced a huge tax bill that heterosexual couples would not have.
The U.S. Supreme Court ruled 5-4 in June 2013 that the provision in the law was unconstitutional, and that legally married same-sex couples are entitled to the same federal benefits that heterosexual couples receive. The opinion became the basis for the wave of federal court rulings that struck down state marriage bans and led to a 2015 Supreme Court ruling giving same-sex couples the right to marry.
“She will go down in the history books as a true American hero,” Kaplan said. Anthony Romero, executive director of the American Civil Liberties Union, called Windsor “one of this country’s great civil rights pioneers.”
“One simply cannot write the history of the gay rights movement without reserving immense credit and gratitude for Edie Windsor,” Romero said.
At the time, Windsor said she was “honored,” “humbled” and “overjoyed” when the decision came down.
Windsor was born in Philadelphia and moved to Manhattan in the early 1950s after a brief marriage to a man that ended after she told him she was gay.
She received a master’s degree in mathematics from New York University in 1957 and went to work for IBM in senior technical and management positions.
Spyer came into her life in 1963, and they became a couple two years later.
In court documents, Windsor said she told Spyer, “`If it still feels this goofy joyous, I’d like us to spend the rest of our lives together.’ And we did.”‘
Concerned that an engagement ring would bring unwanted attention to her sexual orientation from colleagues at IBM, Spyer gave Windsor a diamond brooch.
“Our choice not to wear traditional engagement rings was just one of many ways in which Thea and I had to mold our lives to make our relationship invisible,” Windsor said in court documents.
“We both faced pressures not only in the workplace and in society at large, but also from family and friends,” she added. “Like countless other same-sex couples, we engaged in a constant struggle to balance our love for one another and our desire to live openly and with dignity, on the one hand, with our fear of disapproval and discrimination from others on the other.”
Spyer was diagnosed with multiple sclerosis in 1977, and her physical condition deteriorated over the decades. The women married in Canada when they realized they might not be living when New York state legalized same-sex marriage, which it did in 2011.
Controversial tests taken by England’s seven-year-olds will be scrapped by 2023, but nine-year-olds will have to sit times table tests under new plans.
Announcing the end to compulsory SATs, the government said children would instead have a “baseline” check in reception year, aged four or five.
This would allow their progress to be tracked and would “free up” teachers, the education secretary said.
But times table tests for year four pupils will be introduced in 2019/20.
The Key Stage 1 tests in reading, writing, maths and science – used to monitor schools’ progress – have been compulsory for seven-year-olds in England with around 500,000 children taking them each year.
But they have proved controversial, with many teachers and parents opposed to putting young pupils through the tests.
Those who support the tests argue that they ensure schools are helping children grasp the basics and identify children who are struggling.
The government announced on Thursday that they would no longer be compulsory from 2023.
Instead there would be a baseline assessment of children’s abilities in their reception year, at the start of their schooling, which would then be used to measure their progress throughout the school. Children will still sit SATs at age 11.
Schools would also not be required to submit assessments of pupils’ reading and maths to the government aged 11 – because they were already being tested in year 6.
This would help “free up teachers to educate and inspire young children while holding schools to account in a proportionate and effective way,” Ms Greening said.
But times table tests – initially floated last year for pupils aged 11 – would be sat two years earlier in year four, from 2019/20 to help children’s “fluency in mathematics”.
Kevin Courtney, joint general secretary of the National Education Union, said the tests would be “a waste of valuable time, energy and money and should not be introduced”.
“The reception baseline assessment and multiplication tables check will be of no educational benefit to children and break a promise not to increase the assessment burden on primary schools.”
But Nick Brook of the school leaders’ union NAHT said the baseline assessments at reception were “absolutely the right thing to do” and, if designed properly, would provide useful information for schools while avoiding “unnecessary burdens on teachers or anxiety for young children”.
You’re probably already done with your back-to-school shopping (if you had any), but you may want to make another trip down the art supply aisle after reading about Crayola’s latest news. The crayon company just introduced a new color to freshen up your 24-pack. Crayola’s new blue crayon is called “Bluetiful,” and you’ll want to get your hands on a coloring book pronto to try it out.
According to ABC News, Crayola embarked on the naming process months ago by having fans submit their best ideas. They received over 90,000 submissions, and then narrowed it down to five finalists in July. Before announcing today that Bluetiful is the winner, the other options included Blue Moon Bliss, Dreams Come Blue, Reach for the Stars, and Star Spangled Blue. Crayola took to Twitter to let crayon fans everywhere vote on which name they’d like to see wrapped around the newest blue crayon.
According to Crayola’s press release, 40 percent of the votes went to Bluetiful, and it will be the nineteenth active blue color in your 24-pack. Not only did the company reveal the big name news today, but the company also created the world’s largest crayon to celebrate. The towering crayon was unveiled today in the new Bluetiful color, weighing 1,352 pounds and measuring 15.6 feet long. That was enough to give Crayola its Guinness World Records title for “Largest Crayon.” The celebration continued as globally recognized dancer Leon “Kida” Burns performed upbeat and creative dance numbers. Bluetiful knows how to party.
Crayola also provided some more fun facts about the new crayon. According to the Crayola website, when Bluetiful isn’t being so formal, she goes by the nickname “Bea.” She also enjoys coding apps and DIY projects. While she may be shy at first, she becomes inspired when talking about creative projects and new inventions. When it comes to school, Bluetiful is a “big advocate for arts-infused STEAM (Science, Technology, Engineering, Arts, and Mathematics) education, especially for inspired girls like me!” Sounds like this crayon is woke — with both beauty brains.
Crayola was inspired to create the new blue shade after the discovery of a new pigment called YinMin. According to Oregon State University’s website, scientists at the university accidentally discovered YinMin, which they refer to as “MasBlue,” in 2009. The discovery occurred when graduate student Andrew Smith heated manganese oxide to 1,200 degrees Celcius hoping to get a new, high-efficiency electronic material. But instead, it resulted in a “brilliant blue compound.”
The team was led by Mas Subramanian when they discovered the pigment containing the elements Yttrium, Indium, Manganese, and Oxygen. Crayola loved the new hue, so you have these guys to thank for the latest addition to your stress-coloring session.
It’s a good thing that Crayola finally came out with a new color, because die-hard fans everywhere were recently heartbroken when the company announced in March of this year that the color Dandelion would be retired from future packs of crayons. It was the first time in the company’s history that color was removed from its fellow crayon companions for good.
It’s time to turn those frowns upside-down because Bluetiful is here, and all is well in the crayon-loving world. You might want to run out and buy a new pack of Crayola crayons right this minute to see what’s new with the latest crayon, but you have to wait just a little while longer to hold take Bluetiful for a test drive.
According to Crayola’s press release, the color will be available nationwide in January 2018. If you can’t wait, though, you can pick up Bluetiful exclusively at Walmart, Walmart.com, and Jet.com in early November — just in time for the holidays.
You just might have to add a coloring session to the agenda for your next girls’ night. Bluetiful would approve.
Myron Ebell, who headed the EPAs transition team when Trump became president, said the last decade has been a period of low hurricane activity
Conservative groups with close links to the Trump administration have sought to ridicule the link between climate change and events such as tropical storm Harvey, amid warnings from scientists that storms are being exacerbated by warming temperatures.
Harvey, which smashed into the Texas coast on Friday, rapidly developed into a Category 4 hurricane and has drenched parts of Houston with around 50in of rain in less than a week, more than the city typically receives in a year. So much rain fell that the National Weather Service had to add new colours to its maps.
The flooding has resulted in at least 15 deaths, with more than 30,000 people forced from their homes. Fema has warned that hundreds of thousands of people will require federal help for several years, with Greg Abbott, governor of Texas, calling Harvey one of the largest disasters America has ever faced. Insurers have warned the cost of the damage could amount to $100bn.
Some scientists have pointed to the tropical storm as further evidence of the dangers of climate change, with Penn State University professor of meteorology Michael Mann stating that warming temperatures worsened the impact of the storm, heightening the risk to life and property.
Conservative groups, however, have mobilized to downplay or mock any association between the storm and climate change. Myron Ebell, who headed the Environmental Protection Agencys transition team when Donald Trump became president, said the last decade has been a period of low hurricane activity and pointed out that previous hurricanes occurred when emissions were lower.
Instead of wasting colossal sums of money on reducing greenhouse gas emissions, much smaller amounts should be spent on improving the infrastructure that protects the Gulf and Atlantic costs, said Ebell, who is director of environmental policy at the Competitive Enterprise Institute, a libertarian thinktank that has received donations from fossil fuel companies such as Exxon Mobil.
Thomas Pyle, who led Trumps transition team for the department of energy, said: It is unfortunate, but not surprising, that the left is exploiting Hurricane Harvey to try and advance their political agenda, but it wont work.
When everything is a problem related to climate change, the solutions no longer become attainable. That is their fundamental problem.
Pyle is president of the Institute of Energy Research, which was founded in Houston but is now based in Washington DC. The nonprofit organization has consistently questioned the science of climate change and has close ties to the Koch family.
The Heartland Institute, a prominent conservative group that produced a blueprint of cuts to the EPA that has been mirrored by the Trump administrations budget, quoted a procession of figures from the worlds of economics, mathematics and engineering to ridicule the climate change dimension of Harvey.
In the bizarro world of the climate change cultists … Harvey will be creatively spun to prove there are dire effects linked to man-created climate change, a theory that is not proven by the available science, said Bette Grande, a Heartland research fellow and a Republican who served in the North Dakota state legislature until 2014.
Facts do not get in the way of climate change alarmism, and we will continue to fight for the truth in the months and years to come.
Harvey was the most powerful storm to hit Texas in 50 years, but according to the National Oceanic and Atmospheric Administration, it is premature to conclude that there has already been an increase in Atlantic-born hurricanes due to temperatures that have risen globally, on average, by around 1C since the industrial revolution.
Scientists have also been reluctant to assign individual storms to climate change but recent research has sought to isolate global changes from natural variability in disasters such as Hurricane Katrina, which devastated New Orleans in 2005.
However, researchers are also increasingly certain that the warming of the atmosphere and oceans is likely to fuel longer or more destructive hurricanes. A draft of the upcoming national climate assessment states there is high confidence that there will be an increase in the intensity and precipitation rates of hurricanes and typhoons in the Atlantic and Pacific as temperatures rise further.
Harvey may well fit that theory, according to climate scientist Kevin Trenberth, as the hurricane managed to turn from a tropical depression to a category four event in little more than two days, fed by a patch of the Gulf of Mexico that was up to 4C warmer than the long term average.
When storms start to get going, they churn up water from deeper in the ocean and this colder water can slow them down, said Trenberth, a senior scientist at the National Center for Atmospheric Research. But if the upwelling water is warmer, it gives them a longer lifetime and larger intensity. There is now more ocean heat deep below the surface. The Atlantic was primed for an event like this.
While the number of hurricanes may actually fall, scientists warn the remaining events will likely be stronger. A warmer atmosphere holds more evaporated water, which can fuel precipitation Trenberth said as much as 30% of Harveys rainfall could be attributed to global warming. For lower-lying areas, the storm surge created by hurricanes is worsened by a sea level that is rising, on average, by around 3.5mm a year across the globe.
The oil and gas industry has sought to see off the threat in the Gulf of Mexico with taller platforms post-Katrina, offshore rigs are around 90ft above sea level compared to 70ft in the 1990s but the Houston, the epicenter of the industry, is considered vulnerable due to its relaxed approach to planning that has seen housing built in flood-prone areas.
Barack Obamas administration established a rule that sought to flood-proof new federal infrastructure projects by demanding they incorporate the latest climate change science. Last week, Trump announced he would scrap the rule, provoking a rebuke from Carlos Curbelo, a Florida Republican congressman who called the move irresponsible.
Curbelo, who has attempted to rally Republicans to address climate change, wouldnt comment on the climate change link to Harvey. Ted Cruz and John Cornyn, Texass Republican senators, didnt respond to questions on the climate link, nor did Abbott, the states governor, or Dan Patrick, Texass lieutenant governor. All four of the Texas politicians have expressed doubts over the broad scientific understanding that the world is warming and that human activity is the primary cause.
Its essential to talk about climate change in relation to events like Hurricane Harvey and its sad a lot of reports dont mention it in any way, said Trenberth.
You dont want to overstate it but climate change is a contributor and is making storms more intense. A relatively small increase in intensity can do a tremendous amount of damage. Its enough for thresholds to be crossed and for things to start breaking.
Scientists have revealed the secrets of a mysterious 3,700-year-old Babylonian clay tablet found by the archaeologist who inspired the fictional ‘Indiana Jones’.
Experts at the University of New South Wales Sydney in Australia have uncovered the purpose of the famous tablet, which they describe as the world’s oldest and most accurate trigonometric table. The artifact, they say, may have been used to by ancient scribes to help in the construction of palaces, temples and canals.
The tablet, known as Plimpton 322, was discovered in the early 1900s in what is now Southern Iraq by archaeologist, academic, diplomat and antiquities dealer Edgar Banks, who provided the inspiration for the fictional character ‘Indiana Jones.’
“Plimpton 322 has puzzled mathematicians for more than 70 years, since it was realised it contains a special pattern of numbers called Pythagorean triples,” says Dr. Daniel Mansfield of the School of Mathematics and Statistics in the UNSW Faculty of Science, in a statement.
The tablet’s purpose has long baffled experts. It was not clear why the scribes had performed the complex task of generating and sorting the numbers on the tablet, according to Mansfield.
“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,” he said. “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.”
The tablet, which is thought to have come from the ancient Sumerian city of Larsa sometime between 1822 and 1762 B.C., is now in the Rare Book and Manuscript Library at Columbia University in New York.
A useful mathematical tool before the advent of calculators, trigonometric tables let you use one known ratio of the sides of a right-angle triangle to determine the other two unknown ratios.
The 15 rows on the tablet describe a sequence of 15 right-angle triangles, which are steadily decreasing in inclination, according to the UNSW. The left-hand edge of the tablet, however, is broken, although scientists built on previous research to present new mathematical evidence that there were originally six columns and the tablet was meant to be completed with 38 rows.
Researchers also demonstrated how ancient scribes, who used a base 60 numerical arithmetic similar to our time clock, rather than the modern base 10 number system, could have generated the numbers on the tablet.
The research provides an alternative theory to the widely-held view that the Plimpton 322 was a teacher’s aid for checking students’ solutions of quadratic problems. “Plimpton 322 was a powerful tool that could have been used for surveying fields or making architectural calculations to build palaces, temples or step pyramids,” said Mansfield, who first read about the tablet when preparing material for first-year math students.
UNSW scientists note that Plimpton 322 predates Greek astronomer Hipparchus, regarded as the father of trigonometry, by more than 1,000 years.
“It is wonderful that Mr. Mansfield’s work with Norman Wildberger is bringing more attention to this treasure of Columbia,” explained Jennifer Lee, a curator at Columbia University’s Rare Book and Manuscript Library, in a statement emailed to Fox News.
Plimpton 322 is one of 629 tablets written in ancient cuneiform script held by the Library. The tablet was bequeathed to Columbia by publisher George Arthur Plimpton, who had purchased the artifact from Edgar Banks.
Researchers from the University of St. Andrews have concluded that any programmer that could make a computer solve the famous “Queens puzzle” would change the entire IT industry as well as bag the $1m prize offered by the Clay Mathematics Institute in America.
The Queens puzzle is a very simple conundrum. Can you place eight queens on a chess board in such a way that no two queens can attack each other? So no queen can share the same row, column, or diagonal. It was first devised in 1850 and any human with a bit of patience can solve it.
So where’s the catch? Computers can’t do it as easily. Computers go through all potential options and the more options you have, the more it takes computers to work the solution out. According to the paper, Journal of Artificial Intelligence, after the chess board becomes larger than 1,000 by 1,000 the computers can’t cope anymore.
“If you could write a computer program that could solve the problem really fast, you could adapt it to solve many of the most important problems that affect us all daily,” lead author Professor Ian Gent said in a statement.
“This includes trivial challenges like working out the largest group of your Facebook friends who don’t know each other or very important ones like cracking the codes that keep all our online transactions safe.”
This is just a variation of the famous computer problem known as P versus NP. The crux of it is quite straightforward: can every problem that can be verified quickly also be solved quickly? For example, if I ask to find the divisors of 4,199 it would take you a fair bit of time to try many numbers. But it’s quick and easy to verify that 4,199 is only divisible by 13, 17, and 19 (apart from 1 and itself).
Many believe that not every problem can be solved as quickly as it can be verified, but if you think you can write an algorithm that can do that (or prove that it’s impossible), researchers want to hear from you.
“There is a $1,000,000 prize for anyone who can prove whether or not the Queens Puzzle can be solved quickly so the rewards are high,” co-author Dr Christopher Jefferson added.
So, computer scientists and programming buffs, get coding.
From the time she was little, Jessa has always been used and abused. Her family was part of a group of people who sexually abused her on a regular basis, and as a child, she was forced to pose for pornography. As she grew up, posing turned into performing, and Jessa was no longer appearing to do sexual acts in front of a camera, she was being raped on camera.
The spiral continued, and the pornography turned into profitable exploitation. By the age of 10, this beautiful young woman was being sold to pimps.
Jessa grew up in Canada, and lived in a suburban neighborhood where she was sexually exploited on a daily basis. Her neighborhood was “normal” and probably looked similar to where you and I live, but Jessa had no idea. She wasn’t ever sent to school, and never had the opportunity to even see her hometown. The closest thing she had to an education was a sixth-grade mathematics textbook that was thrown at her.
“I was trafficked domestically in Canada, just as I was often taken to the USA and other international countries for the sole purpose of being trafficked.”
When Jessa was 21, a woman approached her after recognizing that she displayed signs of an abused or trafficked person. She gave Jessa a slip of paper with her name and contact information before telling her to call for help anytime. That woman owned a safe house in Colorado where she helped to protect and rehabilitate survivors of human trafficking.
Escaping wasn’t something the 21-year-old had ever considered at the time—she simply never realized she had a choice.
“I didn’t know that there was an opportunity to get away,” Crisp said. “Growing up I thought it was a normal existence because it was normal for me.”
After months of building courage and communicating back and forth with the gal in Colorado, Jessa finally left. The woman helped her get to the airport and got her a plane ticket.
“My escape wasn’t a fairytale like a Disney movie; instead it was encapsulated by fear and months of preparing. I was terrified of the unknown, frightened that I would be hunted down by my pimps and abusers, and scared of what the future would hold. But in addition to being afraid, I also felt freedom for the first time. Freedom was being able to see the big blue sky and seeing the tumbleweed float around on the road as I was driven to a safe house and it felt like sunshine that kissed my face.”
Jessa was free, but her visa posed a threat for the future. Being that she was a Canadian citizen, her tourist visa was only valid for six months, forcing her to return to Canada. She re-located to Vancouver, and got plugged into a safe house there, but only for three weeks.
It was 2010, and the Winter Olympics were about to get underway in Vancouver at the exact same time that the safe house she’d entered was being forced to shut down for lack of financial funding.
Jessa had nowhere to turn, but she knew that the Olympics posed a major threat to her safety. Research shows a spike in human trafficking surrounding major sporting events.
For the second time in her life, Jessa was approached by a woman who suspected she’d been abused.
She explained to Jessa that she houses a number of girls who are in the same situation as her.
“She told me that she wanted to be my mom and that she has a lot of houses of girls like me and that she wanted to take care of me,” said Jessa.
The 21-year-old was beyond grateful to have someone in her new city who was offering to care for her the way she’d been cared for in Colorado. But her vulnerability had failed her. The woman told Jessa that she now had to work for her, and so began the all-too-familiar cycle of being sexually exploited for money.Once again, Jessa found herself trapped in slavery.
“Men raped me as my body tried to disappear from the deep burning pain, but there was nowhere to go. I wished desperately that this were a nightmare, but without knowing the real names of my pimps, I understood the gravity of my situation. I was a slave once again.”
Jessa says that she felt “numb,” and full of nothing but “shameful pain.” She says she turned the anger she felt toward these men into hatred toward herself.
“I hated the fact that the abuse and trafficking I suffered growing up made me so vulnerable to more abuse and pain. I hated the fact that I trusted someone to help me when I was all alone in a new city. I hated the ways that I longed for safety and for someone to care. And most of all, at that moment, I hated the fact that I was still alive and that I had survived my childhood.”
Unbelievably, Jessa escaped slavery a second time.
She was able to return to the same safe house in Colorado, and with the help of a select few people who had earned her trust, and genuinely cared about her future, Jessa is a completely new person today.
The director of the safe house (and the same woman who originally approached Jessa in 2009) knew that they had to do something to keep her from having to go back to Canada.
She told Jessa that if she enrolled in college, she’d be allowed to stay in the states.
“When the director at the safe house suggested that I enroll in college, I laughed in her face. I thought she was crazy. How could I go to college if I have never had an education growing up? How could I succeed if I had never written a paper in my life and didn’t know how to do simple math problems? In response I was simply told, ‘If you can read, you can learn anything.’ I wrote that phrase on my arm with a black Sharpie every day for over a year.”
After getting her GED, Jessa was accepted into college—something she never dreamed could be possible for someone like her. In 2013, she received the Colorado Authors’ League Scholarship, and she managed to finish college with a 4.0 GPA.
“Last May, when I stood in front of my graduating class to deliver the valedictorian speech, the Sharpie story and many other stories flashed through my mind, including my first day of school when I sat on the parking lot and cried because I was convinced people would shun me if they knew about my past and the things I had been forced to do. Miracles not only happen, but after trauma it is possible to dream again and live life fully.”
Jessa graduated with a BA in Christian counseling and is currently working to get her Master’s Degree in Clinical Mental Health Counseling. She hopes to get aPsy.D. in Clinical Psychology where she’d like to specialize in trauma recovery.
In addition to the academic achievements and incredible strides she’s made in finding freedom, Jessa met the man of her dreams, and the two got married in Colorado last year.
“It’s been a long journey, but through God’s redeeming love, safe people believing in me when I couldn’t believe in myself, and through people choosing to be in my life for the long haul and walking the messy road of healing by my side—I have changed. My past no longer has the power to hold me captive. I am an overcomer, I am a wife, I am a student, I am a professional, I am a speaker, I am an author, I am leader, I am an agent of change, and I am a confident woman who longs to make a difference in society.”
Jessa is currently raising money for her furthered education. Visit her Go Fund Me Page for more information.
Almost a century ago, Edgar Banks – the inspiration for Indiana Jones – dug up a clay tablet in southern Iraq, but it took until now for its meaning to be understood. With this explanation has come insight into Babylonian mathematics, which operated on a different, and in some ways preferable, system than our own.
In 1945, it was realized that the tablet, known as Plimpton 322 after it was sold to collector George Plimpton for $10, had mathematical significance, but the details remained a mystery. New research argues it represents part of a trigonometric table, and one more accurate than those that came afterwards.
Plimpton 322’s burial location in what was once the city of Larsa indicates it’s 3,700 years old, dating from the time of Hammurabi, who established one the earliest surviving legal codes. “Plimpton 322 has puzzled mathematicians for more than 70 years, since it was realized it contains a special pattern of numbers called Pythagorean triples,” said Dr Daniel Mansfield of the University of New South Wales in a statement. Pythagorean triples are any whole numbers a, b, and c that can form a right-angle triangle through the formula a2 + b2 = c2, with 3, 4, and 5 being the most familiar example.
“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,” Mansfield continued.
Mansfield became interested in the problem and collaborated with his colleague Dr Norman Wildberger to try to unravel it. Wildberger is the inventor of a new way of doing trigonometry, based on the ratio of sides rather than angles. In 2005, he published a book, Divine Proportions: Rational Trigonometry to Universal Geometry, demonstrating that any problem that can be solved using traditional trigonometric methods canalso be solved using his technique, and often more easily for those who have taken the time to learn it.
The idea of Plimpton 322 as a trigonometric table had been raised before, and eventually rejected, but this was done in the absence of an understanding of Wildberger’s methods.
Mansfield and Wildberger concluded that the ancient Babylonians had beaten Wildberger to his ideas by almost four millenia, albeit only for right-angled triangles. They report in Historica Mathematica that instead of using sinΘ, cosΘ, and tanΘ as we do – something we inherited from the ancient Greeks – Plimpton 322 could be used by anyone needing to know the length of one side of a right-angled triangle by finding the closest match to the two known sides.
“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,” Mansfield said. “It is a fascinating mathematical work that demonstrates undoubted genius.” The tablet would have been useful to architects or surveyors.
At some point since its making, a section of Plimpton 322 broke off. What remains are the side lengths for 15 right-angle triangles, ordered by inclination. Mansfield and Widlberger believe there were once 38 rows and 6 columns, making a truly impressive store of possible triangles.
The use of ratios in combination with the Babylonian base sixty number system, from which we get the length of our hours and minutes, made for an arguably superior method for calculating trigonometry to the table of chords created by the Greek mathematician Hipparchus more than 1,000 years later.
Mansfield told IFLScience that we have no idea why Babylonian trigonometry was lost. While it is possible that ancient mathematicians decided Hipparchus’ work was superior, it is also possible that Larsa and other centers of this knowledge lost a war, taking valuable knowledge with it. Mansfield noted that there is a gap in our records of the Babylonian civilization lasting several centuries.
When artifacts appear again, what we find comes mixed with influences from other cultures. Still, many Babylonian tablets have yet to be examined in detail, even aside from those that have yet to be dug up, so there may be plenty more we can learn about Babylonian mathematics now that we have a hint.
For all the merits of Wildberger’s system, it has struggled to gain a foothold among mathematicians and teachers well versed in classical trigonometry. However, Mansfield speculates that Plimpton 322 might change this. The use of ratios rather than angles could become a matter of great interest to historians of mathematics, who may learn more about how it was done. Eventually, it may be taught in schools to show there is more than one way to think about trigonometry.
A remarkable archive of letters from the late and brilliant Alan Turing in the mid-20th century has been found hiding in a storeroom at the University of Manchester in the UK.
The find of 148 documents was made by Professor Jim Miles of the School of Computer Science, who had been reorganizing the storeroom when he came across them. The letters date from early 1949 until Turing’s tragic suicide in June 1954.
“When I first found it I initially thought, ‘that can’t be what I think it is’, but a quick inspection showed it was, a file of old letters and correspondence, by Alan Turing,” said Professor Miles in a statement. “I was astonished such a thing had remained hidden out of sight for so long. No one who now works in the School or at the University knew they even existed. It really was an exciting find and it is [a] mystery as to why they had been filed away.”
Although the letters reveal little about Turing’s personal life, they do show how highly regarded he was at the time. This is despite his work at Bletchley Park, when he helped crack the German Enigma machine in World War Two, still being under wraps.
He had numerous offers to lecture at universities or attend events in the US, based on his previous work on artificial intelligence, computing, and mathematics. One of these was from the Massachusetts Institute of Technology (MIT).
However, it seems Turing himself wasn’t that keen on going to the US. In response to one invitation in April 1953, he said: “I would not like the journey, and I detest America.”
Another batch of letters found in 2015 shed more light on Turing’s tortured personal life, which saw him prosecuted for homosexual acts in 1952. He was later pardoned posthumously in 2013, having committed suicide via cyanide poisoning in 1954.
While these latest letters do not reveal any more about his personal life, they do give us more of an insight into his professional life. You can view all of the letters online here.
“The letters mostly confirm what is already known about Turing’s work at Manchester, but they do add an extra dimension to our understanding of the man himself and his research,” said Archivist James Peters in the statement. “As there is so little actual archive on this period of his life, this is a very important find in that context. There really is nothing else like it.”
Female developers are emerging as influential forces in the countrys booming technology sector but the stigma persists that computing is a male industry
The Nigerian tech scene is booming. Last year, Lagos-based startup Andela received $24m (18.5m) in funding from Mark Zuckerberg. In 2015, financial technology startup Paystack one of the first Nigerian tech companies to be accepted into renowned California-based startup accelerator Y Combinator secured approximately $1.3m in seed investment from international investors.
Within this growth, women are emerging as influential forces, and changing the face of technology in Africa, especially in the fields of agricultural and financial tech. This is despite the fact that, as recently as a decade ago, women were grossly underrepresented in and excluded from the industries they are now helping to shape.
I think those who are joining the tech world today have an easier path to tread, says Nnenna Nwakanma, a Nigerian activist for accessible internet. There were situations where people would refuse to recognise my authority, but would patronise or objectify me, or refuse to fulfil contracts they had willingly entered into all because of my gender. Despite this, Nwakanma co-founded the Free Software and Open Source Foundation for Africa (FOSSFA) and is now a senior policy manager for the World Wide Web Foundation, where she supports digital equality and promotes the rights of Nigerian women online.
The negative attitude towards womens involvement in science, technology, engineering and mathematics (Stem) is starting to change, thanks partly to initiatives such as the Stem outreach and mentoring programmes established by the Working to Advance Science and Technology Education for African Women (WAAW) Foundation, which operates in 11 countries. There is also Intels programme She Will Connect Africa, which has trained more than 150,000 women in Nigeria, South Africa and Kenya in digital literacy since it launched in 2013.
The demand for tech talent is now such that it cannot be met by men alone. Rapid digitalisation in Nigeria is heavily concentrated in the countrys metropolitan megacity, Lagos. Here, the startup culture flourishes, while big business have moved in: in 2015, global tech supplier Bosch opened a subsidiary in Ikeja, the capital of Lagos region, and Microsoft has an office in the affluent Lagos neighbourhood of Ikoyi.
Ire Aderinokun the author of web development blog bitsofco.de, a front-end developer and Nigerias first female Google Developer Expert says her love of tech started as a hobby. I used to play an online game called Neopets, which had some HTML capabilities. From there, I got really interested and continued to learn more. But, despite Aderinokuns enthusiasm, her interest was not always encouraged. Its definitely not what society expected of me. I studied psychology for my undergraduate and law for my masters. When I said I wanted to pursue this, there were many people who told me not to.
Rukayat Sadiq, a software engineer and a technical team leader at Andela, also faced opposition. She chose to study electrical engineering a subject in which a class of 150 students might include only 15 women to the surprise of friends and family, who had expected her to become a doctor.
While women entering and participating equally in the labour market is commonplace in Nigeria, computing and engineering are still industries dominated heavily by men. But many women who work in the tech industry are keen to offer support to those coming up. Aderinokun, for example, is funding full scholarships to five women for online programming nanodegrees. These qualifications do not guarantee employment, but they give those who have earned them a distinct advantage in the workplace and are endorsed by top employers, including Google, AT&T and Amazon. Sadiq also spends time teaching and mentoring newbies.
Removing the stigma and assumption that tech is only supposed to be for men is necessary, and I think we need to start from as early in childrens lives as possible, says Aderinokun. We should work towards eliminating negative statements and mindsets that perpetuate the myth that women cant be involved in Stem.
It is hopeful that we will one day get to a point where tech-related fields are level playing grounds for both sexes.
It is a challenge that continues around the globe, but it is one Nigeria is well equipped to handle.