What should I teach my children to prepare them to race with the robots?

I must prepare my sons to adapt to the fourth industrial revolution but that means sending them to schools that are equipped to exceed the averages

Years ago, as a reporter in Seattle, I watched Microsoft CEO Steve Ballmer decry Washington states education system. He said Microsoft couldnt hire enough locals because our schools dont produce the kinds of minds he needed.

At the time, I was angry. He and his cohort, most notably Jeff Bezos of Amazon, contributed serious money to the campaign against a state income tax on the wealthy that would have funneled billions to our schools. Now I feel a pinch deep in my stomach, an emotion so primal I hesitate to name it.

As a mother, my time is come, or nearly done, and my childrens just begun.

Automation will absorb all of the jobs it can reach, whether on the factory floor or in an office. Artificial intelligence has already taken over the corporate earnings analyses I once produced as a business journalist. By the best measures Ive been able to find, machines will displace about half of American jobs by the time my toddlers look for work.

This new era has been called the second machine age, the fourth industrial revolution, the information economy.

From certain angles, Seattle residents seem well positioned to access the highly paid and creative jobs that arise from combining cutting-edge technologies with the exponential powers of computing and big data. My city is now considered a global city not because of the port, which put our state on the maps when they were still being drawn, but because of the presence of Microsoft, Amazon and numerous tech startups.

Amazon occupies one fifth of all office space in downtown Seattle, a short ride from my neighborhood on light rail. Incoming waves of well-educated tech workers have helped double the median home price during the past five years.

Many of these rich young people call themselves progressive. Are they proud to be joining the nations most regressive tax structure? In our state, poor people pay eight times as much of their family income to taxes as the wealthy 1%. Lacking a personal income tax, Washington state relies on sales tax and has long looked to levies to fund schools, parks and other social needs.

When I moved to Seattle in 2004, I marveled that the state didnt take a cut of my income from the now-defunct Seattle Post-Intelligencer. It took me a while to contemplate what it means for an entire society to act against the interests of its children.

College-level tuitions before college

To survive the extinction of an entire class, I must prepare my two- and three-year-old sons to race with the robots, and not against them.

Our kids are going to meet an economy with far fewer entry-level positions and will have to clamber up a receding ladder. That means being in schools equipped to exceed the averages, not rising to meet them.

Washington state has underfunded our schools so long that our governments negligence was deemed unconstitutional by our state supreme court, which fined the state $100,000 a day for failing to provide a future for our children.

Years into this public shaming, the legislature came up with a multibillion-dollar package to fund basic education in our state, though they didnt manage to pass a capital budget before students went back to school after a long, dry summer.

Amazon
Amazon Go opens to Amazon employees in its Beta program in Seattle. Photograph: Paul Gordon/Zuma Press / eyevine

From my porch, I can see the chain-link fence blur into gray around the asphalt playground of our neighborhood public school. On weekday mornings, my closest friends walk to Hawthorne Elementary with their children, ducklings that cluster at crosswalks along streets known for gunfire. A new home just sold for nearly a million dollars at the end of our block, but people keep getting shot and dying at our community playfield.

Despite valiant efforts by its admirable principal, committed educators, engaged parents and resilient students, Hawthorne has been labeled failing since long before my husband and I bought a peeling house from a nice couple who raised their family here.

Less than half of the schools fourth and fifth graders meet the states standards in math, which makes me doubt that our educational system is preparing these kids to thrive in the glittering economy they were born under. Five years ago, the office of the superintendent of public instruction ranked Hawthorne among the bottom 5% of the state, according to test passage rates.

This, in a city known for minting billionaires.

In The Second Machine Age, authors Erik Brynjolfsson and Andrew McAfee, both MIT professors, recommend Montessori programs to prepare children for their future, with a focus on science, technology, engineering, arts and math. Thats Steam, for those not versed in educational acronyms.

Developed to help poor children realize their own innate potential, Montessori schools practice self-directed learning with tactile materials that encourage the freewheeling creativity that formed tech CEOs such as Bezos and Googles co-founders.

The private bilingual Montessori kindergarten I found 30 minutes away costs $20,000 a year.

Despite college-level tuitions, about one quarter of Seattle students opt out of the public school system to study at private or parochial schools. To send my sons to Seattles best private schools would cost more than $700,000, and thats before they get to college.

A survey of public schools in Seattle shows no Montessori options that my children can access, though a nearby program in Leschi was a success at first, drawing wealthier students into the public school system, bringing with them the engagement of their families.

The Leschi teachers were so distressed by the resulting racial, linguistic and housing disparities between the traditional and Montessori classes that they melded the programs, rather than working to recruit more students of color into the Montessori program, which they could not afford to expand. A taskforce opted against including technology in the curriculum, fearful they would attract too many white families.

I believe in diversity; my own blood is blended. A first generation Latinx, Ive invested years of effort to raise my sons to be bilingual. I also want to work toward equity in a city whose neighborhood schools reflect the segregation compelled by redlining and white flight.

Leschis students are learning hard truths about equity, but theyre improving together. Maybe thats enough. But I worry when well-intentioned people lacking the resources to serve their students equally decide against teaching technology, the lingua franca of our world. Even the state administers student tests by computer.

I sought answers from Chris Reykdal, state superintendent of public instruction. The injustice of it all is that we have never seen technology as a core learning, Reykdal said. Do we still consider technology an enrichment, or should it be a more profound part of basic education? The state hasnt made that decision yet.

Washington has hundreds of school districts overseen by elected boards that enact tangled mandates without the resources to see them through. All over the state, schools used levy monies to take care of basics and pay their teachers, rather than acquiring and teaching technology.

Deb Merle is Governor Jay Inslees K-12 education adviser. Merle said that designating technology as part of basic education, which would ensure that the dollars flowed to their purpose, is not a state priority, though she recognized that Reykdals predecessor also advocated for keeping technology funds separate.

I dont think we teach enough science, period. Thats what I spend a lot of time worrying about, not what kind of science, Merle said. Our elementary schools teach less than one hour per week of science.

Steam as a social justice issue

I kept dialing, determined to maintain the education-fueled trajectory of my family.

My kin have lived in dictatorship-induced diaspora since famine swept Spain under Franco; they later fled Batista, who ruled Cuba before Castro. I am not conditioned to expect social stability as a condition of being for any country.

The meeting I most dreaded was closest to home. On the short walk to our neighborhood school, I decided to come right out and tell its principal, Sandra Scott, that I am afraid to send my kids to Hawthorne because the schools test scores, though on the rise, are low enough to make me wince.

Luckily, Scott is a pragmatic visionary, the kind of principal who inspires parents to put down the remote and join the PTA. Since 2009, Scott has led Hawthornes revitalization, winning admiration and awards from Johns Hopkins University for her program of school, family and community partnerships.

Test scores dont define who the students are. Our kids are not a number, Scott said. There were things we needed to do differently or better like improving the academics and the school culture to bring families back into the community.

To
To face the age of automation, it is recommended children are taught a program with a focus on science, technology, engineering, arts and math. Photograph: Will Walker / NNP

Recognizing the opportunity that Seattles tech economy presents, Scott retooled Hawthorne to focus on Steam programming. Rather than cluster the high-performing test takers together which has segregated programs within diverse schools Hawthorne distributes them throughout classrooms. If a student excels in math, outstripping peers in that grades curriculum, the teacher walks that child to the next grade for math.

When it comes to fifth-grade science, those efforts more than doubled the test passage rates over three years, from 20% to 46%. I ache upon rereading that last sentence the hope and pride in the increase, the grimace I cant help but make at where they started, and what remains to be accomplished.

Scott and her staff find ways to make progress. But she doesnt have the funds for a technology teacher or trainings, so the lab will be largely unused this year. As a mother who cares about the kids who go to Hawthorne, I cant afford to wait for someone else to find those resources.

The leaders of this school are working to undo the effects of intergenerational poverty that dates back to slavery and other forced migrations. More than half of the students are eligible for free and reduced lunches. A quarter of the students are learning the language theyre taught in. Scores reflect circumstances, which is why Reykdal is refocusing the state on racial gaps, poverty gaps and English language gaps, down to the school level.

Many of the jobs first displaced by automation belong to peoples of color, women and others who depend on a combination of part-time positions. A federal council of economic advisers found an 83% likelihood that, by 2040, automation would displace jobs paying less than $20 per hour.

In Washington, Steam-related jobs pay double the median wage, for starters. The people moving here to work for Microsoft, Amazon and Boeing make much more. When we choose not to provide public schools with the resources needed to provide educational access to those opportunities, we are consigning local students to lesser-paid sectors of the economy, the very same that are vulnerable to automation. In other words, we are allowing our government to consecrate our children to poverty in real time.

Mass unemployment would make American society more violent, our law enforcement more brutal and our peoples more vulnerable to genocide. Automation is a social justice issue, and if history is any teacher, it shows us that vast swaths of disenfranchised peoples are a harbinger of war.

Problems that reflect the world

Whenever I have a problem thats too big to solve, I call my dad, and we argue about what to do. He told me the solution was simple. I should move. The only financially feasible choice would be the suburbs.

Something in me balks at leaving a city I love, and especially our neighborhood, where my children are happy. As a community, we just celebrated our 10th annual block party, a Cuban pig roast that my husband and I organize for our wedding anniversary. Our neighbors come bearing side dishes, canopies and games, and we dance until the DJs stop playing. The conversations we start on that night have lasted a decade. I want to stay.

As native Spanish speakers, my sons could option into the bilingual public schools on the other side of our gridlocked downtown, north of the covenants which kept people of color from buying homes. Those schools wait lists are legendary, but I am uncomfortable with the mostly white and relatively well-off demographics produced by saving only 15% of seats for native speakers. I want my kids to feel at home in a country that contains multitudes, which is why we moved to one of our nations most diverse zip codes.

Computers solve the problems theyre given. And so we must ask ourselves what we value, and whom.

Not every child wants to be a robotics engineer. But without the modes of thought elicited by learning computer science from an early age, many Washington state students will not be competitive for the jobs that remain. I want my own sons to be chosen and better yet, able to choose as I was, though I fell for a profession whose financial structures imploded five years after my college graduation.

I hope my privileged vulnerability encourages you to reflect on those truly trapped by our system. This essay invokes my worries as a mother, and with them, my socioeconomic position. Hawthorne is a happy place with diverse classrooms whose problems reflect the world, but I am glad of the years I have left to decide what my kids truly need to learn.

There can be no denying that I am one of the gentrifiers of this neighborhood, and with the honor of living here comes the responsibility to contribute. Looking at whats coming in the second machine age tremendous opportunities, to be sure, but also massive loss of what weve known as jobs I feel compelled to join those working toward a better future, minds whirring whenever problems arise.

Two nonprofits, FIRST Washington and XBOT Robotics, have offered support and equipment for Hawthorne to start a Lego robotics league after school. Four parents signed up to lead teams during last nights PTA meeting, my very first.

Its a start.

Get involved

To bolster Steam education for students, hybridized systems have sprung up as non-profits seek to prepare our children for the economy we will leave to them.

First Washington: This nonprofit helps start and sustain after-school Lego robotics leagues from K-12.

XBOT Robotics: Operating in one of the nations most diverse zip codes, offering robotics programming K-12.

Code.org: Free online programming for learners at all levels. Work through problems with your kids.

Technology Access Foundation: Helping people of color access Stem-related education in middle school, high school and beyond.

Washington State Opportunity Scholarship: A non-profit that funds thousands of Stem scholarships for Washingtons college-bound high school graduates. More than half of those scholarship recipients are students of color, women and/or the first in their family to access a higher education, if not all three.

Teals (Technology, Education and Literacy in Schools): Matches professionals with teachers to co-teach computer science in classrooms.

Seattle Mesa (Mathematics Engineering Science Achievement): Provides scholarships, in-class math and science projects, advanced learning opportunities, tutoring, math camp and teacher trainings.

Read more: https://www.theguardian.com/education/2017/oct/18/what-should-i-teach-my-children-to-prepare-them-for-jobs-in-their-era

Collection of letters by codebreaker Alan Turing found in filing cabinet

The correspondence, dating from 1949 to 1954, was found by an academic in a storeroom at the University of Manchester

A lost collection of nearly 150 letters from the codebreaker Alan Turing has been uncovered in an old filing cabinet at the University of Manchester.

The correspondence, which has not seen the light of day for at least 30 years, contains very little about Turings tortured personal life. It does, however, give an intriguing insight into his views on America.

In response to an invitation to speak at a conference in the US in April 1953, Turing replied that he would rather not attend: I would not like the journey, and I detest America.

The letter, sent to Donald Mackay, a physicist at Kings College London, does not give any further explanation for Turings forthright views on America, nor do these views feature in any of the other 147 letters discovered earlier this year.

The correspondence, dating from early 1949 to Turings death in 1954, was found by chance when an academic cleared out an old filing cabinet in a storeroom at the University of Manchester. Turing was deputy director of the universitys computing laboratory from 1948, after his heroic wartime codebreaking at Bletchley Park.

Turing was a visionary mathematician and is regarded today as the father of modern computing who broke the Nazis second world war Enigma code. While his later life has been overshadowed by his conviction for gross indecency and his death aged 41 from cyanide poisoning, a posthumous pardon was granted by the Queen in 2013. His life was featured in the 2014 film the Imitation Game.

Prof Jim Miles, of the universitys school of computer science, said he was amazed to stumble upon the documents, contained in an ordinary-looking red paper file with Alan Turing scrawled on it.

When I first found it I initially thought: That cant be what I think it is, but a quick inspection showed it was a file of old letters and correspondence by Alan Turing, he said.

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 mystery as to why they had been filed away.

The collection focuses mainly on Turings academic research, including his work on groundbreaking areas in AI, computing and mathematics, and invitations to lecture at some of Americas best-known universities including the Massachusetts Institute of Technology.

It contains a single letter from GCHQ, for whom Turing worked during the war, asking the mathematician in 1952 if he could supply a photograph of himself for an official history of Bletchley Park that was being compiled by the American cryptographer William Friedman. In his reply to Eric Jones, GCHQs then director, Turing said he would send a picture for the American rogues gallery.

The collection also contains a handwritten draft BBC radio programme on artificial intelligence, titled Can machines think? from July 1951. The documents were sorted, catalogued and stored by the University of Manchester archivist James Peters and are now available to search online.

Peters said: This is a truly unique find. Archive material relating to Turing is extremely scarce, so having some of his academic correspondence is a welcome and important addition to our collection.

There is very little in the way of personal correspondence, and no letters from Turing family members. But this still gives us an extremely interesting account and insight into his working practices and academic life whilst he was at the University of Manchester.

He added: The letters mostly confirm what is already known about Turings work at Manchester, but they do add an extra dimension to our understanding of the man himself and his research.

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.

Read more: https://www.theguardian.com/science/2017/aug/27/collection-letters-codebreaker-alan-turing-found-filing-cabinet

Malala Yousafzai: notes from my Girl Power trip to Nigeria

In a few months Ill be starting at university. If only more girls around the world had this opportunity

Three days ago, I returned from my second visit to Nigeria.

Nigeria is the richest country in Africa, but it has the highest number of out-of-school girls in the world. When I first visited the country in 2014, the government spent 9% of its budget on education. This year its only 6%. (The international benchmark for spending on education is 20% of the overall budget.)

When planning where I would travel on my Girl Power Trip this summer, I knew I needed to return to Nigeria and advocate again for the millions of girls fighting to go to school.

In some states, particularly in northern Nigeria, extremism terrorises communities and makes education impossible for many children, particularly girls.

During my trip, I travelled to Maiduguri, the birthplace of Boko Haram. In a camp for people displaced by terrorism, I met girls like 15-year-old Fatima, who have faced so much violence and fear in their young lives but are still determined to go to school.

Boko Haram abducted me and wanted to marry me, Fatima told me. I later managed to escape. I was not in school until I came to the camp here.

Malala
Inadequate government spending, corruption and poverty keep girls from getting an education and pursuing their dreams. Photograph: Tess Thomas/Malala Fund

Leaders in this area, like Borno State governor Kashim Shettima, are working against extreme challenges to keep children in school. When we met, Shettima told me hes determined to rewrite history through education for children who suffer so much under Boko Haram.

In other regions of Nigeria, inadequate government spending, corruption and poverty keep girls from getting an education and pursuing their dreams.

Kehinde and Taiwo are 14-year-old twins living in Lagos. In the poor community where they live, there is no public school. When their mother contracted a serious illness and couldnt work, the family could no longer afford to pay $70 per term for their private tuition. Today, Kehinde and Taiwo work 12 hours a day grinding peppers. They earn $2 a day or less, and use the money to feed their family.

Taiwo loves mathematics and wants to be a banker. Kehinde says shed like to be a nurse and help sick people like her mother. But neither of these sisters or millions of Nigerian girls like them can achieve their dreams without education.

Malala
I knew I needed to return to Nigeria and advocate again for the millions of girls fighting to go to school. Photograph: Tess Thomas/Malala Fund

Nigeria has the means to help these girls but the government hasnt prioritised education. Thats why I met with the acting president, Yemi Osinbajo, and asked him to declare an education state of emergency in Nigeria. I urged him, the minister of education and other leaders to triple spending on education, make budgets transparent and encourage all states in Nigeria to pass the Childs Rights Act.

Osinbajo said leaders would meet again in the next two weeks to address the education crisis and he agrees Nigeria must invest significantly in education.

Malala Fund and I will keep monitoring Nigerias progress. I hope my next visit to the country can be a celebration of many more girls going to school, learning and preparing for a brighter future.

My ambitions are high, but so are those of Fatima, Kehinde, Taiwo and all the girls I meet on my travels. I will keep speaking out until all girls can go to school. My sisters and I are fighting for a world where all girls can learn and lead without fear. I hope you will join us.

Follow Guardian Students on Twitter: @GdnStudents.

Read more: https://www.theguardian.com/education/2017/jul/21/malala-yousafzai-girl-power-trip-nigeria-women-education

Maryam Mirzakhani, first woman to win mathematics’ Fields medal, dies at 40

Stanford professor, who was awarded the prestigious prize in 2014, had suffered breast cancer

Maryam Mirzakhani, a Stanford University professor who was the first and only woman to win the prestigious Fields medal in mathematics, has died. She was 40.

Mirzakhani, who had breast cancer, died on Saturday, the university said. It did not indicate where she died.

In 2014, Mirzakhani was one of four winners of the Fields medal, which is presented every four years and is considered the mathematics equivalent of the Nobel prize. She was named for her work on complex geometry and dynamic systems.

Mirzakhani specialized in theoretical mathematics that read like a foreign language by those outside of mathematics: moduli spaces, Teichmller theory, hyperbolic geometry, Ergodic theory and symplectic geometry, the Stanford press announcement said.

Mastering these approaches allowed Mirzakhani to pursue her fascination for describing the geometric and dynamic complexities of curved surfaces spheres, doughnut shapes and even amoebas in as great detail as possible.

Her work had implications in fields ranging from cryptography to the theoretical physics of how the universe came to exist, the university said.

Mirzakhani was born in Tehran and studied there and at Harvard. She joined Stanford as a mathematics professor in 2008. Irans president, Hassan Rouhani, issued a statement praising Mirzakhani.

The grievous passing of Maryam Mirzakhani, the eminent Iranian and world-renowned mathematician, is very much heart-rending, Rouhani said in a message that was reported by the Tehran Times.

Irans foreign minister, Mohammad Javad Zarif, said her death pained all Iranians, the newspaper reported.

The news of young Iranian genius and math professor Maryam Mirzakhanis passing has brought a deep pang of sorrow to me and all Iranians who are proud of their eminent and distinguished scientists, Zarif posted in Farsi on his Instagram account.

I do offer my heartfelt condolences upon the passing of this lady scientist to all Iranians worldwide, her grieving family and the scientific community.

Mirzakhani originally dreamed of becoming a writer but then shifted to mathematics. When she was working, she would doodle on sheets of paper and scribble formulas on the edges of her drawings, leading her daughter to describe the work as painting, the Stanford statement said.

Mirzakhani once described her work as like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out.

Stanford president Marc Tessier-Lavigne said Mirzakhani was a brilliant theorist who made enduring contributions and inspired thousands of women to pursue math and science.

Mirzakhani is survived by her husband, Jan Vondrk, and daughter, Anahita.

Read more: https://www.theguardian.com/us-news/2017/jul/15/maryam-mirzakhani-mathematician-dies-40

After getting pregnant, you are done: no more school for Tanzania’s mums-to-be

Furious campaigners say President John Magufuli is out of touch with public opinion after he endorses law allowing state schools to expel young mothers

A coalition of human rights groups has condemned as unconstitutional the Tanzanian presidents comments that pregnant girls should be banned from school.

President John Magufuli was widely criticised by campaigners after he told a rally last week: As long as I am president no pregnant student will be allowed to return to school After getting pregnant, you are done.

A law dating back to the 1960s allows all state schools in Tanzania to ban young mothers from attending. Over the past decade more than 55,000 Tanzanian pregnant schoolgirls have been expelled from school, according to a 2013 report by the Center for Reproductive Rights.

Womens groups said the ban is out of touch with public opinion and breaks international human rights conventions. It also contradicts a promise set out in the ruling partys 2015 election manifesto, which pledged to allow pregnant school girls to continue with their studies.

Faiza Jama Mohamed, director of Equality Nows Africa office, said campaigners will not stop in their fight against the ban. We have to ensure girls are going to school. Its a right. Even if it means we have to lodge a case in the courts to declare it unconstitutional, thats a route that were considering.

Speaking in Chalinze town, Magufuli said that girls would be too distracted to concentrate on their studies if they had a child, and their presence would be a bad influence on other girls.

After calculating some few mathematics, shed be asking the teacher in the classroom Let me go out and breastfeed my crying baby, he said.

Following his comments, the hashtag #StopMagufuli trended for days, while an online petition opposing the ban and calling for better sex education attracted almost 2,500 signatures.

Equality Now, an international human rights organisation, is supporting a coalition of 29 local campaign groups that gathered in Dar es Salaam on Thursday to voice their concern about the ban. In a statement released before the meeting, the coalition said it was speaking out to defend the countrys young girls, calling on the government to listen.

The statement reiterated that Tanzanian children were guaranteed the right to an education by the constitution and legislation. The rights and protections offered to children, including the right to education, therefore must be available to all those under this age, regardless of parental status. The law is unequivocal on this issue, the statement said.

Failing to educate young women would further entrench poverty, the group warned.

The group pointed to neighbouring countries that have successfully introduced re-entry policies for young mothers. In Zanzibar, since 2010 girls have been allowed back into school after giving birth as a strategy for reducing the number of dropouts. In these countries that offer girls the option to return to school, there is absolutely no evidence of an increase in student pregnancies as a result of young mothers being in school, it said.

About 21% of Tanzanian girls aged 15 to 19 have given birth, according to the Tanzania Bureau of Statistics. Womens campaigners say high numbers of girls become pregnant as a result of rape, sexual violence and coercion.

Instead of blaming girls, the state should tackle the causes of teenage pregnancies, said Jama Mohamed. They need to deal with sexual violence in schools, and with what happens to girls in between schools and home.

There is also a need to improve the quality of reproductive and health education for both boys and girls, she said. Mostly the reproductive health issues are not clear to students and nobody even tells them what will happen if they have sex, for example, she added.

Equality Now is also calling for better access to post-rape healthcare services, including those necessary to prevent pregnancy and sexually transmitted diseases.

Read more: https://www.theguardian.com/global-development/2017/jun/30/tanzania-president-ban-pregnant-girls-from-school-john-magufuli

Can you solve it? The incredible sponge puzzle

This brainteaser will wring out your brain

Hi guzzlers.

For todays puzzle, let me introduce you to the Menger sponge, a fascinating object first described by the Austrian mathematician Karl Menger in 1926. Well get to the problem as soon as I explain what the object is.

The Menger sponge is a cube with smaller cubes extracted from it, and is constructed as follows: Step A: Take a cube. Step B: Divide it into 27 smaller subcubes, so it looks just like a Rubiks cube.

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Step C: Remove the middle subcube in each side as well as the subcube at the centre of the cube, so if you looked through any hole you would see right through it. Step D: Repeat steps A to C for each of the remaining subcubes, that is, imagine that each subcube is made from 27 even smaller cubes and remove the middle one in each side and the central one.

We could carry on repeating steps A to C ad infinitum, on smaller and smaller subcubes, but here lets do it just once more:

Menger
Menger sponge. Illustration: Edmund Harriss/Visions of Numberland

Menger sponges are so loved within the maths community that building origami models of them out of business cards is a thing.

Menger
Menger sponge made as part of Matt Parker and Laura Taalmans MegaMenger project. Photograph: MegaMenger

There are lots* of reasons why Menger sponges are cool and one of them is illustrated by todays puzzle.

How
How to slice a cube in two.

On the left here is how you slice a cube in half such that the cross section is a hexagon.

When you slice a Menger sponge in two like this, what does the hexagonal slice look like?

This question is probably the most difficult one I have ever set in this column, as it requires phenomenal levels of spatial intuition. But I urge you to give it a go, even if just a basic sketch. Send me some images, or post them to me on social media. You may draw something along the right lines…

Please forgive me, though, for posing this toughie. The answer is jaw-droppingly amazing. In fact, I was told about the Menger slice by a respected geometer who told me it gave him probably his biggest wow moment in maths. Come back at 5pm BST and see for yourself.

NO SPOILERS PLEASE! Please talk about Karl Menger and origami instead.

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Photograph: Bloomsbury

Both the Menger sponge and the Menger slice are included in my latest book, Visions of Numberland: A Colouring Journey Through the Mysteries of Maths. The book is a gallery of the most spectacular images that Edmund Harriss, my co-author, and I could find in maths. You can colour them in, or just contemplate them in black and white.

I set a puzzle here every two weeks on a Monday. Send me your email if you want me to alert you each time I post a new one.

Im always on the look-out for great puzzles. If you would like to suggest one, email me.

* Here are a couple. 1) Each time you follow the iteration described in steps A to C you decrease the volume of the sponge, but increase its surface area. After an infinite number of iterations, you will have removed an infinite number of cubes. The sponge will then have zero volume and infinite surface area. 2) After an infinite number of iterations, the object is a fractal, that is, it contains parts that are identical to the whole thing.


Read more: https://www.theguardian.com/science/2017/apr/10/can-you-solve-it-the-incredible-sponge-puzzle

Can you solve it? The incredible sponge puzzle

This brainteaser will wring out your brain

Hi guzzlers.

For todays puzzle, let me introduce you to the Menger sponge, a fascinating object first described by the Austrian mathematician Karl Menger in 1926. Well get to the problem as soon as I explain what the object is.

The Menger sponge is a cube with smaller cubes extracted from it, and is constructed as follows: Step A: Take a cube. Step B: Divide it into 27 smaller subcubes, so it looks just like a Rubiks cube.

undefined

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Step C: Remove the middle subcube in each side as well as the subcube at the centre of the cube, so if you looked through any hole you would see right through it. Step D: Repeat steps A to C for each of the remaining subcubes, that is, imagine that each subcube is made from 27 even smaller cubes and remove the middle one in each side and the central one.

We could carry on repeating steps A to C ad infinitum, on smaller and smaller subcubes, but here lets do it just once more:

Menger
Menger sponge. Illustration: Edmund Harriss/Visions of Numberland

Menger sponges are so loved within the maths community that building origami models of them out of business cards is a thing.

Menger
Menger sponge made as part of Matt Parker and Laura Taalmans MegaMenger project. Photograph: MegaMenger

There are lots* of reasons why Menger sponges are cool and one of them is illustrated by todays puzzle.

How
How to slice a cube in two.

On the left here is how you slice a cube in half such that the cross section is a hexagon.

When you slice a Menger sponge in two like this, what does the hexagonal slice look like?

This question is probably the most difficult one I have ever set in this column, as it requires phenomenal levels of spatial intuition. But I urge you to give it a go, even if just a basic sketch. Send me some images, or post them to me on social media. You may draw something along the right lines…

Please forgive me, though, for posing this toughie. The answer is jaw-droppingly amazing. In fact, I was told about the Menger slice by a respected geometer who told me it gave him probably his biggest wow moment in maths. Come back at 5pm BST and see for yourself.

NO SPOILERS PLEASE! Please talk about Karl Menger and origami instead.

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Photograph: Bloomsbury

Both the Menger sponge and the Menger slice are included in my latest book, Visions of Numberland: A Colouring Journey Through the Mysteries of Maths. The book is a gallery of the most spectacular images that Edmund Harriss, my co-author, and I could find in maths. You can colour them in, or just contemplate them in black and white.

I set a puzzle here every two weeks on a Monday. Send me your email if you want me to alert you each time I post a new one.

Im always on the look-out for great puzzles. If you would like to suggest one, email me.

* Here are a couple. 1) Each time you follow the iteration described in steps A to C you decrease the volume of the sponge, but increase its surface area. After an infinite number of iterations, you will have removed an infinite number of cubes. The sponge will then have zero volume and infinite surface area. 2) After an infinite number of iterations, the object is a fractal, that is, it contains parts that are identical to the whole thing.


Read more: https://www.theguardian.com/science/2017/apr/10/can-you-solve-it-the-incredible-sponge-puzzle

See science come alive with a little help from these amazing illustrations.

Name five women scientists you learned about in school. Go ahead, I’ll wait.

GIF via “Sherlock.”

I got to three very quickly but had to think for a moment to get to five. It’s not because these researchers, explorers, and innovators don’t exist; I simply didn’t learn about their work and contributions to history in school. It just wasn’t a large part of the curriculum. And, sadly, my experience isn’t unique.

You can’t be what you can’t see, which may be why women remain underrepresented in science, technology, engineering, and mathematics (STEM) roles. Just 25% of computer and mathematical science professionals and a mere 13% of engineers today are women.

But one woman is doing her part to help change that. And she’s doing it with comics.

Seriously, comics.

Rachel Ignotofsky is a Kansas City-based artist and designer whose first book is an illustrated look at 50 game-changing women across centuries of scientific discovery and inquiry.

Unless otherwise noted, all images reprinted with permission from “Women in Science,” copyright 2016 by Rachel Ignotofsky, published by Ten Speed Press, an imprint of Random House LLC.

But why comics? It’s the medium that changed her life.

Ignotofsky had a difficult time learning to read and grew frustrated until she found her secret weapon.

“The only thing that … got me through it was educational comic books and cartoons,” Ignotofsky said. “It gave me this push to learn information that was for the ‘smart kids.'”

Ignotofsky grew up loving comics, design, and science. (If a career as an artist didn’t work out, medical school was young Rachel’s backup plan.) So she channeled her passions into “Women in Science: 50 Fearless Pioneers Who Changed the World.” The book is a beautifully curated collection of personal narratives from female scientists from a wide variety of backgrounds and disciplines, with a dash of whimsy thrown in.

Ignotofsky hopes it will open doors to kids and adults interested in learning more about the women who shaped not only science, but history. And after her childhood struggle with reading, she knows firsthand how well comics can deliver information.

“I feel like there’s a real struggle with scientific literacy, especially in this country,” Ignotofsky said. “You have to win people over. And you can convince anyone to do anything with illustration.”

Check out a few of the courageous women in science profiled in Ignotofsky’s book.

1. Edith Clarke, who worked as a human calculator and became General Electric’s first female electrical engineer.

She’s also a Badger. On, Wisconsin!

2. Marie Curie, the two-time Nobel Prize winning physicist and chemist who discovered polonium and radium.

3. Paleontologist and fossil collector, Mary Anning, who at age 12 discovered an intact dinosaur skeleton. Though respected in the field, Anning was never allowed to publish her work because she was a woman.

4. Patricia Bath, a physician, professor, and inventor who brought eye care to people in need and developed the laser probe used to treat cataracts.

5. Rosalind Franklin was a pioneering chemist and x-ray crystallographer who discovered the double helix shape of DNA.

6. Sylvia Earle, a celebrated marine biologist and aquanaut, who explored the recesses of our oceans to study the plants and animals found in the depths.

7. Hypatia, one of the earliest recorded female mathematicians and teachers who was also an expert philosopher.

But even with the amazing women she highlights in her book, Ignotofsky still remembers the women she had to leave out.

Women like pioneering Indian botanist Janaki Ammal, paleoanthropologist Mary Leakey, accomplished physicist and astronaut Sally Ride, and Irene Joliet-Curie, daughter of Marie and Pierre Curie and a talented chemist in her own right. But for this collection, Ignotofsky had to make some tough calls and let variety be her guide.

“I could’ve had 50 women in chemistry if I wanted to, but I really wanted to have a diverse group.”

Physicist Sally Ride became the first American woman in space in 1983. Photo via NASA.

But, luckily, for Ignotofsky and all of us who love women in science there are plenty of women in science for another book or two … or 20.

Women are earning just over half of the undergraduate degrees in STEM fields, and we’re re-writing history and making groundbreaking discoveries every day. The future belongs to these rising stars, and they have these courageous pioneers to thank.

Read more: http://www.upworthy.com/see-science-come-alive-with-a-little-help-from-these-amazing-illustrations?c=tpstream

Yikes, America, If You Like Gold Medals So Much, Why Are We Losing These?

Boy, I wish I could count how many gold medals America is going to win at the Olympics this year, but since America ranks 31st in mathematics, I can’t count higher than the number of fingers I have. Eleventy is a number, right?

Read more: http://www.upworthy.com/yikes-america-if-you-like-gold-medals-so-much-why-are-we-losing-these?c=tpstream

Can you solve it? Are you smarter than a British 11-year-old?

Sharpen your neurons with the maths test just taken by 300,000 UK school pupils

Hello guzzlers.

Today youll be attempting questions from a maths test that 300,000 Britons aged 11 to 13 took just over a week ago. (Thats years 7 and 8 in England and equivalent years in Scotland and Northern Ireland).

The United Kingdom Mathematics Trusts annual Junior Challenge aims to get students excited about maths with 25 appetising and intriguing problems to be solved in an hour. Ive chosen my favourite ten below, and Im giving you no more than 25 minutes to solve them. Did you hear that at the back? You might find the first ones easy, but Im expecting ten out of ten.

Ill be back at 5pm BST today with full explanations of the answers and Ill also compare your marks with the marks of the pupils who sat the test. If you are reading this on mobile, click +Follow Alex Bellos above and youll get a notification when the update appears.

Please make a note of your answers. When you press submit the screen will reveal the correct answers, but not mark individual submissions.

On some devices the image for Q4 is stretching. The image should show that the top angle of triangle C, the bottom left angle of triangle D, and the bottom angle of triangle E are right angles.

Thanks to the United Kingdom Mathematics Trust for letting me reprint these problems. Schools wanting to participate in their national challenges can find out how to do so here.

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I post a puzzle here on a Monday every two weeks.

Im the author of three popular maths books including Alexs Adventures in Numberland and the maths colouring book Snowflake Seashell Star.

You can check me out on Twitter, Facebook, Google+ and my personal website.

And if know of any great puzzles that you would like me to set here, get in touch.

Read more: https://www.theguardian.com/science/2016/may/09/can-you-solve-it-are-you-smarter-than-a-british-11-year-old