Posts Tagged ‘education’
“And these children that you spit on / “As they try to change their worlds / Are immune to your consultations. / They’re quite aware of what they’re going through.”*…
From our friends at The Pudding— specifically, from Alvin Chang— a thorough (and illuminating and bracing) look at how the conditions in which our young are raised have everything to do with how their lives unfold…
In this story, we’ll follow hundreds of teenagers for the next 24 years, when they’ll be in their late-30s. They’re among the thousands of kids who are part of the National Longitudinal Survey of Youth. This means researchers have followed them since their teenage years to the present day – and beyond.
As Matt Muir observes in his invaluable Web Curios…
… Very North America-centric in terms of the data it’s drawing on, but wherever you are in the world the themes that it speaks to will apply – drawing on data about the life experiences of young people tracked by US statisticians….
As you scroll you see visual representations of the proportion of kids in each agegroup coterie who will experience ‘significant’ life events, from crime to poverty and beyond, and how those life events will go on to impact their academic prospects and, eventually, their life prospects – none of this should be surprising, but it’s a hugely-effective way of communicating the long-term impacts of relatively small differences in early-stage life across a demographic swathe…
Data visualization at its best and most compelling: “This Is a Teenager,” from @alv9n in @puddingviz via @Matt_Muir.
* David Bowie, “Changes”
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As we analyze adolescence, we might recall that it was on this date in 1961 that the Cleftones, a group of teens who had formed a vocal group a 3 years earlier in high school, released “Heart and Soul” (a rearrangement of the 1938 standard); it reached #18 on the pop chart and #10 on the R&B chart and was later used in the 1973 movie American Graffiti.
Then fifteen-year-old Duane Hitchings, who went on to win a Grammy award for his work on the Flashdance soundtrack in 1984, played keyboards on the track– his first professional gig. In an interview with Rock United, he recalls that the recording session was cut short when singer Pat Spann, who was dating drummer Panama Francis, was caught in a compromising position with the guitarist. “That ended the session. So the last track we recorded was the record.”
“All reality is a game”*…
If Anna beats Benji in a game and Benji beats Carl, will Anna beat Carl? Patrick Honner unpacks the principle of transitivity…
It’s the championship game of the Imaginary Math League, where the Atlanta Algebras will face the Carolina Cross Products. The two teams haven’t played each other this season, but earlier in the year Atlanta defeated the Brooklyn Bisectors by a score of 10 to 5, and Brooklyn defeated Carolina by a score of 7 to 3. Does that give us any insight into who will take the title?
Well, here’s one line of thought. If Atlanta beat Brooklyn, then Atlanta is better than Brooklyn, and if Brooklyn beat Carolina, then Brooklyn is better than Carolina. So, if Atlanta is better than Brooklyn and Brooklyn is better than Carolina, then Atlanta should be better than Carolina and win the championship.
If you play competitive games or sports, you know that predicting the outcome of a match is never this straightforward. But from a purely mathematical standpoint, this argument has some appeal. It uses an important idea in mathematics known as transitivity, a familiar property that allows us to construct strings of comparisons across relationships. Transitivity is one of those mathematical properties that are so foundational you may not even notice it…
Read on: “The Surprisingly Simple Math Behind Puzzling Matchups,” from @MrHonner in @QuantaMagazine.
* Iain M. Banks, The Player of Games
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As we tackle transitivity, we might spare a thought for Charlemagne; he died on this date in 814. A ruler who united the majority of western and central Europe (first as King of the Franks, then also King of the Lombards, finally adding Emperor of the Romans), he was the first recognized emperor to rule from western Europe since the fall of the Western Roman Empire three centuries earlier; the expanded Frankish state that he founded is called the Carolingian Empire, the predecessor to the Holy Roman Empire.
Committed to educational reform and extension, he began (in 789) the establishment of schools teaching the elements of mathematics, grammar, music, and ecclesiastic subjects; every monastery and abbey in his realm was expected to have a school for the education of the boys of the surrounding villages. The tradition of learning he initiated helped fuel the expansion of medieval scholarship in the 12th-century Renaissance.
Charlemagne is considered the father of modern Europe. At the same time, in accepting Pope Leo’s investiture, he set up ages of conflict: Charlemagne’s coronation as Emperor, though intended to represent the continuation of the unbroken line of Emperors from Augustus, had the effect of creating up two separate (and often opposing) Empires– the Roman and the Byzantine– with two separate claims to imperial authority. It led to war in 802, and for centuries to come, the Emperors of both West and East would make competing claims of sovereignty over the whole.
“A proof tells us where to concentrate our doubts”*…
Number theorist Andrew Granville on what mathematics really is, on why objectivity is never quite within reach, and on the role that AI might play…
… What is a mathematical proof? We tend to think of it as a revelation of some eternal truth, but perhaps it is better understood as something of a social construct.
Andrew Granville, a mathematician at the University of Montreal, has been thinking about that a lot recently. After being contacted by a philosopher about some of his writing, “I got to thinking about how we arrive at our truths,” he said. “And once you start pushing at that door, you find it’s a vast subject.”
“How mathematicians go about research isn’t generally portrayed well in popular media. People tend to see mathematics as this pure quest, where we just arrive at great truths by pure thought alone. But mathematics is about guesses — often wrong guesses. It’s an experimental process. We learn in stages…
Quanta spoke with Granville about the nature of mathematical proof — from how proofs work in practice to popular misconceptions about them, to how proof-writing might evolve in the age of artificial intelligence…
[excerpts for that interview follow…]
How mathematicians go about research isn’t generally portrayed well in popular media. People tend to see mathematics as this pure quest, where we just arrive at great truths by pure thought alone. But mathematics is about guesses — often wrong guesses. It’s an experimental process. We learn in stages…
The culture of mathematics is all about proof. We sit around and think, and 95% of what we do is proof. A lot of the understanding we gain is from struggling with proofs and interpreting the issues that come up when we struggle with them…
The main point of a proof is to persuade the reader of the truth of an assertion. That means verification is key. The best verification system we have in mathematics is that lots of people look at a proof from different perspectives, and it fits well in a context that they know and believe. In some sense, we’re not saying we know it’s true. We’re saying we hope it’s correct, because lots of people have tried it from different perspectives. Proofs are accepted by these community standards.
Then there’s this notion of objectivity — of being sure that what is claimed is right, of feeling like you have an ultimate truth. But how can we know we’re being objective? It’s hard to take yourself out of the context in which you’ve made a statement — to have a perspective outside of the paradigm that has been put in place by society. This is just as true for scientific ideas as it is for anything else…
[Granville runs through a history of the proof, from Aristotle, through Euclid, to Hilbert, then Russel and Whitehead, ending with Gödel…]
To discuss mathematics, you need a language, and a set of rules to follow in that language. In the 1930s, Gödel proved that no matter how you select your language, there are always statements in that language that are true but that can’t be proved from your starting axioms. It’s actually more complicated than that, but still, you have this philosophical dilemma immediately: What is a true statement if you can’t justify it? It’s crazy.
So there’s a big mess. We are limited in what we can do.
Professional mathematicians largely ignore this. We focus on what’s doable. As Peter Sarnak likes to say, “We’re working people.” We get on and try to prove what we can…
[Granville then turns to computers…]
We’ve moved to a different place, where computers can do some wild things. Now people say, oh, we’ve got this computer, it can do things people can’t. But can it? Can it actually do things people can’t? Back in the 1950s, Alan Turing said that a computer is designed to do what humans can do, just faster. Not much has changed.
For decades, mathematicians have been using computers — to make calculations that can help guide their understanding, for instance. What AI can do that’s new is to verify what we believe to be true. Some terrific developments have happened with proof verification. Like [the proof assistant] Lean, which has allowed mathematicians to verify many proofs, while also helping the authors better understand their own work, because they have to break down some of their ideas into simpler steps to feed into Lean for verification.
But is this foolproof? Is a proof a proof just because Lean agrees it’s one? In some ways, it’s as good as the people who convert the proof into inputs for Lean. Which sounds very much like how we do traditional mathematics. So I’m not saying that I believe something like Lean is going to make a lot of errors. I’m just not sure it’s any more secure than most things done by humans…
Perhaps it could assist in creating a proof. Maybe in five years’ time, I’ll be saying to an AI model like ChatGPT, “I’m pretty sure I’ve seen this somewhere. Would you check it out?” And it’ll come back with a similar statement that’s correct.
And then once it gets very, very good at that, perhaps you could go one step further and say, “I don’t know how to do this, but is there anybody who’s done something like this?” Perhaps eventually an AI model could find skilled ways to search the literature to bring tools to bear that have been used elsewhere — in a way that a mathematician might not foresee.
However, I don’t understand how ChatGPT can go beyond a certain level to do proofs in a way that outstrips us. ChatGPT and other machine learning programs are not thinking. They are using word associations based on many examples. So it seems unlikely that they will transcend their training data. But if that were to happen, what will mathematicians do? So much of what we do is proof. If you take proofs away from us, I’m not sure who we become…
Eminently worth reading in full: “Why Mathematical Proof Is a Social Compact,” in @QuantaMagazine.
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As we add it up, we might send carefully calculated birthday greetings to Edward G. Begle; he was born on this date in 1914. A mathematician who was an accomplished topologist, he is best remembered for his role as the director of the School Mathematics Study Group (SMSG), the primary group credited for developing what came to be known as The New Math (a pedagogical response to Sputnik, taught in American grade schools from the late 1950s through the 1970s)… which will be well-known to (if not necessarily fondly recalled by) readers of a certain age.
“Poverty is the worst form of violence”*…
Two economic historians, Peter A. Coclanis and Louis M. Kyriakoudes, on why about 20% of counties in the U.S. South are marked by “persistent poverty”…
For a brief moment in the summer of 2023, the surprise No. 1 song “Rich Men North of Richmond” focused the country’s attention on a region that often gets overlooked in discussions of the U.S. economy. Although the U.S. media sometimes pays attention to the rural South — often concentrating on guns, religion and opioid overdoses — it has too often neglected the broad scope and root causes of the region’s current problems.
As economic historians based in North Carolina and Tennessee, we want a fuller version of the story to be told. Various parts of the rural South are struggling, but here we want to focus on the forlorn areas that the U.S. Department of Agriculture refers to as “rural manufacturing counties” — places where manufacturing is, or traditionally was, the main economic activity.
You can find such counties in every Southern state, although they were historically clustered in Alabama, Georgia, North and South Carolina, and Tennessee. And they are suffering terribly.
First, let’s back up. One might be tempted to ask: Are things really that bad? Hasn’t the Sun Belt been booming? But in fact, by a range of economic indicators — personal income per capita and the proportion of the population living in poverty, for starters – large parts of the South, and particularly the rural South, are struggling.
Gross domestic product per capita in the region has been stuck at about 90% of the national average for decades, with average income even lower in rural areas. About 1 in 5 counties in the South is marked by “persistent poverty” — a poverty rate that has stayed above 20% for three decades running. Indeed, fully 80% of all persistently poor counties in the U.S. are in the South.
Persistent poverty is, of course, linked to a host of other problems. The South’s rural counties are marked by low levels of educational attainment, measured both by high school and college graduation rates. Meanwhile, labor-force participation rates in the South are far lower than in the nation as a whole.
Unsurprisingly, these issues stifle economic growth.
Meanwhile, financial institutions have fled the region: The South as a whole lost 62% of its banks between 1980 and 2020, with the decline sharpest in rural areas. At the same time, local hospitals and medical facilities have been shuttering, while funding for everything from emergency services to wellness programs has been cut.
Relatedly, the rural South is ground zero for poor health in the U.S., with life expectancy far lower than the national average. So-called “deaths of despair” such as suicides and accidental overdoses are common, and rates of obesity, diabetes, hypertension, heart disease and stroke are high – much higher than in rural areas in other parts of the U.S. and in the U.S. as a whole…
Although some people think that these areas have forever been in crisis, this isn’t the case. While the South’s agricultural sector had fallen into long-term decline in the decades following the Civil War — essentially collapsing by the Great Depression — the onset of World War II led to an impressive economic growth spurt.
War-related jobs opening up in urban areas pulled labor out of rural areas, leading to a long-delayed push to mechanize agriculture. Workers rendered redundant by such technology came to constitute a large pool of cheap labor that industrialists seized upon to deploy in low-wage processing and assembly operations, generally in rural areas and small towns.
Such operations surged between 1945 and the early 1980s, playing a huge role in the region’s economic rise. However humble they may have been, in the South — as in China since the late 1970s — the shift out of a backward agricultural sector into low-wage, low-skill manufacturing was an opportunity for significant productivity and efficiency gains.
This helped the South steadily catch up to national norms in terms of per-capita income: to 75% by 1950, 80% by the mid-1960s, over 85% by 1970, and to almost 90% by the early 1980s…
By the early 1980s, however, the gains made possible by the shift out of agriculture began to play themselves out. The growth of the rural manufacturing sector slowed, and the South’s convergence upon national per capita income norms stopped, remaining stuck at about 90% from then on.
Two factors were largely responsible: new technologies, which reduced the number of workers needed in manufacturing, and globalization, which greatly increased competition. This latter point became increasingly important, since the South, a low-cost manufacturing region in the U.S., is a high-cost manufacturing region when compared to, say, Mexico.
Like Mike Campbell’s bankruptcy in Hemingway’s “The Sun Also Rises,” the rural South’s collapse came gradually, then suddenly: gradually during the 1980s and 1990s, and suddenly after China’s entry into the World Trade Organization in December 2001…
A sobering read: “Poor men south of Richmond? Why much of the rural South is in economic crisis.”
* Mahatma Gandhi
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As we dive into the dynamics of development, we might recall that it was on this date in 1718 that the famous pirate Edward Teach– better known as Blackbeard– was killed off the coast of North Carolina.
Edward Teach, also known as Blackbeard, is killed off North Carolina’s Outer Banks during a bloody battle with a British navy force sent from Virginia.
Believed to be a native of England, Edward Teach likely began his pirating career in 1713, when he became a crewman aboard a Caribbean sloop commanded by pirate Benjamin Hornigold. In 1717, after Hornigold accepted an offer of general amnesty by the British crown and retired as a pirate, Teach took over a captured 26-gun French merchantman, increased its armament to 40 guns, and renamed it the Queen Anne’s Revenge.
During the next six months, the Queen Anne’s Revenge served as the flagship of a pirate fleet featuring up to four vessels and more than 200 men. Teach became the most infamous pirate of his day, winning the popular name of Blackbeard for his long, dark beard, which he was said to light on fire during battles to intimidate his enemies. Blackbeard’s pirate forces terrorized the Caribbean and the southern coast of North America and were notorious for their cruelty.
In May 1718, the Queen Anne’s Revenge and another vessel were shipwrecked, forcing Blackbeard to desert a third ship and most of his men because of a lack of supplies. With the single remaining ship, Blackbeard sailed to Bath in North Carolina and met with Governor Charles Eden. Eden agreed to pardon Blackbeard in exchange for a share of his sizable booty.
At the request of North Carolina planters, Governor Alexander Spotswood of Virginia dispatched a British naval force under Lieutenant Robert Maynard to North Carolina to deal with Blackbeard. On November 22, Blackbeard’s forces were defeated and he was killed in a bloody battle of Ocracoke Island. Legend has it that Blackbeard, who captured more than 30 ships in his brief pirating career, received five musket-ball wounds and 20 sword lacerations before dying…
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“Any fool can know. The point is to understand.”*…
… and, Rachael Scarborough King and Seth Rudy argue, to serve a clear purpose…
Right now, many forms of knowledge production seem to be facing their end. The crisis of the humanities has reached a tipping point of financial and popular disinvestment, while technological advances such as new artificial intelligence programmes may outstrip human ingenuity. As news outlets disappear, extreme political movements question the concept of objectivity and the scientific process. Many of our systems for producing and certifying knowledge have ended or are ending.
We want to offer a new perspective by arguing that it is salutary – or even desirable – for knowledge projects to confront their ends. With humanities scholars, social scientists and natural scientists all forced to defend their work, from accusations of the ‘hoax’ of climate change to assumptions of the ‘uselessness’ of a humanities degree, knowledge producers within and without academia are challenged to articulate why they do what they do and, we suggest, when they might be done. The prospect of an artificially or externally imposed end can help clarify both the purpose and endpoint of our scholarship.
We believe the time has come for scholars across fields to reorient their work around the question of ‘ends’. This need not mean acquiescence to the logics of either economic utilitarianism or partisan fealty that have already proved so damaging to 21st-century institutions. But avoiding the question will not solve the problem. If we want the university to remain a viable space for knowledge production, then scholars across disciplines must be able to identify the goal of their work – in part to advance the Enlightenment project of ‘useful knowledge’ and in part to defend themselves from public and political mischaracterisation.
Our volume The Ends of Knowledge: Outcomes and Endpoints Across the Arts and Sciences (2023) asks how we should understand the ends of knowledge today. What is the relationship between an individual knowledge project – say, an experiment on a fruit fly, a reading of a poem, or the creation of a Large Language Model – and the aim of a discipline or field? In areas ranging from physics to literary studies to activism to climate science, we asked practitioners to consider the ends of their work – its purpose – as well as its end: the point at which it might be complete. The responses showed surprising points of commonality in identifying the ends of knowledge, as well as the value of having the end in sight…
Read on for a provocative case that academics need to think harder about the purpose of their disciplines and a consideration of whether some of those should come to an end: “The Ends of Knowledge,” in @aeonmag.
* Albert Einstein
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As we contemplate conclusions, we might recall that it was on this date in 1869 that the first issue of the journal Nature was published. Taking it’s title from a line of Wordsworth’s (“To the solid ground of nature trusts the Mind that builds for aye”), its aim was to “provide cultivated readers with an accessible forum for reading about advances in scientific knowledge.” It remains a weekly, international, interdisciplinary journal of science, one of the few remaining that publish across a wide array of fields. It is consistently ranked the world’s most cited scientific journal and is ascribed an impact factor of approximately 64.8, making it one of the world’s top academic journals.
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