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The geometric zen of solving Rubik’s Cubes

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I’ve never been a great fan of Rubik’s Cubes (or chess, or crossword puzzles, or Scrabble, or most obsession-rewarding, intelligence-test-ish popular puzzle games), but it is rewarding for me to read about the cubes and the people who find themselves in solving the puzzle. (It’s still a $250-million-a-year product! The greatest selling single toy of all time.)

Once you’ve defined your goal—“I want to align this orange face with this other orange face”—you can follow a series of steps to accomplish it. An ease with algorithms, they note, is increasingly important in a world dominated by science, technology, engineering, and math, or STEM. The logic of the Rubik’s cube has, after all, been used by software developers to craft encryption schemes for software for decades. It has 43 quintillion possible combinations—and only one solution.

Puzzling out this 3-D game can also help students hone their spatial thinking skills, according to the presenters. And spatial thinking skills are intimately connected to success in any STEM field. “To think spatially,” the National Academies of Science, Engineering, and Medicine write, “entails knowing about” space, representation, and reasoning. This is the kind of knowledge we tap into every day, when timing our commutes or taking detours, reading maps, and, yes, solving Rubik’s cubes.

Maybe I should give that old cube another try.

Tags: math   toys
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kraymer
2266 days ago
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Mr. Money Mustache, UBER Driver

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kraymer
2566 days ago
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The Dying Art of Disagreement

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So illustrious is the list that, on second thought, I’m beginning to regret that you didn’t disinvite me after all.

The title of my talk tonight is “The Dying Art of Disagreement.” This is a subject that is dear to me — literally dear — since disagreement is the way in which I have always earned a living. Disagreement is dear to me, too, because it is the most vital ingredient of any decent society.

To say the words, “I agree” — whether it’s agreeing to join an organization, or submit to a political authority, or subscribe to a religious faith — may be the basis of every community.

But to say, I disagree; I refuse; you’re wrong; etiam si omnes — ego non — these are the words that define our individuality, give us our freedom, enjoin our tolerance, enlarge our perspectives, seize our attention, energize our progress, make our democracies real, and give hope and courage to oppressed people everywhere. Galileo and Darwin; Mandela, Havel, and Liu Xiaobo; Rosa Parks and Natan Sharansky — such are the ranks of those who disagree.

And the problem, as I see it, is that we’re failing at the task.

This is a puzzle. At least as far as far as the United States is concerned, Americans have rarely disagreed more in recent decades.

We disagree about racial issues, bathroom policies, health care laws, and, of course, the 45th president. We express our disagreements in radio and cable TV rants in ways that are increasingly virulent; street and campus protests that are increasingly violent; and personal conversations that are increasingly embittering.

This is yet another age in which we judge one another morally depending on where we stand politically.

Nor is this just an impression of the moment. Extensive survey data show that Republicans are much more right-leaning than they were twenty years ago, Democrats much more left-leaning, and both sides much more likely to see the other as a mortal threat to the nation’s welfare.

The polarization is geographic, as more people live in states and communities where their neighbors are much likelier to share their politics.

The polarization is personal: Fully 50 percent of Republicans would not want their child to marry a Democrat, and nearly a third of Democrats return the sentiment. Interparty marriage has taken the place of interracial marriage as a family taboo.

Finally the polarization is electronic and digital, as Americans increasingly inhabit the filter bubbles of news and social media that correspond to their ideological affinities. We no longer just have our own opinions. We also have our separate “facts,” often the result of what different media outlets consider newsworthy. In the last election, fully 40 percent of Trump voters named Fox News as their chief source of news.

Thanks a bunch for that one, Australia.

It’s usually the case that the more we do something, the better we are at it. Instead, we’re like Casanovas in reverse: the more we do it, the worse we’re at it. Our disagreements may frequently hoarsen our voices, but they rarely sharpen our thinking, much less change our minds.

It behooves us to wonder why.

* * *

Thirty years ago, in 1987, a philosophy professor at the University of Chicago named Allan Bloom — at the time best known for his graceful translations of Plato’s “Republic” and Rousseau’s “Emile” — published a learned polemic about the state of higher education in the United States. It was called “The Closing of the American Mind.”

The book appeared when I was in high school, and I struggled to make my way through a text thick with references to Plato, Weber, Heidegger and Strauss. But I got the gist — and the gist was that I’d better enroll in the University of Chicago and read the great books. That is what I did.

What was it that one learned through a great books curriculum? Certainly not “conservatism” in any contemporary American sense of the term. We were not taught to become American patriots, or religious pietists, or to worship what Rudyard Kipling called “the Gods of the Market Place.” We were not instructed in the evils of Marxism, or the glories of capitalism, or even the superiority of Western civilization.

As I think about it, I’m not sure we were taught anything at all. What we did was read books that raised serious questions about the human condition, and which invited us to attempt to ask serious questions of our own. Education, in this sense, wasn’t a “teaching” with any fixed lesson. It was an exercise in interrogation.

To listen and understand; to question and disagree; to treat no proposition as sacred and no objection as impious; to be willing to entertain unpopular ideas and cultivate the habits of an open mind — this is what I was encouraged to do by my teachers at the University of Chicago.

It’s what used to be called a liberal education.

The University of Chicago showed us something else: that every great idea is really just a spectacular disagreement with some other great idea.

Socrates quarrels with Homer. Aristotle quarrels with Plato. Locke quarrels with Hobbes and Rousseau quarrels with them both. Nietzsche quarrels with everyone. Wittgenstein quarrels with himself.

These quarrels are never personal. Nor are they particularly political, at least in the ordinary sense of politics. Sometimes they take place over the distance of decades, even centuries.

Most importantly, they are never based on a misunderstanding. On the contrary, the disagreements arise from perfect comprehension; from having chewed over the ideas of your intellectual opponent so thoroughly that you can properly spit them out.

In other words, to disagree well you must first understand well. You have to read deeply, listen carefully, watch closely. You need to grant your adversary moral respect; give him the intellectual benefit of doubt; have sympathy for his motives and participate empathically with his line of reasoning. And you need to allow for the possibility that you might yet be persuaded of what he has to say.

“The Closing of the American Mind” took its place in the tradition of these quarrels. Since the 1960s it had been the vogue in American universities to treat the so-called “Dead White European Males” of the Western canon as agents of social and political oppression. Allan Bloom insisted that, to the contrary, they were the best possible instruments of spiritual liberation.

He also insisted that to sustain liberal democracy you needed liberally educated people. This, at least, should not have been controversial. For free societies to function, the idea of open-mindedness can’t simply be a catchphrase or a dogma. It needs to be a personal habit, most of all when it comes to preserving an open mind toward those with whom we disagree.

* * *

That habit was no longer being exercised much 30 years ago. And if you’ve followed the news from American campuses in recent years, things have become a lot worse.

According to a new survey from the Brookings Institution, a plurality of college students today — fully 44 percent — do not believe the First Amendment to the U.S. Constitution protects so-called “hate speech,” when of course it absolutely does. More shockingly, a narrow majority of students — 51 percent — think it is “acceptable” for a student group to shout down a speaker with whom they disagree. An astonishing 20 percent also agree that it’s acceptable to use violence to prevent a speaker from speaking.

These attitudes are being made plain nearly every week on one college campus or another.

There are speakers being shouted down by organized claques of hecklers — such was the experience of Israeli ambassador Michael Oren at the University of California, Irvine. Or speakers who require hundreds of thousands of dollars of security measures in order to appear on campus — such was the experience of conservative pundit Ben Shapiro earlier this month at Berkeley. Or speakers who are physically barred from reaching the auditorium — that’s what happened to Heather MacDonald at Claremont McKenna College in April. Or teachers who are humiliated by their students and hounded from their positions for allegedly hurting students’ feelings — that’s what happened to Erika and Nicholas Christakis of Yale.

And there is violence. Listen to a description from Middlebury College professor Allison Stanger of what happened when she moderated a conversation with the libertarian scholar Charles Murray in March:

The protesters succeeded in shutting down the lecture. We were forced to move to another site and broadcast our discussion via live stream, while activists who had figured out where we were banged on the windows and set off fire alarms. Afterward, as Dr. Murray and I left the building . . . a mob charged us.

Most of the hatred was focused on Dr. Murray, but when I took his right arm to shield him and to make sure we stayed together, the crowd turned on me. Someone pulled my hair, while others were shoving me. I feared for my life. Once we got into the car, protesters climbed on it, hitting the windows and rocking the vehicle whenever we stopped to avoid harming them. I am still wearing a neck brace, and spent a week in a dark room to recover from a concussion caused by the whiplash.

Middlebury is one of the most prestigious liberal-arts colleges in the United States, with an acceptance rate of just 16 percent and tuition fees of nearly $50,000 a year. How does an elite institution become a factory for junior totalitarians, so full of their own certitudes that they could indulge their taste for bullying and violence?

There’s no one answer. What’s clear is that the mis-education begins early. I was raised on the old-fashioned view that sticks and stones could break my bones but words would never hurt me. But today there’s a belief that since words can cause stress, and stress can have physiological effects, stressful words are tantamount to a form of violence. This is the age of protected feelings purchased at the cost of permanent infantilization.

The mis-education continues in grade school. As the Brookings findings indicate, younger Americans seem to have no grasp of what our First Amendment says, much less of the kind of speech it protects. This is a testimony to the collapse of civics education in the United States, creating the conditions that make young people uniquely susceptible to demagogy of the left- or right-wing varieties.

Then we get to college, where the dominant mode of politics is identity politics, and in which the primary test of an argument isn’t the quality of the thinking but the cultural, racial, or sexual standing of the person making it. As a woman of color I think X. As a gay man I think Y. As a person of privilege I apologize for Z. This is the baroque way Americans often speak these days. It is a way of replacing individual thought — with all the effort that actual thinking requires — with social identification — with all the attitude that attitudinizing requires.

In recent years, identity politics have become the moated castles from which we safeguard our feelings from hurt and our opinions from challenge. It is our “safe space.” But it is a safe space of a uniquely pernicious kind — a safe space from thought, rather than a safe space for thought, to borrow a line I recently heard from Salman Rushdie.

Another consequence of identity politics is that it has made the distance between making an argument and causing offense terrifyingly short. Any argument that can be cast as insensitive or offensive to a given group of people isn’t treated as being merely wrong. Instead it is seen as immoral, and therefore unworthy of discussion or rebuttal.

The result is that the disagreements we need to have — and to have vigorously — are banished from the public square before they’re settled. People who might otherwise join a conversation to see where it might lead them choose instead to shrink from it, lest they say the “wrong” thing and be accused of some kind of political -ism or -phobia. For fear of causing offense, they forego the opportunity to be persuaded.

Take the arguments over same-sex marriage, which you are now debating in Australia. My own views in favor of same-sex marriage are well known, and I hope the Yes’s wins by a convincing margin.

But if I had to guess, I suspect the No’s will exceed whatever they are currently polling. That’s because the case for same-sex marriage is too often advanced not by reason, but merely by branding every opponent of it as a “bigot” — just because they are sticking to an opinion that was shared across the entire political spectrum only a few years ago. Few people like outing themselves as someone’s idea of a bigot, so they keep their opinions to themselves even when speaking to pollsters. That’s just what happened last year in the Brexit vote and the U.S. presidential election, and look where we are now.

If you want to make a winning argument for same-sex marriage, particularly against conservative opponents, make it on a conservative foundation: As a matter of individual freedom, and as an avenue toward moral responsibility and social respectability. The No’s will have a hard time arguing with that. But if you call them morons and Neanderthals, all you’ll get in return is their middle finger or their clenched fist.

One final point about identity politics: It’s a game at which two can play. In the United States, the so-called “alt-right” justifies its white-identity politics in terms that are coyly borrowed from the progressive left. One of the more dismaying features of last year’s election was the extent to which “white working class” became a catchall identity for people whose travails we were supposed to pity but whose habits or beliefs we were not supposed to criticize. The result was to give the Trump base a moral pass it did little to earn.

* * *

So here’s where we stand: Intelligent disagreement is the lifeblood of any thriving society. Yet we in the United States are raising a younger generation who have never been taught either the how or the why of disagreement, and who seem to think that free speech is a one-way right: Namely, their right to disinvite, shout down or abuse anyone they dislike, lest they run the risk of listening to that person — or even allowing someone else to listen. The results are evident in the parlous state of our universities, and the frayed edges of our democracies.

Can we do better?

This is supposed to be a lecture on the media, and I’d like to conclude this talk with a word about the role that editors and especially publishers can play in ways that might improve the state of public discussion rather than just reflect and accelerate its decline.

I began this talk by noting that Americans have rarely disagreed so vehemently about so much. On second thought, this isn’t the whole truth.

Yes, we disagree constantly. But what makes our disagreements so toxic is that we refuse to make eye contact with our opponents, or try to see things as they might, or find some middle ground.

Instead, we fight each other from the safe distance of our separate islands of ideology and identity and listen intently to echoes of ourselves. We take exaggerated and histrionic offense to whatever is said about us. We banish entire lines of thought and attempt to excommunicate all manner of people — your humble speaker included — without giving them so much as a cursory hearing.

The crucial prerequisite of intelligent disagreement — namely: shut up; listen up; pause and reconsider; and only then speak — is absent.

Perhaps the reason for this is that we have few obvious models for disagreeing well, and those we do have — such as the Intelligence Squared debates in New York and London or Fareed Zakaria’s show on CNN — cater to a sliver of elite tastes, like classical music.

Fox News and other partisan networks have demonstrated that the quickest route to huge profitability is to serve up a steady diet of high-carb, low-protein populist pap. Reasoned disagreement of the kind that could serve democracy well fails the market test. Those of us who otherwise believe in the virtues of unfettered capitalism should bear that fact in mind.

I do not believe the answer, at least in the U.S., lies in heavier investment in publicly sponsored television along the lines of the BBC. It too, suffers, from its own form of ideological conformism and journalistic groupthink, immunized from criticism due to its indifference to competition.

Nor do I believe the answer lies in a return to what in America used to be called the “Fairness Doctrine,” mandating equal time for different points of view. Free speech must ultimately be free, whether or not it’s fair.

But I do think there’s such a thing as private ownership in the public interest, and of fiduciary duties not only to shareholders but also to citizens. Journalism is not just any other business, like trucking or food services. Nations can have lousy food and exemplary government, as Great Britain demonstrated for most of the last century. They can also have great food and lousy government, as France has always demonstrated.

But no country can have good government, or a healthy public square, without high-quality journalism — journalism that can distinguish a fact from a belief and again from an opinion; that understands that the purpose of opinion isn’t to depart from facts but to use them as a bridge to a larger idea called “truth”; and that appreciates that truth is a large enough destination that, like Manhattan, it can be reached by many bridges of radically different designs. In other words, journalism that is grounded in facts while abounding in disagreements.

I believe it is still possible — and all the more necessary — for journalism to perform these functions, especially as the other institutions that were meant to do so have fallen short. But that requires proprietors and publishers who understand that their role ought not to be to push a party line, or be a slave to Google hits and Facebook ads, or provide a titillating kind of news entertainment, or help out a president or prime minister who they favor or who’s in trouble.

Their role is to clarify the terms of debate by championing aggressive and objective news reporting, and improve the quality of debate with commentary that opens minds and challenges assumptions rather than merely confirming them.

This is journalism in defense of liberalism, not liberal in the left-wing American or right-wing Australian sense, but liberal in its belief that the individual is more than just an identity, and that free men and women do not need to be protected from discomfiting ideas and unpopular arguments. More than ever, they need to be exposed to them, so that we may revive the arts of disagreement that are the best foundation of intelligent democratic life.

The honor the Lowy Institute does tonight’s nominees is an important step in that direction. What they have uncovered, for the rest of you to debate, is the only way by which our democracies can remain rational, reasonable, and free.

Correction: September 26, 2017

An earlier version of this article misidentified Charles Murray’s host for his speech at Middlebury College. He was invited by the campus American Enterprise Institute Club and the political science department, not by Prof. Allison Stanger.

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kraymer
2626 days ago
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Philippot : le couscous de la discorde

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On se plaint parfois que l'Internet démarre au quart de tour pour la moindre polémique. Mais là, franchement, y a de quoi.

Le patriote Florian Philippot a été photographié en train de manger un couscous à Strasbourg. Rien que ça. La fachosphère est depuis en ébullition et de nombreux militants FN crient au scandale, comme l'a remarqué Buzzfeed.

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2638 days ago
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100+ exceptional works of journalism from 2016

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Each year, in one of my favorite media traditions, Conor Friedersdorf picks dozens of articles, essays, podcasts, and stories from the previous year “that stood the test of time”. Here’s his just-published installment for this year.

Friedersdorf has a keen eye (and ear) for good stories. Shamefully, I’ve read maybe 10% of the articles listed here…I’ve dropped my longform reading in recent years in favor of books, TV, and being out in the real world. Maybe on my next vacation, instead of a book, I’ll tackle this list instead.

Tags: best of   best of 2016   Conor Friedersdorf   lists
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2647 days ago
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The Nuclear Potato Cannon Part 2

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As described in an earlier post (see above) in 1957, the Soviet scientists launched Sputnik from the Baikonur Cosmodrome in what is now Kazakhstan. But was it the first man made object shot into space? Maybe, maybe not.

The nuclear test code named Bernalillo had a nuclear device which was relatively puny, having explosive equivalent of less than a kiloton of high explosive. But, small in nuclear terms is still very large and loosing large amounts of energy has hard-to-predict effects.

Dr. Brownlee said that the the scientists working on Bernalillo were trying to figure out what happens during the few micro-moments of the nuclear explosion. The Los Alamos team was testing the feasibility of underground nuclear testing, as an alternative to spreading radiation in the atmosphere with above ground tests. If underground testing was to suceed, then the experiments had to be designed such that scientists could track what kind of nuclear particles were emitted, how many there were, and where they were going.

The data they needed to collect had to be measured in the first few "shakes" after the detonation. A "shake," Brownlee told me, is a unit of time peculiar to nuclear scientists. It is the amount of time it takes light to travel 10 feet. Since light travels at 186,000 miles per second, that makes a shake about equal to 10 nanoseconds, or 1/100,000,000 of a second. That's a small time interval.

When the device was triggered, the scientists evidently got a bit more than they bargained for. The fissioning core emitted high energy particles of light, called photons. In the first few shakes of time, the photons, (or in the quaint lingo of Los Alamos’ tech community, the "shine"), bombarded the steel pipe lining the well, vaporizing it into superheated iron gas. About one third of a millisecond after detonation, the shockwave of gas, shine, and radiation blasted against the steel cover plate at the top of the well.

Brownlee and team had mounted high speed cameras near the well cover to record the blast effects. What the film showed is this: in one frame the steel cover plate is there. In the next frame, it is gone. Where did the 4-foot diameter, Jersey-cow-sized steel plate go? The area was searched carefully, but wasn't found. In fact, in the 40 plus years since project Bernllilo, no trace of the plate has ever been found, anywhere.

Dr. Brownlee told me about the high speed cameras used to record the test. In the film sequence, the plate was there in one frame of the high speed film, and gone in the next. I'm told that the film ran at 160 frames per second, so obviously the time interval between frames was 1/160 of a second. He also said that the field of view, or the vertical area in view in the camera frame captured an area of roughly about one quarter of a mile. Therefore, I reason that the steel plate traversed an area of one quarter mile in less than 1/160 of a second. That calculates out to a speed of an amazing 41 miles per second.

My understanding of Newtonian physics is that you throw something hard enough and fast enough, you can make it through the gravitational attraction of the earth and break free into outer space. The speed required to break free is what Newton called "escape velocity" and on earth is calculated to be just less than seven miles per second on earth. The Los Alamos plate was propelled by the atomic cannon into the summer sky at a speed of more than five times escape velocity.

So, it looks to me that the Los Alamos nuclear potato cannon won the space race. At least, that’s my theory. I’m not stuck on it, but I’ll stand by it until somebody proves (not speculates) otherwise.

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2652 days ago
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