Brain Pickings

Posts Tagged ‘education’

25 SEPTEMBER, 2012

Measurement: Exploring the Whimsy of Math through Playful Patterns, Shape and Motion

By:

“What makes a mathematician is not technical skill or encyclopedic knowledge but insatiable curiosity and a desire for simple beauty.”

Math, as Vi Hart’s stop-motion doodles, Robin Moore’s string portraits, and Anatolii Fomenko’s stunning black-and-white illustrations have previously shown us, can be the conduit of great fun and great beauty. In Measurement (public library), mathematician Paul Lockhart invites us to “make patterns of shape and motion, and then [try] to understand our patterns and measure them.” (Because, lest we forget, we have a natural penchant for patterns.) What results as we step away from physical reality and immerse ourselves in the imaginary — and imaginative — world of mathematical reality is a thing of infinite beauty and infinite fascination.

Lockhart writes in the introduction:

Physical reality is a disaster. It’s way too complicated, and nothing is at all what it appears to be. Objects expand and contract with temperature, atoms fly on and off. In particular, nothing can truly be measured. A blade of grass has no actual length. Any measurement made in the universe is necessarily a rough approximation. It’s not bad; it’s just the nature of the place. The smallest speck is not a point, and the thinnest wire is not a line.

Mathematical reality, on the other hand, is imaginary. It can be as simple and pretty as I want it to be. I get to have all those perfect things I can’t have in real life. I can never hold a circle in my hand, but I can hold one in my mind.

[…]

The point is I get to have them both — physical reality and mathematical reality. Both are beautiful and interesting… The former is important to me because I am in i, the latter because it is in me.

Lockhart underpins this excitement with a fair warning:

Mathematical reality is an infinite jungle full of enchanting mysteries, but the jungle does not give up its secrets easily. Be prepared to struggle, both intellectually and creatively.

And yet, he’s quick to reassure that the gold standard of math, not unlike that of science, isn’t the answer but the driver of curiosity:

What makes a mathematician is not technical skill or encyclopedic knowledge but insatiable curiosity and a desire for simple beauty.

But what makes Lockhart particularly compelling is his ability to relate mathematics to parallel concepts from disciplines and aspects of life that are more familiar, more comfortable, more ingrained in our everyday understanding of the world — for instance, in comparing math to storytelling:

A mathematical argument [is] otherwise known as a proof. A proof is simply a story. The characters are the elements of the problem, and the plot is up to you. The goal, as in any literary fiction, is to write a story that is compelling as a narrative. In the case of mathematics, this means that the plot not only has to make logical sense but also be simple and elegant. No one likes a meandering, complicated quagmire of a proof. We want to follow along rationally to be sure, but we also want to be charmed and swept off our feet aesthetically. A proof should be lovely as well as logical.

In a nod to the value of “useless” knowledge and figuring things out, Lockhart argues:

People don’t do mathematics because it’s useful. They do it because it’s interesting … The point of a measurement problem is not what the measurement is; it’s how to figure out what it is.

He ultimately offers several pieces of advice on engaging with math:

  1. The best problems are your own. Mathematical reality is yours — it’s in your head for you to explore any time you feel like it… Don’t be afraid that you can’t answer your own questions — that’s the natural state of the mathematician.
  2. Collaborate. Work together and share the joys and frustrations. It’s a lot like playing music together.
  3. Improve your proofs. Just because you have an explanation doesn’t mean it’s the best explanation. Can you eliminate any unnecessary clutter or complexity? Can you find an entirely different approach that gives you deeper insight? Prove, prove, and prove again. Painters, sculptors, and poets do the same thing.
  4. Let a problem take you where it takes you. If you come across a river in the jungle, follow it!
  5. Critique your work. Subject your arguments to scathing criticism by yourself and others. That’s what all artists do, especially mathematicians… For a piece of mathematics to fully qualify as such, it has to stand up to two very different kids of criticism: it must be logically sound and convincing as a rational argument, and it must also be elegant, revelatory, and emotionally satisfying. [But don’t] worry about trying to hold yourself to some impossibly high standard of aesthetic excellence.

Lockhart elaborates on the latter point with a poignant reflection that applies to math just as much as it does to life itself:

Part of the problem is that we are so concerned with our ideas being simple and beautiful that when we do have a pretty idea, we want so much to believe it. We want it to be true so badly that we don’t always give it the careful scrutiny that we should read. It’s the mathematical version of ‘rapture of the deep.’ Divers see beautiful sights that they forget to come up for air. Well, logic is our air, and careful reasoning is how we breathe.

Indeed, much of math sounds an awful lot like the art of living itself: Take for instance, that same old fear of failure that often stands in the way of creativity, which also holds us back from immersing ourselves in the art of figuring things out:

The important thing is not to be afraid. So you try some crazy idea, and it doesn’t work. That puts you in some pretty good company! Archimedes, Gauss, you and I — we’re all groping our way through mathematical reality, trying to understand what is going on, making guesses, trying out ideas, mostly failing. And then every once in a while, you succeed… And that feeling of unlocking an eternal mystery is what keeps you going back to the jungle to get scratched up all over again.

Here’s a little teaser for the whimsical jungle of mathematical reality and the logical aesthetic of math:

Measurement, from Harvard University Press, comes seven years after Lockhart’s exquisite critique of math’s tragic fate in contemporary education, A Mathematician’s Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form.

Brain Pickings has a free weekly newsletter and people say it’s cool. It comes out on Sundays and offers the week’s best articles. Here’s what to expect. Like? Sign up.

24 SEPTEMBER, 2012

Neil deGrasse Tyson on Scientific Literacy, Education, and the Poetry of the Cosmos

By:

“Science is a way of equipping yourself with the tools to interpret what happens in front of you.”

“People,” lamented Richard Feynman in 1964, “I mean the average person, the great majority of people, the enormous majority of people — are woefully, pitifully, absolutely ignorant of the science of the world that they live in.” In the half-century since, we’ve sequenced the human genome, put a man on the moon and rovers on Mars, confirmed the existence of the Higgs “God particle” boson, and achieved innumerable scientific miracles, small and large, that enhance our daily lives in fundamental ways. And yet, bad science spreads, good science journalism is fighting an uphill battle against media reductionism and distortion, and the general public remains as just as woefully and pitifully distrustful of or, worse yet, unconcerned with science as in the Feynman days.

In this fantastic conversation with Stephen Colbert, Hayden Planetarium director Neil deGrasse Tyson — passionate crusader for space exploration, eloquent champion of the whimsy of the cosmos, modern-day Richard “Great Explainer” Feynman — brings his characteristic blend of sharp insight, quick wit, and unapologetic opinion to the issue of scientific literacy and how it relates to everything from education to government spending to morality.

Highlights below, though the entire hour-long conversation — including the most brilliant and hilarious James Cameron Titanic critique you’ll ever hear — is more than worth the time.

On the ethics of discovery vs. the broader morality of application:

We are collectively part of a society that is using or not using, to its benefit or its detriment, the discoveries of science. And at the end of the day, a discovery itself is not moral — it’s our application of it that has to pass that test.

On the misunderstanding of science:

[Science] is distrusted not because of what it can do, but because people don’t understand how it does what it can do — and that absence of understanding, or misunderstanding, of the power of science is what makes people afraid. … Just because you don’t understand it, doesn’t mean it’s bad for you — go figure out how it works! That’s why we need a scientifically literate electorate — so that when you go to the polls, you can make an informed judgment and you can draw your own conclusions rather than tune into a particular TV station to have your conclusions handed to you.

On the poetry of astrophysics:

Some of the greatest poetry is revealing in the reader the beauty of something that is so simple you had taken it for granted. That, I think, is the job of the poet. The simplicity of the universe, if it doesn’t drive you to poetry it drives you to bask in the majesty of the cosmos.

On what’s wrong with education:

Our academic system rewards people who know a lot of stuff and, generally, we call those people ‘smart.’ But at the end of the day, who do you want: The person who can figure stuff out that they’ve never seen before, or the person who can rabble off a bunch of facts?

A brilliant addition to history’s best definitions of science:

[Science] is a way of equipping yourself with the tools to interpret what happens in front of you.

On our broken yardsticks for assessing the value of scientific research:

Today, you hear people say, ‘Why are we spending money up there when we’ve got problems on Earth?’ And people don’t connect the time-delay between the frontier of scientific research and how it’s going to transform your life later down the line. All they want is a quarterly report that shows the part that comes out of it — that is so short-sighted that it’s the beginning of the end of your culture.

He goes on to point out that people grossly misperceive how much is actually being spent “up there,” assuming anywhere between 10 and 15% of taxpayer money, whereas the real number is a mere 6/10 of a penny on the tax dollar, or 0.6%. The solution:

The greatest need is to be able to have the foresight necessary to make investments on the frontier of science even if, at the time you make those investments, you cannot figure out how that might make you rich tomorrow.

Finally, when Colbert asks the grandest cosmic question of all — why there is something instead of nothing — Tyson answers with a brilliant haiku-esque retort that hints at the power of ignorance as a tool of science:

Words that make questions
May not be questions
At all

Tyson’s latest book, Space Chronicles: Facing the Ultimate Frontier (public library), is a must-read.

Swiss-Miss

Donating = Loving

Bringing you (ad-free) Brain Pickings takes hundreds of hours each month. If you find any joy and stimulation here, please consider becoming a Supporting Member with a recurring monthly donation of your choosing, between a cup of tea and a good dinner:





You can also become a one-time patron with a single donation in any amount:





Brain Pickings has a free weekly newsletter. It comes out on Sundays and offers the week’s best articles. Here’s what to expect. Like? Sign up.

12 SEPTEMBER, 2012

This Is Water: David Foster Wallace on Life

By:

Revisiting the tragic literary hero’s only public insights on life.

On September 12, 2008, David Foster Wallace took his own life, becoming a kind of patron-saint of the “tortured genius” myth of creativity. Just three years prior to his suicide, he stepped onto the podium at Kenyon College and delivered one of the most timeless graduation speeches of all time — the only public talk he ever gave on his views of life. The speech, which includes a remark about suicide by firearms that came to be extensively discussed after DFW’s own eventual suicide, was published as a slim book titled This Is Water: Some Thoughts, Delivered on a Significant Occasion, about Living a Compassionate Life (public library).

You can hear the original delivery in two parts below, along with the the most poignant passages.

On solipsism and compassion, and the choice to see the other:

Here is just one example of the total wrongness of something I tend to be automatically sure of: everything in my own immediate experience supports my deep belief that I am the absolute centre of the universe; the realest, most vivid and important person in existence. We rarely think about this sort of natural, basic self-centredness because it’s so socially repulsive. But it’s pretty much the same for all of us. It is our default setting, hard-wired into our boards at birth. Think about it: there is no experience you have had that you are not the absolute centre of. The world as you experience it is there in front of YOU or behind YOU, to the left or right of YOU, on YOUR TV or YOUR monitor. And so on. Other people’s thoughts and feelings have to be communicated to you somehow, but your own are so immediate, urgent, real.

Please don’t worry that I’m getting ready to lecture you about compassion or other-directedness or all the so-called virtues. This is not a matter of virtue. It’s a matter of my choosing to do the work of somehow altering or getting free of my natural, hard-wired default setting which is to be deeply and literally self-centered and to see and interpret everything through this lens of self. People who can adjust their natural default setting this way are often described as being ‘well-adjusted’, which I suggest to you is not an accidental term.

On the double-edged sword of the intellect, which Einstein, Steve Jobs, and Anne Lamott have spoken to:

It is extremely difficult to stay alert and attentive, instead of getting hypnotized by the constant monologue inside your own head (may be happening right now). Twenty years after my own graduation, I have come gradually to understand that the liberal arts cliché about teaching you how to think is actually shorthand for a much deeper, more serious idea: learning how to think really means learning how to exercise some control over how and what you think. It means being conscious and aware enough to choose what you pay attention to and to choose how you construct meaning from experience. Because if you cannot exercise this kind of choice in adult life, you will be totally hosed. Think of the old cliché about ‘the mind being an excellent servant but a terrible master.’

This, like many clichés, so lame and unexciting on the surface, actually expresses a great and terrible truth. It is not the least bit coincidental that adults who commit suicide with firearms almost always shoot themselves in: the head. They shoot the terrible master. And the truth is that most of these suicides are actually dead long before they pull the trigger.

And I submit that this is what the real, no-bullshit value of your liberal arts education is supposed to be about: how to keep from going through your comfortable, prosperous, respectable adult life dead, unconscious, a slave to your head and to your natural default setting of being uniquely, completely, imperially alone day in and day out.

On empathy and kindness, echoing Einstein:

[P]lease don’t think that I’m giving you moral advice, or that I’m saying you are supposed to think this way, or that anyone expects you to just automatically do it. Because it’s hard. It takes will and effort, and if you are like me, some days you won’t be able to do it, or you just flat out won’t want to.

But most days, if you’re aware enough to give yourself a choice, you can choose to look differently at this fat, dead-eyed, over-made-up lady who just screamed at her kid in the checkout line. Maybe she’s not usually like this. Maybe she’s been up three straight nights holding the hand of a husband who is dying of bone cancer. Or maybe this very lady is the low-wage clerk at the motor vehicle department, who just yesterday helped your spouse resolve a horrific, infuriating, red-tape problem through some small act of bureaucratic kindness. Of course, none of this is likely, but it’s also not impossible. It just depends what you want to consider. If you’re automatically sure that you know what reality is, and you are operating on your default setting, then you, like me, probably won’t consider possibilities that aren’t annoying and miserable. But if you really learn how to pay attention, then you will know there are other options. It will actually be within your power to experience a crowded, hot, slow, consumer-hell type situation as not only meaningful, but sacred, on fire with the same force that made the stars: love, fellowship, the mystical oneness of all things deep down.

On false ideals and real freedom, or what Paul Graham has called the trap of prestige:

Worship power, you will end up feeling weak and afraid, and you will need ever more power over others to numb you to your own fear. Worship your intellect, being seen as smart, you will end up feeling stupid, a fraud, always on the verge of being found out. But the insidious thing about these forms of worship is not that they’re evil or sinful, it’s that they’re unconscious. They are default settings.

They’re the kind of worship you just gradually slip into, day after day, getting more and more selective about what you see and how you measure value without ever being fully aware that that’s what you’re doing.

And the so-called real world will not discourage you from operating on your default settings, because the so-called real world of men and money and power hums merrily along in a pool of fear and anger and frustration and craving and worship of self. Our own present culture has harnessed these forces in ways that have yielded extraordinary wealth and comfort and personal freedom. The freedom all to be lords of our tiny skull-sized kingdoms, alone at the centre of all creation. This kind of freedom has much to recommend it. But of course there are all different kinds of freedom, and the kind that is most precious you will not hear much talk about much in the great outside world of wanting and achieving…. The really important kind of freedom involves attention and awareness and discipline, and being able truly to care about other people and to sacrifice for them over and over in myriad petty, unsexy ways every day.

That is real freedom. That is being educated, and understanding how to think. The alternative is unconsciousness, the default setting, the rat race, the constant gnawing sense of having had, and lost, some infinite thing.

On what “education” really means and the art of being fully awake to the world:

[T]he real value of a real education [has] almost nothing to do with knowledge, and everything to do with simple awareness; awareness of what is so real and essential, so hidden in plain sight all around us, all the time, that we have to keep reminding ourselves over and over:

‘This is water.’

‘This is water.’

It is unimaginably hard to do this, to stay conscious and alive in the adult world day in and day out. Which means yet another grand cliché turns out to be true: your education really IS the job of a lifetime.

In the altogether excellent Magic Hours: Essays on Creators and Creation, Tom Bissell writes:

The terrible master eventually defeated David Foster Wallace, which makes it easy to forget that none of the cloudlessly sane and true things he had to say about life in 2005 are any less sane or true today, however tragic the truth now seems. This Is Water does nothing to lessen the pain of Wallace’s defeat. What it does is remind us of his strength and goodness and decency — the parts of him the terrible master could never defeat, and never will.

Complement with the newly released David Foster Wallace biography.

Donating = Loving

Bringing you (ad-free) Brain Pickings takes hundreds of hours each month. If you find any joy and stimulation here, please consider becoming a Supporting Member with a recurring monthly donation of your choosing, between a cup of tea and a good dinner:





You can also become a one-time patron with a single donation in any amount:





Brain Pickings has a free weekly newsletter. It comes out on Sundays and offers the week’s best articles. Here’s what to expect. Like? Sign up.

11 SEPTEMBER, 2012

Richard Feynman On The One Sentence To Be Passed On To The Next Generation

By:

“In that one sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied.”

The great Richard Feynmanchampion of scientific culture, graphic novel hero, crusader for integrity, holder of the key to science — may have earned himself the moniker “the Great Explainer,” but when Caltech invited him to take over the introductory course in physics in 1961, they took an enormous chance on a theoretical physicist with no particular interest in students. What resulted, however, was nothing short of magic — his lectures went on to become a cultural classic, blending remarkably articulate explanations of science with poignant meditations on life’s most profound questions, and were eventually collected in The Feynman Lectures on Physics (public library).

From the very beginning of his first-ever lecture comes this timeless gem (mentioned in Daniel Bor’s excellent The Ravenous Brain) that set the tone for both Feynman’s academic contribution and his broader cultural legacy:

If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis that all things are made of atoms — little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied.

Donating = Loving

Bringing you (ad-free) Brain Pickings takes hundreds of hours each month. If you find any joy and stimulation here, please consider becoming a Supporting Member with a recurring monthly donation of your choosing, between a cup of tea and a good dinner:





You can also become a one-time patron with a single donation in any amount:





Brain Pickings has a free weekly newsletter. It comes out on Sundays and offers the week’s best articles. Here’s what to expect. Like? Sign up.

10 SEPTEMBER, 2012

Design, Knowledge, and Human Intelligence: RIP Bill Moggridge, Designer of the First Laptop

By:

“You can’t really, truly expect to explain design unless you explain intelligence.”

Sad days for the design world: We’ve lost Bill Moggridge (1943-2012) — visionary pioneer, designer of the world’s first laptop, director of the Cooper-Hewitt National Design Museum, and one infinitely kind man. No attempt to capture the full scope of his legacy and cultural imprint would be remotely adequate, but revisiting his inimitable insight into the essence, purpose, and sociocultural capacity of design is a poignant reminder of just what we’ve lost with his passing — and how much we’ve gained through his timeless wisdom.

In 2007, shortly after the publication of his now-iconic Designing Interactions, Moggridge gave an interview for Ambidextrous Magazine, in which he articulates with his signature blend of insight and irreverence some of the most critical issues that still keep design a culturally misunderstood discipline and design education a broken model.

One of the paradoxes Moggridge addresses is that of the usefulness of “useless” knowledge and the fetishizing of factual knowledge:

[Academia is] all about explicit knowledge. And design, by definition — along with the other arts like poetry or writing — is mostly not so explicit. It’s mostly tacit knowledge. It has to do with people’s intuitions and harnessing the subconscious part of the mind rather than just the conscious. And the result is if you try and couch the respectability of a professor or some form of research grant in terms that are normal for science, then it looks very weak. And so you have to have a different attitude, really, in order to see the strength that it could offer or the value that it could offer. And that’s a big difficulty both in academia and in terms of foundations.

[…]

If you think about the structure of the mind, there just seems to be a small amount that is above the water—equivalent to an iceberg—which is the explicit part…And most academic subjects are designed to live in that explicit part that sticks out of the water. If you can find a way to harness, towards a productive goal, the rest of it, the subconscious [understanding], the tacit knowledge, the behavior — just doing it and the intuition — all those, then you can bring in the rest of the iceberg. And that is hugely valuable.

NASA astronaut using the first notebook computer, Moggridge's GRiD Compass, on a space shuttle flight.

Moggridge draws a fascinating parallel between design and science, echoing the idea that intuition is essential to both scientific discovery and creativity:

Every scientist is an intuitive person, and most ‘ahas’ come from intuition anyway. And we all know that we fall in love with things and that we’re interested in subjective qualitative values. It’s just whether you recognize it as having something that you can use in a respective environment or a respectable sense.

Ultimately, and perhaps precisely because it requires this kind of abstract knowledge and combinatorial creativity, Moggridge frames design as a form of intelligence:

I really don’t think you’re going to understand design and art until you understand intelligence [and how the brain works]. So you can dent it, you can sort of make things so there are interesting insights and will help people, and you can explain process, but you can’t really, truly expect to explain design unless you explain intelligence.

He leaves us with a seemingly simple but infinitely important reminder, wrapped in a hope for better design writing and education:

So few people seem to realize that everything’s designed. And until we get some good people telling the story, that’s probably going to continue to be the case. So I’d love it if there was a consciousness in the public mind that mathematics and reading and writing is not enough — you also need to learn how to do design. Because everything is designed, and the way our world exists around us depends on how well it’s designed.

Fortunately, we’ve had some really good people telling design’s story. But what tragedy to lose one of the best of them — Bill Moggridge, you will be missed.

In 2010, Moggridge followed up with Designing Media — a modern treasure.

Images via Smithsonian courtesy IDEO, Associated Press

Donating = Loving

Bringing you (ad-free) Brain Pickings takes hundreds of hours each month. If you find any joy and stimulation here, please consider becoming a Supporting Member with a recurring monthly donation of your choosing, between a cup of tea and a good dinner:





You can also become a one-time patron with a single donation in any amount:





Brain Pickings has a free weekly newsletter. It comes out on Sundays and offers the week’s best articles. Here’s what to expect. Like? Sign up.