Brain Pickings

Posts Tagged ‘science’

25 SEPTEMBER, 2012

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


“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.

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24 SEPTEMBER, 2012

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


“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.


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21 SEPTEMBER, 2012

The Science of Procrastination and How to Manage It, Animated


This is where you insert the meta-joke about what else you’re actually supposed to be doing this very moment.

From AsapSCIENCE — who have previously brought us the scientific cure for hangovers, the neurobiology of orgasms, and how music enchants the brain — comes this illustrated explication of the science of procrastination and how to manage it, a fine addition to these five perspectives on procrastination. Among the proposed solutions is the Pomodoro technique, a time-management method similar to timeboxing that uses timed intervals of work and reward.

Human motivation is highly influenced by how imminent the reward is perceived to be — meaning, the further away the reward is, the more you discount its value. This is often referred to as Present bias, or Hyperbolic discounting.

For a more metaphysical take on the subject, see the fantastic anthology The Thief of Time: Philosophical Essays on Procrastination.

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:

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20 SEPTEMBER, 2012

The Best Science Writing Online 2012, In a Print Book


A far more brilliant and necessary idea than it first appears.

At first, the idea of publishing some of the web’s finest journalism in a print book might seem counterintuitive, if not downright absurd — after all, half the beauty of online journalism is the magical Rube Goldberg machine of references, strung together via hyperlinks that offer riffs and context without the cumbersome expository bulk of text. So what happens when you strip the writing of its linked context, of the dynamism of hypertext, and confine it to the static printed page?

In The Best Science Writing Online 2012 (public library), editors Bora Zivkovic and Jennifer Ouellette demonstrate precisely what happens — and it’s something rather curious and whimsical.

Once you’re able to get past seemingly anachronistic footnotes awkwardly compensating for the linklessness, you find yourself immersed in the writing in a way that the web’s blinking, demanding, ad-infested pages never quite allow. But, most importantly, you begin to see connections between critical issues, to understand how things fit together and why, as Charles Eames once observed, “the quality of the connections is the key to quality per se.” And therein lies the magic of the anthology’s thoughtful curation — a potent mix of critical analyses, witty personal reflections, absorbing feature profiles, illuminating commentary on the intersection of science and social policy, and even long-form investigative journalism, covering everything from the last space shuttle launch to fluid dynamics to gender politics.

In “The Renaissance Man,” the inimitable Ed Yong shows us that rigorous science journalism and exquisite long-form feature profiles can coexist, and when they do, it’s a thing of beauty:

Aiden is a scientist, yes, but while most of his peers stay within a specific field — say, neuroscience or genetics — Aiden crosses them with almost casual abandon. His research has taken him across molecular biology, linguistics, physics, engineering and mathematics. He was the man behind last year’s ‘culturomics’ study, where he looked at the evolution of human culture through the lens of four per cent of all the books ever published. Before that, he solved the three-dimensional structure of the human genome, studied the mathematics of verbs, and invented an insole called the iShoe that can diagnose balance problems in elderly people. ‘I guess I just view myself as a scientist,’ he says.

His approach stands in stark contrast to the standard scientific career: find an area of interest and become increasingly knowledgeable about it. Instead of branching out from a central speciality, Aiden is interested in ‘interdisciplinary’ problems that cross the boundaries of different disciplines. His approach is nomadic. He moves about, searching for ideas that will pique his curiosity, extend his horizons, and hopefully make a big impact.

‘I don’t view myself as a practitioner of a particular skill or method,’ he says.


Aiden naturally gravitates to problems that he knows little about. ‘The reason is that most projects fail,’ he says. ‘If the project you know a lot about fails, you haven’t gained anything. If a project you know relatively little about fails, you potentially have a bunch of new and better ideas.’ And Aiden has a habit of using his failures as springboards for success.

In “On Beards, Biology, and Being a Real American,” molecular biologist Joe Hanson, everyone’s favorite Feynman of the Tumblr era, brings his signature blend of the personal and the universally insightful to explore the bacterial ecosystems that inhabit the token signifier of hipster street cred, painting, as he always does, science as as anything but boring. Amidst the fascinating microbiology, you also find such priceless sentences as:

Unsurprisingly, when a live chicken is rubbed across an unwashed beard containing a lethal titer of avian viral particles, then ground up in a blender and injected into fertilized eggs, the rates of survival are not good. Beard-wearing scientists must take care to ensure that they do not repeat this extremely precise and odd sequence of events, lest they ruin dozens of perfectly good eggs.

Vintage ad accompanying Christie Wilcox's original Scientific American article 'Why do women cry? Obviously, it’s so they don’t get laid'

But the anthology’s greatest curatorial feat is the purposefulness with which it debunks the myth that science is dry, passionless, objective, and devoid of emotional investment. Take, for instance, Scientific American’s Christie Wilcox, who in “Why do women cry? Obviously, it’s so they don’t get laid” takes MSNBC’s Brian Alexander’s appallingly sexist pseudoscience reportage head-on and brings to it with equal force the dual lenses of hard science and eloquent, unabashedly opinionated analysis:

Alexander’s reporting of the actual science was quick and simplistic, and couched in sexist commentary (like how powerful women’s tears are as manipulative devices). And to finish things off, he clearly states what he found to be the most important find of the study:

‘Bottom line, ladies? If you’re looking for arousal, don’t turn on the waterworks.’

It’s no wonder that the general public sometimes questions whether science is important. If that was truly the aim of this paper, I’d be concerned, too!


Of course, Brian Alexander missed the point. This paper wasn’t published as a part of a women’s how-to guide for getting laid. Instead, the authors sought to determine if the chemicals present in human tears might serve as chemosignals like they do for other animals — and they got some pretty interesting results.

She goes on to cite a number of studies that suggest alternative, more complex evolutionary explanations, then concludes:

Why do I care so much? It’s not just that they got it wrong. It’s that their interpretation of research isn’t labeled as opinion. It’s that the vast majority of people who have any interest in science news are going to read inaccurate (if not downright insulting) news articles and think studies like this one are either misogynistic or frivolous. It’s that journalists like Brian Alexander undermine good science for the sake of attention grabbing headlines. And as a scientist and a writer, I am doubly insulted.

The rest of The Best Science Writing Online 2012 is just as stirring and stimulating — do yourself a favor.

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