Archive for the ‘books’ Category

My Friends’ Birthdays

May 2, 2011

Malcolm Gladwell’s Outliers describes how elite hockey players in Canada are far more likely to be born in the first half of the year than the second. There’s a simple explanation – Canadian youth hockey leagues bin age group teams according to the calendar year of birth. Two young players, one born January 1, 2003 and the other December 31, 2003 are considered the same age and play in the same league.

Being born in at the beginning of the year makes you a few months older than most of your peers. When you’re eight year old, those few months equate to a big advantage in physical maturity. Being more mature, you perform better, get selected for elite teams, and receive better training. You get better and better while your peers born near the end of the year are left behind.

The data shown in the book are convincing. The phenomenon is seen not just in Canadian hockey, but in a host of other sports where a similar age cutoff exists, and when the cutoff date changes from January 1, the distribution of birth months changes, too. (Basketball in the US is one exception, presumably because kids learn on the streets regardless of their birth month, and don’t need to be selected for elite training until later on.)

Then Gladwell goes on to suggest that the same effect dominates academic achievement in the US.

Parents with a child born at the end of the calendar year often think about holding their child back before the start of kindergarten: it’s hard for a five-year-old to keep up with a child born many months earlier. But most parents, one suspects, think that whatever disadvantage a younger child faces in kindergarten eventually goes away. But it doesn’t. It’s just like hockey. The small initial advantage that the child born in the early part of the year has over the child born at the end of the year persists. It locks children into patterns of achievement and underachievement, encouragement and discouragement, that stretch on and on for years.

Recently, two economists — Kelly Bedard and Eliza­beth Dhuey—looked at the relationship between scores on what is called the Trends in International Mathematics and Science Study, or TIMSS (math and science tests given every four years to children in many countries around the world), and month of birth. They found that among fourth graders, the oldest children scored somewhere between four and twelve percentile points better than the young­est children. That, as Dhuey explains, is a “huge effect.” It means that if you take two intellectually equivalent fourth graders with birthdays at opposite ends of the cutoff date, the older student could score in the eightieth percentile, while the younger one could score in the sixty-eighth percentile. That’s the difference between qualifying for a gifted program and not.
pp 28

The first paragraph seems like a rather wild extrapolation, based solely on the second.

I wanted to know if I could see this birthday effect in some data I had readily available – that generated by my Facebook friends.

I have about 700 Facebook friends, many of whom were Caltech students. These people represent an academic elite, so if the birthday effect is extraordinarily strong, I ought to have friends whose birthdays come in a clump, assuming they are educated in the US.

I tallied the birth months of all my Facebook friends who are or were students at Caltech and who listed themselves as being from somewhere in the US. (I wound up throwing out a lot of people from the US because they didn’t list a home town, but I thought it was better to have a uniform data collection policy than to guess.) 110 people made the cut.

I made a plot of their birth months, and it looked like maybe there was some sort of signal in there. So then I made seven fake plots by randomly generating birth months from a flat distribution. Here are the eight plots. Can you tell which one is the real data?

One of these plots is real data from the birth months of students at one the world’s top universities. The other seven plots are as random as Python can make them. I challenge Malcolm Gladwell to tell me which one is which.

This challenge is a bit unfair. What I really ought to plot is not birth month, but age when starting kindergarten. These aren’t the same, largely because people born near the end of the year (like me) can wind up either old for their grade or young for it. Still, January babies are almost uniformly old for their grade in the US, and August babies are almost uniformly young. If the effect is as powerful as Gladwell suggests, we ought to see it at play here.

If birth months were evenly distributed and I took 110 data points, the expectation value for a each month is 9.2 and the standard deviation is 2.9. Since the standard deviation is pretty big compared to the expectation value, we would need a large signal in order to see an obvious effect in the data. So to make a strong case, I really ought to have more data.

Still, we actually expect whatever effect there is to be magnified when looking at this data. The reason is that, with Caltech students, we’re looking far out on the tail of the distribution of academic ability.

Here are two normal distributions that are the same except that one is shifted to the right.

The original gaussian, centered on zero, represents students born late in the year, and the shifted one represents students born near the beginning. (This is only supposed to be a heuristic, of course.)

I’ve added two vertical lines. The first vertical line shows a cut off for students who are “good at school”. There are about three times as many students from the shifted distribution that make it beyond this cut off.

The second line shows students who are “very good at school”. There are about ten times as many students from the shifted distribution that make it beyond this tougher cutoff.

Even though I don’t expect the age-selection effect to work in such a simple way, the main idea is simply that if you give one population a small advantage over the other, the effect becomes magnified when you look at the frequency of outliers. So, in the birthdays of my Caltech friends, I ought to see a pretty strong signal, if the basic effect exists.

So, for now I’d say that, lacking further data, either the effect is not very large, or it is not very simple, so that somehow it allows Caltech students form an exceptional bunch.

Book Review: How I Killed Pluto and Why It Had It Coming

January 4, 2011

This review is for The California Tech, where it should appear later this week. You can listen to the full audio of my interview with Mike Brown here

Amazon Link

If you read enough pop sci books, you’ll learn that black holes ain’t so black and that our genes are selfish. Along the way, you’ll pick up a few tidbits about the lives and research of Stephen Hawking or Richard Dawkins. If you read enough memoirs by scientists you’ll learn that Feynman could crack the safes at Los Alamos (and knew the codes for something else men want to access), or that James Watson didn’t use modesty to discover the secret of life. You’ll also get a few tidbits about the character of physical law or the structure of the double helix. But if you read Mike Brown’s new book, you’ll learn that a scientist’s work and a scientist’s life are separate but inextricable, that the motion of the planets really can affect the path of a life, and that sometimes there is no distinction between teacher and raconteur.

“The amusing thing that I get now,” Brown told me about the hate mail he’s received since publishing How I Killed Pluto and Why It Had It Coming, “are these obscene phone messages.” He’s smiling as he tells the story. “They sound like drunk fraternity boys who were probably thirteen when Pluto got demoted. They were pissed off then and now they’re drunk and pissed off.”

Brown, of course, did not kill Pluto. It’s still there, and still cold. What he really did was help it. He found it some friends. “The singular thing for which I am most famous is the discovery of Eris,” he said. “It’s not the most important thing I’ve done, scientifically. I don’t think there’s any question that the discovery of Sedna and this whole story I’ve been telling you is far and away the most important thing.”

Brown has been telling me the story about his discovery of several large Kuiper Belt objects – balls of rock and ice orbiting in slow, frigid ellipses beyond Neptune. Eris and Sedna are among them. Using the nearly-derelict 48-inch Schmidt Telescope at the Palomar observatory, Brown and his teams conducted several surveys of the outer solar system to search for these objects. His first search failed. His second did not.

They first discovered Quaoar, then Sedna, an object somewhat smaller than Pluto, but scientifically fascinating due to its extremely distant orbit, which separates it gravitationally from the influences of the gas giants. “Sedna never comes close [to the gas giants], and if you integrate the orbit backwards for 4.5 billion years, it never did,” Brown explains.

Since Sedna can maintain its orbit unmolested, it serves as the Solar System’s time capsule. “It’s this window into the earliest Solar System – into the formation of the Solar System. This is what really excites me. I want to understand what the earliest Solar System was like, how it led to what we have today, and what it tells us about the formation of other plantery systems. These objects out there are, I think, the best tools for understanding that we have.”

In other words, Brown wants another story to tell. He’s been hitting me with them since I entered his office, leaning in to tell me the good parts, then suddenly swiveling back from his desk, calling up online pictures of the Russian Venera lander’s panoramic photos of Venus, and holding them up next to an ultrasound of his daughter for comparison.

How I Killed Pluto is a repository of Brown’s stories. It recounts his obsessive data-recording and analysis, not of planetary motion, but of his infant daughter’s sleeping and eating schedules. Other anecdotes discuss the way Jupiter and Saturn looked on the epiphanous night when he first understood that the planets really are hanging up there in the sky, or just how relaxed his post-doc Chad Trujillo was when he announced their first Kuiper Belt discovery, or the gradual evolution from disappointment, to inkling mistrust, to deep suspicion as he learned that a particular discovery was perhaps not scooped, but stolen by a team of researchers in Spain. We learn Brown’s opinions on the weather near telescopes (nasty), the moon (his nemesis), living in the woods (good deal for a single guy), and, of course, whether Pluto should be called a planet (definitely not).

“I find that stories draw people in more,” Brown says. All the major events in his life – the beginning of his career at Caltech, his courtship and marriage, and the start of his family – occurred during the few years surrounding his search for planets past Pluto. For Brown, the personal context of the search is as important as the scientific context. If the book is about how he killed Pluto, it’s necessarily about those personal stories as well.

Brown says that even “scientific papers are more compelling and more readable when they have a story that they’re telling. Even if it’s a scientific story with data and analysis, it’s better if it’s a story.”

And if ever there has been a great story in need of telling, it’s the story of how a ball of gas twirling in deep space collapsed to form the Sun, the planets, and all rest of our Solar System. “It’s a huge set of phenomena. If you want to understand the entire Solar System and why it is the way it is, you need to understand details from quantum physics to organic chemistry to hydrodynamics to electrical discharge. I mean, there’s so many crazy things that go on that you’ll never be able to put all these pieces together in a predictive way and say, ‘I know exactly what happened.’”

Brown believes that careful scientific study of Kuiper Belt objects can still help fill in pieces of that story. For example, astronomical evidence from analyzing their orbits is currently giving insight into the mechanism of planet formation and whether the Sun formed in a cluster of other stars.

A story, to Brown, is not just a trick to hold your interest. It’s the essence of science, an active process of discovery. He told me that to write about science, “I walk though the whole process of how I think about it, and why I come to that conclusion. I think it’s much more interesting to understand the process, in addition to just saying, ‘Here’s the answer.’”

Brown doubled the number of words he’s written, lifetime, in writing How I Killed Pluto. The effort will be repaid in full as thousands of people learn how mysterious our Solar System still is. Our understanding continues to evolve, with new evidence like that of Brown’s discoveries continually challenging and inspiring our stories about the Solar System. Brown, with his hallmark enthusiasm and joviality, tells me, “We’re really starting to be able to not as much rewrite those stories, as write them for the first time.”

Let’s Be Serious

August 11, 2010

I have read many bad book reviews (shame on me), but one that sticks out as exceptionally absurd was an Amazon reader review of an exercise book. “This book is pure genius!” wrote the reviewer. “I only bought it yesterday, but it’s so good I read it twice already!”

I imagine this anonymous reader so enthralled by The New Secrets of Phenomenal Fitness, or whatever it was, that they stayed up all night reading about the Secrets that would finally get them in great shape after all these years. The next day they blabbed the secrets to anyone they could find, including their office-mates, their boss, their neighbor who is 94 years old, and their uncle who got hit by a bus and has been in a coma for six months.

They stayed up the next night, too, rereading all the secrets and trying over and over to craft an review that was worthy of a small fraction of the book’s genius. As dawn broke, the reviewer collapsed while attempting to climb the short flight of stairs to the bathroom, concluding two days of maniacal devotion devoid of sleeping or eating. They were still clutching The Secrets to their weakened, flabby chest.

Though I mock this aspiring connoisseur, I wonder how frequently I commit the same sort of error. When I recently read Dan Ariely’s book on the patterns in humans’ irrational decisions, I thought it was so great that I talked about it to people for weeks, then read the sequel. Still, I can’t name a single habit or behavior of mine I’ve definitely altered after reflecting on the book.

Maybe I should stick to mystery novels and Sudoku – the literary equivalent of Tootsie Pops (because you want to skip to the end) and alphabet soup (because the numbers are missing). These things are not meant to be nourishing – you consume them because you like how it feels, and that’s all.

I don’t like mystery novels, though. And frequently, when I sit down to solve a Sudoku puzzle or read about chess, I get the feeling that I am wasting my time, because I could be doing something serious with this oh-so-precious brainpower I’m throwing at toy puzzles.

Somehow, I’ve gotten it into my mind that reading a math or physics book is a good, serious thing to do. But on the other hand, it’s hard. I frequently don’t understand what they’re talking about in those books, and that makes me feel bad. I compromise by reading a popular level book on math or physics.

I just read Timothy Gowers’ Mathematics: A Very Short Introduction, and I’m having a hard time saying what I got out of it. The book was well-reviewed, which I took as justification for reading it. Indeed, it is well-written. I did get enjoyment of the Sudoku / mystery novel kind. Gowers writes clearly and succinctly, with a view creating, as much as is possible, an overall view of mathematics in the reader’s mind. The book is fun.

But most of the content was stuff I already knew. I have read plenty of popular math books before, and even if this was the best there are certainly diminishing returns. There was a nice little proof that the golden ratio is irrational on pages 43-45, and I was interested in the discussion of the Poincaré disk model of hyperbolic geometry on pages 98 – 104, but for the most part, reading this book simply made me feel good. I think that’s fine, as long as I don’t deceive myself that I’m being serious while I read it.

Also, I’m having a hard time figuring out what’s so great about being serious, anyway, and why I so frequently feel an urge to do it.


June 12, 2010

I took a short break from reading Steven Strogatz’s Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life earlier today and checked Facebook. Usually, the status updates of my Facebook friends are a seemingly-random menagerie of links to news stories, jokes, anecdotes, and these things: ^_^. Today, though, I found that in just the last twenty minutes, ten or so of my friends had posted nearly identical messages. They had somehow synced.

In this case, it’s not surprising. They were restating the result of the recently-concluded World Cup soccer game, but with more exclamation points than I’d get from Reuters. (Actually, Facebook status updates are the primary way I keep in touch with mainstream sports.) My Facebook synced today because of a strong, external signal influencing all the individual updates. That’s the way we normally think about synchrony. If you want it, you need some sort of a central clock for everyone to follow. A computer chip’s parts sync this way. Coworkers on a project are synced by a manager. Orchestras have conductors. Tug-of-war teams count to three.

By contrast, Strogatz is interested in spontaneous synchrony – synchrony where you won’t expect it and no one’s in charge. A great visual and audio introduction is Strogatz’s own TED talk.

Sync is a broad survey of nonlinear systems from spirals in oscillatory chemical reactions to synchronized menstruation induced by armpit sweat. What’s captivating about it is the story. Like James Gleik’s Chaos or Kip Thorne’s Black Holes and Time Warps, it carries you along from a few researchers diddling around with a curious idea to the creation of a large scientific field. We explore different branches where the original research lead, all the time seeing the different ways scientists and mathematicians approach their problems. From Strogatz, you also get a sense of the way these different approaches contribute to a complete understanding. At different times, Strogatz describes analytical work (solving equations), computer simulations, visualization (including building models from string and clay), laboratory experiments, and field research. Each endeavor feeds back into the others in this story about the science of synchrony.

I was curious, as I read the book, what it would be like if it had been technical as well. What if Strogatz had included didactic discussions of the solvable systems he’d worked on, or outlined the topological proofs he mentioned, or showed the results of the research as he would in a technical scientific talk, all integrated into the same story? A skeptical answer would be that lay readers wouldn’t touch the book and that technical readers would not be interested in the fluff. Strogatz already wrote an introductory textbook on nonlinear dynamics (which I haven’t read, but I’m told it’s good). I’ve seen textbooks that have little biographies inserted here and there, and I’ve seen popular books that use some equations or put technical appendices at the end. I am curious about a book intended to teach an undergraduate course that’s a truly integrated historical story and didactic text. There is an extensive bibliography allowing me to pursue the technical aspect of whatever ideas interest me the most, but that is something quite different from an organized presentation.

I picked up Sync while browsing, and read it because I remembered both the TED talk I linked above and Strogatz’s amusing math columns in the New York Times.