# Because the World Needs Nightmares

You know what the Scientifick Blogohedron needs more of? Well, besides introductions to basic subjects, so that we can be more than chatterbots reacting to whatever news story incenses us the most?

Gosh, you people are demanding.

No, I’m talking about nightmare fuel!

And as only children’s television can deliver. You remember Square One TV, right? It came on PBS in the afternoons, after Reading Rainbow and before Where in the World is Carmen Sandiego?. Like every other aspect of my generation’s formative years, it can be relived via the video tubes. Our lives have already been uploaded: the Singularity came and went, and we were all too busy arguing to notice.

Looking back, Reimy the Estimator Girl was fairly cute, and the “Angle Dance” is somewhat frightening in that in-1983-this-was-the-future way, but one bit of sheer irrational terror stands out. I refer, of course, to the mask which Reg E. Cathey wears in the title role of “Archimedes”:

Archimedes!
Archimedes!
A mathematician and scientist
Born in 287 BC
He lived in the city of Syracuse
On the island of Sicily

He said he could move the world
If he only had a place to stand
A fulcrum and a lever long
And the strength of an average man

He solved the problems of his days
Using math in amazing ways
His great work lives on today
Archimedes!
Archimedes!
Continue reading Because the World Needs Nightmares

# Squaring Numbers Near Fifty

And now, a brief break from non-blogging:

Today, I’d like to start with a specific example and move on to a general point. The specific example is a way to approximate the squares of numbers and then refine those approximations to get exact answers, and the general point concerns the place such techniques should have in mathematics education.

My last calculator broke years ago, so when I have to do a spot of ciphering, I have to work the answer out in my head or push a pencil. (If the calculation involves more numbers than can fit on the back of an envelope, then it’s probably a data-analysis job which is being done on a computer anyway.) Every once in a while, the numbers teach you a lesson, in their own sneaky way.

It’s easy to square a smallish multiple of 10. We all learned our times tables, so squaring a number from 1 to 9 is a doddle, and the two factors of 10 just shift the decimal point over twice. Thus, 502 is 2500, no thinking needed.

Now, what if we want to square an integer which is near 50? We have a trick for this, a stunt which first yields an answer “close enough for government work,” and upon refinement gives the exact value. (I use the “close enough for government” line advisedly, as this was a trick Richard Feynman learned from Hans Bethe while they were calculating the explosive power of the first atomic bomb, at Los Alamos.) To get your first approximation, find the difference between your number and 50, and add that many hundreds to 2500. The correction, if you need it, is to add the difference squared. Thus, 482 is roughly 2300 and exactly 2304, while 532 is roughly 2800 and exactly 2809.

I wouldn’t advise teaching this as “the way to multiply,” first because its applicability is limited and second because it’s, well, arcane. What a goofy sequence of steps! Surely, if we’re drilling our children on an algorithm, it should be one which works on any numbers you give it. The situation changes, though, after you’ve seen a little algebra, and you realize where this trick comes from. It’s just squaring a binomial:
Continue reading Squaring Numbers Near Fifty

# The Giant’s Shoulders #1

The inaugural edition of The Giant’s Shoulders, our blog carnival for explaining and discussing the influential golden oldies of science, is online at A Blog Around the Clock. Want to know where Petri dishes come from, and who Petri was? Which planet narrowly escaped being named George? What kind of beverage is Ethroxylon Classic? This carnival will tell you!

# Pretentious Document Format

I love the Interblagotubes.

Where else could you dump thousands of grumpy and disaffected words on unsuspecting readers and have them come back asking for more, and in a more easily printable format? Seriously: if you know a better venue for long-winded, gloomy rambles, I’ll go there instead.

Recently, Scott Hatfield asked me if I could convert one of my lengthier essays into a PDF or some other such format. In the spirit of excessive and unwanted generosity, I did a quick-and-dirty conversion job on not one, but two posts. Here they are:

The next time I need to procrastinate on something dreadfully important, I might try this again.

# What Science Blogs Can’t Do

No cosmic law says that when you gaze into your navel, you have to like what you find.

My thesis is that it’s not yet possible to get a science education from reading science blogs, and a major reason for this is because bloggers don’t have the incentive to write the kinds of posts which are necessary. Furthermore, when we think in terms of incentive and motivation, the limitations upon the effects of online science writing become disquietingly clear. The problem, phrased without too much exaggeration, is that science blogs cannot teach science, nor can they change the world.

INTRODUCTION

Notice how short the “basic concepts in science” list is, compared to the “basic concepts” which we know are the foundation of our fields? It has eleven entries — count them — for all of physics. Translated into lectures, that might be a couple weeks of class time. Chemistry is even worse off, and while the biology section is big, it’s also remarkably scatter-shot. Such introductory lessons as get written don’t get catalogued, and thus become damnably difficult to find again.

And, the problem hardly stops there. As the magician Andrew Mayne recently pointed out,

People only know what they can understand. There’s a lot of great information out there, but not enough is being doing to make it widely accessible to the masses. Most science entries in Wikipedia read like they’re written by graduate students for other graduate students. Even the basic science stuff is written that way.

We need to put ourselves into the perspective of someone who hasn’t had the science exposure that we’ve had and find ways to help make this information more accessible.

Why is introductory material so poorly represented?

Well, what do we science bloggers write about, anyway? This is how I caricature what I see:

0. Fun posts about random non-science stuff — entertaining, humanizing, but not the subject I’m focusing on right now.

1. Reactions to creationists and other pseudo-scientists.

2. Reactions to stories in the mainstream media, often in the “My God, how did they screw up so badly” genre.

# Woe

Las Vegas is a town of bottled water, not just because they’re hawking it on the street corners, but on general principles: the city takes things which should not be encapsulated — risk, chance, sex, scenery — packages them and sells them at exorbitant prices. I’m glad I’m out of it, except that on the way home, I was caught in a monsoon downpour which lasted almost exactly the duration of the walk from the T station to my front door. The next day, my trusty laptop developed an interesting new behavior: when I turned it on, it turned itself off. I suspect the containment around it failed, to use a Star Trek-ism, and its power supply had a delayed allergic reaction to the rainwater. It remains to be seen whether I can extract the data from its hard drive.

Fortunately, the so-called social circle in which I move is a giant geek support system.

While I try to get my act together, Maria Brumm has a couple good posts on the troubles mathphobia causes in a geology education. To an aspiring high-school science teacher, she writes,

# The Necessity of Mathematics

Today, everything from international finance to teenage sexuality flows on a global computer network which depends upon semiconductor technology which, in turn, could not have been developed without knowledge of the quantum principles of solid-state physics. Today, we are damaging our environment in ways which require all our fortitude and ingenuity just to comprehend, let alone resolve. More and more people are becoming convinced that our civilization requires wisdom in order to survive, the sort of wisdom which can only come from scientific literacy; thus, an increasing number of observers are trying to figure out why science has been taught so poorly and how to fix that state of affairs. Charles Simonyi draws a distinction between those who merely “popularize” a science and those who promote the public understanding of it. We might more generously speak of bad popularizers and good ones, but the distinction between superficiality and depth is a real one, and we would do well to consider what criteria separate the two.

Opinions on how to communicate science are as diverse as the communicators. In this Network age, anyone with a Web browser and a little free time can join the conversation and become part of the problem — or part of the solution, if you take an optimistic view of these newfangled media. Certain themes recur, and tend to drive people into one or another loose camp of like-minded fellows: what do you do when scientific discoveries clash with someone’s religious beliefs? Why do news stories sensationalize or distort scientific findings, and what can we do about it? What can we do when the truth, as best we can discern it, is simply not politic?

Rather than trying to find a new and juicy angle on these oft-repeated questions, this essay will attempt to explore another direction, one which I believe has received insufficient attention. We might grandiosely call this a foray into the philosophy of science popularization. The topic I wish to explore is the role mathematics plays in understanding and doing science, and how we disable ourselves if our “explanations” of science do not include mathematics. The fact that too many people don’t know statistics has already been mourned, but the problem runs deeper than that. To make my point clear, I’d like to focus on a specific example, one drawn from classical physics. Once we’ve explored the idea in question, extensions to other fields of inquiry will be easier to make. To make life as easy as possible, we’re going to step back a few centuries and look at a development which occurred when the modern approach to natural science was in its infancy.

Our thesis will be the following: that if one does not understand or refuses to deal with mathematics, one has fatally impaired one’s ability to follow the physics, because not only are the ideas of the physics expressed in mathematical form, but also the relationships among those ideas are established with mathematical reasoning.

This is a strong assertion, and a rather pessimistic one, so we turn to a concrete example to investigate what it means. Our example comes from the study of planetary motion and begins with Kepler’s Three Laws.

KEPLER’S THREE LAWS

Johannes Kepler (1571–1630) discovered three rules which described the motions of the planets. He distilled them from the years’ worth of data collected by his contemporary, the Danish astronomer Tycho Brahe (1546–1601). The story of their professional relationship is one of clashing personalities, set against a backdrop of aristocracy, ruin and war. From that drama, we boil away the biography and extract some items of geometry:
Continue reading The Necessity of Mathematics

# Help, Help, I’m Being Oppressed!

I just noticed a post at Michael White’s Adaptive Complexity entitled, “Bad Science Journalism and the Myth of the Oppressed Underdog” (9 March 2008). It’s good. Go read it.

[I]n our culture we love the underdog, who sticks to his or her guns, in spite of heavy opposition. In this narrative, we have heroes, villains, and a famous, brilliant scientist proven wrong.

I’m sure you could pick out instances in science history where this story is true, but more often it is not. You wouldn’t know this from the pages of our major news media though; in fact you’d probably get the impression that the underdog narrative is the way science works. And many journalists may think that too; after all, most of them read (or misread) Thomas Kuhn when they were in college, and Kuhn brought this kind of narrative to a new high.

This is the narrative which I called the “David vs. Goliath of Scientific Establishment” story. White gives a specific example, concerning the public presentation of evolutionary biology; in physics, the problem can be even more fun, since the actual relationship between David’s revolutionary idea and Goliath’s orthodoxy often requires a hefty dose of mathematical reasoning to understand. When a typical statement by a physicist trying to sort the mess out might read, “Any embedding of your gauge group in either noncompact real form of E8 will always give you a nonchiral fermion spectrum,” well. . . the temptation will always be to plump for the “social” angle and emphasize the personalities of the physicists involved. The “oppressed underdog” story emerges quite naturally.

To be fair, or at least spread the misery around, biology can suffer from Popularizer Mathophobia, too. White’s example comes from sexual selection theory and relates to the role game theory might play in understanding the dynamics of a population. Oooh! Math! Scary!

(My “typical statement” is a paraphrase of Jacques Distler, who pointed out this problem almost six years ago.)

# Brain Damage and Journalism

Dan Hurley writes of Katherine P. Rankin’s neurological research on sarcasm,

To her surprise, though, the magnetic resonance scans revealed that the part of the brain lost among those who failed to perceive sarcasm was not in the left hemisphere of the brain, which specializes in language and social interactions, but in a part of the right hemisphere previously identified as important only to detecting contextual background changes in visual tests.

That’s from a New York Times piece, “The Science of Sarcasm (Not That You Care),” 3 June 2008. The abstract for Rankin et al.‘s presentation says, in part,

This study provides lesion data suggesting that the right posterior temporal lobe and dorsomedial frontal cortex are associated with recognizing and interpreting sarcastic irony using paralinguistic vocal and facial cues, consistent with functional imaging research examining neural correlates of voice prosody, facial emotion recognition, and perspective taking.

Trust the alchemy of science journalism to turn a result consistent with prior research into a great surprise. As Vaughan Bell points out, by the early 1980s people had already found out that damage to the brain’s right hemisphere can cause “disorders of affective language,” i.e., problems with recognizing emotion in speech. More recently, Shamay-Tsoory et al. (2005) found that lesions in the ventromedial section of the right prefrontal cortex impaired test subjects’ abilities to handle tasks which required understanding sarcasm.

This is the sort of gaffe which makes neurocurmudgeons file a story under “chaff” instead of “wheat.” I wonder: can fMRI detect a cortical lesion which makes all interesting and worthwhile research be perceived as revolutionary? The problem is not just restricted to neuro-journalism, of course — revolution disease is a general trope, right up there with “Think of the children!” and “David vs. the Scientific Goliath.” One begins to appreciate why Eric Roston, author of The Carbon Age (2008), said of his research practices, “I wanted to avoid secondary literature, media,” even though this meant a masochistic journey through peer-reviewed articles.

As for the research itself. . . . To my knowledge (and that of the Neurocritic), Rankin et al.‘s results have not yet appeared in a journal, only at an American Academy of Neurology conference, so pickings are as yet rather thin. No doubt more details will be available anon.

# “The Magic Word is Beauty”

PZ Myers, doyen of science blogging, was recently at Berkeley to attend the IEDG 2008 symposium (the letters stand for “Integrating Evolution, Development, & Genomics”). Now, the conclusion of his talk, which capped off the conference, is available on the ‘tubes:

Thanks go to Scott Hatfield for recording and providing the video.

# Medical Journalism is Ill

Is the news media doing a good job of reporting on new treatments, tests, products, and procedures? Ray Moynihan and colleagues analyzed how often news stories quantified the costs, benefits, and harms of the interventions being discussed, and how often they reported potential conflicts of interest in story sources [1]. Of the 207 newspaper and television stories that they studied, 83 did not report the benefits of medications quantitatively, and of the 124 stories that did quantify the benefits of medications, only 18 presented both relative and absolute benefits. Of all the stories, 53% had no information about potential harms of the treatment, and 70% made no mention of treatment costs. Of 170 stories that cited an expert or a scientific study, 85 (50%) cited at least one with a financial tie to the manufacturer of the drug, a tie that was disclosed in only 33 of the 85 stories.

Moynihan et al. (2000) inspired some Australians to do a similar survey in 2004, which found after six months that Australian print and online news coverage of medical advances was “poor.” Now, Schwitzer has done a more extensive survey of United States media. The punchline is as follows:

In our evaluation of 500 US health news stories over 22 months, between 62%â€“77% of stories failed to adequately address costs, harms, benefits, the quality of the evidence, and the existence of other options when covering health care products and procedures. This high rate of inadequate reporting raises important questions about the quality of the information US consumers receive from the news media on these health news topics.

Details are available at PLoS Medicine. Now, we just need somebody to pay for a similar survey of non-medical science reporting.

(Tip o’ the fedora to Steve Novella.)

# Gah! But Yay!

I grew up (to the extent that I have grown up) reading the works of Larry Gonick, expositor of science and history in cartoon format. As Cosma Shalizi wrote, “When I think about it, I realize a truly substantial proportion of my basic knowledge of the world derives from reading Larry Gonick’s Cartoon Guides and Cartoon History of the Universe.” So it was with great interest that I read in the Mercury News of 10 April 2008 that Gonick “hopes to work on a cartoon book about calculus” once he’s finished The Cartoon History of the Modern World Part II, which is really the fifth installment in the Cartoon History of the Universe series. However, that Mercury News article commits a serious gaffe:

Gonick hasn’t actually yet put in cartoon form a subject he knows at least as well as history: mathematics.

Ahem. The Cartoon Guide to Statistics (1994), coauthored with Woollcott Smith of Temple University. And that’s not even mentioning his “Science Classics” feature in Discover magazine, a regular two-page comic which often covered mathematical topics. We could go on to list the mathy subjects addressed in his other science books and even in his histories, but really.

# An Alloy of Pleasures

REVIEW: The Oxford Book of Modern Science Writing, edited by Richard Dawkins. Oxford University Press, 2008. ISBN 978-0-19-921680-2. A PDF copy of this review is available here.

PRELUDE

During the Christmas holidays last year, my mother and I were visiting a bookshop, and we passed by a display of general-audience science books. As a child, I had devoured such things, and propelled by sentiment mixed with curiosity, I looked over the titles, browsing for ones which I’d seen recommended or were written by authors I knew. Momentarily, however, a harsh edge cut through my sentimental reverie. “Look at this,” I said. “This book props up its thesis with phony numbers and citations which point to papers that don’t even discuss what the book says they do! And this one, here, tells a version of 1990s physics history which, to put it mildly, doesn’t match up with what other physicists remember. Oh, and this author, well, everybody is just astonished at how the clarity of his thinking implodes halfway through, when he stops thinking and starts faith-ing. And what’s this — quantum healing?

If the Gentle Reader were to deduce a “moral” from the story, it might be that I am a cantankerous individual with an acerbic disposition, and the reader would not be gravely in error. Beyond that, one could say that a science education nearly killed the general-interest bookshelf for me, and what University did not do, the science-blogging world definitely tried to finish. Caught up in this electronic tangle of opinions, discoveries and arguments, where new findings and reactions to them are all free for the taking, I’d seen the flaws of a great many books exposed. Precisely because online science writing makes irascible iconoclasm a way of life, though, it teaches the joy of discourse and the admiration of written words which, finally, work. Both of these aspects play into the value of The Oxford Book of Modern Science Writing, edited by Richard Dawkins.

This book collects passages written by seventy-nine scientists over the previous hundred years; though Dawkins himself has more than proven his talents as an expositor, his own writings are confined to introductory remarks giving context for each selection. Biology is represented quite strongly, and physics makes a good showing. Astronomy, other than the cosmological variety, makes mostly cameo appearances, and chemistry seems rather the poor stepchild. (Max Perutz, a Nobel Laureate, contributes a bit on X-ray crystallography which is largely an admiring biographical sketch of fellow laureate Dorothy Hodgkin, and the well-known neurologist Oliver Sacks is roped in to give a quirky reminiscence about tungsten! Primo Levi‘s tale of a carbon atom, though, is not to be missed.) Truly commendable is Dawkins’s inclusion of mathematics, a subject which provokes an unnatural fear even in literate readers who appreciate science and enjoy reading about the latest fossil or the most newly discovered extra-solar planet. The selections chosen for The Oxford Book are clear, memorable and not infrequently poetic. Upon occasion, they deliver on that great promise of science education: to provoke the learner into seeing the natural world and the products of the human mind in a new and unforgettable light. After reading what Stephen Jay Gould wrote about Charles Darwin‘s take on the humble earthworm, for example, it is difficult to see in the same way such a simple thing as worms coming out on a pavement after the rain.

The Oxford Book would serve as an excellent smÃ¶rgÃ¥sbord of introductions for the reader who has grown interested in science but doesn’t know where to begin. Likewise, those who catch the biggest headlines and read about the flashiest new breakthroughs will likely benefit from a book about science which has stood the test of time, about discoveries which have kept on inducing breathlessness for several decades. A specialist trained in one scientific field could also enjoy an interlude of lateral thought, poking into a new domain of learning to flex the thought-muscles.

When I’ve heard people talk about a movie or a book being “an unalloyed pleasure,” they mean it to be joy without stopping, all good and nothing bad. Given that an alloy is a mixture of metals, the phrase also carries a trace contamination of the idea that the book or the movie being talked about only offers one kind of goodness — all drama and no comedy, let’s say. Consequently, I find myself describing The Oxford Book of Modern Science Writing as an alloyed pleasure, a mixture of different satisfactions, in unequal amounts. The amazing facts, the flashes of wit, the moments of rapturous wonder are all there to be had, but Dawkins has also provided a series of portals to debate. I’m not talking about a nasty kind of political infighting, with accusations and character assassination, but rather the academic version of the same process: the rolling up of sleeves, the setting down of the teacup and the declaration of intellectual combat.

The book club meetings for this volume can, and should, be. . . volatile places.
Continue reading An Alloy of Pleasures

# Survey: Teachable Controversies

Today, John Timmer posted on the ‘tubes a brief summary of current debates in evolutionary biology, as unfolded at a recent Rockefeller University symposium. Timmer takes the position, and PZ Myers agrees, that these controversies don’t belong in the high-school curriculum. They require too much background knowledge to understand, and if the students haven’t spent time learning the basic principles, they’ll be sunk. On these specific points, I’d tend to agree; however, other debates might provide “teachable moments.” If trying to build lesson plans around the questions currently rocking the symposia is going too far, what about the problems which have been wrapped up in the last ten years or so? For example, in a post-Bullet Cluster world, a high-school physics class could well include some talk of dark matter.

# The Web Spinning ‘Round

Both T. Ryan Gregory and Abbie Smith have moved into new digs. In the former case, the move was voluntary, while in the latter, it appears to have been a choice expedited by the mysterious vanishing of her old site. Update your blaggregators, and say hello to them both!

I’m actually somewhat skeeved that the old ERV site upped its chucks and huffed the æther. Last summer, before Michael Behe’s The Edge of Evolution had turned out to be a complete flop, I had started compiling a list of debunkings, several of which resided at the old ERV. Hopefully those pages can get pulled from the various archives and republished at the new site.

Other stuff of note which I’ve seen lately in my local neighborhood of Network nodes:

Both Isabel Lugo and Brian Switek have discussed the relative roles of concrete examples and abstract reasoning in mathematics education. Elsewhere, Glennda Chui points us to a description of an “ILC Fan Club” in Tokyo. Which is better: that the International Linear Collider has a fan club, or that it meets in a bar basement? Two weeks ago, the ILC Fan Club hosted an all-women panel discussion on gender equality, an area in which physics has plenty of problems still to solve.

We fret a lot these days about how to “communicate science with the public,” but reading about the “Accelerator Ladies’ Night” reminded me, in an odd way, that while science is a global enterprise, the public to which we’re trying to communicate is divided into all the diverse cultures of the human species. Consider the analogy which novelist Aya Kaida proposed for explaining neutrino experiments:

Some experiments, like the Sudbury Neutrino Observatory, have measured particles zinging our way from the Sun. Other investigations produce neutrinos here on Earth; for example, K2K uses the proton synchrotron at the KEK facility in Tsukuba to make a beam of neutrinos, which is fired toward the Super-Kamiokande detector in Kamioka, 250 kilometers away. By measuring the neutrinos which arrive at Super-K, physicists can figure out what happened to them en route. Aya Kaida says that the neutrinos in the K2K beam are “cultivated fishes,” while the ones from the Sun are “wild.”

Vive la diffÃ©rence! In the U. S. and A., we might speak of animals “raised on a farm” versus “caught in the wild,” but when it comes to fish, I’m not sure we care. By and large, it’s not a distinction to which we are sensitive, and a person explaining neutrino research would reach for a different analogy. While the physics is the same everywhere on this spinning world of ours, its encounters with culture vary in all the ways we maddening mammals are able to differ.

Finally, David Guarrera, a string theory Ph.D. student at the Institvte, has posted the first in a series of essays on false vacua. Happy reading!

# Open Books

Hmmm. It appears that I get to spend this week working on something which is not this website. However, it’s not in my nature to leave whatever readers I’ve got without something else to read, and fortunately for me, the Internets have delivered some juicy material recently. Two books are in the works, and you, Gentle Reader, have a chance to contribute to both of them.

Both are mathematical in nature. The one geared to a more general audience is Jason Rosenhouse’s big book on the Monty Hall Problem. He’s finished the first draft, and is gathering feedback on the first chapter. Go, read the PDF, and offer your comments!