Cocktail Party Physics

change and motion

It's here! Today is the official publication date for The Calculus Diaries: How Math Can Help You Lose Weight, Win in Vegas, and Survive a Zombie Apocalypse -- two and a half years of hard work finally comes to fruition. There are zombies, of course, and rollicking good tales about probability theory in craps, surfing in Hawaii (more than you ever wanted to know about the Fourier transform), and ferreting out parabolas and vectors at Disneyland. It's peppered with colorful historical math-y characters. There's even a couple of appendices with actual, you know, equations and stuff, for those readers who crave something a bit mathier, while still making sure the book appeals to my fellow math-phobes. I like to think of The Calculus Diaries as a gateway drug to the hard stuff. Sure, you think you're just taking a light hit, reading about catenary curves and architectural arches, but soon the Math Monkey is on your back, and you're staying awake for three days straight, solving differential equations and obsessing over whether P = NP. Not that I would know anything about that. I just sell the stuff.

Calculus is all about change and motion, and this seems as good a time as any to announce another impending change. For the last two years, I've been director of the Science & Entertainment Exchange, a fledgling program of the National Academy of Sciences to foster creative collaborations between scientists and the entertainment industry. We've had a very successful first two years, and all that hard work is beginning to bear some tangible fruit -- I'm excited about the potential of the program as it moves into Phase II. But I won't be actively involved for that phase. Effective September 24th, I'll be stepping down as director to return to writing full-time. The new director will be Marty Perreault, an industrial engineer by training who's been working at the Academy for several years, most recently heading up their President's Circle program, and recently relocated to Los Angeles.

This was not an easy decision. The short version: I'm exhausted. There just aren't enough hours in the day. I managed to write The Calculus Diaries on evenings and weekends while running the daily operations of the Exchange, but it's been tough juggling two very demanding, very different kinds of work. It became abundantly clear that I would have to choose between them. Everyone recites the mantra, "Follow your heart!", but what if your heart is divided between two equally amazing options? Still, as fulfilling as the Exchange has been, when the chips are down, writing wins out in the end. I miss being able to regularly delve deeply into nifty science, and am eager to get back in the writing game with renewed vigor. I'll still be tangentially invested in the future fortunes of the Exchange -- just on an informal, watching-from-the-sidelines basis, cheering the program on.

The next couple of months will be far from restful, as I wind down my tenure as Exchange director and work to promote the new book; you can keep track of various book-related appearances here. For those who care, I also set up a separate page on Facebook for The Calculus Diaries, making sure the feed isn't just all promo, all the time -- because don't you just hate that? There's a generous sampling of fascinating math-bits gleaned from all over the Interwebs as things catch my fancy. A sampling of cool links is below, just to whet your appetite for more things mathematical.

The Mathematics of Viking Jewelry. The beautiful bracelets and necklaces made by Viking artisans from rods of gold and silver are all twisted together into double helices. That's true regardless of whether the jewelry was found in Ireland, Scotland, the Orkney Islands or Scandinavia -- an impressive degree of regularity. Is it just a coincidence? Or could math be to blame? A couple of mathematicians at Denmark's Technical University think they've cracked the case in a paper recently submitted to the arXiv: Kasper Olsen and Jakob Bohr say that two wires become maximally twisted when no more rotations can be added with deforming the double helix. You guessed it: Viking jewelry is maximally twisted.

Mathematicians: Behind the Music. Forget mad scientists, how about mad mathematicians? Adam (Paco) Hanlon brings a refreshing dose of snark to this historical overview of some of the more colorfully insane math-y sorts during Nerd Nite NY. You gotta love any talk with slides captioned, "David Hilbert: Trash-Talking Mathematician Badass." (If Hilbert were alive today, I bet he'd put that on his business cards.)

 

The Mathematics of Balloon Animals. Man, there's a math paper for everything these days. In "Computational Balloon Twisting: The Theory of Balloon Polyhedra," the authors introduce the idea of ‘Bloons’: mathematical idealisations of real-world balloons (eg a doggie balloon, pictured with its associated 'bloon' below). Per Improbable Research: "The research not only provides '…algorithms to find the fewest balloons that can make exactly a desired graph or, using fewer balloons but allowing repeated traversal or shortcuts, the minimum total length needed by a given number of balloons.'”

A Math-y Take on the Perfect Roller Coaster Loop. Physics Buzz reports that Swedish mathematicians have used the same equations that describe how the planets orbit the sun to design a bunch of roller coaster loops that would give riders the visual experience of a loop without any whiplash. Good times!

Tasting the Limit, with Pie! Back in March, Ethan Siegel of Starts With A Bang took a break from blogging about astrophysics to pump out a tasty twist on infinite series and the limit -- illustrated with yummy photos of various kinds of pies. It's a fun explication, but it might make you hungry for something sweet. Forewarned!

Sunday with the St. Petersburg Paradox. Matt Springer of Built on Facts has a regular feature called the Sunday Function that quickly became one of my favorites. In this post, he takes a look at the St. Petersburg Paradox: a hypothetical gambling scenario where you win money based on the outcome of a coin toss. Per Matt: "Play this game enough times and it doesn't matter how much it costs to play, you will certainly come out ahead in the long run." There's a catch, of course: you have to play for, like, infinity. But it's a fascinating discussion, all the same.

Futurama Unveils Prisoner of Benda Theory. Psst! Did you know that Futurama writer Ken Keeler has a PhD in mathematics? Well he does! And he put his training to good use a couple of weeks ago, devising (and proving) a theorem based on group theory to explain a plot twist in the episode “The Prisoner of Benda.” (APS News leaked a spoiler back in May in an interview with executive producer David X. Cohen.) Basically, the Professor and Amy use a new invention to switch bodies. But the same two brains can’t switch twice, so they need an equation to prove that, "with enough people switching, eventually everyone will end up in their rightful form." Also? Most disturbing animated sex scene ever. Just sayin'.

NP Hard Problems Frustrate Hitler. Earlier this month, the Internet was abuzz with a new paper claiming to have solved the P vs NP conundrum. It's an esoteric math question relating to the speed at which a computer can accomplish a task such as factorising a number (eg, the Traveling Salesman problem). If P = NP, every problem that can be checked quickly can also be completed quickly. If it doesn't -- as the new proof claims -- well, that could have huge repercussions for internet security, since we keep our data safe from hackers using factoring of very large numbers. But it has an even bigger impact on Hitler, who needs to find the best route to get a KFC DoubleDown in Reichstag and doesn't have eternity to wait. ("Everyone who failed Theory of Computation, leave the room!")

Cracking Plato's Mathematical Code. Science historian and philosopher Jay Kennedy claims that Plato understood the mathematical structure of the universe quite well, 2000 years before Newton and Galileo. He bases this conclusion on analysis of Platonic texts using stichometry: the measure of ancient texts by standard line lengths. Per the Guardian: "What he found was that within a margin of error of just one or two percent, many of Plato's dialogues had line lengths based on round multiples of twelve hundred. The Apology has 1,200 lines; the Protagoras, Cratylus, Philebus and Symposium each have 2,400 lines; the Gorgias 3,600; the Republic 12,200; and the Laws 14,400." Paging Dan Brown! I smell a sequel to The Da Vinco Code!

Herbie Hancock Says Do the Math! What's the secret to a successful music career? Herbie Hancock insists it's math and science, in this LA Times exclusive interview. A taste: "I've always been interested in science. I used to take watches apart and clocks apart, and there's little screws, and a little this and that, and I found out if I dropped one of them, that thing ain't gonna work. When I was a kid, I put things back together and they never worked anyway! But just, like, going into those details, it's kind of a scientist's thing. And I have that kind of [mind], it's part of my personality.... So when synthesizers came in, they used terminology I knew. I knew what an amplifier was and I knew what it did.... I knew about wave forms. I knew what a 'sawtooth' was. I mean, if you studied physics, you'd learn those things. I was really good in math and I was good in science." Read the whole thing.

Marco Fusinato Fuses Math, Music and Art. "Music is what numbers feel like," io9 declared in this post about artist Marco Fusinato. He "brings together avant garde music and art in his work, creating imagery that looks like the results of a mad scientist's musings on how sound functions. In this series of drawings, called Mass Black Implosion, he's transformed scores for avant garde works into suggestions for what he calls "free noise," by changing the order of the notes and suggesting new relationships between them. Basically he's suggested a way to make something abstract even more abstract. In the process, he's created charts that are gorgeously strange." The whole gallery of images is worth a gander.

The Calculus of Saying I Love You. This ranks as possibly my favorite blog post ever, courtesy of Inkling Magazine, via the irrepressible Anna Gosline. She applies basic calculus to the conundrum to determine the optimal moment when the engineer her roommate is dating shoud declare his affection. The solution? "The Engineer should in fact solve for zero in the second derivative to the love-time function and say 'I love you' when love has stopped accelerating. This solves the concerning problem of having to wait until his love has stopped growing. Because zero growth in the love function is likely to make any woman, chemist, calculus enthusiast or otherwise, pretty goddamn pissed off." Wise words!

Mathematically Modeling Marital Breakups. Apparently math can also shed light on what happens when love sours. A new paper appeared in May purporting to analyze marital breakups (see graph below). Per the article: "The results of the mathematical analysis showed when both members of union are similar emotionally they have an 'optimal effort policy,' which results in a happy, long-lasting relationship. The policy can break down if there is a tendency to reduce the effort because maintaining it causes discomfort, or because a lower degree of effort results in instability. Paradoxically, according to the second law model, a union everyone hopes will last forever is likely break up, a feature Rey calls the failure paradox.'"

Teaching Calculus in Haiti.One of the Spousal Unit's former students, Eugene Lim, took some time off from his postdoc to spend a summer teaching calculus at a university in Haiti. He wrote a guest post for Cosmic Variance about his experiences as a volunteer teacher -- "a powerful and affecting look into conditions there, and the spirit of the students."

Math Skills Declined Back in 1804? Apparently the challenge of inspiring apathetic students in the face of declining math and science literacy isn't an especially new problem. Skulls in the Stars unearthed a fascinating article by one Reverend John Toplis, A.M., “On the decline of mathematical studies, and the sciences dependent upon them,” which appeared in Philosophical Magazine 20 (1805), 25-31. Among other things, Toplis lamented the pending loss of England's competitive edge: "We have long ceased to study those sciences in which we took the lead and excelled, and are content to follow, at a very humble distance, the steps of the philosophers of the continent, in those which they have in a manner discovered and made plain by their glorious exertions. We, after having discovered and conquered regions in science, suddenly quit them to be possessed and cultivated by other nations, that we may pick up a few gleanings in the countries found out and cultivated by their exertions." Plus ca change, anyone?

Math Class Needs a Makeover. I wish I could be a high school student again just to take Dan Meyer's high school math classes. He gave a fantastic TED talk on what's wrong with math education in this country, echoing many of my own thoughts and experiences -- namely, that we focus on the computational aspect (numbers crunching), which most of us forget when we leave high school, but is easy enough to relearn as an adult -- provided you also have a solid grounding in reasoning ability. And that's what high school students aren't getting. Meyers is a funny man, admitting that as a high school math teacher, "I sell a product to a market that doesn't want it, but is forced by law to buy it." But as I learned while writing The Calculus Diaries, math is still relevant outside of high school -- and it's far, far cooler than I ever imagined it could be. Folks like Meyers could change our minds about math for the better.

 

mucus, slime and killer snot monsters

Dragon*Con is nigh, and I'll be heading out to Atlanta next Thursday to participate in several panels over that weekend, including one on "The Science of the Whedonverse," wherein I will join fine folks like JPL's Kevin Grazier (tech consultant for Eureka) analyzing the science behind Joss Whedon's most beloved series: Firefly/Serenity, Dollhouse, and of course, Buffy the Vampire Slayer and Angel.(I'll also be on a few panels on the Skeptic track, and talking about The Calculus Diaries, given that the book's release is -- yikes! -- this Tuesday.)

There's far too much to discuss in one hour (I wrote an entire book on Buffyverse physics, and you could easily do the same for Firefly and the neuroscience of Dollhouse), but I hope we'll touch on some of my favorite topics: the Gentlemen's exploding heads in the Emmy-nominated episode "Hush"; the time-tinkering physicist in "Happy Anniversary" (Angel, Season 2); the thermodynamics of magic in the Buffyverse; and some of the real-world biological counterparts to demons and monsters, like the Queller demon in "Listening to Fear" (Buffy, Season 5). As the episode opens, Willow and Tara are gazing at the constellations when they a meteor streaking across the sky. It’s not an ordinary meteor: this one has a soft chewy demon center, unleashing an overgrown, slimy lizard-like creature onto a community already overrun with demons. The Queller demon vomits a sticky, odiferous substance onto its victim’s face, which then hardens, suffocating said victim. Xander resents being forced to spend his weekend researching a killer snot monster, and an exasperated Giles upbraids him that it's important because "it's a killer snot monster from outer space!" I'm still waiting for the SyFy original movie on that one: Killer Snot Monsters from Outer Space would give Sharktopus a run for its money.

I was reminded of all things slimy and snot-like this past week, upon reading a short post by Brian of Laelaps about a new method for extracting DNA-rich tissue from dolphins. In the past, the standard techique has been dart biopsies: you shoot the creature with a small harpoon-like device and when you pull it out, there's a bit of tissue attached, ideal for genetic analysis. Jen-Luc Piquant sniffs that if she were a dolphin, she would find this very irritating, if not outright painful. And indeed, dart biopsies can't be used on very young dolphins for fear of injury.

Get a dolphin to blow in a tube, however -- the dolphin equivalent of a breathlayzer -- and you collect a sample of "dolphin blow" (oh, stop sniggering!): air infused with a mix of proteins and liquids to comprise a sort of "lung surfactant." Per Brian, prior work showed that dolphin blow contains traces of reproductive hormones, so why not  genetic material? To find out, the University of Queensland researchers held polyproplene tubes -- which look disturbingly akin to a solidified condom in the photo below -- over the dolphins' blowholes and collected enough genetic material to produce DNA profiles that closely matched that obtained by analyzing the dolphins' blood. One more challenge remains: the dolphins used in the study were from the National Aquarium in Baltimore, who are far more likely to cooperate with such procedures than dophins reared in the wild. But I'm sure if we just explained to them that they can either be pinged with sharp darts and lose a bit of tissue, or breathe into a tube for a few minutes, they'll see reason.

From Brian's description, dolphin blow seems quite similar to what a materials scientist might term a "viscous colloid," a class of materials that includes mucus, a substance with which we all have had firsthand experience. When the Spousal Unit appeared on The Colbert Report this past March, I went with him to NYC, only to be felled by a nasy cold virus during our stay. For three days, my morning ritual included the ceremonial Clearing of the Mucus -- undertaken while the Spousal Unit was off getting his morning coffee to spare him the horror of witnessing something akin to a scene from The Exorcist. (A good marriage needs a bit of mystery.) Having witnessed what was expelled form my nasal passages, I can readily believe Wikipedia's assertion that "the average human body produces about a liter of mucus per day."

Usually, though, mucus is beneficial, helping ward off infection by trapping nasty paticles that enter through the nose (or mouth) before they can get down into the respiratory tract. It's a bit sensitive to temperature: in cold weather, for instance, our mucus can thicken, only to "melt" when we come in from the cold for a nice hot bowl of soup, thereby causing one's nose to run at the table in a most unappetizing fashion. I hate being "that person" at the dinner table. We have all been that person at some point.

Elsewhere in Nature, mucus and other slimy substances have some very desirable properties of great interest to scientists – not to mention celebrities of advancing years. Slug mucus is enjoying a renaissance of sorts as an anti-aging compound in high-end cosmetics. Beyond the pursuit of vanity, it also provides a useful model in the development of new synthetic lubricants, which could one day be used to combat friction in molecular-scale nanomachines. And then there's the lowly hagfish, a pretty darn ugly eel-like creature that excretes copious amounts of slime from pores all along its body when it feels threatened in any way. That slime mixes with saltwater to transform into a sticky goo.

The hagfish puts the human mucus production system to shame: it can churn out 1 liter of mucus in less than a second, according to hagfish guru Douglas Fudge, a marine biologist at the University if Guelph in Canada. Hence the creature's Latin name, Myxine glutinosa, from the Greek myxa ("mucus") and the Latin gluten ("glue"). The resulting slime bonds to the gills of an attacking fish and blocks respiratory flow: the victim perishes by choking on snot. Should the victim attempt to chew its way through the slime to escape, the stuff will just expand further, and the victim will suffocate that much faster. The hagfish gets out of its own mess by tying itself into a knot, then pushing the knot down the length of its body to scrape off the slime.

And that brings me to another gratuitious Buffyverse reference! The long-suffering Giles turns into a Fyarl demon in “A New Man” (Buffy, Season 4), gaining the ability to shoot a sticky mucus through his nostrils that hardens into a solid and immobilizes an opponent. Excreting large globules of snot it not as showy as, say, shooting searing laser beams from his eyes, but Spike declares the ability dead useful in a fight. Just ask the hagfish. Or Peter Venkman in Ghostbusters.

 

 

Mucus is what’s known as a “phase-change” material because it moves from liquid to solid. The change is usually triggered by temperature (hot to cold, or vice versa) or environmental factors (wet to dry, dry to wet). Mucus is made up of protein-and-sugar molecules (mucin), as well as lots of water, which gives the material its slippery texture. As the substance loses moisture, it becomes more rigid, undergoing a sort of phase transition, although scientists who study these strange materials prefer to describe the process in more vague terms: the substance goes from a “fluid-like” to a “solid-like” state. Once ejected, the substance rapidly cools down and begins losing moisture. As it dries out, it forms a hard shell.

Unlike other forms of mucus, hagfish slime doesn’t harden. It stays slimy even in very chilly water, in part because both the hagfish and its victim are immersed in salty seawater, so it never has a chance to dry out. But hagfish slime has a secret ingredient:  the usual protein-and-sugar concoction also contains long threadlike fibers. The technical term is "intermediate filaments," and these fibers are finer than spider's silk, and as strong. The fibers form protein strands that expand rapidly once the mucins comes into contact with seawater, causing the substance to “blow up” into a sticky gel. The consistency is a bit like half-solidified Jell-O, or watered-down hair gel. The fibers are so stretcy, they can enlongate like taffy to three times their length before finally snapping. Fudhe designed his own apparatus to stretch the filaments: something akin to a ping pong paddle, except with a filament where the paddle part should be. (Diagnostic electronics are embedded in the handle.)

Intermediate filaments can be found in most animal cells, creating a kind of scaffolding so that the cells are rigid enough to maintain their shape, yet still flexible enough to have a bit of give and take. That's an interesting finding, because until quite recently, most biologists had assumed cell structure was rigidly inflexible. So they were initially skeptical of Fudge's model, until French researchers traced a 3D contour of the fibers using an atomic force microscope, and also found them to be stretchy rather than inflexible.

Fudge is one of the leading experts on hagfish, which might be a dubious distinction if the creature weren't so fascinating... and if its slime weren't so complex. There's still a lot to learn about hagfish slime. For instance, the goo is ejected as a mix of disc-shaped vesciles and wound-up protein fibers (just like balls of yarn), and the vesicles burst when they come into contact with sea water, and the fibers unwind. The resulting mixture traps sea water, and that's what causes it to swell. But what keeps those vesicles from bursting prematurely? There has to be a stabilizaing compound among the ingredients.

In 2003, Fudge thought he'd found the answer when an analysis revealed very high concentrations of methylamines, notably trimethylamine oxide. That's a compound often found in shark tissue, for instance, to keep salt water from leaching bodily fluids out of the shark through osmosis. But it turned out to be something of a red herring. His team actually "milked" the glands of drugged-up hagfish, releasing the substance into air instead of salt water -- and still there was an explosion of slime. The hagfish is full of surprises. Fudge surmises that the gland might be pressurized -- kind of like how Reddi-Wip doesn't foam up until it's released from the can.

All promising materials have potential applications and hagfish slime is no exception. Its unique properties could help save human lives by curtailing bleeding in an accident victim during surgery, for example. The mucus would expand upon contact with the blood (which is mostly water and salt), staunching blood flow. That stretchy property is another bonus for potential applications. Fudge compares them to the plastic rings tha hold together a six-pack of beer: pull them apart and they syart to loosen and deform; in the case of the fibers, they actually rearrange into new molecular formations, eerily similar to spider silk. So those amazing fibers could be used -- or synthesized -- to make ultra-light yet super-strong textiles ("bio-steel"), as well as biomedical devices, tissue engineering and biosensors. And as any hagfish could attest, mucus is a terrific defense mechanism, which is one reason why the U.S. military is investigating its properties for military applications.

More frivolously, a group of students in British Columbia figured out how to use hagfish slime as an egg substitute in scones; they believe it could also serve as a thickening agent in eggnog. They failed to include the recipe in their report, but an interpid blogger at the Museum of Awful Food adapted a recipe for just that purpose, which we reproduce here (duly credited) for those in need of some fresh-baked hagfish slime scones for Sunday morning. If you make them, be sure to let us know how they taste; we share the blogger's skepticism that hagfish slime will be an effective substitute, given that egg yolk plays a big role in emulsification and texture....

Hagfish-Slime Cheddar-Gruyere Scones

4 cups all-purpose flour
2 tablespoons baking powder
4 teaspoons sugar
1/2 teaspoon salt
1 cup (two sticks) chilled unsalted butter, cut into 1/2-inch cubes
2 cups (packed) coarsely grated extra-sharp yellow cheddar cheese (about 9 ounces), or a mix of 6 ounces cheddar and 3 ounces gruyere.
1-1/2 cups chilled heavy whipping cream
6 tablespoons hagfish slime

Preheat oven to 375F

In a food processor, blend flour, baking powder, sugar, and salt. Cut in the butter using quick pulses until the mixture resembles coarse meal. Add cheese and cut in using quick pulses. In a small bowl, whisk together the cream and hagfish slime. With the food processor running, add cream mixture through feed tube. Process until dough just holds together – don’t overmix!

Turn dough out onto a lightly floured work surface. Gather the dough together and divide into quarters. Pat each quarter into a round just short of 1 inch high (it should be about 6-7 inches in diameter). Using a clean, sharp knife, cut each round into six wedges. Transfer half the wedges to ungreased baking sheets lined with parchment paper, spacing them about 2 inches apart.

Bake the first batch of scones until the edges just start to brown and a toothpick comes out clean, about 20 minutes. Transfer them, still on their parchment paper, to a wire rack to cool at least 10 minutes, during which time put in the second batch of scones.

Serve warm or at room temperature. The scones will stand for about 8 hours. Do not refrigerate. If you want to reheat them, warm them in a 350F oven for about 5 minutes.

 

what do we mean by "how much oil is left" in the gulf?

If Shakespeare were alive today, he might suggest that PR/branding/marketing people should go before lawyers.  The spin doctor's job is to make their company look good - even when it shouldn't.  The existence of spin doctors is reason number one why we must fix our badly broken education system.  If science teaches one thing, it is skepticism:  People shouldn't be so anxious to be told what to think.

This week marked the first peer-reviewed study of the Gulf Coast oil spill.  Big disclaimer here - it takes weeks (sometimes months or years) for research to make it from research to print, so the results are from measurements made in June; however, there are many more research reports to come.  The Truth is likely to be known only after multiple research groups have published on different aspects - probably on a timescale of years - and all of their data is analyzed in aggregate.  Science aims for precision, not speed. 

The last few weeks have brought heated debates on radio and television arguing over exactly "how much oil is left in the Gulf".  Estimates vary from "none" to "more than seventy-five percent".  How can people looking at the exact same system come up with numbers that are so different?

How much oil was released into the Gulf?  The National Incident Command (mostly the federal people in charge of managing the cleanup) uses a figure of about 5 million barrels and, on August 2nd, noted that about 17 percent of the oil released from the spill has been removed.

On August 19th, Ian MacDonald (a biological oceanographer from Florida State) testified in Congress and presented a very interesting fact:  the 5 million barrel total includes oil that was pumped directly from the well onto ships after the first capping attempts.  Initially, this larger figure doesn't make sense - why would the government use a bigger number? 

Because if you include the oil pumped directly from the well to a tanker, you've "removed" a higher percentage of the oil.  MacDonald (who argues that the total amount of oil that actually was released into the water was 4.1 million barrels) says that six percent was burned and four percent was skimmed.  If you use his numbers, a total of 10 percent of the oil was 'removed' from the environment.  The government number of 17 percent isn't wrong - but you can't compare the two numbers head to head.  The higher number sounds better, but it's important for the consumer (of information) to know what that number actually represents.

A report from NOAA (National Oceanic and Atmospheric Administration) in early August estimated - and that's an important word - that 74 percent of the oil from the leak had been: captured directly from the well; skimmed; burned; dispersed chemically; dispersed naturally; evaporated;  or dissolved into microscopic droplets. The rest of the oil washed ashore.  On August 4th, Carol Browner said on the Today Show that "more than three-quarters of the oil is gone."

Salad dressing made with oil and vinegar (or water) presents a challenge in mixing, as I've written about in the past.  Oil molecules don't like water molecules and water molecules don't like oil molecules.  You need to either whisk in the oil or shake it vigorously to form an emulsion.  An oil-in-water emulsion consists of very small droplets of oil suspended in water.  Most salad dressing recipes include dispersants of some type. Homemade dressings rely on things like mustard and egg yolk.  Commercial salad dressings use more exotic dispersants.  Few people call them dispersants, but these additives encourage the formation and persistence of the emulsion, which is pretty much what a dispersant does. 

I don't see any oil after shaking the bottle of vinaigrette in the fridge.  Is it 'gone''?  Evidently not, because the calorie count doesn't have separate columns for 'shaken' and 'not shaken'.  It's definitely 'not visible', but it sure the heck isn't 'gone'.

I happen to like my vinaigrette more on the vinegar side than the oil side, so I typically use a lower ratio than the recommended 3:1 oil:vinegar ratio for a classic vinaigrette.  My eating companions rarely agree with my acidic preferences, so I usually make the salad dressing with the 3:1 ratio and then add additional vinegar to a small container just for me.  That decreases the oil concentration, but not the absolute amount of oil - it's just spread out more than it was before.  That's not 'gone' either.

It would be really nice to have an equation that predicts how long oil takes to break down in seawater.  Such an equation does exist - in fact, a number of different models exist.  MacDonald's Congressional testimony makes the point that federal report (which makes no secret that its numbers/predictions are based primarily on theory) doesn't indicate which scientific formulae, models or predictors they used for their estimates. 

The Science paper researchers (along with researchers at other institutions that have peer-reviewed papers coming out soon) dropped sensors into the water and some even sent a submersible to look various 'plumes'.  The lead researchers on the Science paper (from Woods Hole Oceanographic Institute) reported on over 57,000 chemical analysis on a plume "only" 200 meters thick and about 2 kilometers wide over two weeks in June.  The plume measured was about 3,600 feet below the surface and extended more than 20 miles southwest of the well, traveling at about four miles a day.  The caveats, of course, are that this study occurred before the well was capped and two months ago. 

The use of the word 'plume' may be a little misleading because this is a collection of small oil droplets, presumably formed by the dispersant or natural actions.  It's not the billowing cloud you might picture. The Science paper reports significantly higher concentrations of a number of toxic compounds, including benzene at a rate of 50 micrograms per liter (which is 0.05 parts per million).  One part per million is about one drop in 40 gallons. The maximum allowable concentration of benzene in drinking water is 5 parts per billion, which is 0.005 parts per million or ten times less than the concentrations they measured. (Incidentally, commercial salad dressing is required to contain 30% oil.)

Dispersing is (in my opinion) not the same thing as removing.  How do we actually remove oil?

Crude oil is a collection of many different types of hydrocarbons, the exact composition of which varies from location to location.  The molecules, all of which are carbon and hydrogen atoms in various configurations, are separated into fractions according to their boiling points. The lighter fractions have fewer carbon atoms (and by association, fewer hydrogen atoms) and lower boiling points.  The pie chart below is representative of what might flow through a pipeline carrying Gulf Coast crude (See Appendix 6-A). Boiling points are shown in parentheses after the specific fraction name.

The light ends through medium naptha generally have a composition like gasoline, while the heavier components are more like oils.  A representative molecule from the gasoline range would be octane or isooctane (both C₈H₁₈), while a representative molecule from the oils side would be paraffin wax (C₂₅H₅₂).  The heaviest components of crude oil are like the binders for asphalt.

What everyone is counting on to actually 'remove' the oil are specific types of marine bacteria that eat oil.  The bacteria with the best PR appear to be Alcanivorax borkumensis, which loves hydrocarbons for breakfast, lunch and dinner.  They prefer alkanes, which are saturated hydrocarbons and very prevalent in crude oil.  David Valentine of UCSB has a nice video showing the dispersant and the bacteria's effects on oil in water on the PBS Newshour website.

If you've ever watched bacteria grow on bread (either due to a science project or reluctance to clean the fridge), you know that the growth of a bacterial colony depends on specific environmental conditions.  A. borkumensis likes water temperatures in the range of 20-30 C, and a 3-10 percent salt concentration, which makes it ideal in marine applications. 

A group at Bangor University studies the limiting factors this bacteria's growth. We already know that the bacteria population won't grow unless there is plenty of food (not a problem in this case).  The Bangor group has been studying whether you can 'fertilize' these bacteria to get them to grow faster.  They are examining how nitrogen and phosphorus may stimulate growth of the bacteria to allow them to deal with very large oil spills.

These oil-gobbling bacteria need oxygen to survive.  You may also have heard reports that scientists are concerned that the bacteria colonies could grow so large that they significantly de-oxygenate the water.  So far, that doesn't look like a problem.

The federal report, which has been widely quoted, says that early signs suggest the oil is “biodegrading quickly."  A number of scientists quickly challenged this assertion.  Bacteria's metabolism decreases as the temperature decreases.  Water gets colder with depth, so bacteria metabolizing oil will be less efficient at lower depths. One of the problems with dispersants is that, at some oil droplet size, the force of gravity exactly counterbalances the buoyant force, so droplets are stuck at a particular depth.  It may take a very long time for these smaller droplets at lower depths to be eaten - remember that the Science paper looks at a plume 3600 feet below the surface.

There are also a lot of unknowns.  We have precious little data about how the dispersants used may change the bacteria's ability to digest oil.  I've been looking for hard information about exactly which components of crude oil the bacteria eat and - sort of importantly - the by-products of the eating process. Some groups have engineered bacteria so that they eat oil and produce plastic. I am suspicious that CO₂ might be a by-product of the metabolism, since it's released in human metabolism of sugars (hydrocarbons with oxygen) and combustion of gasoline. 

This is an interesting case study in communicating science.  The federal report that came up with the 75% 'gone' number was very specific about what they meant by 'gone', even though they included some things I wouldn't necessarily include.  By the time the information got reduced to a soundbite, though, the details were 'gone'.

Research scientists have been pretty unanimously vocal about their skepticism of the 75% figure. It is interesting because we usually go out of our way to emphasize the limits of validity of our conclusions, we make all kinds of caveats and generally put so many conditions on our results that our PR people want to pull out their hair (or ours).  I think the vocal outcry from the scientific community is because conclusions are being presented as 'known', when in fact, they are very tenuous.  There is nothing like drawing conclusions before the data are all in to get scientists riled up.

A very important role of science education - usually overlooked because it isn't easy to test - is teaching people how to think logically and rationally.  This becomes even more important when people are inundated with information from all sides, including professionals whose job it is to promote specific agendas.  It ought to be an attractive theme for today's students:  Don't take anyone's word - prove it for yourself.

here, listen to this while I'm away

While you're waiting for fresh blogging fare at the cocktail party (it's coming soon! we promise!), let me point you to the hot new diavlog I did for BloggingHeads.tv, featuring me and author Mary Roach, whose latest book is the excellent Packing for Mars. Regular readers know I'm a longstanding fan of Mary's work, and she's just as fun and engaging over the phone as she is in print. We chatted about zero gravity (she got to ride on the Vomit Comit!), what freefall is really like during a spacewalk, the psychological complications pertaining to sex in space, Mary's foray into space toilet training, and she also had the chance to redeem the reputation of Enos the Space Chimp, unfairly maligned for masturbating during his NASA space mission. (Although if he had, Roach says, that would have given Enos the dubious honor of achieving first orgasm in space.) Go on, you know you want to give it a listen. And we'll be back soon with new posts before you know it.

FROM THE ARCHIVES: down the rabbit hole

It's madness preparing for a book launch (August 31, y'all), which means it's time yet again for a trip to the cocktail party archives. This week's offering is inspired by Annalee's post over at io9 reporting on two new papers published this week, in Science and Nature, confirming that hallucinogenic drugs stimulate healthy brain activity -- possibly even promoting the growth of neurons. I happen to have blogged about the possible useful purposes for LSD back in November 2007, inspired by a Dali exhibit in Los Angeles.

While vast numbers of Angelenos stormed the malls in search of holiday shopping bargains over the weekend, the Spousal Unit and I attempted to inject a bit of culture into our Saturday evening by meeting local pals at the Los Angeles County Museum of Art to take in the new Salvador Dali retrospective. Dali is my favorite of the Surrealist painters, but the experience proved even more surreal than expected. Also shorter. I never made it past the halfway point of the exhibit, thanks to a sudden onset of illness. (Yes, I'd been feeling odd earlier. I just didn't realize I was getting genuinely sick.) I was standing there, taking in the dream-like imagery of early sketches and paintings and intermittently watching dueling film screens showing Un Chien Andalou (really disturbing stuff!) and L'Age d'Or, when there was a roaring in my ears and the images started blurring together into a kaleidoscope of color. I barely made it to the ladies' room without passing out. The Spousal Unit gallantly took me home shortly thereafter, whereupon I proceeded to sleep for the next 14 hours.

In retrospect, it was rather fitting that I saw the exhibit (okay, the first half of it) in what amounted to a semi-fugue state, since Dali incorporated his own dream-like imagery in his paintings -- clearly much more Freudian and twisted than my own dreams, which tend to focus on more mundane frustrations, like trying to pack in time for a flight. (This might explain why I am a science writer with a practical bent, rather than a famous Surrealist painter.) The only thing that might have been more appropriate would have been to view the exhibit while under the influence of LSD or magic mushrooms. Speculation about Dali's possible use of LSD or 'shrooms abounds, but LSD didn't appear on the scene until the late 1930s,  and didn't become popular until the 1960s. Dali's paintings were weird long before that. The artist liked to experiment, but didn't advocate habitual drug use: "Everyone should eat hashhish, but only once," he observed. He didn't need drugs to be creative. As he once wrote to LSD advocate Timothy Leary, "Why do you need LSD, when you have Salvador Dali?" Leary himself admitted that Dali was "the only person who can paint LSD without having to take LSD."

Personally, I have never dropped acid, or eaten magic mushrooms, or ever done much in the way of drugs apart from a few exploratory puffs of marijuana in college -- not for moral reasons, it just didn't interest me. I was more about exploring and experiencing reality than escaping it, and I suspect Dali was, too. This was a man with a powerful lust for life -- maybe a bit too powerful at times. But his passion and appetites extended beyond the physical to the intellectual: early on, he was devoutly Freudian, clearly evidenced in his paintings from that era, but he was also fascinated by mathematics, geometry, and physics. The famed melting clocks in The Persistence of Memory may have been at least partially inspired by Einstein's theory of relativity (time is relative, not absolute), and in the 1950s, Freud was supplanted by Werner Heisenberg (particularly the Uncertainty Principle) as Dali's intellectual father-figure: Dali painted The Disintegration of the Persistence of Memory in 1954 to symbolize that transition from his early to his later work. (The painting almost looks like it's being quantized.) He was one of the first modern artists to incorporate holography into his work, and also experimented with visual representations of a fourth spatial dimension.

And if his comments about hashhish are to be believed, he also had an interest in chemistry. I wasn't able to find any record about whether Dali ever tried LSD, but I wouldn't be surprised if he had -- just once. It's a fascinating substance in its own right. Technically, it's lysergic acid diethylamide, a member of the tryptamine drug family. It's derived from ergot, a grain fungus commonly found on rye, and was first synthesized in 1938 by a Swiss chemist named Albert Hoffman. He wasn't looking for psychedelic drugs; initially, at least, he had hopes that it could be used as a circulatory and respiratory stimulant. (He did eventually develop another ergot derivative that became a widely used medication in obstetrics, called Methergine.) However, animal tests showed no such effects -- although he did notice that the animals became "restless" under the compound's influence.

Hoffman didn't realize what he'd synthesized for another five years, when he accidentally absorbed some of the compound through his skin. He became dizzy (just like me in the Dali exhibit... hmmm...), went home to bed, and experienced a "dreamlike state" filled with intense, kaleidoscopic colors and "extraordinary shapes." Those effects were just from trace amounts of the stuff. Three days later, Hoffman repeated the experiment with a much larger dose of 150 micrograms (20-30 micrograms is sufficient to cause mild effects).

That day -- April 19, 1943 -- became known in his journals as Bicycle Day, because Hoffman was so incapacitated by the dosage that he had to ask his lab assistant to give him a ride home on the latter's bike. Hoffman had a pretty bad trip to start with, becoming convinced he was demon-possessed, that his next-door neighbor was a witch, or that he had gone insane, but after a few hours, the pleasant pretty images and psychedelic colors returned, along with a bit of synesthesia: he wrote that every sound was transformed into optical perceptions. And far from being hungover the next day, he was a bit tired, but cheerful and optimistic, with heightened senses.

Hoffman's discovery was initially embraced as a possible drug treatment for mental illness, most notably schizophrenia, but by the 1950s this proposed connection had been disproved. The CIA notoriously -- and controversially, since the subjects didn't know they were participating in such a trial -- experimented with LSD as a possible mind control drug during the Cold War, eventually concluding that it was of little practical use in that application. (So did the British government; in fact, one 19-year-old British test subject reported seeing "walls melting, cracks appearing in people's faces... eyes would run down cheeks, Salvador-Dali-type faces...")

It wasn't until 1961 that Leary, then a psychology professor at Harvard, and his colleague Richard Alpert, brought the substance into the popular culture at large. They conducted a study of 400 test subjects who were administered LSD, and noted that 90% wanted to repeat the experience, 83% said they had "learned something or had insight," and 62% believed the experience had changed their life for the better. As Leary and Alpert delved deeper into the drug's effects, they became less about the science, and more about spiritual enlightenment, turning into hallucinogenic gurus of the Flower Power movement with their slogan, "Turn on, tune in, drop out." By 1971, LSD had been banned in the US, even for scientific study, and many other countries followed suit.

And yet, LSD has, if not exactly flourished, done a pretty brisk business over the years, maybe because it's pretty easy to make. You just take the liquid solution and spray it onto a substrate of some kind. Initially, people soaked sugar cubes in the substance, and then started encapsulating the LSD in pill form. Next came thin squares of gelatin, dubbed "windowpanes," and finally, makers hit on the idea of using blotter paper: sheets of paper soaked in LSD, which is dried and cut into small individually dosed squares that the user could simply pop onto his/her tongue, or swallow. This approach appealed artistically, as well, since the various distributors could print their own unique designs on the blotter paper -- kind of a trademark, or signature. LSD-related blotter paper is kind of an art form all its own

For all its reputation, LSD isn't particularly addictive. Most users are young (18-25), and their interest quickly wanes, especially if they have a bad trip. Tobacco, cocaine, and alcohol produce far more addictive behaviors. True, LSD is powerful stuff: a single dose between 100 and 500 micrograms, about one-tenth the mass of a grain of sand, is sufficient to induce several hours of psychedelic visions. But while people may be injured while under its influence, there are currently no fatalities on record directly attributable to an overdose of the drug. We always hear about LSD-related flashbacks, but there is evidence that these tend to occur primarily in those already prone to some psychological problems. And the tales that LSD crystallizes in spinal fluid or in fat cells where it can dislodge and cause nasty flashbacks many years later isn't supported by medical evidence. LSD breaks down completely in the body within hours, and any metabolites are purged within a few days.

In fact, there is evidence that it might be an effective treatment for cluster headaches. (This was actually featured in an episode of House, wherein magic mushrooms were used to treat the cluster headaches of a young chess champion.) Cluster headaches are like migraines, only much, much worse: they are characterized by excruciating pain that can last from 15 minutes to three hours, and attacks can occur anywhere from two to eight times a day in the midst of a cycle. Peter Goadsby, the world's leading researcher on cluster headaches, has described the pain as being "worse than natural childbirth or even amputation without anesthetic." Given that, and the profound ineffectiveness of most conventional drug therapies to date, it's not surprising that chronic sufferers are turning to illicit substances like LSD and magic mushrooms (technically, psilocybin).

The Multidisciplinary Association for Psychedelic Studies (MAPS) supported one of the first scientific studies of this reported efficacy, conducted by Andrew Sewell and John Halpern of the Alcohol and Drug Abuse Research Center at McLean Hospital in Belmont Massachusetts. It's affiliated with Harvard, where Leary and Alpert did their controversial LSD research in the early 1960s, but the similarities end there. Sewell and Halpern show no signs of turning into New Age gurus of any sort; they're interested in the science. They interviewed over 50 sufferers of cluster headaches who admitted to self-treating with psychedelics to alleviate their symptoms (medical records verified that those studied did indeed have the condition). And they found that ingesting psilocybin or LSD reduced cluster headache pain, and even could interrupt cluster headache cycles to that no more headaches occurred. Eighty-five percent said that the illegal drugs aborted attacks, stopping them altogether in 52% of those surveyed.

The study is admittedly flawed in its design, since there are so many potential sources of bias, but Sewell and Halpern think their findings warrant greater study, and applied to the FDA for permission to conduct a randomized, double-blind, carefully controlled experimental study of the effects of LSD and psilocybin on cluster headaches. No one is quite sure why the drugs might be effective, but the working hypothesis is that LSD and psilocybin are both tryptamines, with chemical structures very similar to natural neurotransmitters like serotonin. MAPS is partially funding the study, as well as investigations into psilocybin as a treatment for obsessive-compulsive disorder, or ecstasy as a treatment for post-traumatic stress disorder. Not surprising, MAPS describes itself as "a nonprofit alliance of scientists and campaigners that funds research into the benefits of psychoactive drugs, and lobbies for changes in US laws." I guess we'll all have to stay tuned in to see what transpires next.

All that research into LSD from my sickbed (*cough, moan*) made me grateful that I don't suffer from cluster headaches, and placed my own mild discomfort and general wooziness into proper perspective. And I'm almost feeling back to my normal self, although that might partly be due to euphoria over the shiny new iPhone the Spousal Unit purchased for me as an early Christmas present. That, and plying me with bowls of chicken soup and pomegranate juice, seems to have kicked that nasty ol' virus to the curb. We have the bestest Spousal Unit ever. Now I can answer email, make calls, and download nifty YouTube videos, like this clip of the incomparable Grace Slick performing "White Rabbit" with Jefferson Airplane -- a song she has publicly admitted is in part about LSD, albeit mostly inspired by (and openly alluding to) Lewis Carroll:

One pill makes you larger
And one pill makes you small
And the ones that mother gives you
Don't do anything at all
Go ask Alice
When she's ten feet tall

And if you go chasing rabbits
And you know you're going to fall
Tell 'em a hookah smoking caterpillar
Has given you the call
Recall Alice
When she was just small

When men on the chessboard
Get up and tell you where to go
And you've just had some kind of mushroom
And your mind is moving low
Go ask Alice
I think she'll know

When logic and proportion
Have fallen sloppy dead
And the White Knight is talking backwards
And the Red Queen's "off with her head!"
Remember what the dormouse said:
Feed your head*

*Actually, the Dormouse never said that, per Chapter XI of Alice in Wonderland: "'But what did the Dormouse say?' one of the jury asked. 'That I can't remember,' said the Hatter." So the Divine Ms. Grace took some artistic liberties.

_+3=5+7=_: it depends what 'equals' equals

Pop quiz!  Answer the following before reading further:

A:  6+9=__+4

B:  __+8=12+5

C: __+3=5+7=__

D:  True or False:  6+8=3+11

E:  160=___

I've become painfully aware recently how sloppy communication can be.  I am surprised how many times I have to reply to an email asking for clarification because of unclear writing or simply not taking the time to think things through.  And that's with other scientists.

The GK-12 program I run at the University of Nebraska places graduate students in upper elementary, middle and high schools to work with teachers on improving math and science education for their students.  We spend an entire day of the week-long orientation discussing communication.  I break it down roughly into "scientific" communication and "normal person" communication.  That's probably not a fair breakdown, but we really have to emphasize to the students that, although it is perfectly OK to reply to a scientist's idea with "here's why that won't work", it's a death knell for the relationship if you do that with a teacher (or, often, a spouse).

At the end of the year, one of my students made an observation I wholeheartedly endorse.  "I like scientific communication better," she said, "It's just faster."  And clearer, I would add. 

Although Jennifer and I come from very different disciplinary backgrounds, I think one of the reasons we've hit it off is that we share the trait of wanting to use words properly.  Jennifer recognizes that scientists and mathematicians use words and symbols to convey very specific meanings.  If I use the word "velocity", she's likely to ask if there's a reason I didn't say "speed".  (Speed is a scalar, velocity is a vector.  Sometimes it makes a difference, sometimes not.)

Nowhere, perhaps, is the specificity of symbols more rigorous than in mathematics.  My mother was a graduate student in math, then economics, while I was in elementary and middle school.  I remember seeing her scribblings filling up scads of yellow legal pads and asking her once "when do I get to learn this language?"  And math is definitely its own language.  One of the biggest problems teaching (or communicating) science and math is that sometimes words mean different things in the discipline than they do everyday life.

But the equal sign should be an easy one, right?  It means, well, equal.

Apparently, American students have a much less clear idea of the meaning of the equal sign than their Chinese, Korean and Turkish compatriots.  A study by Capraro, et al in Psychological Reports (106(1), 49-53 (2010)), which draws on their previous data in Li, et al. (Cognition and Instruction, 26, 195-217 (2008) compares 6th grade students from different countries.  Both papers originate from the research group of Mary Margaret Capraro and Robert M. Capraro at Texas A&M University.  Incidentally, "et al." translates literally in Texan to "and them".

The results from the first two questions I posed from their study (6+9=__+4 and __+8=12+5) were surprising/appalling.  Only 28.6% of American students got these questions right.  The Chinese and Korean rates were in the 90+% range and the Turkish rates were 61% and 79% respectively.

As is often the case, we learn more by looking at the wrong answers than the right ones.  The first two problems were designated "Type A" and "Type B" - similar, except the missing numbers are on opposite sides of the equal sign.  The third problem - the one that lent itself to the title of this blog - is classified as "Type C" and provides a slightly different probe of the understanding (or misunderstanding).

For the "Type C" problem __+3=5+7=__, American students got the first blank right 23.8% of the time, while the rates for other students were 98.6% (Chinese), 86.5% (Korean) and 60.2% (Turkish).  Interestingly, the correct rates for the second blank were much more comparable:  86.7% (American), 97.9% (Chinese), 93.3% (Korean) and 86.0% (Turkish). 

What this strange disparity between the first and second blanks tells us, the authors argue, is that American students disproportionately don't understand the equals sign.  The most common wrong answer for the first blank was "2".  It is true that 2+3 = 5, but 2+3 definitely doesn't equal 5+7.  Almost 90% of the students recognized that "5+7=12", but a significant number of those got the first blank wrong.  This is apparently a common misconception among American students that isn't seen nearly as much in student from the other countries studied: the belief that the answer is the number immediately following the equal sign.

In their previous study, the authors used the True/False question "6+8=3+11?" to test understanding of the reflexive property of the equal sign.  Reflexive, which I had to look up, means a=a. The popular phrase "it is what it is" embodies the mathematical philosophy of reflexivity.  The educators doing the study,  though, realized that students with the misconception I mentioned above - the answer is the number immediately after the equals sign - would get this question wrong for that reason and not because they don't understand that a=a.

In their new study, they replaced that question with "160=___", and expected the blank to be filled in with "160".  But a number of students put an operation in that blank, like 80*2 or 40+120. Those answers are not wrong, but (strictly speaking), but they indicate that those students look at the equal sign as indicating that a mathematical operation is required and not solely as a representation of equality.

I've always thought of the equal sign as the pivot on a see saw.  Whatever is on the left has to balance with whatever is on the right. If I fill in the blank with a 6, there's only 9 on the left and 12 on the right, so the see saw isn't balanced.  OK, I can't draw a picture for the multiple equals signs on one line, but you get the idea.  Who ever thought that something as seemingly simple as 'equal' could be so complicated?

At this point, you might be thinking that this seems like a bunch of quibbling over a precise definition of interest only to the highly mathematical.  One of the original motivations for this study was the low performance of American students relative to their international counterparts on standardized tests like the TIMSS and the PISA tests.  There apparently isn't much explicit attention to the equal sign in middle school curricula and, the authors (along with other math educators) believe that not understanding the equal sign puts students at a distinct disadvantage when it comes time to learn algebra.  If you put 'x' in place of the blank, you realize you're actually doing algebra answering the questions I posed at the start of the blog.

These misconceptions carry over to physics.  For example, consider the force on an object falling:  F = mg.  The force gravity exerts on a ball falling through the air is equal to the product of its mass times the acceleration due to gravity (in the absence of air resistance - sorry, I felt compelled as a professor to add that.  I couldn't help myself.) 

Students identify gravity as a force, but a significant number of them also identify a force "F" in the above equation as distinct from the force of gravity.  The problem gets worse when there are multiple terms on the right-hand side of the equation due to multiple forces.

It is amazing that something so seemingly fundamental can so impact a student's education.  One of the (many) reasons I am looking forward to Jennifer's book is that I speak fluent calculus.  Imagine trying to explain to someone how to walk.  That's what me teaching calculus is like.  One of the best reasons for using peer teaching (students teaching each other) is that they explain things in ways I wouldn't have thought to use.  Listening to them explaining how they understand an idea helps me realize how I can explain it better.  It's research like this that reminds me that sometimes the better part of teaching is listening.

ADDED 8/13/10:  An interesting study notes the need for better prepared mathematics teachers, as well as a significantly strengthened math curriculum.  Jennifer and I have been talking a lot here recently about stereotypes. Although we've focused on those in the media, this article, by researchers at the University of Chicago in PNAS, suggests a scary chain:  Female first and second grade teachers who are anxious about math pass that anxiety along to their female students. More female students are likely to agree with the suggestion that boys are better than girls at math after being exposed to this anxiety, and the female students who did agree with this stereotype performed worse in math as the year went on.  Great article and PNAS makes the full text publicly available.

AND:  A Christopher E. Granade speaks on the topic of 'equal' - a very nice post focusing on the importance of relationships and how that is really at the base of math and science.

we can haz diversity?

A couple of months ago, co-blogger Diandra wrote about scientist stereotypes she encountered in a 4th grade class, in which very few of the kids believed she and the other female scientists who visited were, you know, actual scientists, because everyone knows scientists are all nerdy white guys in lab coats, right? And she trotted out the familiar refrain of how the media fosters such inaccurate stereotypes, particularly film and TV. We had a spirited email exchange at the time, and this seems like a good time to revisit the topic, since I'll be talking about it quite a bit during SETI-Con this coming weekend. (If you're in the Bay Area, stop in and say hi.)

We can certainly debate the extent to which popular culture reflects a society's values, and to what extent it shapes those values in turn; it's probably a bit of both. And I'm not sufficiently familiar with the kinds of films and TV shows your average 4th grader might be watching to build an effective counter-argument to Diandra's charge at the K-12 level. But I can make a very strong case that, especially when it comes to the current crop of adult-oriented TV shows, there's an astonishing -- and likely unprecedented -- diversity in the range of fictional characters who happen to be scientists. We've come a long way, baby, over the last 50 years, in terms of how scientists are portrayed in film and TV.

I was reminded of this back in April, when the Science & Entertainment Exchange sponsored a screening of an independent documentary by David Gargani called Monsters from the Id, as part of the Los Angeles United Film Festival. Gargani's film weaves the intersecting themes of over thirty classic films in order to tell the untold story of the Modern Scientist and his role in inspiring a nation. (Science fiction buffs will recognize that the title alludes to the 1950s classic film, Forbidden Planet, itself a reworking of Shakespeare's The Tempest.) Check out the trailer:

We held a panel discussion after the screening, with JPL scientist Kevin Hand, marine biologist turned filmmaker Randy Olson, and Scripps Institute biologist Kristen Baldwin, moderated by yours truly. I think we all pretty much agreed that while we enjoyed the film, we weren't crazy about the basic premise, namely, that during this Golden Age of science fiction films, the mad scientist stereotype gave way to the scientist as hero and family man, and this was a Positive Thing for science. I suppose it's accurate enough, but the operative word here is "man" ("white man"). Women are mostly decorative in films from this era, and/or damsels in distress, and Forbidden Planet was no exception (Altaira merely exists to order shiny new dresses from Robbie the Robot, and tempt good men away from their duties). They certainly weren't depicted as strong, smart, independent scientists in their own right. And scientists of color (any color) are nowhere to be found.

Such is no longer the case. Sure, the time-honored stereotypes still exist -- mad scientists, social misfit nerds, bookish Plain Janes -- but they're part of a much broader landscape of scientist characters. In fact, I'd argue that we might just be in the midst of a different kind of Golden Age of science-themed film and TV -- one where diversity is the name of the game. Consider this random sampling of Hollywood scientists just from the last five years or so (warning: there may be a few inadvertent spoilers):

NCIS. How could you not love Abby, the pig-tailed punk/Goth sassy lab technician with mad hacking skills, who is so hip and edgy, she makes the cool kids look like nerds? She is rightly the most recognizable (and wildly popular) regular cast member on that show.

Numb3rs. You've got dreamboat mathematician Charlie Eppes, along with his best friend Larry the absent-minded physicist. Larry might be a bit of a stereotype, but Amita, Charlie's brilliant computational physics girlfriend, most definitely is not: she is a beautiful, strong woman in a traditionally male field, she's Indian (but not an obvious ethnic stereotype), and she contributes as much to solving FBI cases as any of her male counterparts. (Ditto for the female FBI agents on the show.) For a season or two, we also had a female physicist heading up the CalSci math and physics departments, played by the Rubenesque Kathy Najimy, who ended up dating Charlie's father (a retired civil engineer).

C.S.I. (Vegas edition). A.k.a., "pretty people doing science." It proved to be a winning formula. Gil Grissom brought the catchphrase "follow the evidence," into millions of households, along with science-minded characters of all shapes, colors and sizes. Greg the DNA technician (he later became a full-fledged field agent) is a white male in a lab coat, true, but he's cute, smart, listens to great music, and has a passion for Las Vegas history. And he's surrounded by smart attractive cohorts with colorful personal histories: a former stripper/single mom turned CSI, a black CSI with a gambling problem, a female CSI with a tragic family history, etc. The show's strength is its diverse cast, since their varied backgrounds drive some fascinating subplots and supply necessary conflict... and personal growth.

Bones. Head vs. heart is a major theme in this series, which is why the lead character of Temperance Brennan often struggles to steer clear of jargon when she communicates with non-scientists, and with reconciling her messy emotions with her rational scientific training. But she's beautiful, spunky (with martial arts skills), idealistic, and she has romantic entanglements just like anybody else. And like Grissom, she has a lab filled with smart, attractive scientists of diverse backgrounds. Okay, Zack's social awkwardness led to him being imprisoned for colluding with a crazy serial killer early on in the series, but ya gotta love Jack Hodgins, who revels in analyzing bugs and various icky substances, and devising nifty -- and often risky -- lab experiments to test his hypotheses ("King of the Lab!"). The man is passionate about his science, he's rich, smart, good-looking, and chivalrous, and he makes science look good by being so.

Lost. Sure, there was a lot of magic and mysticism in this series, but they had some terrific science-minded characters, most notably Season 5's heartthrob physicist Daniel Faraday. There was also Charlotte, the beautiful archaeologist, and Sayid, the sexy, morally ambiguous Iraqi assassin with mad electrical and mechanical engineering skills (he rebuilt his share of radios out of salvaged parts).

Eureka. You want diversity? Eureka gives you a whole town full of brilliant scientists, in lots of different fields. There are men, women, blacks, whites, Asians, all of them brilliant and valued for being so. Tesla High School's "cool kids" are the science whizzes and honors students, not your stereotypical jocks and cheerleaders. An average IQ is grounds for ridicule and being a social outcast. My favorite transformation on the show occurred with Carter's daughter, Zoe: a runaway rebellious sort who found her true self in Eureka when she discovered she was actually incredibly smart and talented in the sciences. She might never have figured that out on her own, and provides a terrific role model for high school students.

Fringe. Okay, Walter Bishop fits the "mad scientist" stereotype -- he's literally mad, having been rescued from an asylum to help Olivia and his son Peter solve the weekly mysteries and ferret out the Big Multi-Dimensional Mystery that forms the narrative arc of the series. But he's charming and lovable, a truly original character, and his troubled relationship with Peter forms the heart of the show. Audiences adore Walter; he's the main reason they tune in, week after week.

Breaking Bad. Chemistry teacher Walter White finds out he has a terminal illness and turns to manufacturing meth to raise enough money to provide for his wife and family after he's gone. He's not a hero, he's a basically good guy driven to desperate measures. And the result is a gritty, emotionally compelling drama with lots of real science woven into the background (although according to one of the technical consultants, some of the meth lab details are deliberately wrong -- for obvious reasons).

Big Bang Theory. Yeah, I know, this is the show many physicists love to hate, particularly the character of Sheldon, who is the poster child for socially inept scientists, and the root of much of the show's humor. But, like Walter Bishop, he is also the most beloved of the main characters, as evidenced by the huge cheer that went up during a Comic-Con panel last month when a clip from the series was shown featuring Sheldon. There's some validity to the criticisms. The sitcom genre traffics in stereotypes more than your average drama -- do you think Seinfeld was representative of real New Yorkers? -- and some episodes are better than others about rising above cheap laughs. But at its best, the characters on this show are smart, funny, likable people, and it's really about their relationships. It's also the top rated sitcom these days, and just snagged a record-breaking syndication deal of $1 million per episode. Bad for science? I doubt it. It means there are likely to be more scientists on TV in the future, because that's been shown to be a commercially successful model.

The point is, when I flick through the channels these days, I see a lot of diversity in how scientists are depicted. There are men and women, with varying degrees of attractiveness, some geeky, some cool, representing many different ethnic backgrounds, some socially awkward, some suave and sexy, some thin, some heavyset, some short, some tall, and so on. They have friends and families, they struggle with balancing the personal and professional, they grapple with ethical dilemmas -- in short, they are complex human beings, not two-dimensional caricatures, and they interact with each other in very interesting ways. This gives the writers a lot more creative fodder to work with, week after week, season after season, to keep the show fresh and compelling (because ultimately we're talking about fictional entertainment here, not earnest documentaries).

If scientific stereotypes persist despite all of this, can we still credibly place the blame firmly on film and TV? I just don't think it's that simple. I'm sure popular culture plays an important role in shaping public perception, but it does so in conjunction with other influences that are far more nebulous and tough to pin down. If we're too quick to take the fallback position that it's all popular culture's fault, we won't get very far in furthering our understanding of the myriad influences that shape our perceptions of science and scientists -- which in turn will give us clues about how to effectively change the negative perceptions.

GUEST POST (#PDEx): the scientist and the anarchist (part I)

NOTE: Among those who left the SEED Science Blogs fold in the wake of PepsiGate is Eric Michael Johnson, proprietor of the excellent Primate Diaries blog. While he's casting about for a new home, he hit upon a novel idea: a Primate Diaries in Exile blog tour! We at the cocktail party are delighted to serve as one of many stops on the tour, and that Eric has written a fantastic historic account about Huxley, science and anarchy. Good times! You can follow other stops on this tour through his RSS feed or at the #PDEx hashtag on Twitter. In the meantime, welcome to Cocktail Party Physics, Eric! And if this is someone's first time visiting, feel free to browse our archives.

How East London defined "Darwin's Bulldog" and brought him into conflict with the world's most dangerous anarchist.

Applicants For Admission To A Casual Ward by Luke Fildes (1857) shows a crowd of East London poor waiting in the snow, trying to gain access to a homeless shelter. Source

The first thing you noticed was the smell. It was an oppressive, suffocating odor. It assaulted your senses day and night, at work, at rest, preparing a meal, or enjoying children’s games. It pervaded every aspect of your life and soiled the very experience of living, and dying. It was the birth of modern civilization. East London in 1841 was a society on the brink of collapse. Charles Dickens used the words “pestiferous and obscene” to describe what he experienced. However, a poor resident of Soho put it much more elegantly, "We live in muck and filth . . . all great and powerfool men, take no notice wasomedever of our complaints." Open sewers, garbage littered streets, contaminated water, and overflowing cemeteries had transformed the detritus of overpopulation into a veritable miasma and the result was simply repugnant. [1]

Ignored by politicians and abandoned by those able to escape its slums, East London during the latter half of the 19th century represents one of the most profound failures of urban planning the world has ever seen. Starting in the late 1700s, modern industry and agrarian capitalism had made the open-field farming system of feudal lords and their laboring peasants obsolete. Over six million acres, or a quarter of the country’s cultivated area, were enclosed under parliamentary acts between 1750 and 1850 (and most occurred during the Napoleonic war years from 1793 to 1815). What had previously been communal lands were now off limits. Without a means of subsistence people migrated to the cities en masse, nearly tripling the size of London in a single generation (from 675,000 to 1,945,000). [2]

This was a social reengineering project of massive proportions. In much the same way that privatization of land today (backed by free trade policies) has pushed the landless poor of Latin America into the great northern cities, so the Industrial Revolution sent millions of English tenant farmers flooding to urban centers at the ushering in of the 19th. Most of them ended up in the slums of East London. Steven Johnson cites one report from the time that estimated a densely packed 432 people per acre (even with our modern skyscrapers Manhattan only houses about 110 per acre). In many slum tenements large families or groups of laborers would crowd into a single room. Without any resources for public health or sanitation – aspects of social life that had yet to be invented – and with wages depressed from the legions of poor workers, these slum dwellers were forced to survive in any way they could. In this way, London in the mid-19th century parallels many parts of our world today: teeming cities of the impoverished, lacking resources and meaningful employment, left to suffocate in their own filth. [3] It was into this environment that Thomas Henry Huxley emerged. If the city is an ecosystem, Huxley embodies the phrase “survival of the fittest.” Lanky and high-strung, estranged from his father at an early age, and the youngest of six children, Huxley was primed from birth to view life as a struggle. Born on May 4, 1825 above a butcher’s shop on London’s outskirts, Huxley was the son of a poor schoolteacher and a member of England’s newly emerging middle class (in culture though not in wealth). As such he was determined to separate himself from the ranks of the working poor. In the years to come he would claw his way out of obscurity and establish himself as a celebrated anatomist, President of the Royal Academy of Sciences, and evolutionary theorist widely hailed as “Darwin’s bulldog.” He would forge a path of his own and create a revolution in the way science was practiced. As his biographer, Adrian Desmond, would later put it:

The young hothead scrambled to the top of his profession; indeed he made a profession of science. With him the ‘scientist’ was born. [4]

An important theme that is found throughout Huxley’s life and work is one that can only be understood from his early experiences in East London: the brutal conditions of the poor. At the age of sixteen Huxley was apprenticed to a "lowlife doctor" named Thomas Chandler whose patients lived exclusively in the East London slums. In later years Huxley would describe in vivid detail the depravity he experienced:

Men, women, and children are forced to crowd into dens wherein decency is abolished and the most ordinary conditions of healthful existence are impossible of attainment; in which the pleasures within reach are reduced to bestiality and drunkenness; in which the pains accumulate at compound interest, in the shape of starvation, disease, stunted development, and moral degradation; in which the prospect of even steady and honest industry is a life of unsuccessful battling with hunger, rounded by a pauper's grave.

In one incident during a house call Huxley encountered a deformed girl nursing her ill sister. There was little he or his mentor could do for her and, out of compassion, Huxley suggested that the sick child needed a better diet than simply "bread and bad tea." In response, according to Huxley:

[The girl] turned upon me with a kind of choking passion. Pulling out of her pocket a few pence and halfpence, and holding them out, "That is all I get for six-and-thirty hours’ work, and you talk about giving her proper food."

Surrounded by such crushing poverty, Huxley anguished over the conditions that seemed to afflict both good people and bad without remorse. “I see no fault committed that I have not committed myself,” he wrote at the time, quoting Goethe. Already moved towards religious skepticism because of his voracious appetite for knowledge and his pursuit of science, Huxley now moved closer to the agnosticism that would define his life. After all, what sort of loving God could allow such horrors to persist? Where was the justice in a divine plan that forced more righteous men than he to a life of squalor, "I confess to my shame," he wrote, "that few men have drunk deeper of all kinds of sin than I." Late at night, cackles emanated from the busy pubs along Paradise Street where Chandler's slum-row surgery was located. Prostitutes offered their wares to the drunken and downtrodden while knife-wielding gangs clashed in the dark alleys, sometimes leaving a fresh corpse for the “bone-pickers” to scavenge a few pennies worth of clothing from.

With so many of his days and nights spent in the ramshackle surgery, just a hundred paces from the festering Thames, Huxley experienced “gloom with every breath” and felt his ambitions stifled. He had only one hope of advancement: a university degree. However, with only two years of formal education he was greatly outclassed by his social betters. And so, by the thin light of his lantern the young man sat grinding drugs late into the night, and reading. Humes’ History of Great Britain, Müller’s Elements of Physiology, Hutton’s Theory of the Earth. Whenever he could fit in time for personal study, Huxley maintained a punishing schedule. On Tuesdays and Thursdays he studied physiology, other days of the week he focused on “a chronological abstract of reigns”, he spent evenings devoted to mathematics, Saturday’s were for chemistry and physics with an hour of German daily. “I must get on faster than this”, he chided himself, “and let me remember this – that it is better to read a little & thoroughly than cram a crude undigested mass into my head.” He studied Latin and Greek and wrote his mother to ask for a copy of Euclid’s Geometry. The university entrance exams required a solid background in the classics and he had a great deal of catching up to do.

Interestingly, there is one title on Huxley’s reading list during this time that doesn’t seem necessary for college admission: Thomas Carlyle’s Chartism. Published a year earlier in 1840, the book was a passionate manifesto of the struggles that the poor experienced, explaining the backdrop of what would became the first major labor struggle of the Industrial Revolution. “To me,” Huxley reflected, “this advocacy of the cause of the poor appealed very strongly.” That August as Huxley ground drugs and studied anatomy, factory workers took to the streets outside demanding the right to vote, for decent wages, and a ten-hour workday. By 1841 the Chartist movement was already several years old but was still a profound mystery and a source of great anxiety to Victorian England. In 1837 six sympathetic members of Parliament and six working men wrote the first draft of The People’s Charter, a document that advocated universal male suffrage, annual elections, and an end to property qualifications for membership in Parliament. The Charter was then taken around the country to eventually be signed by 1.3 million people (nearly twice the number of propertied voters) before being presented to the House of Commons in 1848.

The Great Chartist Meeting on Kennington Common, April 10, 1848, photograph taken by William Kilburn. Crowd estimates range from 50,000 to 100,000 people. Source

The aristocracy viewed this movement as dangerous, if not outright seditious. In the year prior to Carlyle’s book, Lord John Russell (a liberal Whig in the House of Commons who would later serve as Prime Minister) had a letter sent to The Times of London requesting that reporters report on “any meeting convened by persons calling themselves Chartists” so that their “illegal transaction” could be prosecuted. Carlyle, however, referred to the democracy movement among the poor as, "the bitter discontent grown fierce and mad . . . of the Working Classes of England. It is a new name for a thing which has had many names, which will yet have many." [5] For young Huxley this struggle, and the conditions which gave rise to it, became pivotal in his development and can be seen to have influenced his thinking as well as his scientific theories many years later. “I had had the opportunity of seeing for myself,” he wrote of the time, “something of the way the poor live. Not much, indeed, but still enough to give a terrible foundation of real knowledge to my speculations.” However, while it’s clear that Huxley sympathized with the plight of the poor and found the conditions of East London both shocking and unacceptable, he was already developing a distinctly middle-class sensibility. The destitute of East London were as strange to him as “the savages of Australia,” he would later write. Even so, no Aborigine was “half so savage, so unclean, so irreclaimable as the tenant of a tenement in an East London slum.” He went on to write:

I used to wonder sometimes why these people did not sally forth in mass and get a few hours’ eating and drinking and plunder to their hearts’ content, before the police could stop and hang a few of them. But the poor wretches had not the heart even for that. As a slight, wiry Liverpool detective once said to me when I asked him how it was he managed to deal with such hulking ruffians as we were among, "Lord bless you, sir, drink and disease leave nothing in them."

Morally offended by many of the vices that people turned to in an environment that offered little hope of social betterment, Huxley found inspiration in Carlyle’s missionary solutions. As Carlyle wrote in Chartism:

Light has come into the world, but to this poor peasant it has come in vain. . . Education is not only an eternal duty, but has at length become even a temporary and ephemeral one, which the necessities of the hour will oblige us to look after.

To teach the moral qualities that he viewed as central to his own future success, Huxley would emulate Carlyle in his own policy recommendations for the poor:

[W]hat dweller in the slough of want, dwarfed in body and soul, demoralized, hopeless, can reasonably be expected to possess these qualities?...[I]n a densely populated manufacturing country, struggling for existence with competitors, every ignorant person tends to become a burden upon, and, so far, an infringer of the liberty of, his fellows, and an obstacle to their success. Under such circumstances an education rate is, in fact, a war tax, levied for purposes of defence.

For Huxley then, as it was for Carlyle, the crisis of poverty was one of proper training. The reality of their economic condition may make them poor in material goods, but it was their poverty of mind that made them truly destitute and unable to rise in the world. It was only through proper education that the poor would be able to pull themselves up by their own bootstraps. The call from the radicals for economic and political change were ultimately addressing the wrong problem. As Huxley read and dreamed of escape into university life and upper-class respectability, Carlyle's sermon brought a glean to the young agnostic's eye.

Intellect is like light; the Chaos becomes a World under it, the discernment of order in disorder; it is the discovery of the will of nature, of God’s will.

Huxley had no use for God, but what did nature say on the question of order and disorder? It was something he would spend much of his life contemplating and his final years obsessing over. It would also bring him into direct conflict with one of the most influential political radicals in the world, a fugitive already wanted in three countries who was now intent on bringing anarchy to the UK. The Scientist and the Anarchist - Part II will be published next week at Skulls in the Stars.

References:

[1] Roy Porter (2006). London: A Social History, Cambridge: Harvard University Press, 1995; Liza Picard (2006). Victorian London: The Life of a City, 1840-1870. New York: St. Martin’s Press.

[2] John E. Archer (2000). Social Unrest and Popular Protest in England, 1780-1840, Cambridge: Cambridge University Press.

[3] Steven Johnson (2006). The Ghost Map, New York: Riverhead Books.

[4] Adrian Desmond (1997). Huxley: From Devil's Disciple to Evolution's High Priest. Massachusettes: Addison-Wesley.

[5] The Times, Tuesday, Mar 26, 1839; pg. 6; Issue 16999; col E

snowball fight in saturn's f-ring

Some interesting news broke last week from NASA's Cassini spacecraft, which has been orbiting Saturn since, oh, 2004 or thereabouts, checking out the planet's mysterious rings. The infamous "F" ring, discovered in 1979 by Pioneer 11, is one of the most unpredictable in its appearance: it's not a smooth thin band of icy particles, but has lots of kinks in it, and is flanked by two small "shepherding" moons, Prometheus and Pandora (no relation to the Na'vi).

Here's some handy background information (adapted from an earlier blog post from 2008). Scientists have been fascinated by Saturn's rings ever since Galileo Galilei trained a rudimentary telescope on the planet in 1610 and noticed their blurry outlines. The instrument's resolution wasn't quite sufficient for Galileo to make out what those blurry bits actually were, but by 1655, the technology had improved to the point where Christian Huygens  could accurately describe them as a disk surrounding the planet. Ever-better telescopes provided ever-better views of Saturn's rings in the ensuing centuries, but eventually we had to go see for ourselves. Voyagers 1 and 2 sent back loads of images in 1980 and 1981, and as is often the case in science, the images raised as many questions as they answered.

Sure, the rings are pretty and all. But there's some really fascinating physics going on, too. Here's what we do know: The rings are made of lots of small particles that range in size from microns (very tiny) to meters, with the bulk falling in the range of the size of seashells to the size of surfboards, as Burns colorfully described them. Those particles have clumped together as they orbit Saturn, "innumerable small objects orbiting a dominant central mass." They're made of water ice, mostly, with bits of dust and other chemicals creeping in from time to time.

What don't we know? Well, for one thing, scientists aren't sure how old the rings are; Saturn's rings guard that secret as zealously as any aging star in Hollywood. The rings could be a mere 100 million years old, given the relative brightness and purity of the "water ice" that make up the ring particles. Incoming meteoric dust should have darkened the rings substantially by now. They might be ancient, dating back to when the planet first formed. Maybe the particles are the remnants of an old moon broken apart by a collision. Those pieces in turn collided with each other, losing energy in the collisions while still conserving angular momentum, with the end result that the systems flattened out into the thin disks we now see around Saturn.

The most likely circumstances for such an initial "trigger collision" (an old moon with another celestial object) existed during a period known as the Late Heavy Bombardment (would Wikipedia lie to me?) some four billion years ago. But even so, if collisional physics were the sole mechanism for the ring formation, there would be more diffusion, i.e., the edges would be blurry. They're not: they're sharply delineated, although they do show evidence of "sinusoidal scalloping" along the edges: waves that kind of "flow" along the rim. Also, there are areas where the ring's texture becomes ropy in places and strawlike elsewhere, indicating that the simple angular momentum model is insufficient to explain all the rings' features.

There are three main rings, rather unimaginatively dubbed A, B and C, by far the densest of the rings with larger particles. There are also several fainter rings (Dusty Rings) that have been discovered in recent years. The D ring is faintest, and closest to the planet itself. Just outside the A ring, one finds the narrow F ring, and beyond that are two very faint rings known as G and E.

While we tend to think of Saturn's disk as a series of little ringlets, there are very few true "gaps"  in the disk. The best known gap is the Cassini Division that separates rings A and B, and has its own Huygens Gap near its inner edge; the inner C Ring contains the Colombo Gap, while the outer C Ring contains the Maxwell Gap; and within the A Ring we have the Encke and Keeler Gaps. Those gaps aren't always empty, either: both the Encke Gap and the narrower Keeler Gap contain embedded moons, for instance. In 2006, Cassini images revealed evidence of four tiny "moonlets" in the A ring, roughly 100 meters in diameter, too small to be directly observed. But they produce propeller-shaped disturbances that span several kilometers. Scientists now believe the A ring could contain thousands of similar objects; 250 "propeller" moonlets have been detected to date.

Why do things like these gaps occur? Perhaps the spreading outward is interrupted by destabilizing orbital resonances -- essentially gravitational relationships -- that arise when the local orbital period of a particle corresponds in a simple ratio to the orbital period of a nearby satellite (a moon or moonlet). For instance, the G ring is basically a faint, rubble-filled arc that orbits Saturn seven times for every six orbits of Mimas, one of Saturn's moons. So that would be, say, a 7:6 ratio orbital resonance. At these resonant locations, a moon's gravity can stir up a ring's mass distribution, giving rise to spiral density or bending waves, which transfer angular momentum between the moons and the rings and ultimately drive them apart." Such a process (a kind of shepherding mechanism) would serve to "truncate rings and pry open gaps." Should Cassini identify changes in any moon's motion, this hypothesis could be verified.

Scientists are interested in studying all these features of Saturn's rings in greater detail because the processes at work are analogous to other systems, including protoplanetary disks (the nurseries where nascent planets are born), our own asteroid belt, the formation of spiral galaxies (such as the whirlpool galaxy), and even the accretion disks around black holes. It's not the exact same processes at work, but there are striking similarities, so the expectation is that studying Saturn's rings can teach us about the mysterious underlying physics of some of these other celestial objects, as well as the origins of our own solar system. How do hordes of orbiting bodies crowd together? How does material accumulate in such systems to form moons or planets? And how do nearby masses disturb -- and are in turn perturbed by -- adjacent disks?

The latest images from Cassini shed some light on what might be going on specifically inside the F ring, giving rise to its uniquely complex structure. The culprit: Prometheus! Apparently the little potato-shaped moon can't leave well enough alone; it's just got to shake things up now and then. Every time Prometheus passes by the F ring, all the tiny icy particles within it get agitated by the moon's gravitational pull, and start engaging in the particle equivalent of slam-dancing.

These rippling perturbations create "streamer channels," and the particles start to bunch up and clump together into much bigger "snowballs" -- and I do mean big. Some measure as much as 12 miles in diameter, which means they are large enough to have "self-gravity" -- that is, they can attract more icy particles and continue to grow.

Prometheus swings by this particular segment in Saturn's F ring roughly every 68 days, and most of the smaller snowball clumps get ripped apart with the next pass. But that's not enough time for the streamer channels to subside, and with each pass, more channels are created and complicate an already complex kinky pattern. It's like a giant churn in space.

"Every time [the snowballs] survive an encounter [with Prometheus], they can grow and become more and more stable," said Cassini imaging scientist Carl Murray of Queen Mary, University of London. While it's likely that even the largest snowballs have a lifetime of just a few months, the new data could improve our current understanding of how space debris gets transformed into denser objects.

You can see this whole process in action in the animation below. Cassini scientists believe this could be why the F ring's structure is so surprisingly complex. And it just might help explain another mysterious objects first detected by Cassini scientists back in 2004: it's called S/2004 S 6 -- being too new to warrant a more formal moniker -- measures between 3 to 6 miles in diameter, and every now and then it bumps into the F ring and produces a spray of debris. Maybe it's one of those giant surviving snowballs. Maybe it's something else entirely. We'll have to wait to see what else Cassini tells us.