Cocktail Party Physics

picture this

It's been an incredibly busy week, so I'm just now getting around to writing about Chad's post about how it's not science without graphs. Basically, in a fit of procrastination, he plotted his latest blog traffic stats into a nice little graph, drew a line through the data points, and analyzed the results. It's all very meta of him. But who am I to point fingers? Chad's post made me realize that I am officially an uber-geek. See, back in late January, I got sidelined by the flu and spent a couple of days with a high, spiking fever, unable to do much except moan in between gulps of Theraflu. Bored with flipping channels and the meager offerings of daytime television, I started checking my temperature every hour and recording it, with the aim of plotting it onto a graph when I was done. I had some vague, drug-fogged notion of finding the slope of the tangent curve and thereby practicing my calculus by taking a derivative using a "real-world" example: the rate of change of my body temperature as the fever ran its wicked course.

It didn't quite work out that way: that particular calculus trick only works if the graph gives you a smooth curve. I had so few data points that the result was a series of spiked lines. If I took my temperature every 5 minutes and plotted it out, the end result might have been closer to a curve -- or not. Given the relative crudeness of my digital thermometer, the differences at that point would be so minimal that it probably would have just looked like a straight line. Still, before I started my amateur dabbling into self-taught calculus, I would not have realized that the closer one gets to an infinite number of ever-smaller data points, the more like a curve the resulting graphed data will appear. And it would never have occurred to me to try to create my own real-world calculus problem tracking the rate of change of my own body temperature. Maybe I ended up somewhere other than where I'd intended when I started my little sickbed exercise, but I learned something quite valuable from the experience -- and I'm not likely to forget the "lesson," either.

Real-world examples while learning abstract mathematical principles work for me, despite the recent findings by researchers at Ohio State University that this widespread assumption among educators may be wrong. Ed Yong at Not Exactly Rocket Science has an excellent summation of the study specifics, accompanied by a thought-provoking comment thread. For instance, more than one person said that the so-called "real world" problems one finds in, say, calculus textbooks bear very little resemblance to anything most students would want to solve -- like that silly train analogy that leads off both the New York Times article and Ed's blog post on the study's results. (Jen-Luc Piquant  has her own snide response to when Train A, departing at 6 PM and traveling at 40 MPH toward Station B, will pass Train B, departing at 7 PM and traveling at 50 MPH toward Station A: "When everyone on board is long past caring.") Far from making math "come alive," it's just one more way to make students' eyes glaze over in boredom.

I do not, however, conclude from this that "real world examples don't work." I think it depends on which examples you choose, and how you use them. They are a useful starting point for piquing student interest, but you still have to make the critical connection -- "This relates to that abstract principle, which can be broadly applied to other situations" -- and put in the work to grasp the abstractions.

Jennifer Kaminski, the OSU researcher who spear-headed the study, thinks such an approach obscures the underlying mathematical principle, rather than illuminating it, and actually hinders students' ability to transfer their knowledge to new problems. "They tend to remember the superficial, two trains passing in the night," she told the New York Times. "It's really a problem of our attention getting pulled to superficial information." I can see how that might happen, but I think it's more of a translation problem. Honestly? I sucked at textbook story problems in my K-12 math classes, and received excellent grades in high school geometry and algebra.

But here's the thing: I didn't actually understand the abstractions; I was just blindly following the "rules," manipulating meaningless symbols. And it bored me. I needed some kind of context, just not the equally pointless exercises routinely used in classrooms. The real world examples in textbooks don't really correspond to our daily experiences, or how we might typically approach such a problem. As one of Ed's commenters put it: "If I wanted to know Frankie's and Johnny's ages, I'd ask them, not work out some weird algebra problem." Yet another commenter observed, "'Real-world examples may be treated by students as confusing symbolic concepts that look like real things they know about but act like abstract notions that are defined by the teacher."

I was pleased to read that Kaminski isn't suggesting that we eliminate all real-world examples in classrooms; rather, she thinks that they should augment the abstract principles -- which should be taught first -- rather than being deeply grounded in one specific context. I agree this might increase a student's chances of extrapolating the general principles and applying them to new problems as they arise. Perhaps letting the students choose a real-world problem they'd like to solve -- like my little experiment plotting out my changing rate of body temperature -- is a better way of incorporating a practical context.

You're more likely to pique their interest if they're involved in creating the problems and then figuring out how to solve them -- the "lessons" they learn along the way are more likely to "stick," plus it's a lot more similar to what a working scientist actually does for a living. Is it a calculus problem? A statistical one? How does one go about "translating" that situation into a meaningful mathematical format? This is more of a ground-up approach, akin to taking apart an alarm clock and putting it back together to gain a more comprehensive understanding of how it works. Personally, Jen-Luc would like to see more LOLCats in math and science classes:

This kind of choose-your-own-problems approach also might address the perennial problem of over-generalization -- we all learn differently, and suggesting there is only one correct way to teach a subject like math or physics is likely to leave behind as many students as such a pedagogical approach would advance. And sometimes teachers under-estimate the difficult of new concepts because it's been so long since they learned the material for the first time themselves. As commenter Sam C. said, "Once one has learned something, it's difficult to appreciate what it looks like to someone who hasn't learned it." Something that seems perfectly obvious to the teacher, probably needs to be spelled out, step by step, for many of his/her students.

Case in point: I started my informal calculus "studies" with a DVD lecture series from The Teaching Company. The lectures were pretty good, conceptually: visual elements, real-world examples, but tying them to the abstract principles and then showing how they could be broadly applied. The first thing I learned was how I could (a) use the derivative to figure out the speed of my car from the car's position, and (b) use the integral to figure out how far I'd traveled in my car based on speed. The two are flip sides of the same coin, two different approaches to solving the same problem, depending on the information at one's disposal. And there's a handy real-world context: this is basically what's going on in your car's speedometer and odometer all the time.

Frankly, finding the integral is a labor-intensive process of multiplication and addition take to ridiculous extremes (i.e., infinity). There is a short-cut to the much-harder integral however: if I know both my beginning and ending position, for example, I could just subtract the first from the second to figure out how far I'd traveled. What if I don't know my ending position (and my odometer is broken), just my speed (the velocity function)? Per my DVD instructor, "all" I have to do is figure out which position function generates the known velocity function, and voila! I can do a bit of math-y hocus-pocus to essentially "retrace my steps" backward and use the easier derivative approach. Fair enough, but he never once explained how one goes about finding that position function. There's a lot of them. Still, he insisted it was a simple matter, and silly me -- I believed him.

My DVD instructor lied. It's actually a non-trivial thing for someone just starting out, and/or a bit rusty in their basic algebra and geometry. Don't take my word for it; listen to Johann Bernoulli, a contemporary of Newton and Leibniz who made significant contributions to then-brand-new field of calculus in the 17th century: "But just as much as it is easy to find the differential (derivative) of a given quantity, so it is difficult to find the integral of a given differential," he wrote. "Moreover, sometimes we cannot say with certainty whether the integral of a given quantity can be found or not."

Fortunately, I know a lot of physicists and a smattering of mathematicians, most of whom are happy to weigh in now and then with their own insights and "tricks" for the kind of road-block described above. And I'm persistent. I only bring it up because I think it's always interesting to see where different people get hung up when learning new mathematical concepts. Sometimes it's just a language problem, mixing up terminology, or not realizing that you do know what a particular term means -- you just didn't realize that's what your mental concept was called. You hadn't made the connection. Sometimes the instructor has inadvertently left out a step, or doesn't realize that some of his/her students need to be walked through something a bit more carefully.

Because we all learn and think differently -- newsflash: even scientists don't all think and learn alike! -- I'm interested in hearing from readers about similar experiences in their math and science education -- or even their humanities education. I admit, I have an "intuitive" feel for words and writing, and have been guilty in the past of just not understanding why someone couldn't grasp some "trivial" aspect of composition. I've noticed that many "gifted" math sorts can make similar intuitive leaps with numbers. What were your most significant roadblocks? Have you ever stopped to really analyze what happened? How did you overcome them? What are some of the "tricks of the trade" you find useful when applying abstract math principles to "real world" problems?

I think it's a conversation worth having....

crime scene craziness

Last year, the Spousal Unit and I attended a friend's 40th birthday party here in Los Angeles. Among the many guests was one of the writers for Bones -- one of my favorite current TV shows, as regular readers may know. We exchanged the usual pleasantries, I said how much I liked the show, and then he asked what I did for a living. As soon as I said "science writer," he tensed up, with a slightly panicked, hunted look in his eye, and launched into a litany of his supposed "sins against science": "I know, I know, we take liberties with the science, DNA testing can't be done in just a few hours, Angela's holographic system for recreating faces doesn't exist...." I quickly interrupted his impromptu "confessional" to assure him I wasn't one of those sorts who constantly feel compelled to nitpick science-themed fictional TV shows for --basically -- not being science-themed documentaries.

Personally, I think it's quite telling, and more than a little sad, that this man's first reaction to encountering a science-oriented person (even one who admitted to being a Bones fan) was to recoil and start defending himself. I can only imagine how often he's encountered such individuals who dispensed with the usual pleasantries and simply attacked him for doing his job: producing a compelling, entertaining crime drama. It reflects quite poorly on scientists, frankly. Scientists mean well, but all the  judgmental finger-wagging gets pretty old, pretty darn fast. And soon, they're just not being heard because people have stopped listening. Who likes to be nagged and nitpicked all the time? Would it kill the scientific community to hand out a few kudos once in awhile, to offset the constant griping?

So in today's monster blog post, I come not to bury science-themed TV shows (death by nitpicking?) but to praise them -- specifically, to praise Thursday night's new episode of C.S.I., or, as Jen-Luc Piquant has dubbed it, "the episode that launched a thousand Google searches." Maybe it was because of May Sweeps, or perhaps the whole writing staff got exposed to laughing gas that made them collectively giddy, but the episode ("The Theory of Everything") managed to cram together a record number of weird, stranger than fiction forensic oddities. (The writers of House are probably seething with envy; extremely rare and bizarre medical anomalies are their stock in trade.) And as I discovered when I Googled the relevant terms, they're all pretty solidly based on scientific fact. [SPOILER ALERT! The rest of this post gives away key plot points -- solely in the interests of science -- so if you didn't catch the episode, you might want to hold off reading further until you've checked it out: it's available on the CBS official Website.]

We get an inkling of the craziness to come in the opening sequence, set in the Vegas police station, where Detective Brass is questioning a suspect while, in the main room, a mentally disturbed homeless woman named Evelyn expounds on string theory and the coming alien invasion. We quickly discover that the suspect is in jail for killing a deer with a bolt from a cross bow and, um, putting a dress on it. He's recently divorced, drunk as a skunk (blood alcohol level of 2.8!), and suddenly makes a break for it, bolting through the station until he's cornered. The assembled officers use pepper spray to subdue him, but he's too smashed for it to have much effect. So Brass gives the order to tase him, using the unfortunate phrase, "Light him up." As if on cue, the suspect bursts into flames. Soon he joins the dead deer in the morgue for autopsy, and Brass is taking heat for having a suspect die in custody.

First, a brief word about tasers. I tend to think of them in terms of those smaller handheld electroshock devices, but the kind more commonly used by law enforcement -- and depicted in the episode -- are a bit more complicated. A taser fires two small darts (electrodes) connected to the main unit by conductive wire, with a maximum range of about 35 feet. The darts are pointed to penetrate clothing and touch the skin. Earlier models required them to pierce the skin, but today's version uses a "shaped pulse" that is more effective in penetrating clothing. The handheld devices are more commonly marketed to the general public these days. In fact, Jen-Luc Piquant was thrilled to discover a surprisingly large number of pretty pink tasers for women, from a standard issue model, to a taser disguised as a couple of pink tampons, to this adorable pink seal taser -- and yes, it was made in Japan, along with the infamous Hello Kitty "personal massage wand." (Think I'm kidding? Think again! A Hello Kitty taser is practically inevitable.) Jen-Luc totally covets her own pink seal taser.

Anyway, tasers, or stun guns, are fairly controversial, since there have been several cases of suspects dying, ostensibly as a result of being tased -- the most recent case was last year, involving a Polish immigrant in Canada who died after being tased by police in Vancouver's airport. That man didn't burst into flames, however. Combustion isn't typically one of the risks. Nick Stokes figures it has to be either the moonshine the man had been consuming, the pepper spray, or some chemical in the man's shirt, but a controlled experiment involving three Jell-O Men shows that none of those could account for the poor man's sudden immolation.

Eventually, Stokes discovers that there is more than one type of pepper spray. This is quite true. All types contain the same active ingredient: capsaicin, a chemical derived from the fruit of plants like chilis. But the episode is correct that the sort used by the police is water-based and hence non-flammable -- precisely because of the growing use of tasers by police officers. Some consumer brands have alcohol-based propellants, however, which are highly flammable.

In the case of Burning Man, the officer at fault had used a consumer version after his girlfriend accidentally took his pepper spray with her to work. Nick repeats the experiment with the other type of pepper spray, and voila! The Jell-O Man bursts into flame. And yes, that was the Mythbusters looking on approvingly from behind the glass as Nick performs his final test -- an uncredited cameo to keep obsessive fans happy. (Obsessive? Moi? Jen-Luc is the one who writes Mythbuster-themed slash fanfic. And if that doesn't take you to a scary mental place, I shudder to think what it would take to do so.)

Really, that's weird enough for one episode right there, but when  police finally track down the unfortunate Evelyn, she's dead, the victim of a collision with a semi. The truck driver was temporarily blinded by the sun reflecting off her tinfoil costume, and didn't even see her. The clincher: she's bleeding green blood -- yes, just like Mr. Spock; perhaps she really was in touch with aliens. (Or not; certain species of lizards known as skinks also have green blood, along with some marine worms.) The whole green blood thing turns out to be a mini-epidemic: two more victims soon show up: another homeless man, dead from blunt force trauma to the head, and his killer: a pest control specialist named David Bohr, a.k.a. "Atomic Dave" (one of several cheeky nods to physics).

Bohr is alive when they find him, but not for long: he soon starts seizing and the same green blood, um, oozes out of his face. He joins the other victims in the county morgue, where we have the added twist of all his internal organs being various shades of green, including his brain. It turns out that all the green blood victims suffered from migraines and were taking massive doses of a medication without a prescription -- supplied by Bohr the exterminator, who was taking the stuff himself in enormous quantities. Except Bohr thought he was suffering from migraines, when in fact, he had a massive brain tumor -- hence the headaches, crazed behavior, and hemorrhaging. That's the danger of self-medication: what if your original diagnosis is wrong?

Hodges and Wendy (who is emerging as his unlikely love interest) conclude -- along with Grissom -- that the culprit is high levels of sulphur in the blood, caused by the large doses of migraine medication the victims had been taking. (The drug is identified as thiocyte, but this might be a fictional version -- perhaps for legal reasons? -- since the only Google hits that showed up on that drug name were related to this particular episode of C.S.I.) And naturally, they invoke Mr. Spock, although Wendy rightly reports that Spock's green blood, according to the series, arose from copper instead of iron in the hemoglobin. She knows a whole bunch else about Star Trek, as it happens, prompting Hodges to observe, "You're like a geeky nerdy guy trapped in a woman's body." Not to be outdone, Wendy zings back, "So are you."  Yeah, those two are made for each other....

This "Vulcan Blood" phenomenon isn't fictional. In fact, it's ripped right from last year's science headlines, when an article appeared in The Lancet describing a very odd case of a 42-year-old Canadian man (why are they always Canadian?) who appeared to have dark-green blood coursing through his arteries. The case was already a bit strange before the whole Vulcan-blood thing. The patient had fallen asleep in a chair for so long, and in such a position, as to severely restrict the blood flow to his limbs, resulting in localized tissue and nerve damage that required surgery to correct, before he lost his legs. The man also suffered from chronic migraines and had been prescribed sumatriptan to treat them. Apparently he'd been consuming a whopping 200 milligrams of the stuff per day, giving rise to a rare condition called sulfhaemoglobinaemia, in which high levels of sulphur wind up up in the oxygen-carrying compound hemoglobin, found in red blood cells.

Meanwhile, Catherine Willows gets called to a nearby home where a 60-something couple has been found dead in their sleep. The husband was a physics professor, and they named their cat Schroedinger -- except poor Schroedinger in this case isn't in a superposition of states, but very much dead and buried in the back yard, which is littered with the bodies of dead squirrels.

Initially, Willows surmises the exterminator's equipment -- which employs electromagnetic pulses to chase away the squirrels -- interfered with the couple's matching pacemakers, but lab tests definitively rule that out: the pulses were too weak to have any effect on the pacemakers' operation. It's a very real health risk, however: most Websites concerned with pacemakers warn those considering the surgery to avoid MRIs altogether afterward, and use with caution such devices as cell phones, iPods microwave ovens, metal detectors, industrial welders, and electrical generators.

A tox screen reveals that both the squirrels and the couple died of cyanide poisoning, the squirrels via ingested pellets, and the couple by inhaling a hydrogen cyanide gas. Victims of foul play? Yes for the squirrels; the jewelry-maker next door admitted to using cyanide in her electroplating (a common application for cyanide) and dosing the pesky squirrels (not to mention the unfortunate Schroedinger, by accident), but as for the elderly couple -- not so much. Turns out the cyanide that killed them came from the old carpet -- since overlaid with a new one -- which contained polyvinyl chloride as a flame retardant. A fire broke out when a fleeing squirrel chewed through some electrical wiring, the old carpet kept things to a low smolder and the chemicals in the carpet fibers, when burnt, produced hydrogen cyanide gas. At least the couple died peacefully in their sleep.

All of the above is pretty scientifically accurate, give or take the occasional liberty for Purposes of the Plot -- at least as far as I could tell from my hour of Googling. If one were going to nitpick on the cyanide front, one might note that Hodges is credited with the rare gift of being able to smell the bitter almond odor associated with hydrogen cyanide. It's true that not everyone can do so, but those that can't are in a minority (one out of four). Three out of four people can detect the telltale odor; if anything, it's surprising that Hodges is the only person in the Vegas lab who can do so. Then again, Hodges is known for exaggerating his gifts, so constantly proclaiming the uniqueness of his ability is entirely in keeping with his character.

Recapping the day, the C.S.I. team marvels at the unlikely string of coincidences that connected the various cases. First, a suspect goes up in flames while in police custody, and the last person he came into contact with -- Tinfoil Evelyn -- ends up dead and oozing weird green blood from migraine medication she'd copped from Atomic Dave, hired by the elderly couple to get rid of the squirrels. The late, great Immolated Deer-Killer turns out to be the ex-husband of the couple's next-door neighbor. The Deer Killer only ended up in police custody (and thus, dead) because he was so upset about the end of his relationship with the jewelry maker. Grissom says there's no such thing as coincidences and attributes the phenomenon to (wait for it!) string theory -- thereby tying him to crazy Tinfoil Evelyn.

Okay, citing string theory as an explanation for a series of unlikely coincidences is stretching things very far indeed -- in fact, unlikely coincidences do arise quite frequently, and they are rarely (if ever) evidence of anything more than that. But the brief layperson's sound-bite summation that Grissom gives of the essence of string theory is dead-on. The writers did their due diligence, even if they added their own fanciful metaphorical embellishment. And that's good enough for me.

NEW VOICES: love bytes

For the last eight months or so, I've been encouraging various aspiring young science writers I encounter to submit the occasional guest post to Cocktail Party Physics. First, sometimes I just get tired of the sound of my own voice, or need a break. Second, I think it's critically important to encourage fresh new voices in the science writing sphere -- because they will become the voices of "authority" tomorrow. Maybe they're not quite ready to take the plunge with their own blog, but I try to make this blog a place where it's okay to take the occasional creative risk, and receive helpful feedback from a (mostly) receptive audience so that they can keep refining their science writing skills.

Frankly, many of the aspiring science writers I've approached have been a bit intimidated about venturing into an admittedly rowdy (at times) public forum, but I'm finally optimistic that at least a few brave souls will be coming on-board for my little project over the next few months. So on this May Day, I inaugurate a new, occasional series called "New Voices." Today we welcome back Brian Frank, a student in KC Cole's science writing class at the University of Southern California, who guest blogged a couple of weeks ago about "Doomsday Physics." In this post, he shares the result of an in-class assignment on imagining a unique story-telling approach to a scientific topic -- the workings behind a simple email -- aimed at a very general target audience, for our consideration. Without further ado, we present "Love Bytes: A Fantasy of Networks and Bits." (Jen-Luc Piquant thinks we should all forward the post to any members of Congress -- *cough* Ted Stevens *cough* -- who remain mystified by how these Intertubes actually work.)

Johnny's sitting there, trying to decide how to sign his email to Liz. He taps out "-- Johnny." He reconsiders, hits the Backspace key, and taps a few more keys. There it is: "Love, Johnny." He pauses. The cursor darts erratically around the screen as he wobbles the mouse. Then it hovers over the Send button. There's still time to change the signature line, but he's certain now. He clicks.

Normally, Johnny wouldn't think twice about what happens next to his message, but he's in a rather sentimental mood. With a modest background in computer science, he knows how that message will cross the nearly 3000 miles of networked wires from his apartment in Los Angeles to Liz's in New York. Through the filter of his romantic brooding, though, that electrical transmission seems as grand and romantic as some lone adventurer crossing the Sahara to reach his beloved. He imagines the L that started the one word that seemed to convey the whole of his message.

L is exactly one byte, but he isn't traveling alone. Each letter, each comma, each period of the message amounts to a byte. In Johnny's imagination, time is compressed, and L and all his compatriots are about to embark on an odyssey that in fact occurs countless times every second on the Internet.

But first, they have to wait while the E-mail program gets them in proper order. This gargantuan application (from L's point of view) works like a factory, padding the message with extra information in the form of even more bytes. These extra bytes will travel at the head of the pack (in the header, no less), delivering special instructions on how to handle everything that comes after them. It's like sending a company representative ahead of a shipment to explain to the people on the receiving end how to unpack the freight trucks and reassemble the contents into a house.

With the header finished, the E-mail application prepares L and all the other bytes for travel. First, L is turned into something that can be easily read by computers. He gets crunched into bits -- not smashed, really, but assigned "bits," the 0s and 1s that, in clusters of eight, make one byte. L translates to "01001100" in bits (which is binary, the universal language of computers). In a sense, that string of digits will act like L's identification tag.

Now properly identified, L gets crammed together with his neighbors into a long stream of digits. It's impossible to tell where one byte ends and another begins, really. All those letters and commas and periods blend together until they look like this: 01001100101011101010110100100101, and so on.

L and the other bytes are now ushered down to the network card, where they find their seats, as it were, on one of a caravan of buses -- the packets that make it more efficient to send information across a network. These packets come in various sizes, but many hold up to 4000 passengers, which are bytes just like L. That seems like a lot of characters for one message, but actually a substantial portion of those bytes are part of the header that will tell the receiving computer what to do with all these 0s and 1s.

The packets line up in an orderly fashion and point to the cable that connects Johnny's computer to the Internet and ultimately to Liz's computer. But here's the beauty of it for L. The bytes are sent in groups, one packet at a time, but they don't actually have to travel at all. The computer just reads the information on the identification tags, and in a kind of Morse code, calls out the 0s and 1s across the network. Instead of using the blips of light or sound characteristic of traditional Morse code, the computer will send electromagnetic pulses. Each 1 is a pulse. Each 0 is a pause. With the perfect rhythm of a clock, the computer will either pulse or pause.

The packet in front of L's moves forward and all its bytes have their identification tags read and relayed down the line. L's packet has to wait briefly before it follows, because if all the packets went in a row, the line would be tied up too long, preventing other computers from sending other heartfelt messages.

Finally, L's packet has its turn. Each byte in front of his has its 0s and 1s transmitted. Then L's ID is read: "01001100." The computer measures out the beats like this: wait, pulse, wait, wait, pulse, pulse, wait, wait.

The pulses and pauses travel in their packets for hundreds of miles at a time -- Los Angeles to Houston, Houston to Denver, Denver to Detroit, and so on until they reach New York. At each hub, a computer receives the signal and records it as bytes in a packet. It signals the next hub and so on down the line. When a line is temporarily busy, the computer hub holds the packet for a short layover. And they don't all have to travel together. Part of the job of that header was to tell the receiver, "Hey, there are 100 packages en route, so don't try reassembling all this stuff until you have all of them."

Eventually all the packets arrive in New York, in Liz's computer, in fact. The computer watches for pulses and pauses, keeping the same rhythm as the sender. For each pause it records a 0, and for each pulse a 1. Gradually it has a long string to work with. It snips every eighth bit and reads the subsequent string as a byte. All those bytes are sent up to Liz's E-mail application, where the factory transforms the digits back into characters. At some point, the application comes across the by-now-familiar byte "01001100," and shoots an L onto her screen. And at last, the journey is complete.

Of course, all this happens in a matter of seconds. Johnny and Liz have already traded numerous email messages today. This time, Liz sees the "Love, Johnny," panics, and sends a quick reply. Her message takes the same fantastic route, all the characters changing to bits and then pulsing across the Web to Johnny's computer. Unfortunately for Johnny, preceding Liz's name is not the "01001100" that would start the L word. Instead, he message reads, "I think we're better off as friends. -- Liz."

birds of a feather

Let me clarify, for the benefit of any concerned readers, that my post over the weekend bidding a fond farewell was not a departure from the blogosphere, but from my tenure as Journalist in Residence at the Kavli Institute for Theoretical Physics (KITP), the pretty peach-colored building in the photograph. It was a terrific experience, although not 100% comfortable -- which I consider a good thing, because if one is not pushed beyond one's comfort zone once in awhile, one never makes any significant developmental progress. Not only was much of the subject matter unfamiliar (and often incomprehensible) to me, but I was compelled to crystallize my various random thoughts and approaches to science communication into a workshop-type format that would appeal to theoretical physicists (or at least some of them). Did I succeed? Sometimes. The only flat-out failure was my attempt to use PowerPoint Karaoke to jump-start a discussion about communicating across disciplinary boundaries. Talk about a deflating experience. In retrospect, I think I "framed" it incorrectly for my target audience. Next time, it will take place in a local bar and feature copious amounts of alcohol. That seems to have worked very well for the PowerPoint Karaoke event organized by this group of Australians from McCann Sydney.

Anyway, after my final workshop (a post on that is forthcoming later this week), I jumped into my shiny red Prius and navigated my way one last time from Santa Barbara to Los Angeles, just like a homing pigeon seeking to reunite with its avian equivalent of a Spousal Unit. I relied on past experience and my trusty GPS display to find my way home, but apparently, birds use the earth's magnetic field to help them navigate. According to a recent entry on the physics arXiv blog maintained by the mysterious "KFC," "A growing body of evidence points to the possibility that a weak magnetic field can influence the outcome of a certain type of chemical reaction in bird retinas involving radical ion pairs." In fact, it's possible to confuse the navigational abilities of birds by zapping them with magnetic fields that, apparently, disrupt this reaction.

KFC explains that while this proposed mechanism has substantial experimental evidence, to date, it's been a little incomplete theoretically. The ion recombination effect that gives rise to a preferred chemical reaction happens far too quickly to allow for any influence from earth's magnetic field -- and yet, the experiments indicate that this field does play a vital role. Hmmm. In a recent paper posted to the arXiv, Iannis Kominis at the University of Crete has outlined an intriguing idea about how to resolve the paradox, namely, by evoking another one: arguably one of the most famous paradoxes in quantum physics, known as the quantum Zeno effect. Per KFC, "It states that the act of observing a quantum system can alter its evolution in a way that maintains the state for longer than expected." A more colloquial phrasing would say, "A watched quantum pot never boils."

Say what? There are quantum teapots? Well, no, not literally. But it's a useful analogy if one takes a bit of extra time to bone up on the broader context. And that means hopping into the Way-Back Machine for a brief visit to ancient Greece. Zeno was a Greek philosopher who logically constructed an argument to prove the (clearly) nonsensical assertion that motion is impossible. (Philosophers often like to play devil's advocate and argue for the impossible.) Zeno envisioned an archer shooting an arrow from his bow. Imagine Legolas Greenleaf from The Lord of the Rings doing just that. Assuming he shoots directly in front of him -- it's tradition in physics to hypothesize idealized situations -- the arrow will travel in a straight line indefinitely until it is stopped by an opposing force,  ideally, by piercing the heart of an evil Orc.

Zeno asked what would happen if you divided the distance the arrow must travel to its target into an infinite number of increasingly smaller increments, halving the distance every step of the way. He argued that this would mean the arrow would get closer and closer to its Orc-target but would never be able to reach the creature's heart. All motion would seem to stop. This sort of thing doesn't happen in the macroscopic world of our daily experience, of course: eventually Legolas' arrow will find its mark, and the Orc will perish. (Good riddance!) Zeno's abstract argument rests on the notion that the progression will continue for infinity, but in physical reality there is always some kind of limit. An endless series can still have a finite sum. There's lots of ways to describe the notion of a limit -- it's a key concept in modern calculus -- but just from a practical standpoint, the arrow has a fixed length (at least over the distance it travels). The distance the arrow must travel would eventually be subdivided to the point where the increments would be smaller than the arrow itself. And at that point, the arrow would hit its mark.

But the quantum world is a much weirder place, governed not by exact absolutes but by probabilities and uncertainty. On the subatomic level, something akin to Zeno's paradox actually happens. Physicists have argued for decades over the nature of a measurement or observation and its implications for quantum mechanics, ever since Werner Heisenberg first proposed his Uncertainty Principle. That's the one that says we can never know the precise momentum (or the precise velocity) associated with a particle, or we can know its exact location, but we can't know both at the same time. The very act of making the measurement changes the state of the atom.

It sounds like magic, but it's really not; it's the result of an actual physical force. We measure and observe atoms via electromagnetism, i.e., light of varying wavelengths. But how much we can see depends on the wavelength (and energy) of the light -- a photon's energy is inversely proportional to its wavelength, so the shorter the wavelength of light, the higher the energy of its constituent photons. And the smaller the object we wish to observe, the higher the energy of light we must use in order to get the resolution we need to see that object. An atom is really, really tiny. To locate its precise position, we'd need to hit it with a photon of such high energy that significant amounts of that energy would be transferred to the atom itself, thereby altering it (changing its speed or direction). Basically, we know where the atom was, not where it now is, because our ham-fisted "observation" has knocked it out of its prior position.

Ergo, Heisenberg concluded that the mere act of observation can determine the outcome of a quantum experiment. But experimental measurements are made in single, fixed, brief moments in time. What if it were possible to continuously observe an experiment? And at what point does observation become continuous? Scientists actually know the answer to both questions. Back in 1977, researchers discovered that a radioactive atom would never decay if it were "observed continuously." And the critical transition point is one measurement every four-thousandths of a second.

We have that precise figure thanks to the work of scientists at the National Institute of Standards and Technology (NIST) in Colorado. In 1989, they trapped 5000 charged beryllium atoms in a magnetic field and then tried to "boil" them by zapping them with a radio frequency field to raise their temperature. They expected the atoms to absorb the extra influx of energy and jump to higher ("hotter") energies. But this only happened if they didn't make any further measurements in the interim. The more often, they tried to measure the energy state of the atoms, the fewer of those atoms would reach the higher energy level. And at the rate of one measurement every four-thousandth of a second, no atoms at all jumped to the higher energy state. They just wouldn't heat up. It still happened even when the scientists used an automated measuring device.

Why does this happen? Blame it on uncertainty: the act of measurement interferes with the atoms' ability to absorb extra energy. The Spousal Unit once penned a classic blog post about this topic, employing quantum puppies to discuss the notion of quantum interrogation, which explains things beautifully even if the cuteness of the puppies tends to overpower all else. 

I like to think of it in the more concrete terms of Legolas' arrow. Let's imagine that this arrow is imbued with some elfin magical property by which it can grow longer over short intervals of time. That's a pretty decent analogy for what's happening to the uncertainty associated with two atomic energy states. At some point the uncertainty becomes large enough to bridge the two energy states -- akin to lengthening Legolas' arrow to the point where it can reach an Orc's heart -- the atom shifts to the higher energy state (and the arrow downs the evil Orc). The "uncertain arrow" then collapses back down to its original length and the whole process starts over again.

But every time we make a measurement of an atom's energy, or the length of Legolas' magic arrow -- and no, that is not a euphemism! Get your minds out of the gutter and back onto the curb with the rest of us! -- we reduce uncertainty, so it can't increase. Every time someone tries to measure Legolas' magic arrow, it becomes just a little bit shorter (oh, stop it!), to the point where it's never long enough to reach the Orc's heart. That's what happens to the energy states of atoms in the quantum Zeno effect. Uncertainty gets smaller with every measurement, because each measurement yields new information about the atoms, reducing the "fuzziness" of their energy states. Make those measurements often enough, and uncertainty never becomes sufficiently large to enable to atom to heat up. So a "watched" quantum pot never boils.

I know -- it's really weird, and utterly counter-intuitive. That's quantum physics for you. By now you're probably wondering what the hell any of this has to do with birds and their navigation skills -- assuming folks have even read this far. But according to Kominis in Crete, it is indeed relevant! Let's recap: scientists think that a weak magnetic field (like that of the earth) influences "the outcome of a certain type of chemical reaction in bird retinas involving radical ion pairs," but the sticking point is that the ion recombination happens too quickly for earth's magnetic field to have an actual impact. And yet it really does seem to influence the avian navigational process.

Per KFC, Kominis knew that it's "possible to slow down the rate at which molecules convert from ortho to para isomers when they are constantly involved in collisions." Something similar, he believes, happens in birds, namely, "The presence of a geomagnetic field extends the lifetime" of that recombination process, thereby giving the magnetic field more time to influence the outcome of the recombination. This really could turn out to be an extraordinary insight, since it means that birds have a built-in quantum sensor -- roughly akin to a GPS chip, perhaps, or at least a compass -- that determines their macroscopic behavior (i.e., navigation). It would also explain why birds occasionally are afflicted by a 30-degree "heading error," and why these built-in "compasses" only seem to be sensitive to a certain type of magnetic field strength.

Kominis even speculates that a similar mechanism might play a role in photosynthesis. It could be a brave new world out there, indeed, if it turns out that quantum effects can impact macroscale behavior. As KFC rightly notes, in his trademark style: The quantum consciousness people are going to be all over this like freshmen at a sorority party." Let the arguments begin!

a fond farewell

it's just a flesh wound

Martial arts and personal injury seem to go hand in hand. In my decade or so of jujitsu training, I broke two toes, dislocated my wrist, endured countless bruises and sprains, fractured my right elbow, and had my back thrown seriously out of whack thanks to a powerful guillotine choke administered by an over-enthusiastic ex-Marine. Most notably while practicing self-defense techniques against a long bo (actually a stickball bat) for my black belt test, I miscalculated during a duck-under technique, came up too soon, and received a nasty thwack! on the forehead that dropped me to one knee. It didn't actually hurt; I was mostly stunned. Then the blood began to gush, and I realized mat time was over, and I'd be spending several hours in the ER instead. The slash went clear down to the skull cap, and required 14 stitches to close. I still have a jagged scar across my forehead, although few people notice unless I point it out. (Also? No need for future botox treatments in that area, since the tiny muscle that causes frown wrinkles got sliced clean through. I literally cannot frown in that portion of my forehead.)

And I still loved every minute of my training. It's just part of the rite of passage when one is seriously studying the martial arts, but to outsiders, it can seem a bit, well, extreme. (A friend of mine became so upset at the perceived brutality of my black belt test, he literally had to leave the room at one point.) I was reminded of my halcyon days sweating and bleeding with my fellow jujitsu practitioners when I received an email from my friend Jim D., who started training in Tae Kwon Do a few years ago with his teenaged son, and recently passed his brown belt exam. Jim fractured his wrist this past week when he agreed to hold six pine boards while his instructor attempted to break them with a kick. Apparently, the instructor missed the central target area and the full force of his kick landed off to the side, so all that kinetic energy (or should one say momentum? Terminology can be so confusing!) went into Jim's wrist instead of into the board. Ouchie! At least he has a very impressive looking cast with which to impress the laydeez:

Anyway, Jim took the injury in stride, like any respectable martial artist. But he's the curious sort, so he emailed me asking if I knew anything about what went on from a physics standpoint to bring about his injury. I've done lecture/demos on the topic, focusing on broad concepts as opposed to specific calculations, so I knew a little, even though I never featured board-breaking in any of my lectures. Frankly, I've never understood the point of such an exercise. I'm an adherent of the Bruce Lee philosophy, immortalized in Enter the Dragon: "Boards don't hit back."

Except in the strictest physics sense, they kinda do. Per Newton's third law, momentum is conserved, and that translates into the well-known maxim of equal and opposite reaction. Many of us remember this from our introductory physics classes (or the equivalent thereof): If an object exerts a force on another object for a specific length of time, the second object will react by exerting an equal but opposite force for the same amount of time. So a board does "hit back" in that sense. The force generated by Jim's instructor created a reaction force in the opposite direction when his foot made contact with the boards; the boards gained exactly the amount of momentum the instructor's foot lost, or almost as much; some would have been lost via conversion into heat or noise energy, for example. The boards accelerated in the opposite direction in response to the kick.

A board will break when the part that is hit -- ideally the center -- is infused with more energy than its structure can handle, causing it to crack and/or break. But not every part of the board accelerates uniformly. The part that took the brunt of the kick -- again, ideally the center, although unfortunately for Jim, in his case it was off to the side -- accelerate much more than the surrounding piney-parts. This produces a localized strain, and if the strain becomes too great, the board will crack in that locale. As for how much force went into Jim's poor wrist, I could only offer the grossest generalities. For someone weighing 140 pounds, traveling at a final velocity of about 10 MPH when s/he hits the target, that person's body would have about 504 joules of energy. But that's assuming a full-tilt run and putting one's entire body mass behind a kick. Chances are, only a portion of one's body mass will be used -- although a TKD instructor, one assumes, would have excellent technique, and would therefore employ a greater percentage of his/her overall body mass than the average untrained kicker.

I told Jim if he wanted a truly thorough answer to his question, rather than the generalities I could offer, he should contact Jearl Walker, physics professor at Cleveland State University in Ohio, longtime contributor to Scientific American, and general all-around daredevil scientist, trying his hand at firewalking, lying down on a bed of nails, and investigating the physics of the martial arts. (He has a book -- and a Website -- called The Flying Circus of Physics detailing various real-world illustrative examples of physics concepts, as well as a blog.)

Per Walker, the force required to break a standard single 3/4-inch pine board is about 3000 Newtons; the force required to break a solid pine block of the same thickness as six stacked standard pine boards is astronomically higher: six times higher, as one might expect (6 x 3000 Newtons), [CORRECTION: I didn't read my hastily scrawled notes correctly: that should be 6 CUBED x 3000 Newtons. Yowza! 6 pine boards would be about 18,000 Newtons and change.] although there are numerous variables, such as whether the boards are warped, how many have knots (which make them harder to break), and how much space is between each board. Still, that's a pretty good ballpark figure. To phrase it in slightly different units, it takes about 5 joules of energy to break one board, and about 30 joules to break six. And a large fraction of that energy went into Jim's wrist instead of into the board. (Also per Walker, it was the focused shock wave that broke Jim's arm, not a static wave of energy.)

I think it would be a bit more difficult to determine the force of impact of my old head injury, although if any of you are bored over the weekend and care to give it a shot, we'd all be interested in hearing what you came up with. The mass of the stickball bat could probably be estimated, along with the respective body masses of me and my friend Jordan, who was swinging the stick. Then we'd need to estimate the speed of the swing (Jordan's pretty big, and strong, and to his credit, respected me enough to not pull his punches, so to speak), and how fast the stickball bat was traveling when it struck my head. The hardness of my head might also be a factor; all materials have their own varying degree of elasticity, after all. Complicating matters is the fact that both Jordan and I were moving when the injury occurred, and because of that, it was more of a sharp, glancing blow that slashed across my forehead at a downward angle. That's probably why I escaped without a concussion or more serious skull fracture.

Of course, like most head wounds, it bled like crazy. There are a lot of arteries, veins and capillaries in the head, since the brain requires a constant supply of oxygen- and glucose-rich blood to function properly. Also, I'd been exercising for a good hour by then, so the blood was really pumping. Funny side story: My chief instructor was chatting with a visitor to the dojo when my head injury occurred, his back to the mat. The visitor, gazing at the gushing blood in horror, mentioned that I'd been hurt, and really, oughtn't someone to do something? My instructor was used to people worrying about my welfare (there were very few women in my chosen style, and a hard fall from, say, a judo throw can look much worse than it really is). So he just waved it off and said, "It's okay -- she gets back up." Quoth the guest, "But... but... she's bleeding all over the mat!" That got his attention. He swung around, and immediately warned, "Don't you bleed on my mat!" Too late!

Ironically, when I examined my gi upon getting home, there was hardly any blood on it at all, just a bit of staining around the collar when the ER doc rinsed the matted blood from my hair. It had spurted outward in impressive gushes, hitting pretty much everyone in the vicinity except me -- just like the Black Knight's arterial sprays in Monty Python and the Holy Grail. ("It's just a flesh wound!") That's not what I would have expected.  Granted, we aren't talking about arterial spatter of the sort one sees routinely these days on C.S.I. Still, the blood pumping through my head at that point was clearly moving at a high enough pressure to cause an arterial-like spurt. Which meant I didn't need to soak my gi in bleach for two days, like a few of my unfortunate fellow students. (One guy -- who kindly administered pressure to my wound to stem the bleeding while waiting for the ambulance to arrive, and thus had my blood all over him -- just gave up bought a new gi. Thanks, Vito!)

The C.S.I. franchise certainly has its critics when it comes to how it depicts forensic science, but in fact, there is such a thing as bloodstain pattern interpretation that can be used to piece together the events that gave rise to a particular pattern of spatter or bloodstains. Experts trained in this approach consider such qualities as the viscosity of blood, the specific gravitational forces acting upon it, and the role of surface tension. (For instance, a bit of blood that falls off a pricked finger will round out into a sphere because surface tension acts to reduce surface area to the absolute minimum possible.) Here's some fun facts I learned about blood spatter (illustrated by some handy photos) from this excellent Website:

* Blood cast from a moving source will make smaller droplets than blood cast from a stationary source.

* Blood follows the same basic laws of physics as any projectile in motion. (This means it should be possible, in principle, to calculate the trajectory of the blood spurting from my head wound and predict where it would land on the mat, so everyone could steer clear of that spot.)

* The terminal velocity of a falling blood drop depends on its size: smaller drops have a lower terminal velocity and reach that point after a shorter fall distance that larger droplets (which accelerate over a greater distance and thus reach a greater terminal velocity).

* The shape of the blood spot depends in part on the texture of the surface on which it calls. If it falls on smooth glass, it will be circular and fairly uniform in shape. If it calls on a textured surface, such as paper, or wood (or a judo mat), the shape won't be nearly as regular. In general, the harder the surface, the less spatter there will be. If a blood drop hits a surface that is both hard and smooth, it will break apart upon impact into smaller droplets -- and those offspring droplets will continue to move in the same direction as the parent drop.

* The angle of impact also determines a blood drop's final shape. For instance, a vertical drop onto a smooth target tilted at 90 degrees results in a circular stain, and as the angle decreases, the stain becomes more elongated, and its length-to-width ratio increases accordingly.

* Finally, blood spatter patterns are classified according to the velocity with which the blood struck a given surface. For instance, spatter patterns occur when blood is projected at a velocity greater than the force of gravity, such as what occurs when blood is cast off a weapon. (Per the site, "The direction and origin of the backswing is often clearly discernible.") Low-velocity blood spatter is basically what happens when the stuff just drips downward from a cut. A blow with a baseball bat would constitute medium-velocity blood spatter, producing spots of about 4 mm in diameter, while a gunshot will produce high-velocity spatter and a "fine mist" of spots less than 1 mm in diameter. Arterial spurting is a category all its own.

The Black Knight would have been fascinated, I'm sure, to hear King Arthur ruminate on these matters (far more interesting than determining the air speed velocity of an unladen sparrow, both African and European varieties). There's much, much more to do with the science of blood spatter, and the physics of the martial arts (judo throws are a specialty all their own), but I suspect I've grossed everyone out enough for one day.

let me explain

I found myself chuckling in amused recognition on Sunday while reading Rebecca Solnit's Op-Ed in the Los Angeles Times, "Men Who Explain Things." Solnit, for those unfamiliar with her work, is the author of A Field Guide to Getting Lost and River of Shadows: Eadweard Muybridge and the Technological Wild West, among other tomes. Her Op-Ed is a wry commentary on a familiar phenomenon, per the subhead: "Every woman knows what it's like to be patronized by a guy who won't let facts get in the way." She opens with the story of an upscale party at a chalet in Aspen; most of the guests were old enough that she, in her 40s, was considered quite young. So perhaps it shouldn't have been surprising when the host mentioned he'd heard she'd written a couple of books, and condescendingly asked what they might be about, "in the way you encourage your friend's 7-year-old to describe flute practice."

Solnit has actually written six or seven books, but rather than give him a laundry list -- correctly guessing he was less interested in her work than in figuring out how he could use the topic to jump-start his own literary soliloquy -- she started to tell him about the latest book (published in 2003), on Muybridge. In record time, her host interrupted and proceeded to expound at length on the "very important" Muybridge book that had been published that year, which she really must read if she was interested in Muybridge, and launched into a summation of that revered tome for her edification. His soliloquy was delivered "with that smug look I know so well in a man holding forth, eyes fixed on the fuzzy far horizon of his own authority." (That Solnit has quite a way with words, doesn't she?) Not even the news that Solnit had written the "very important" book he was pontificating about was enough to dissuade him for long, beyond a moment of ashen-faced embarrassment. Small wonder he couldn't remember her name. He had not, it turned out, actually read the book on which he was holding forth with such authority. He'd merely skimmed an article about it in The New York Times Book Review.

Now, this sort of unmasked literary pretension is quite common in certain pseudo-intellectual circles, and is not gender-specific per se. (Frankly, certain women can be just as preening and pretentious, with the same need to hold center stage. They can also be absolutely brutal when it comes to the art of diminishing the stature of perceived rivals via the subtly condescending put-down.) Solnit is very careful to point out that she is not describing all men, only a particularly annoying sub-species, and acknowledges that "my life is well-sprinkled with lovely men... Still, there are these other men, too." Explaining Men are the in-your-face embodiment of what Solnit decries as a much broader "archipelago of arrogance." It bespeaks an underlying attitude towards women as "empty vessel[s] to be filled with their [i.e., men's] wisdom and knowledge," and the worst part is, women themselves often buy into this skewed under-assessment of their relevance and abilities.

"Men explain things to me, and to other women, whether or not they know what they're talking about.... Every woman knows what I mean. It's the presumption that makes it hard, at times, for any woman in any field; that keeps women from speaking up and from being heard when they dare; that crushes young women into silence by indicating... that this is not their world. It trains us in self-doubt and self-limitation just as it exercises men's unsupported over-confidence. This syndrome is something nearly every woman faces every day, within herself too, a belief in her superfluity, an invitation to silence...."

My own experiences with Explaining Men are a bit more complex, in part because I am a science writer, and thus quite often I want someone to explain something esoteric to me, and welcome the attempt at edification. (It helps that I am naturally curious, too.) In the male-dominated field of physics, that explainer is usually going to be a man -- although the percentage of women is inching upwards every so slowly with each passing decade -- and for the most part, those men have been very decent about it, with a few rare exceptions.

That's not what Solnit is describing, however. She's talking about the sort of patronizing condescension that pervades all kinds of daily interactions between men and women; Men Who Explain Things are among the more benign examples. So I tend to agree in principle with Solnit when she writes, "Most women fight wars on two fronts, one for whatever the putative topic is, and one simply for the right to speak, to have ideas, to be acknowledged to be in possession of facts and truths, to have value...." This harsh reality hit me full force with the publication of my first book a few years ago, and my very first radio interview to promote it: an hour-long call-in program in San Francisco. Something about a former English major thinking she could effectively communicate physics concepts to a general audience stuck in the craw of one cranky male physicist, who called in specifically to harangue me on the air for my chutzpah is daring to presume to "speak for physics" (a claim I never made). He didn't actually call me uppity English major scum, but the implication was clear.

"But surely that had nothing to do with your gender," some of you might be thinking. I suspect it did. After all, he didn't merely take issue with the substance of what I said (the cornerstone of any healthy debate); he questioned my right to say anything publicly on the topic at all.

A similar incident occurred about two months later when I appeared on a radio call-in show in Washington, DC. Another male physicist called in, highly irate, to take issue with my off-the-cuff summation of the uncertainty principle. It was a nitpicky technical point, plus, it was a live show, so for all I knew, I could have mis-spoken, and said so. I hadn't, as it turns out; I'd simplified the explanation for the public radio audience, but within those constraints, it was a perfectly acceptable summation. A couple other male physicists of my acquaintance who heard the show were incensed that the caller had attacked me for no good reason -- and, frankly, a bit disappointed that I hadn't defended myself more aggressively. Mea culpa. I let self-doubt hold sway. The caller claimed to be a physicist, and I was just a first-time author, and a girl at that. Some small part of me just assumed I'd made a mistake, rather than concluding that he was being a jerk.

I have a lot more confidence these days in my right to speak and be heard; now, I'd come out swinging and make mincemeat out of that irate Explaining Man. But three years ago, I was still a bit lacking in confidence, despite all the hard work I'd done to research the book, running all the sample chapters past PhD physicists to check for technical accuracy, and so forth. Even Solnit, a far more seasoned writer, has fallen victim to this phenomenon: "There was a moment there when I was willing to believe Mr. Very Important and his overweening confidence over my more shaky certainty." And it was her book he was pontificating about!

Would I have been attacked so vigorously had I not been a young woman, with a degree in English, daring to speak about the caller's pet topic? Everyone mis-speaks occasionally when talking off-the-cuff, including the Spousal Unit. But he's a man, with a PhD in physics, so when he mis-speaks, it's assumed that he's made an honest error. When I mis-speak, it's usually assumed I am ignorant. Or sloppy. Or both. At least by men. Honestly, there were times, during the year of the First Book, when it felt less like I was being interviewed about a book I'd written, and more like I was being grilled before some self-appointed Inquisition of Popular Physics Writing to make sure I had earned the right to even be there in the first place. Generally speaking, the women who interviewed me (or reviewed the book) were interested and friendly (even if they had criticisms); several men were condescending at best, harshly critical and combative at worst.

Don't get me wrong: I'm not one of those writers who thinks her words are sacred; I rely on thoughtful, constructive criticism to improve my skills, and deliberately seek it out. I'm also a bit of a perfectionist. Like most writers, I'd dearly love to rewrite portions of that first book, so it could benefit from everything I learned in the process of writing it. That sort of input is not the same thing as a subtle power play, an attempt to put the little lady in her place, thinly disguised as helpful criticism, the better to puff up one's own ego and sense of superiority. (Jen-Luc Piquant acidly comments that if you take such faux-criticism otherwise, you're denounced as clearly "over-sensitive." Hey, must be "that time of the month!" Insert deprecating chuckle here. Cut her some slack. She's still bitter over a recent confrontation with a pompous Lacanian Avatar Who Explains Things about deconstructing Jane Eyre.)

Sometimes I envy Explaining Men this over-weening confidence in their own authority -- even when they actually know very little about the particular topic at hand. In this era of superficial dialogue, the appearance of knowledge is often all that's required.  Then again, the constant reminders of my own supposed irrelevance have made me stronger, more confident with each storm I weather that yes, I do deserve to be here, and to be heard.  All those years as a struggling writer have given me a hard-won expertise that no patronizing Explaining Man can take away from me.

Maybe I'm more appreciative of the freedom to speak because I had to fight so hard to find my voice in the first place. These days, I'm more inclined towards rueful amusement when encountering Men Who Explain Things. But as Solnit points out, that's because we've had to learn to publicly stand our ground as authors; millions of other women don't get that particular boost, and never learn to push back. That's the underlying tragedy of what would otherwise be an amusing oddity of social discourse. Per Solnit: "The battle with Men Who Explain Things has trampled many women... [including] the countless women who came before me and were not allowed into the laboratory, or the library, or the conversation, or the revolution, or even the category called human."

Certainly, throughout the ages, women have not enjoyed many exalted positions in intellectual circles, especially in math and science. Usually, they had to teach themselves, unless they came from wealthy and/or noble families. Such was the case with an 18th century Italian mathematician named Maria Gaetana Agnesi. The eldest of 21 children -- I was relieved to learn her father married three times, since the thought of one woman enduring that many pregnancies boggled the mind -- Agnesi was very much a child prodigy, known in her family as "the Walking Polyglot" because she could speak French, Italian, Greek, Hebrew, Spanish, German and Latin by the time she was 13.

Agnesi had the advantage of a wealthy upbringing; the family fortune came from the silk trade. And she also had a highly supportive father, who hired the very best tutors for his talented elder daughter. Unfortunately for the shy, retiring Agnesi, he also insisted she participate in regular intellectual "salons" he hosted for great thinkers hailing from all over Europe. The young Maria delivered an oration in defense of higher education for women in Latin at the age of 9 (she had translated it from the Italian herself and memorized the text).

There is evidence from contemporary accounts that Agnesi loathed this sort of thing and hated being put on display, even though her erudition earned her much admiration. One contemporary, Charles de Brosseslde Brosses, recalled, "she told me that she was very sorry that the visit had taken the form of a thesis defence, and that she did not like to speak publicly of such things, where for every one that was amused, twenty were bored to death."

Unlike the men in her father's salon, Agnesi didn't much care for Explaining Things. De Brosses  admired her intellectual prowess greatly, and expressed his horror upon learning that she wished to become a nun. What a waste! was the implied sentiment. And perhaps it was. But I'm thinking maybe she was far too intelligent for her own good; she just couldn't take the self-aggrandizing intellectuals of her father's acquaintance seriously. And perhaps she realized that she would always be proving herself, and that her accomplishments, no matter how impressive, would always be treated with some degree of patronizing amazement. ("Look at the smart woman discoursing in Latin!")

Agnesi did, eventually, become a nun, but not before spending 10 years writing a seminal mathematics textbook, Analytical Institutions, which was published in 1748. (Most biographies, while admiring, feel compelled to note that the tome contained "no original mathematics.") She was also the first woman to be appointed as a mathematics professor at a university -- the University of Bologna -- although there's no record she ever formally accepted the position. She died a pauper in 1799, having given away everything she owned. At least there's a crater on Venus named in her memory. And she need never be forced to perform like a trained circus monkey again, or listen to any more Explaining Men eager to find some means to edify such a prodigy. She can just let her life's work speak for itself.

I'll give Solnit the last word, since she writes so eloquently:

"Men explain things to me still. And no man has ever apologized for explaining, wrongly, things that I know and they don't. Not yet, but according to the actuarial tables, I may have another 40-something years to live, more or less, so it could happen. Though I'm not holding my breath."

these boots weren't made for walking

Every now and then, shoe-frenzy makes a cameo appearance the blogosphere. Okay, it's omnipresent in blogs dealing with fashion and shopping, but most of us (male and female) have to shop for footwear at some point. And some of us feel compelled to blog about our particularly noteworthy finds, at least in passing. You know, like the incomparable Heather Armstrong at Dooce, who has waxed ecstatic about silver-metallic ballet flats (dismissed by her husband as "elf shoes"), and once wrote this wonderful paean to the joy of finding the perfect pair. Armstrong is known for detailing the minutiae of her daily life on her blog, but that doesn't mean the rest of us don't occasionally bliss out over an especially nifty pair of pumps. Which is exactly what happened in comment threads this week over at Bitch PhD and Shakesville. (Fair warning to the easily offended: why are you clicking on a link to a blog called Bitch PhD in the first place? Because you thought it would be about knitting while sipping mint juleps and nibbling cucumber sandwiches? Duh!)

Ah, but there are lots of killjoys out there on teh Internets, no doubt wearing too-tight or ill-fitting shoes (or, worse, clunky "sensible" shoes), which might explain why they're so cranky, and why they feel compelled to spoil other people's fun. Apparently some people criticized Shakesville's Melissa McEwan for departing from her usual hard-hitting feminist political fare to focus on something as trivial as shoes. I'm guessing this is something women scientists face as well. We aren't allowed, it seems, to take pleasure in the small joys of life and still be Serious Women, respected professionals in our chosen fields.

Um, screw that. I'm the patron saint of comfy sensible shoes -- I'm known for it among my female friends, in fact (who are not always complimentary about my workmanlike choices) -- but that doesn't mean I can't branch out once in awhile and be truly stylin'. Who says women can't be smart, serious, 100% professional, and still totally rock a pair of hot pink pumps if they want to? (Or asphalt-stomping Doc Martens, if that's your preference. To each his/her own.) In honor of Melissa, Bitch PhD, Heather, and all you other shoe-lovers out there, today's post will focus on the science of footwear.

First, a look at this week's featured products before we delve into the science. Bitch PhD offered these multi-colored beauties:

Then Melissa weighed in with these innocent-seeming pink pumps that launched a thousand angry comments (UPDATE: Oops! Apparently it was only a couple of negative comments, but it did inspire her to write a blog post on the topic):

Followed by these plaid ballet flats, for the more sensible-minded of her readers: