“So I was talking to…to…oh, you know, that guy, the one in the head office, big hair, bad teeth, only listens to Perry Como records…geez, why can’t I remember his name? It’s on the tip of my tongue!”

It’s a common phenomenon, and it’s not just people’s names. Sometimes you can’t think of the name of a place, or a food, or a car, or…just about anything. You can feel that the information is in your head, but you can’t shape it into a word.

It may be a well-known phenomenon, but it isn’t well-understood. However, new research may have shed a little light on the mechanism involved.

One leading explanation for tip-of-the-tongue torment is that when we’re trying to think of a specific word, some other, similar-sounding word pops up in the brain instead and blocks our ability to access the correct one. This is called “phonological blocking,” and it was that idea that the new research was designed to test.

Interestingly, though, the researchers didn’t turn to people who speak with their tongues, but people who speak with their hands: fluent speakers of American Sign Language.

Karen Emmorey, director of the Laboratory for Language & Cognitive Neuroscience at San Diego State University, is interested in the similarities and differences between signed language and spoken language. Other of her recent research has shown, for example, that when a gesture is used for sign language, a different part of the brain is activated than when that same gestture is used for pantomime: in other words, the brain distinguishes between a gesture that has linguistic meaning and a gesture that’s just a gesture.

Emmorey knew previous research has shown that bilingual people have more tip-of-the-tongue moments than unilingual people do. The phonological-blocking explanation of this would be that those with two languages in their heads have twice as many words to get in the way of other similar-sounding words.

She reasoned that if that explanation were correct, then the general rule that bilingual people have more tip-of-the-tongue moments shouldn’t hold true for those who were bilingual in both English and sign language, because obviously half the words in one language not only don’t sound the same as the words in English, they don’t make a sound at all!

In sign language, tip-of-the-tongue moments are called tip-of-the-finger moments. Just like tip-of-the-tongues, tip-of-the-fingers occur spontaneously, often involve proper names, and frequently include partial access to the word. In speakers, this frequently means you can remember the first sound of the word but not the rest of it. In signers, that may mean they can remember the sign’s hand shape, location and orientation, but not its movement.

Unfortunately for the phonological-blocking contingent, Emmorey discovered that those bilingual in English and ASL had tip-of-the-tongue…or, in the one case, tip-of-the-finger….incidents pretty much as often as people bilingual in English and Spanish.

That would seem to indicate that phonological blocking is not the mechanism underpinning tip-of-the-tongue moments at all.

If you’re going to throw out one explanation, you need to suggest another one, and Emmorey has done so. She believes tip-of-the-tongue/tip-of-the-finger moments are due to forgetfulness, brought about by infrequency of use. In other words, the less often you use a word, the harder it is for your brain to come up with it when needed, she suspects.

That would explain why all bilinguals, whether they use two spoken languages or one spoken and one unspoken, have those moments more often: all the words they know are used less frequently than the words known by someone who only speaks one language.

It’s just a possible explanation at this point, of course. To see if it holds water, there’ll have be additional…um…

Oh, you know, starts with “r,” that thing scientists do in laboratories, involves experiments…

Research! That’s it.

Now why couldn’t I remember that?

Morrison invented the Frisbee.

Since millions of these and other flying discs have been sold since the 1950s, it’s perhaps a bit humbling to discover, though, that even though throwing a Frisbee well is a skill that can be acquired, nobody has pinned down all the details of the science involved.

Morrison, born in Richfield, Utah, said the inspiration for the Frisbee went back to a Thanksgiving Day picnic in 1937 when he and his girlfriend (and future wife), Lu Nay, began throwing the lid of a popcorn tin back and forth.

They soon found that a tin cake pan flew even better, and shortly after that started selling “Flyin’ Cake Pans” on the beach at Santa Monica, California, for 25 cents each.

Morrison flew P-47 Thunderbolts during the Second World War, no doubt developing a new appreciation of aerodynamics, and shortly after the War, in 1946, created his first flying disc, the Whirlo-Way. In 1948, with backing from another former pilot, Warren Franscioni, he began molding what he then called the “Flyin’ Saucer” in plastic.

In 1955 he and his wife began producing their own discs with a deeper, thicker rim, calling them “Pluto Platters.” Wham-O bought the rights in 1957, and changed the name to Frisbee (which Morrison didn’t like), the name apparently based on the pie tins from the Frisbie Pie Company that students from East Coast colleges had long been flying.

A Wham-O designer, Ed Headrick, added the flight ridges to the top of the disc in 1964, improving its stability and speed.

So…how does a Frisbee fly, exactly?

Like an airplane wing: it generates lift by creating a difference in air pressure between its top and bottom sides. The top of a Frisbee is slightly convex, and the bottom is flat. That forces the air flowing over the top of the disc to move faster than the air flowing beneath it. Faster-flowing air has a lower air pressure, and so the higher-pressure air underneath forces the disc up. This is known as Bernoulli’s principle.

But a Frisbee is also very different from an airplane wing. Its curved rim disrupts the airflow on the bottom of the disk, creating turbulence. This means the airstream at the back of the disc tends to move much more slowly than the airstream at the front, creating an imbalance in pressure…which is why Frisbees often turn over in flight.

The other big difference between a Frisbee and an airplane wing is that the Frisbee is spinning. This is why the Frisbee, when it does turn over, tends to turn onto its side, rather than flipping front to back: spinning objects, through something called gyroscopic progression, tend to show the effect of a force in a spot perpendicular to where the force is applied.

At the same time, though, spinning helps the Frisbee stay stable. A spinning object resists being tipped. This “angular momentum” is why a moving bicycle, with its spinning wheels, is stable, but a stopped bicycle is not.

Some of the subtleties of a Frisbee’s flight, such as why it can make slight turns at the end of its flight, are still not well-understood. In the past few years, researchers have put Frisbees on a motorized rod and spun them in a wind tunnel to try to learn more, and have discovered that how fast a Frisbee tips over in its flight depends on the angle of attack (you want to tip it slightly upward as you throw it) and how fast it spins relative to its airspeed. A really dedicated and mathematically minded Frisbee thrower could, using the results of this study, figure out exactly what angle the Frisbee should be thrown at to make it go as far as possible or stay in the air as long as possible.

This kind of work has more “practical” applications: space probes, for instance, are often spun to improve stability, and Frisbee studies have figured into work on their design.

But who cares? Morrison’s invention has brought more happiness to more people over the years than any number of “practical” inventions. And for that, he deserves your thanks next time you spend a sunny afternoon on the grass with a Frisbee.

Actually, he deserves your thanks twice: once for yourself, and once for your dog.

It sounds even more like a 2 a.m. infomercial product when you see headlines about it that claim it is “about to revolutionize everything.”

Maybe it’d sound more impressive if I used its more formal name, which is “SiO2 ultra-thin layering,” but that’s hard to type, so I’m going to stick with “spray-on liquid glass.”

Besides, that’s exactly what it is: an extremely thin layer of glass that can be sprayed onto…well, just about anything.

Though it was invented in Turkey, the patent for spray-on liquid glass is held by the German company Nanopool.

It consists of almost pure silicon dioxide, a.k.a. silica, extracted from quartz sand. Water or ethanol is added, depending on what kind of surface is to be coated: the water-based versions are good for absorbent surfaces such as stone, wood and fabrics, while the ethanol-based versions are suitable for metal, glass, plastic and painted surfaces. There are no other additives: a bottle of liquid glass contains only water or ethanol, and molecules of silica. And not too surprisingly (since silica is the most abundant mineral in the Earth’s crust), the coating is non-toxic and environmentally harmless.

The glass binds to the surface through quantum forces that come into play at the extremely small scale of these tiny glass particles. The coating is only about 100 nanometers thick–that’s only 1/500th the width of a human hair.

An article in the June, 2009, issue of the U.K. magazine Cleanroom Technology has a pretty complete list of the coating’s benefits.

First of all, it’s flexible, meaning it can be used to coat, not just hard surfaces like countertops and sinks, but fabric, conveyor belts, medical devices such as endoscopes, and more.

It’s highly durable, able to withstand tens of thousands of cleaning cycles, and heat tolerant, unaffected by temperatures as low as -150 C and as high as 450 C. It also resists both acid and alkaline substances.

It doesn’t kill bacteria, but it also doesn’t provide them with a friendly surface to attach themselves to and multiply. Wash a coated surface with hot water, and the bacteria are wiped away more effectively than you can achieve with bleach on an uncoated surface (as tests in an Austrian cheese-packaging plant have proven).

It’s so thin that it’s invisible to the human eye and can’t be felt; while it’s slippery at the micro level, at the macro level (our level), it isn’t. In fact, since bacteria can be so easily cleaned off of it, a coated shower floor would probably be less slippery, because of the lack of bacteria-produced biofilms.

The stuff is easy to apply: even large areas such as floors, walls and windows can be coated with it in minutes, and no special equipment is needed. And finally (and even more amazingly), it’s cheap: the cost to cover a square metre ranges from about 40 cents to $1.80.

Sounds too good to be true, doesn’t it? Surely it must be full of little tiny glass particles that are going to get into our lungs and cause asbestos-fibre like problems?

Nope. The coating contains no discrete or potentially harmful engineered nanoparticles.

Spray-on liquid glass is already available in Germany for domestic use, for about $8.50 a bottle. In the home, it could conceivably make existing cleaning products obsolete, since hot water would do the job chemicals are doing now. It could be used in the oven, bathrooms, tiles, sinks, and on almost any other surface, and the coating is expected to last about a year with normal use.

Outside, the uses are endless. A silk shirt coated with it would shrug off a spilled glass of red wine. Stone coated with it could be more easily cleaned of graffiti. Seeds sprayed with it are protected from fungal and bacterial attacks and germinate and grow faster than untreated seeds. Wood treated with it has survived undamaged after being buried in a termite mound for nine months.

A Lancashire hospital has had “very promising” results using it as a coating for everything from equipment to medical implants, catheters, sutures and bandages.

It sounds amazing.

But it also still sounds like a 2 a.m. infomercial product.

I guess time will tell.

But there’s an obvious problem with this. That stuff we’re turning into fuel is also food for humans and feed for animals.

(And as an aside, how come we always call it “animal feed” as opposed to “animal food”? And why don’t we ever refer to “human feed”? Hmm?)

A lot of the plant is wasted when you grow crops for fuel or food. The leaves and stems, with their tough cell walls made of cellulose, hemicellulose and lignin, are more of a nuisance than anything else. Wouldn’t it be great if there were a use for what is now plowed under or burned?

There is, or there soon will be, thanks to research aimed at using bacteria to convert this “lignocellulosic biomass” into fuel in its own right.

A just-published article in Nature reveals the state of the art. Titled “Microbial production of fatty-acid-derived fuels and chemicals from plant biomass,” it describes the successful engineering of the common bacterium Excherichia coli–better known as E. coli and generally in the news when it contaminates water or meat and makes people sick–into a producer of biodiesel.

One of the co-authors of the research study is Jay Keasling, chief executive officer for the U.S. Department of Energy’s Joint BioEnergy Institute (JBEI). “We’ve got a billion tons of biomass every year that goes unused,” he says, adding that fuel produced from that biomass could make up for as much as half of U.S. oil imports, turning “the U.S. Midwest into the new ‘Mideast’.”

That’s not hyperbole: by one estimate, lignicellulosic biomass could produce more than 7,500 litres of renewable petroleum per acre.

The researchers modified the E. coli genome, inserting genetic code for the production of an enzyme called hemicellulase, which can break down hemicellulose into smaller sugar molecules which E. coli can then turn into fatty acids.

E. coli normally produces only as much of the fatty acids as it needs for its own cell membranes. But the researchers’ E. coli were further modified so that the fatty acids just kept coming, turning each bacterium into a microscopic biodiesel factory.

The process takes place in fermentation vats, into which the bacteria expel little drops of oil. Turn off the impellers, and the oil floats to the top, where it can be skimmed off.

Even better, by tweaking the process, chemical products ranging from solvents to lubricants to jet fuel could conceivably be produced.

Of course, it’s important to note that the research reported in Nature is just a proof of concept. There’s no commercially viable process for doing any of this yet–but Keasling hopes there will be within a very few years. Work will continue as the researchers search for ways to make use of even more of what’s in the feedstock–not just the hemicellulose.

There’s already a company standing ready to market fuels and other microbe-produced chemicals. Based in California, LS9, founded by a geneticist and a plant biologist, helped fund the research reported in Nature. LS9 points out that the crude oil produced by bioengineered bacteria has none of the contaminating sulfur of regular crude oil, so it’s cleaner. And despite its unorthodox origins, it can be refined like any other crude oil in a standard refinery.

There are other companies pursuing their own paths. Amyris Biotechnologies, for example, says it has also created bacteria capable of providing renewable hydrocarbon-based fuels. There are many more.

Why would this be preferable to ethanol production as it is currently carried out? Aside from the aforementioned fact that we’re presently turning food into fuel, hydrocarbon fuels are more efficient than ethanol, packing about 30 percent more energy into any given quantity. And even better, they take less energy to produce: ethanol production, which involves distilling, requires 65 percent more energy than hydrocarbon production does.

Perhaps the oil industry will slowly evolve away from the purview of drilling companies and into the realm of agriculture.

As for the marketing slogan for this new germ-produced form of fuel, I think I’ve come up with a winner: “E. coli. It’s not just for food poisoning anymore.”

What do you think?

The fact is, we’re all influenced by the people around us…and we often think of that influence as a bad thing.

As the Bible puts it, “Evil companions corrupt good morals.” And other kinds of companions can have other effects.

For instance, an analysis of 12,067 people that appeared in The New England Journal of Medicine in 2007 revealed that you are more likely to be obese if your best friend is obese. (Overstuffed siblings or spouses also makes a difference, but the greatest negative effect comes from fat friends.)

To a certain extent, it seems, obesity is a kind of societal disease, rather like the mysterious fainting disorders Victorian women seemed to be heir to, or the bizarre disorder koro, which in South China convinces men that their genitals are shrinking inward and they will die once they disappear.

Which they don’t, of course, but the affliction is real even if the symptoms are imagined.

High anxiety, depression, anorexia and bulimia are also contagious, and if you believe all these things are being foisted upon us by a secret government agency, perhaps you have fallen prey to another contagious state of mind, paranoia.

But not all social contagions are bad.

Back around Christmas of 2008 I wrote a column on the discovery that happiness is contagious, spreading rather like influenza. It seemed a particularly fitting column for the holiday season…and the newest research along those lines seems particularly fitting for a post-holiday column, because now comes word that self-control is also contagious.

At the University of Georgia, psychology professor Michelle vanDellen and colleagues were able to measure the effect in the laboratory, through a variety of studies over two years.

In one, they randomly assigned 36 volunteers to think about a friend with either good or bad self-control. They found that those thinking about a friend with good self-control squeezed a handgrip (a standard method of measuring self-control, since you have to force yourself to keep squeezing it as your hand gets more and more tired) longer than those who were asked to think about a friend who had poor self-control.

In a second test, 71 volunteers were again randomly assigned to either watch other people exert self-control by choosing to eat a carrot rather than a cookie when presented with both options, or fail to exert self-control by eating a cookie rather than a carrot. The mere act of watching those acts of good and bad self-control altered the volunteers’ performances on a later test of self-control.

In a third experiment, 42 volunteers were randomly assigned to list friends with both good and bad self-control. Then, as they were working their way through a computerized test designed to measure self-restraint, the computer would flash, for just 10 milliseconds–too fast to be read, but enough to bring the names to mind–the names of those friends. Volunteers who were flashed the name of a self-disciplined friend did better on the test than those who were flashed the name of a non-self-disciplined friend.

VanDellen believes that the influence is great enough that hanging around with friends who exhibit self-control could help us keep from eating an extra high-calorie snack at a party, or drive us to go to the gym for a workout at the end of a hard day at work. It’s only a nudge, but sometimes a nudge is all that’s needed.

And just why are we so susceptible to peer pressure?

Because we’re primates, and, as science writer Meredith F. Small puts it, “A primate’s day is all about everyone else.”

Chimpanzees and other primates spend all their time touching each other, keeping track of each other, and building interpersonal relationships…and in a very real sense, so do we. We are constantly influenced by those around us…and influence them, in turn.

Rather alarming, if you ask me. I think I’ll just sit in my office from now on and not talk to anyone.

I wouldn’t want to catch anything.

It’s easy, when you’re one of the little guys in any creative field, be it fashion, books, movies or music, to envy the runaway successes and wonder what, for example, Stephenie Meyer’s got that you ain’t got. Are her books, objectively, truly so much better than everyone else’s? Or, more to the point, than mine?

Probably not, suggests recent research: in fact, runaway successes are runaway successes in part because they’re runaway successes…and efforts to figure out what “the next big thing” will be are largely wasted, because there’s no way to know.

That’s because people simply don’t make decisions as independently as we like to think.

A recent research project at Columbia University, led by Duncan Watts and Matthew Salganik, showed just how big an impact social influence can have on the popularity of something.

Through a website called Music Lab, the two registered more than 14,000 participants for their study. These participants were asked to listen to, rate and, if they chose, download songs by bands they had never heard of.

Some participants were only shown the names of the songs and bands. Others also saw how many times other participants had already downloaded the songs. Those who could see how often songs were downloaded were further split into eight separate “social-influence worlds”: they could only see the number of downloads a song received from other members of their “world.” This allowed the popularity of songs to evolve independently, eight times over.

If people made their choices completely independently, the scientists predicted, the most successful songs would draw about the same market share among both the participants who saw only band and song names and those who also saw how often the songs had been downloaded. As well, they predicted, the same songs, the “best songs,” would become hits in all eight social-influence worlds.

Instead, the most popular songs were much more popular, and the least popular songs less popular, in the social-influence worlds than in the independent group. Not only that, different songs became hits in each of the separate worlds.

This is where the idea of “cumulative advantage” comes in.  Initially, all the songs were equal. But random choice by the participants soon meant that some songs were downloaded more than others. And once that happened, more participants started downloading them than the other songs, because they thought there must be a reason for their popularity–even though that popularity arose mostly by chance.

It may offer some slight solace to those who cling to their belief that they can’t be swayed by mass opinion that perceived quality did play some role in popularity. When downloads across all eight social-influence worlds were added together, songs the participants rated as higher in quality–“good” songs–had higher market share on average than “bad” ones. But the effect was miniscule. One song squarely in the middle of the quality rankings was number one in one social-influence world and number 40 in another one.

Or, as Watts put it in his New York Times article about his research, “A song in the Top 5 in terms of quality had only a 50-percent chance of finishing in the Top 5 of success.”

All of this indicates that things don’t become popular solely because they meet some previously unsuspected public desire or somehow match up with the public’s changing tastes. Instead, things become popular almost by chance, and then their very popularity changes the public’s taste. The market, in other words, influences itself.

Or, as the publisher of Lynne Truss’s bestselling book Eats, Shoots & Leaves put it when asked to explain its success, “it sold well because lots of people bought it.”

I’m not entirely convinced, so I’d like all my readers to help me conduct an experiment. I’d like each of you to go out and buy a dozen–better yet, two dozen–better yet, 100!–copies of my science fiction books Marseguro and Terra Insegura, just to see if we can artificially drive them to the top of the bestseller charts.

I’ll compile the royalties…um, I mean, the results…and report back just as soon as I can.

Well, if Oprah and Cameron will quit pestering me long enough, that is.

But that’s all recorded music. Live music remains far rarer. Live musicians may occasionally show up in a public space, but you generally have to seek them out.

Which raises an interesting question. Do we perceive music differently when we watch it being played than we do when we are only listening to a recording?

Michael Schutz is both a noted percussionist and a noted researcher. Currently an assistant professor at McMaster University, he runs a research lab dedicated to studying the cognitive science of music, and the visual component of music is something he’s very interested in.

As he notes in an article published by the Acoustical Society of America, “while purists may argue that music is an auditory experience and therefore visual information is irrelevant, the enormous investment in clothing, lighting, smoke machines and other visual effects in live concerts demonstrates audiences clearly respond to and appreciate visual information as part of the musical experience.”

“Clothing, lighting, smoke machines and other visual effects” is rather too broad a collection of items to serve as the focus of a practical experiment, so Schutz decided to look at a much narrower question, i.e., “Do the gestures used by percussionists have any musical value irrespective of their acoustic consequences?”

This has long been a matter of debate. Some percussionists are adamant that using a sharp wrist motion produces a more staccato sound than a fluid motion. Others are adamant that gestures don’t matter: a percussion instrument will make the same sound if struck with the same amount of force no matter what gesture is used to produce the blow.

It turns out that they’re both right–or both wrong, depending on how you look at it–because there’s a difference between sound (acoustics) and the way that sound is experienced (perception).

Schutz and colleagues conducted two experiments. In the first, they recorded a world-renowned percussionist performing notes using long and short gestures on a professional-quality marimba. Participants rated the duration of each note twice: once while viewing the gesture, once just by listening.

The result: notes produced by long and short gestures were indistinguishable when judged by audio alone, but were judged to be significantly different when the accompanying gesture was seen…even though the participants had been specifically instructed to ignore visual information when making their ratings. Or, as Schutz puts it, in what at first glance seems a self-contradiction, “while gesture fails to alter the sound of the note, it…alters the way the note sounds.”

Earlier studies had suggested that visual information does not influence ratings of note length, but Schutz suspected his experiment revealed such an influence because of the particularly strong visual connection between the gesture of the marimba player and the sound produced. He predicted the results would only apply to percussive sounds, where the motion producing the sound is clearly visible.

To test that prediction, the researchers paired the original videos with notes produced, not only by the marimba, but by piano, French horn, clarinet and voice. A second set of participants followed the same procedure as before…and found that non-percussive sounds were unaffected by the visuals…not too surprising, since we obviously know that a man hitting a marimba won’t produce the sound of someone singing. (Interestingly, some visual influence was found in the piano…which is technically a percussive instrument.)

All of which seems to indicate that, at least for percussion, there is a very strong link between the sight of a live musician playing an instrument and the listeners’ perception of the sound…and that watching a percussionist play live is a very different experience from listening to a recording.

Percussionists, Schutz suggests, use this “musical illusion” to “align audience perception with performer intent.”

Quite likely, other musicians make use of similar illusions. Pete Townshend’s wind-milling arm may not produce any different sound from an electric guitar than the less flamboyant display of another musician–but that’s not the way we perceive it.

Our brains are so strongly affected by visual stimuli that we literally cannot ignore them…which means that, while recorded music has its uses, it can never replace the impact of hearing, and seeing, music performed live.

Bonus: no silly, uncomfortable earbuds required.

’Twas the nocturnal time of the preceding day
To the day we call Christmas (which is, by the way,
Just a modern twist on the eons-old fight
To use feast and fire to end winter’s night).
And all through our dwelling (a.k.a. the house),
Not a creature was stirring, not even a mouse.
(Mus musculus—really a terrible pest,
But even a pest needs a bit of a rest.)
The stockings were hung by the chimney with care,
In hopes that Saint Nicholas soon would be there
(Though that old-fashioned chimney’s so energy-poor
That next year I’m making him use the front door!).
Our genetic descendants lay snug in their beds,
While sucrose-based snack foods danced jigs in their heads,
And mamma in her kerchief, and I in my cap,
Had just settled our brains for a long winter’s nap
(You wear hats to bed when you lack central heat;
It helps keep you warm from your head to your feet),
When out on the lawn there arose such a clatter,
I sprang from my bed to see what was the matter.
(I’m not really jumpy, but a noise in the night
Sets off animal instincts to flee or to fight.)
Away to the window I flew like a flash,
Tore open the shutters and threw up the sash
(Well, not really flew, it was more like a dash—
And my wife didn’t wake even after the crash).
The moon on the breast of the new-fallen snow
Gave a luster of midday to objects below
(Which makes sense, since the moon gets its glow from the sun,
Which means moonlight and sunlight in one sense are one!);
When what to my wondering eyes should appear,
But a miniature sleigh and eight tiny reindeer
(Rangifer tarandus, you could call them, too—
Here in Canada we know them as caribou).
With a little old driver, so lively and quick,
I knew in a moment he must be St. Nick.
(St. Nick is the patron of Russia, you know;
He was born fifteen hundred or more years ago!)
More rapid than eagles his coursers they came
(As fast as a peregrine diving on game),
And since his old sleigh had no window or door,
He shouted their names o’er the slipstream’s loud roar:
“Now, Dasher! now, Dancer! now, Prancer and Vixen!
On, Comet! on, Cupid! on, Donder and Blitzen!”
(An interesting mixture of names old and new—
Astronomy-biology-mythology stew!)
“To the top of the porch, to the top of the wall!
Now dash away, dash away, dash away all!”
As dry leaves that before the wild hurricane fly,
When they meet with an obstacle, mount to the sky
(That’s ’cause air piles up when it meets with a wall,
And the leaves, weighing little, rise too, and don’t fall),
So up to the house-top the coursers they flew,
With the sleigh full of toys—and St. Nicholas too.
And then in a twinkling I heard on the roof
The prancing and pawing of each little hoof
(Not to mention the cracking of each little shingle:
Reindeer weigh quite a lot, as does dear Mr. Kringle!).
As I drew in my head, and was turning around,
Down the chimney St. Nicholas came with a bound.
(I can only assume, since his legs didn’t crack,
That friction ’twixt him and the bricks held him back.)
He was dressed all in fur from his head to his foot,
And his clothes were all tarnished with ashes and soot
(And since so much creosote blackened his hide,
I no longer fear carbon mono-oxide);
A bundle of toys he had flung on his back,
And he looked like a pedlar just opening his pack.
His eyes, how they twinkled (reflecting the light)!
His dimples, how merry (one to left, one to right)!
His cheeks were like roses, his nose like a cherry
(I thought for a sec he’d been drinking my sherry);
His droll little mouth was drawn up like a bow,
And the beard on his chin was as white as the snow.
(And did you know that white hair is not really white?
It looks white because it’s transparent to light.)
The stump of a pipe he held tight in his teeth,
And the smoke it encircled his head like a wreath.
(We must forgive Santa this unhealthy sin;
He was born before all of the studies were in.)
He had a broad face and a little round belly
That shook, when he laughed, like a bowl full of jelly.
(It’s amazing, you know, that he’s lived for so long,
What with all of the things that he eats that are wrong!)
He was chubby and plump, a right jolly old elf,
And I laughed, when I saw him, in spite of myself.
(Laughter benefits heart, lungs and brain, it’s been said;
Maybe laughter’s why cheerful old Santa’s not dead!)
A wink of his eye and a twist of his head
Soon gave me to know I had nothing to dread.
(Body language, to Santa, is nothing unique;
He speaks every language, from Zulu to Greek.)
He spoke not a word, but went straight to his work,
And filled all the stockings; then turned with a jerk,
And laying his finger aside of his nose,
And giving a nod, up the chimney he rose.
(Apparently Nick spends his off-season time
At a school in Nepal, where he’s learned how to climb.)
He sprang to his sleigh, to his team gave a whistle,
And away they all flew like the down of a thistle
(Its surface is large, but it’s so very light,
That the slightest of breezes can make it take flight);
But I heard him exclaim, as he vanished away,
With his anti-grav reindeer and miniature sleigh,
“Though I may not be real, in the physical sense,
“Though I may not have mass, and I may not be dense,
“Though it’s true, scientifically, this isn’t right,
Happy Christmas to all, and to all a good-night!”

(OK, maybe pizza is not the most traditional of foods, but it’s still a popular holiday choice, so humor me.)

Pizzas normally come pre-sliced. The question is, and I’m sure you’ve asked yourself this a lot, “How do we eat this pre-sliced pizza in a way that ensures nobody gets an unfair share?”

That’s the question, as New Scientist reported on December 11, that Rick Mabry and Paul Deiermann kept asking themselves when they used to share pizza for lunch at Louisiana State University in Shreveport. They kept getting into discussions about the mathematics of slicing it up while the pizza itself congealed on their plates.

Here’s the problem that bothered them: If the waiter cuts the pizza off-centre, but all the cuts from edge to edge cross at a single point, and the angles between all the adjacent cuts are identical, will two people taking turns eating adjacent pieces get equal shares by the time they’ve worked their way around the whole pizza…and if not, who will get more?

Like I said, it’s a problem that has baffled most of us at some time or other…hasn’t it?

Well, whether it has or hasn’t, it baffled them, and after years of work, the two mathematicians have arrived at the solution that works in all cases.

It’s that “all cases” that makes it special. It’s fairly easy to see that if a pizza is sliced just once, and the cut doesn’t pass right through the centre, the piece that includes the centre is larger and hence the person who eats it gets more.

A pizza cut twice, into four parts, works the same way: whomever eats the slice that contains the centre gets the bigger portion. After that, as long as there are an even number of cuts and the diners alternate taking pieces, they end up with the same amount of pizza each.

But if there are an odd number of cuts, things get more complicated. If you cut the pizza with 3, 7, 11, 15… cuts, and no cut goes through the centre, then whomever gets the slice that includes the centre gets more pizza. But if you use 5, 9, 13, 17… cuts, then the person who gets the centre ends up with less.

There’s been a “pizza theorem” that postulates this since the late 1960s (naturally). The problem has been rigorously proving it.

That’s what Mabry and Deiermann achieved. First they came up with elegant solutions to the “three-cut problem” and the “five-cut problem.” They thought they could just proceed from there, but things got messy (sorry) as they cut the pizza more times, or, as New Scientist puts it, “the solution still included a complicated set of sums of algebraic series involving tricky powers of trigonometric functions,” summed up more succinctly as “ugly.”

So Mabry and Deiermann continued to work on it. For 11 more years. (Well, they did other things, too, but they kept revisiting it from time to time.)

The breakthrough came in 2006. Mabry was on a vacation in southern Germany, where, he says, “I had a nice hotel room, a nice cool environment, and no computer…I started thinking about it again and that’s when it all started working.” He rewrote the algebra in more elegant form, discovered there were some simple-looking sums in the middle of it, went searching to see if anyone had already worked them out, and discovered a 1999 paper that referenced a mathematical statement from 1979 that showed them what they needed to do to flesh out the proof.

If that seems like a lot of work for a trivial problem, just consider the important practical applications of it:

OK, there aren’t any. But, says Mabry, “It’s a funny thing about some mathematicians. We often don’t care if the results have applications because the results themselves are so pretty.”

Which makes this a better Christmas topic than you might have thought when I first mentioned pizza. Christmas is, among many other things, a celebration of beauty.

You may not be able to hang a mathematical proof on your Christmas tree, but that doesn’t make it any less beautiful in its own way.

What’s that? Yes, zombies are big in pop culture right now, but what’s that go to do with…? Oh, I get it.

No, sorry, this column isn’t about zombies. It’s about husbands going shopping with their wives. It turns out there’s a solid scientific explanation for why women shop the way they do…and why men find it baffling.

At least, that’s the claim of Daniel Kruger of the University of Michigan School of Public Health. According to his study, about to be published in the Journal of Social, Evolutionary, and Cultural Psychology, it all goes back to our evolutionary heritage.

“It’s perfectly natural that men often can’t distinguish a sage sock from a beige sock or that sometimes women can’t tell if the shoe department is due north or west from the escalator,” is how the university’s press release about the study puts it.

“From an evolutionary perspective, it all harkens back to the skills that women used for gathering plant foods and the skills that men used for hunting meat.” the press release continues.

Kruger conducted his study during a winter holiday trip with friends across Europe.  (Nice work if you can get it!)

He says that after exploring sleepy little villages and finally reaching Prague, the first thing the women wanted to do was shop–and the men couldn’t understand why.

It makes sense, though, if you think of it in terms of a gathering strategy, Kruger says. “Anytime you come into a new area you want to scope out the landscape and find out where the food patches are.”

He points out that in hunter-gatherer societies, gathering edible plants and fungi is traditionally done by women. The women return to the same patches of land where they have previously successfully found food, usually staying close to home and using landmarks as guides.

Foraging is a daily activity, often social, he goes on, and can include young children if necessary. The gathering women have to be adept at recognizing the colours, textures and smells that ensure safe, quality food, and must also be able to recognize how long it takes a patch of land to regenerate a quantity of food after it has been harvested.

How does that translate to modern terms? Women, says Kruger, are much more likely than men to know when a specific type of item will go on sale, and spend much more time choosing the perfect fabric, colour and texture. They’re usually willing to take their kids shopping with them.

Men are usually the hunters in hunter-gatherer societies. Once they’ve killed something, it’s important to get meat home as quickly as possible. Taking children along on a hunt isn’t safe and could make success harder to achieve.

Fast-forward to modern times: men usually have a specific item in mind from a store, and want to go in, get it, and get out as quickly as possible, preferably unhindered by having to look after a child at the same time.

Having made that connection, though, Kruger backs away from it a little bit, admitting that of course these behaviors aren’t genetically determined and don’t apply to everyone. Nevertheless, they’re common enough stereotypes that he believes there’s value in considering them as a result of what his paper calls “Evolved foraging psychology.”

“The value is in understanding each other–both your own shopping strategy and the strategy of the complementary sex,” Kruger says. “It helps demystify behaviors–guys, myself included, have been puzzled by why women shop the way they do.”

Similarly, women can have a hard time understanding a man’s aversion to shopping, he says.

As for practical applications beyond mutual understanding–well, Kruger doesn’t mention any, but personally I think the next time I’m asked to go shopping, I’ll demur on the grounds I have to go kill a woolly mammoth for supper.

I’m sure that will be an acceptable excuse. Won’t it, dear?