The More Your Friends Change, the More Your Social Network Stays the Same

For the most part, people move in and out of our lives at a trickle: a new coworker becomes a friend; a neighbor moves away. But there's at least one cataclysmic monsoon in a young person's social life, and that's high school graduation. So long, hometown chumps! Hello, dorms! When scientists used cell phone records to track the social networks of people graduating from high school and starting the next phase of their lives, they saw a huge turnover in friends and acquaintances. Remarkably, though, the overall structure of each person's network stayed the same.

"We wanted to see what happens to social networks when there is a big disruption," says Jari Saramäki. A professor at Aalto University in Finland, he leads a research group studying complex networks.

In 2007, Saramäki and his coauthors gave cell phones to 24 soon-to-graduate high schoolers in a large city in the United Kingdom. The phones came with an 18-month contract and a guarantee that all their call data during that time would be collected by researchers. After graduating, a quarter of the subjects stayed in their home city and got jobs; the rest went off to universities nearby or in other cities.

At three points during the study, the young people filled out questionnaires about their phone use. They listed all the friends, acquaintances, and family members for whom they had contact information, and rated the closeness of their relationships with each person. The researchers combined this information with the call records to piece together each person's network: who were they calling, how often, and how close were they to the people they called?

Researchers didn't calculate the absolute numbers of people in each subject's social network, Saramäki explains, because a graph of anyone's call frequencies shows a long "tail" of numbers dialed just once or twice. Are these doctor's office receptionists? School administrators? Does a virtual stranger count as a member of someone's network? Instead, Saramäki says, they focused on the top of the graph. Each subject's acquaintances were ranked by the number of phone calls they got, then graphed according to the fraction of total calls this was. Here's an example. "Ego" is the person we're interested in, and A-J are the people he or she called the most:

The graph on the right is this person's "social signature." There were some patterns among subjects. For example, an average of 20 to 25 percent of calls went to each person's top-ranked acquaintance, and nearly half of calls to their top three acquaintances. Nevertheless, each subject's social signature had a distinct shape. 

Over time, the graduating students had huge turnover in their networks. Within all top-20 contacts, 42 percent were people added in the middle section of the study. Yet statistical analysis showed that for the most part, the shapes of these social networks stayed the same.

"I would have expected that when the participants begin their first university year, there is some dramatic, temporary effect on their network shapes," Saramäki says. "What was really surprising is that [network structures] do not change much, even when this turnover is there."

Of course, phone calls don't give a complete picture of a person's social activity—there are also text messages, for one thing. But Saramäki says texts can be "problematic." Not everyone's parents text, for example, and some interactions might be completed in one message while others take a dozen back-and-forth volleys. "We do have data on text messages for this study and are working on it," Saramäki says. "But judging from what we have seen so far, it looks like the text message data tells pretty much the same story."

Even when people overhaul nearly all their friends at once, they seem to just slot the new acquaintances into the old social structure. The researchers point out that people have a limited amount of time to spend on their friends, and the brain may have a finite capacity for keeping track of others. So it's possible that people allot those resources in a consistent way, no matter which friends they currently have. It seems you can't shake your social network—wherever you go, there you (and they) are.

Jari Saramäki, E. A. Leicht, Eduardo López, Sam G. B. Roberts, Felix Reed-Tsochas, & Robin I. M. Dunbar (2013). Persistence of social signatures in human communication. PNAS : 10.1073/pnas.1308540110

Image: Mine. All mine.

This post has been edited from an earlier version.

The Elderly Make Even Worse Decisions Than Teens

The wisdom of aging may not apply to economic decisions. In a study of choices make about money, the oldest people performed the worst—even beating out the usual bad-decision champions, adolescents.

Agnieszka Tymula, a decision scientist at the University of Sydney in Australia, studies economic decision making in humans (and sometimes monkeys). With colleagues at Yale and New York University, she gathered 135 total subjects in four different age groups: teens (12-17), young adults (21-25), "midlife" adults (30-50), and older adults (65-90). All the elderly subjects were screened for dementia to make sure they had healthily aging brains.

At the start of the experiment, researchers gave the subjects $125 in cash. It was theirs to lose—or to more than double, depending on the choices they made. Then subjects made a series of quick decisions. For example, would you rather take a guaranteed loss of $5, or play a "lottery" where you're equally likely to lose $8 or $0? What about a guaranteed gain of $5, versus a lottery an unknown chance of winning $20 that's somewhere between 25 and 75 percent?

In these kinds of experiments, it's normal for people to avoid risk when making money—to accept a guaranteed $5, say, even if a 50-percent shot at winning $12 is a better choice on average. With losses, people act the opposite way; we'd rather enter the lottery than take a guaranteed loss.

There are other decisions that are just plain wrong, though. For example, if given a choice between a guaranteed gain of $5 and a lottery with a chance of winning $5, everyone should take the sure money. But people didn't always do this in the experiment. The two middle age groups made these wrong choices around 5 percent of the time. Teens, 10 percent. And older adults, when given a choice with a clear right and wrong answer, chose incorrectly almost 25 percent of the time.

Over the course of the experiment's 320 decisions, the oldest adults were also the most likely to behave inconsistently, choosing the opposite of what they'd done earlier when facing the exact same choice. (Teens, again, were in second place.)

At the end of the experiment, the researchers gave subjects actual cash (or took it away) based on a subset of the choices they'd made. If every decision had been for real money, the oldest adults would have walked away with a walloping 39 percent less cash than young adults. Middle-aged adults did roughly as well as young adults, and teens did a bit worse—though not nearly as badly as the elderly.

Agnieszka Tymula says the choices in her experiment, which was sponsored by a grant from the National Institute on Aging, are simplified versions of real choices we make all the time. "Most important real life decisions are taken under conditions of uncertainty," she says. When we invest in the stock market or choose a health insurance plan, we have to weigh unknown risks and payoffs. And we may have a harder time making those decisions as we age. The authors write, "Elders borrow at higher interest rates, use credit balance transfers suboptimally, misestimate property value, and pay more fees to financial institutions."

In future studies, Tymula wants to try to pin down what biological changes lead an aging brain to worse choices. "Ideally, we would like to follow a very large sample of people throughout their whole lives," she says, "to precisely identify when changes in decision-making occur and identify risk factors." This might help researchers design treatments that will dial back the brain to a younger mode of decision-making—though not, of course, all the way back to the teenage years.


Image: by Artis Rams (via Flickr)

Agnieszka Tymula, Lior A. Rosenberg Belmaker, Lital Ruderman, Paul W. Glimcher, & Ifat Levy (2013). Like cognitive function, decision making across the life span shows profound age-related changes. PNAS DOI: 10.1073/pnas.1309909110

Baseball Players Make Worse and Worse Decisions as the Season Goes On

If their goal were to frustrate fans, they couldn't plan it any better. Major-league baseball players reach a low point in their decision making in September, just in time for playoffs. Across all teams, batters swing at more and more pitches they shouldn't as the season goes on.

They may just need a nap.

"Consistently getting too little sleep—even if it's just [by] one hour a night—can lead to a state of chronic sleep deprivation that can compromise performance," says Vanderbilt University neurologist Scott Kutscher. "Specifically, things like judgment and reaction time."

Judgment and reaction time are just what a baseball player needs when a ball is hurtling toward his body at 90 miles an hour: he has to decide whether to swing, then react quickly enough to actually get it done. And sleep deprivation is familiar to pro ball players, who have a packed schedule and frequently travel back and forth across the country.

To see whether baseball players suffer the effects of sleep loss as the season drags on (or skips along for six non-tedious months, depending on your inclinations), Kutscher and his colleagues looked at data from 2011 back to 2006, after the MLB cracked down on steroid use. For each team, they tracked how often players swung at pitches outside the strike zone.

Over the course of the season, the researchers saw a steady increase in how many out-of-the-strike-zone pitches players swung at. These badly judged swings went up by about six-tenths of a percent each month.

Then Kutscher and his colleagues tested that model on the data from the 2012 season. When the numbers from all the MLB teams were pooled together, the model was a tight fit. Out of 30 teams, 24 were swinging at more balls in September than in April. Kutscher presented the findings at a recent conference on sleep.

Other factors aside from sleepiness may be at work. Pitchers might be throwing better curveballs as the months pass, for example. But Kutscher says pitchers threw pretty much the same ratio of balls and strikes throughout the season; if they were improving a lot, you'd expect to see them throwing more strikes. (Not to mention that batters, too, are practicing and honing their skills during the season.)

Since the researchers looked at whole teams rather than individuals, it's also possible that a change in the roster during the season—say, the addition of less experienced players who are called up from the minors—has an effect. Kutscher doesn't think this could account for all the deterioration he witnessed, though.

"I am hesitant to argue that fatigue is 100% of the story," Kutscher says. "But we have findings that are consistent with what we know about fatigue and chronic sleep loss."

Pro ball players, and other athletes, might see their performance improve if they could avoid sleep deprivation. So stop shouting at that guy on your screen who just struck out—he needs to go home and get some rest.


Image: Ed Gaillard (via Flickr)

Ants Reveal How to Build a Tunnel You Can't Fall Down

It's hard to keep your footing in a steep tunnel made of loose dirt while others are scrambling around and over your body. Harder still in pitch blackness. That's why fire ants build tunnels that will catch them when they fall—a strategy human engineers might want to steal.

"Slips and missteps are likely a constant, recurring feature of life underground," says Nick Gravish, a graduate student in Daniel Goldman's rheology and biomechanics lab at Georgia Tech. Yet ants have to traverse their tunnels quickly, especially when there's a colony emergency like a flood or destruction by a gardener's spade.

To study how ants engineer their tunnels, Gravish brought the fire ant Solenopsis invicta into the lab. Invasive to countries around the world and packing a nasty sting, these South American ants deal out plenty of hardship. But Gravish was interested in how they handle adversity themselves.

First, the ants were put into "laboratory soil" (actually tiny glass balls) to dig. Researchers took x-ray CT scans of the resulting tunnels and found that no matter the moisture of the "soil" or the size of the glass beads, ants dug circular tunnels of approximately the same diameter. That diameter was just a little bit more than the length of their bodies, not counting legs or antennae.

This suggested that the diameter of the tunnel was crucial to the fire ants. To see how well the ants moved within these tunnels, the researchers recorded video of them climbing as fast as they could. ("We startled them into climbing at high speed by exhaling gently into the nest," Gravish says.) They saw that ants were able to navigate their tunnels quickly, reaching speeds of more than 9 body lengths per second. They also saw that sometimes the ants slipped and had to recover their footing.

In addition to their tunnels, the researchers recorded ants climbing in vertical glass tubes. To get a better idea of how ants corrected their falls, the scientists jolted the tubes to knock the ants off the walls while they were climbing. (If you enjoy videos in the falling-bugs genre, this study generated several new additions. Here's one video of several ants falling and stopping themselves.)

Now the reason ants build tunnels so close in diameter to their own body length became clear. Ants responded to a fall by spreading all their appendages wide and waiting until they jammed to a stop. "One of the coolest things we found was that fire ants used their antennae to brace themselves," Gravish says. While falling, the ants turned these delicate sensors into extra load-bearing limbs.

When the glass tube width increased to 1.3 times the ants' body length, the strategy began to fail. The tunnels ants built themselves had an average diameter of just 1.06 times their body length, the authors report in PNAS. It seems fire ants put most of the responsibility for stopping falls on the tunnels themselves. After that, all a plummeting insect has to do is stretch out its limbs.

Gravish likens this strategy to the way humans build stairs. Steps are engineered to fit our bodies. If they're too tall or short, we struggle to use them (or maybe just fall down them). But with the right design, our environment works with us to get us where we're going.

This strategy could inspire how we design robots for confined spaces such as search-and-rescue zones, Gravish says. For instance, "falling is usually considered a failure mode for a robot." But fire ants seem to use little falls to descend more quickly through their tunnels. If engineers knew the size of the cracks and crevices in a disaster area, they might be able to send in many inexpensive robots designed to tumble through those spaces—rather than one very expensive robot built to keep its footing.

What about humans ourselves: would we benefit from building tunnels that were only as wide as our head-plus-torso length, like the ants? Gravish points out that fire ants often fall many body lengths before catching themselves, making this not such a great strategy for people. "Ants have a robust exoskeleton," he says. "We humans are quite soft in comparison."


Images: ant in tunnel by Laura Danielle Wagner; ants falling by Gravish et al.

Gravish, N., Monaenkova, D., Goodisman, M., & Goldman, D. (2013). Climbing, falling, and jamming during ant locomotion in confined environments Proceedings of the National Academy of Sciences DOI: 10.1073/pnas.1302428110

Kids Learn Better When Teachers Wave Their Hands

Maybe it's no mistake that we talk about "grasping" new ideas. When we find our hands moving wildly as we try to explain something, maybe we shouldn't feel ridiculous. Research in math classrooms has found that kids learned better when a teacher used gestures—and their grip on the new material improved even more after the lesson ended.

Teachers who gesture more or less while they speak can have other differences too, of course: they might use different intonation or vocabulary, or have more or less energy. University of Iowa psychologist Susan Wagner Cook and her coauthors, though, were only interested in the effect of teachers' hand motions. To isolate this factor, they created a series of videos.

In the videos, aimed at elementary schoolers, a teacher taught a single scripted lesson. The subject of the lesson was equivalence, the idea that what's on one side of an "=" must be equal to the other side.

In one set of videos, the teacher used her hand to indicate "one side" and "the other side" of an equation. A second set of videos showed the same teacher reading the same script, but she kept her hands at her sides. The researchers made several recordings and chose the ones in which the teacher's intonation was the most consistent, ensuring that the only difference between the lessons was her hands.

The kids who watched the videos were 184 boys and girls from 22 classrooms in central Michigan schools. Most were in second or third grade, and a few were in fourth. The kids had taken a pretest to make sure they weren't already familiar with this mathematical idea.

Each classroom watched a videotaped lesson, either the one with hand gestures or the one without. Immediately afterward, they took a test with questions such as:

7 + 2 + 4 = 7 + __

Kids who had understood the lesson would answer "6."

A day later, the kids had a second set of test questions spring on them. First they answered the same type of questions that they had the day before. Then they saw a second set of questions designed to make them "transfer" the rules they'd learned to new situations. For second graders, this meant trickier addition problems such as:

6 + 4 + 2 = __ + 3

in which none of the numbers on the right side matched the left. Third and fourth graders had to transfer their new skills to multiplication problems such as:

5 x 2 x 3 = __ x 3

Kids who had seen the lesson with gestures did significantly better than the no-gesture kids on the first test. A day later, they again outperformed the hands-free group—and beat their own test scores from the day before. Their understanding of the lesson seemed to have gotten even better in the 24 intervening hours. (This wasn't true of kids who watched the hands-free lesson.) Finally, the gesture group did better on the test of transferred skills.

A couple factors could explain why students learned better from a gesturing teacher, the authors write. Hand movements might help them pay better attention to the teacher, for example. And seeing a repeated hand motion across different problems might reinforce how those problems are similar.

That doesn't answer the question of why students continued to improve over the next 24 hours. Susan Wagner Cook explains that shortly after we form new memories, those memories are stabilized or "consolidated" in our minds. Consolidation can make new memories even stronger.

"We do know that motor memory is often consolidated during sleep," Cook says. Seeing another person's hands moving may have built motor (movement) memories in kids' minds, as if they were pointing and waving their own hands. "One possibility is that memories encoded with gesture are more likely to be consolidated during sleep," Cook says. "We are trying to figure this out!"

Although being able to point to the two sides of an equation seems like a clear advantage in this particular lesson, Cook says the benefit of gesturing goes beyond arithmetic—or even math. Other studies have shown that hand motions help kids learn in a wide range of subjects.

What's new is the idea that gestures help in the future, not only the present. Cook points out that even though some kids learned the lesson just fine without gestures, they didn't show the same improvement over time that the other kids did. Instead of only clarifying, gestures may help kids grasp their new knowledge more tightly. (Please imagine a fist-closing gesture to drive home this idea.)


Image: sleepinyourhat (via Flickr)

Cook, S., Duffy, R., & Fenn, K. (2013). Consolidation and Transfer of Learning After Observing Hand Gesture Child Development DOI: 10.1111/cdev.12097

Why Fish Raise Foster Kids (and Give Up Their Own)

A fish swims along a sandy lake bottom, carrying one of its babies in its mouth. It approaches the nesting cave of another family of fish. With a furtive "ptooey," it leaves the baby behind for adoption. For certain fish, this seems to be a common scene: giving up your young and taking on others' may be the best way to ensure your offspring grow past snack size.

The fish in question is Neolamprologus caudopunctatus, a type of cichlid (pronounced like a compliment for someone's hat).* Just a couple of inches long, the diminutive fish lives only in East Africa's Lake Tanganyika. Males and females form monogamous pairs. They raise their young in burrows under rocks; carrying sand in their mouths, they pile it up around the rocks to build narrow entrances.

For the first 40 days or so in the lives of the young fish (called fry), both parents work to protect them from predators. They guard the nest and attack any other fish that come by looking for a meal. Cichlids can also protect their young by carrying them inside their mouths.

As the fry grow older and start swimming on their own, they may wander away from their parents' nests and into nearby ones. However, cichlids have also been spotted carrying young in their mouths and leaving them at other nests. Scientists at the Konrad Lorenz Institute of Ethology in Vienna set out to see how much of the baby swapping among N. caudopunctatus is intentional.

Researchers scuba dived down to the home of the cichlids, mapped the locations of their nests, and collected DNA samples. Back on land, like the crew of a daytime talk show for African lake bottoms, they analyzed the DNA to find out just how these fish were related.

Out of 32 nests, more than half held adopted fry, the authors report in Behavioral Ecology. Within nests that housed adopted fish, those outsiders made up anywhere from 10% to 77% of the nest.

The researchers took their DNA analysis a step further for a dozen adopted fry, hunting down their biological parents. They found that while some fry had been adopted from nearby nests, others were a very long way from home—as far as 40 meters or more. "It is virtually inconceivable that they swam there alone," says senior author Richard Wagner. The lake is packed with hungry predators. It would be, he says, "like a toddler walking across a busy city without mishap." It's more likely that parents deliberately carried these young fish in their mouths from one nest to the other.

There was another piece of evidence that adoptions happened on purpose. Adopted fish were on average larger (which is to say older) than non-adopted fish across the whole sample. But within each nest, the size difference wasn't significant. This suggests that when cichlid parents give up their young, they select nests with fry that are close in size to their own. Such a strategy might make the adopted fish less conspicuous to predators.

Parents who leave their fry at other nests may be hedging their bets, making sure that at least some of their offspring survive if their own nest is wiped out by a predator. As for adoptive parents, they could just kick out the freeloading fry. But keeping adopted fish around means that when predators attack, there's a smaller chance of your own offspring ending up in another fish's mouth.

"Our paper adds evidence that adoption is an adaptive strategy," Wagner says, rather than simply the result of wandering babies. We humans aren't the only animals that regularly choose to raise others' young. One hopes, though, that human foster parents aren't in it for the reduced predation.


Schaedelin, F., van Dongen, W., & Wagner, R. (2012). Nonrandom brood mixing suggests adoption in a colonial cichlid Behavioral Ecology, 24 (2), 540-546 DOI: 10.1093/beheco/ars195

Image: N. caudopunctatus by Varmer (via Flickr)

*"Sick lid!"

NOTE: It's been pointed out to me by an astute reader (my mother) that the hat compliment could also be "chic lid." Fair point, Mom. 

Good Coot Parents Let Kids Starve, Make It Up to Them Later

Too many mouths to feed? Just make your babies fight each other to the death! That's a strategy some bird parents have been using since even before The Hunger Games was popular. It means the strongest chicks get stronger while the weakest ones conveniently stop showing up to the table.

One type of bird takes this family drama a step further: after letting the biggest chicks bully their siblings for a while, parents suddenly decide the runts are their favorites and begin beating up the older chicks themselves. Authors looking for the next dystopian mega-hit, take note.

"Many species of birds show 'hatching asynchrony,'" says Daizaburo Shizuka of the University of Nebraska, Lincoln. This means they stagger the hatching of the eggs within a nest. When some chicks emerge from their eggs days later than others, the younger birds are doomed to be outweighed and outcompeted by their older siblings. Blue-footed boobies, for example, produce two mismatched chicks; one may peck the other to death or shove it out of the nest. (If you think that's horrifying, you haven't heard about sand tiger sharks, which eat each other inside their mother's womb.)

The polite way to say "letting half your babies die" is "brood reduction." Why hatch a runty egg at all? Parents may allow more siblings to live if food is plentiful. Or a second egg might be a kind of insurance in case the first doesn't hatch.

American coots are waterbirds that lay large clutches of eggs and may space out their hatching over a week or more. This means some siblings end up much heftier than others. At first, young coots follow their parents around, relying on their parents to feed them insects and plant material they find by diving. Siblings don't physically attack each other, but older birds easily out-jostle smaller ones for food. Half of all chicks die of starvation.

Over several years, Shizuka and Bruce Lyon, an ecologist at the University of California, Santa Cruz, monitored 75 American coot families on a lake in British Columbia. They snuck every new chick away as it hatched to give it a color-coded tag. Spying on these families while their chicks ate or starved, the researchers discovered a highly unusual system at work.

During the first 10 days after hatching, younger coot chicks often died of starvation. But any runty chicks who survived this period saw their luck turn around. Parents suddenly started playing favorites. Each coot parent picked one preferred chick out of those who'd hatched last, and gave that chick the most food. Heightening the drama, moms and dads each chose a different favorite.

To discourage bigger siblings from asking for so much food, the parents spent more time "tousling" these birds. In humans this means "affectionately messing up someone's hair," but in birds it means "grabbing your baby by the head and shaking it." As you might imagine, it's pretty convincing. The beefy siblings backed off.

Once parents switched to spoiling the runts and beating up the bigger kids, late hatchers became just as likely to survive as their siblings. The youngest chicks even grew slightly larger than their older brothers and sisters.

This system may be a way "for parents to try to get the best of both worlds," Shizuka says. First, coot parents allow brood reduction to happen, watching their chicks compete to the death. Once the family reaches its optimal size, he says, "parents can take matters into their own hands to make sure that the youngest chicks that are still surviving end up getting enough."

Don't throw out your parenting books yet. Although this method seems to work for the coots, scientists still aren't sure why so many birds have evolved elaborate strategies that require siblings to murder each other—or why chicks go along with it. Shizuka says, "It's safe to say the matter is not resolved."


Shizuka, D., & Lyon, B. (2013). Family dynamics through time: brood reduction followed by parental compensation with aggression and favouritism Ecology Letters, 16 (3), 315-322 DOI: 10.1111/ele.12040

Image: Bruce E. Lyon

In Our Partners' Heights, We Get What We Want

If you ask most heterosexual people what height they're looking for in a partner, they'll describe basically what a children's-book illustrator would draw: the man taller than the woman but not towering over her. But those of us who aren't pen-and-paper must settle for real human partners in human shapes and sizes. Nevertheless, new research says most people end up with a reality that matches the fantasy.

Researchers led by Gert Stulp of the University of Groningen in the Netherlands wondered whether people's professed height preferences matched who they ended up with. Earlier studies had shown that within Western cultures, there are clear trends: Taller people are interested in other tall people; shorter people like short people. And both sexes prefer that the male be taller.

But not too tall! One study combed through thousands of personal ads from a dating site that let users indicate the tallest and shortest person they'd consider dating. On average, women said they weren't interested in men more than 17% taller than themselves. For a 5-foot-5 woman, for example, that means  a man over 6 foot 4 seems like a little much.

To compare these preferences to a real population, Stulp and his coauthors used data from the Millennium Cohort Study, a broad sampling of almost 19,000 babies born in the United Kingdom in the year 2000. Among other things, the parents of these babies had been asked for their heights, and 12,502 couples had answered the question.

To see what it would look like if people paired off with no regard to height, the researchers created 10,000 random reshufflings of their UK couples. They then compared these chance pairings to reality.

First, they tested whether people seek out their own kind. Sure enough, taller people had taller partners, and shorter people had shorter partners.

The next question was whether people really care about the man being taller. Of course, since men are on average taller than women, randomly pairing people off is likely to get you a taller male anyway. In the randomized UK couples, the male was taller 89.8% of the time. But in reality, 92.5% of couples had a taller male, a significant difference. And when the woman was taller, it was likely to be only by a tiny bit.

Finally, people say they prefer height differences that aren't too exaggerated. But do they follow through? The authors looked for height gaps of 25 centimeters or more. In the random pairings, this occurred in 15.7% of couples. But in real life, only 13.9% of couples had a height difference this huge.

More often than chance would predict, these couples had followed traditional height preferences. That suggests that when we choose our partners, height does matter.

The study doesn't address the preferences (or reality) of couples who are not heterosexual, not parents, or not in the United Kingdom. Stulp says research has shown that across Western cultures, heterosexual people report very similar preferences for a partner's height. (The Netherlands, where the 6-foot-7 Stulp lives, is home to the tallest people in the world. But he says he believes height preferences in this land of giants are the same, just shifted upward.) In non-Western cultures, he says, those preferences are slightly different and more variable.

Stulp, in fact, was surprised that height preferences didn't have an even stronger affect on the results. He expected reality to be further from random chance than it was. But, writing in PLOS ONE, he acknowledges that many factors affect our choice of partner. "Height," he writes, "is but one of many characteristics valued in a mate."


Stulp, G., Buunk, A., Pollet, T., Nettle, D., & Verhulst, S. (2013). Are Human Mating Preferences with Respect to Height Reflected in Actual Pairings? PLoS ONE, 8 (1) DOI: 10.1371/journal.pone.0054186

Image: Peter Rukavina (Flickr)

Math Shows Penguins Only Care about Themselves

Don't let the adorable mini-orchestra-conductor look fool you: penguins aren't that nice. When emperor penguins huddle together during Antarctic storms, they act like they're all in it together. But a new mathematical model shows just how the clusters of birds keep warm, accounting for everything from their geometry to the speed of the wind. Concern for one's fellow bird, it turns out, isn't a factor.

Regardless of your motivations, huddling together in a group is a great way to wait out a frigid storm. Instead of burning up their own energy reserves trying to warm their bodies, emperor penguins can rely on the warmth of a bunch of big feathery animals pressed together. There may be ten or hundreds of bodies in the huddle. Inside, the temperature is between 20 and 37.5 degrees Celsius (a cozy 68 to 99.5 degrees Fahrenheit). In the chilliest storms, penguins squeeze as tight as 10 birds every square meter.

Those huddles aren't motionless, though. With a continuous slow shuffling, the penguins rotate through the formation. Birds with their backs exposed to the wind creep away from it, up the sides of the huddle, until they find some protection. Meanwhile, birds that were formerly on the warm interior find themselves on the outside.

Three applied mathematicians at the University of California, Merced, set out to create a computer model of penguin huddling. Aaron Waters, François Blanchette, and Arnold Kim wanted to find out how well the birds' strategy works—and whether any penguins are left out in the cold.

To pack their penguin huddle as tightly as possible, the mathematicians imagined the birds on a grid of hexagons. This is the best way for circles to squeeze into a plane (think of a honeycomb), and scientists in the field have observed that real penguins arrange themselves roughly this way. The researchers also assumed that "penguins in this huddle have uniform size and shape."

Next, they added wind to the model, which flowed around the huddle differently depending on its overall shape. Then they calculated the rate at which each computerized penguin was losing body heat. They sent the coldest penguin shuffling around the outside of the huddle until it found the warmest spot it could stand in, then started over with the new coldest penguin.

The simulated penguins constantly shifted positions within the huddle, just as real penguins do. Over time, the model huddle tended to take on the shape of a flat-sided oval and travel slowly downwind (as penguins on the windward side continuously moved away from it).

When they calculated the flock's heat loss, the authors discovered that their model huddle was very fair: every penguin lost approximately the same amount of body heat. But these model penguins were only programmed to maximize their own warmth, not to consider the warmth of other penguins or the group as a whole. This means that even if penguins are only looking out for themselves, the whole huddle stays warm, as the authors report in PLOS ONE.

Just because emperor penguins can be totally selfish doesn't mean they are, the authors point out. It's still possible that penguins are altruists, organizing their huddle by thinking about the group as a whole. But it's not necessary to explain how they behave in the wild.

There's one flaw in the penguins' strategy: the elliptical shape a huddle tends to take on isn't optimal. A less stretched-out formation would help the whole group stay a little warmer. Maybe the emperor penguins should consult with a mathematician.

*********

ADDENDUM: Francois Blanchette, who was traveling when I first contacted him, says that this research was inspired by (what else?) March of the Penguins. While watching the movie, he noticed that factors in the penguins' environment, such as wind flow and heat transfer, were relevant to his own field of fluid dynamics. "I figured there should be a problem I could address that had to do with penguins," he says. "I was looking to do something different than my usual line of research."

With penguins out of the way, Blanchette and his coauthors are now interested in modeling other groups of living things, such as bacterial colonies. "However, not being biologists," he says, "we are not very familiar with other biological systems where such a model could be useful." If you're a biologist with a clump of organisms you'd like to model, let him know.


Image: Emperor penguins, by Mtpaley (Wikimedia Commons)

Waters, A., Blanchette, F., & Kim, A. (2012). Modeling Huddling Penguins PLoS ONE, 7 (11) DOI: 10.1371/journal.pone.0050277

P.S. If you enjoy reading about math and self-interested animals, you may like my earlier post Geometry Proves Sheep Are Selfish Jerks.

Math-Phobes Experience Arithmetic like Bodily Pain

If subtraction makes you sweat, division gives you diarrhea, and the Pythagorean theorem inspires panic attacks, you might be afflicted with math anxiety. Others may not always be sympathetic to your fear of tipping in restaurants without your cell phone. Brain scans, though, show that people like you suffer from more than just nerves. In people who are highly anxious about math, the threat of doing arithmetic activates the same brain areas as a punch in the stomach.

Researchers at the University of Chicago's Human Performance Lab study how humans think and what makes us succeed—or not—under pressure. Anxiety has been found to heighten our awareness of our bodies and make us more sensitive to pain. So Ian Lyons and Sian Bielock wondered whether feelings of anxiety might have a direct connection to pain centers in the brain.

For their anxious guinea pigs, Lyons and Bielock used humans with "high math anxiety." They measured math anxiety using a survey in which subjects rated how anxious they'd feel in various scenarios, including "walking to math class" and "being given a set of addition problems to solve on paper." From their potential subjects, the authors selected 14 people who scored especially high on this test and 14 others who scored especially low. Subjects were also tested for general anxiety (to make sure their math fears weren't part of an allover nervous disposition) and working memory (to ensure that their problem-solving capacity was normal).

Then all the subjects solved a series of math and word questions while inside an fMRI scanner. For the math questions, subjects saw equations like (3 * 5) – 4 = 11 and had to decide whether they were true or false. Some of the equations involved larger numbers to make them harder. For the word questions, subjects saw sets of letters such as yrestym and had to decide whether they spelled a real English word backward.

Subjects with high math anxiety struggled with the harder arithmetic problems more than subjects with low math anxiety did. And in the high-math-anxiety subjects, math problems lit up brain regions involved in sensing pain. Specifically, pain in the gut.

These brain areas, the dorso-posterior insula and mid-cingulate cortex, "are active during the experience of visceral pain—for example, a stomachache or a gut punch," says Ian Lyons. "These areas are also involved in detection of threat to the body." So while people with a lot of math anxiety may not feel bodily pain when facing a math test, their brains seem to interpret each arithmetic problem like a physical threat.

Earlier research found that those same brain areas were activated when people experienced social rejection, Lyons says. Our brains apparently view getting ditched by our friends, or (for some of us) solving for x, like being kicked in the liver.

But what was most surprising about the results, Lyons says, was the timing of that kick-in-the-gut reaction. It happened not when subjects were actually facing those dreaded arithmetic problems, but a few seconds before.

Subjects saw a yellow circle or a blue square, indicating whether a math or word question was coming their way. When they saw the shape and started anticipating a math problem, high-anxiety subjects' pain centers lit up. But once they actually started working on the problem, those brain centers retreated again.

"This underscores the fact that anxiety is very much about the psychological interpretation of an event or phenomenon, and not so much about the event itself," Lyons says. He and Bielock write that once people focus on solving an equation or other problem, they may not have the mental resources left over to keep feeling anxious. To stop the pain of anticipation, serious math-phobes—and perhaps the rest of us too—should just do it already.


Lyons, I., & Beilock, S. (2012). When Math Hurts: Math Anxiety Predicts Pain Network Activation in Anticipation of Doing Math PLoS ONE, 7 (10) DOI: 10.1371/journal.pone.0048076

Image: Shurik_13 (Flickr)

Geometry Proves Sheep Are Selfish Jerks

Sometimes what looks like friendly behavior is really an attempt to get one's neighbor eaten by a wolf before oneself. Sheep, for instance, seem cozy enough in their flocks. What's a better way to travel than surrounded by 100 percent merino? But the real reason they stick close to their neighbors is to save their own woolly rear ends.

The question of what motivates seemingly community-minded animals is a classic one in biology. Do the birds in a flock, or the fish in a shoal, just enjoy each other's company? Do they rely on each other's eyes to spot a predator before it gets too close? In an often-cited 1971 paper, British evolutionary biologist W. D. Hamilton suggested that the answer was simple geometry.

An animal never wants to be the nearest potential prey to a predator, Hamilton said. To increase its odds of survival against a lion, a wildebeest should put itself closer to other wildebeest. And even better than being near a few other defenseless grazers is being surrounded by a pack of them. The more edible neighbors are between you and a hungry mouth, the safer you are.

Hamilton's theory was called the "selfish herd." To find out whether a non-hypothetical herd really behaved as selfishly as Hamilton predicted, researchers led by Andrew King at the University of London used a flock of sheep wearing GPS-equipped backpacks. And one sheepdog.

Three times, the team gave the Australian kelpie the command to round up the flock of 46 sheep. With their backpacks on, the sheep responded as usual by running around in a panicked clump. Then the researchers used the GPS data from the backpacks to map exactly how each sheep had moved, second by bleating second.

They saw that the sheep started reacting when the running dog was about 70 meters away. A few moments later, the sheep had formed as tight a flock as they could.

A sheepdog (approaching from the top right corner) drives sheep into a clump in seconds.

In keeping with the selfish herd theory, the sheep used their flock to buffer themselves from a threatening attack. But the way they did it was surprising. Hamilton had suggested that animals might condense their herd, when a predator approached, by following an easy rule: Move toward your nearest neighbor. King's team found that the sheep were following a different guideline: Always move toward the center of the group. As if armed with a protractor and a map, sheep zoomed toward the middle of the flock, however dispersed it was to start with.

It's a slightly more complicated maneuver, since sheep must consider the positions of many neighbors at once. The authors write that while "a precise calculation of the flock centroid may be unlikely"—as sheep brains probably aren't equipped for much geometry—"sheep may be able to approximate where that target location ought to be."

King is interested in flocking, selfish or not, as a social behavior. His research group has also studied how individual fish "personalities" affect schools; how baboon troops forage for food and coordinate their travel; and even (using GPS baseball caps) how groups of humans move. But King's coauthor Jenny Morton has a different motivation. She studies brain degeneration in Huntington's disease and uses sheep as an animal model. By learning what rules the sheep in a flock usually follow, she hopes to better understand what happens as their brain cells—and their geometry skills—break down.

Andrew J. King, Alan M. Wilson, Simon D. Wilshin, John Lowe, Hamed Haddadi, Stephen Hailes, & A. Jennifer Morton (2012). Selfish-herd behaviour of sheep under threat. Current Biology, 22 (14) : 10.1016/j.cub.2012.05.008

Images: Sheep with GPS backpacks on. King et al., Current Biology Volume 22 Issue 14.

Brain Scans Predict When Poker Players Will Bluff

Your gray matter doesn't have much of a poker face. Even if your stony expression reveals nothing, two bits of brain tissue behind your ears leap into action when you decide to make a bluff. But it's not just about lying. Your brain is deciding whether your foe is a worthy opponent whose actions should affect your own.

Poker playing taps into a skill called social cognition. This is the mental power that lets us assess what other people are up to, figure out what they're thinking, and anticipate what they'll do next. It comes in handy not just for guessing when an opponent has pocket aces, but for everyday activities like negotiating a four-way stop or remembering which of your friends can't keep secrets.

To find out what goes on in our brains while we're judging different opponents, researchers at Duke University set up a very simple game of poker. Don't expect to see this new variant on ESPN anytime soon. The game is played between two players, each of whom is dealt either a high card or a low card. (Rather than numbers, each card reads simply "H" or "L.") The player who goes first decides whether to bet a set amount of money or to fold right away, ceding the ante to the other player. If the first player bets, the second player must decide whether to call the bet or fold.

The game had to be simple, since the 18 study subjects were playing inside a brain scanner. At the beginning of the experiment, subjects were introduced to Player Two (the same person each time). Inside the scanner, they played eight seven-minute rounds of the poker game by hitting buttons on a screen. But there was a twist: At the beginning of half of those rounds, subjects learned they'd be playing against a computer instead of a human.

Subjects were also reminded before playing that bluffing some of the time—that is, betting with a low card and hoping their opponent folded, leaving them the ante money—was a good strategy. The computer opponent was programmed to call players' bets half the time. The human Player Two had been promised extra payment from the researchers if he, too, called bets close to half the time. The result was that the computer and human opponents played the game the same way, says senior author Scott Huettel.

While this nail-biter of a competition was going on, researchers gathered fMRI data from their subjects. They searched everywhere in the brain for areas that lit up with activity when subjects were bluffing. Certain brain regions that had previously been tied to social cognition showed up, indicating the researchers were on the right track.

But there was only one brain region that distinguished between human and computer opponents, the authors reported last week in Science. When the subjects lying in the scanner decided to bluff against a human component—but not against the computer—an area called the temporal-parietal junction (TPJ) suddenly blazed with activity.

Breaking down their results subject-by-subject, the researchers discovered a final twist. After the poker games, they'd asked each subject: Who was a better opponent, the computer or human? "Eleven of the participants said the human," Huettel says, "and the effect was present in those people, but not in the others." In other words, the TPJ only jumps into action when people are bluffing against a human opponent whom they respect.

The TPJ effect was so pronounced that the researchers could use it to tell the future. Huettel says they created a model using one part of their fMRI data, then returned to the rest of the data to test that model. Based on activity in the TPJ when subjects were shown a low card, the researchers could successfully predict whether that subject would bluff or fold about six seconds later.

"There has been an ongoing debate about whether this region is involved in social cognition," Huettel says. The poker study suggests that we do use our TPJs for social cognition, but only in cases where we're basing our actions on another person's behavior. People who thought the computer was a more formidable opponent might have ignored their opponents altogether while deciding whether to bet or fold.

In a real poker game—where there are 52 possible cards rather than two, and decisions about betting or folding are complicated—the TPJ might be at work more often. The activity that predicted a bluff in this study might simply show players are thinking hard about their opponents' cards in a true game of Hold 'Em. Either way, until someone develops remote brain imaging technology, there's probably no need to purchase cerebral sunglasses.

Carter RM, Bowling DL, Reeck C, & Huettel SA (2012). A distinct role of the temporal-parietal junction in predicting socially guided decisions. Science (New York, N.Y.), 337 (6090), 109-11 PMID: 22767930

Image: Rob Watkins/Paf (Flickr)

When It Comes to Numbers, We're All Late Bloomers

Good news for aspiring jelly-bean jar estimators who are under 30! Your intuitive grasp of numbers may not have peaked yet. Unlike other cognitive skills, the ability to approximate keeps improving well into adulthood. Since the skill is tied to mathematical smarts, this news might bring hope to struggling students.

Scientists call our intuitive understanding of numbers the approximate number system, or ANS. It lets us compare amounts or guess at the size of a solution without putting our thinking into words. An approximate number system has been observed in adults, kids, infants, remote Amazonians who don't have number words, chimpanzees, and pigeons.

Just because you have an approximate number system, though, doesn't mean it measures up to everyone else's. For English-speaking humans with internet access, an easy way to test your ANS is with a simple computer test. Available at panamath.org, the test flashes sets of dots and asks whether you see more yellow ones or more blue. Afterward, if you dare, you can find out how your skill compares to that of other people who have taken the test (though not pigeons, sadly).

A whole lot of people, in fact, have taken this test. When researchers led by Justin Halberda at Johns Hopkins University posted a version at www.testmybrain.org, a site where you can participate in ongoing psychology experiments, they got over 10,000 responses in just 3 months. This giant dataset became a new paper in Proceedings of the National Academy of Sciences. 

Before taking the test, participants had filled out a questionnaire that included items such as their age (subjects ranged from 11 to 85) and how they felt they did in various school subjects compared to their peers. From this heap of information, two patterns emerged.

The first was that subjects' approximation skill was tied to their self-reported math ability. People who answered the dot questions faster and more accurately said that they were (or had been) good at math, compared to their classmates. This held true across all ages, from kids currently in school to retirees who hadn't seen a math class in 60 years.

Of course, people can misremember how well they did in school. But when the researchers asked a smaller group of subjects about their SATs, the math scores corresponded to self-reported math ability. And while the math SAT score also correlated to performance on the number sense test, verbal SAT scores didn't. This suggests the better ANS scores are truly related to math ability, not to overall intelligence or a tendency to inflate one's resumé. 

The second finding was that number sense changes over a person's lifetime—and it peaks late. The accuracy of people's answers on the test steadily improved up until age 30 or so, before beginning a long decline. (As for speed, teenagers answered the fastest, even though they were less accurate than adults.)

Although the trends were clear across the 10,000 subjects, people within in each age group varied widely in their number sense scores. For example, the authors write, one out of eight adults in their study had a less precise number sense than the average 11-year-old. Since these scores seem to be linked to math performance in school, this variation might help explain why certain students sail through class while others struggle. But Justin Halberda says the results are a cause for optimism. 

"That the gut number sense continues to improve up into our thirties means that it is malleable, and that we may be able to help those struggling with the number sense," Halberda says. Since the number sense is flexible throughout our lifespans, there may be ways to enhance it—and that might make people better at math in general.

Halberda adds, "I remain hopeful that we will be able to improve people's abilities even later in life." In other words, you might never be too old to return to your second-grade classroom and dominate a round of Guess How Many Pennies.

Halberda J, Ly R, Wilmer JB, Naiman DQ, & Germine L (2012). Number sense across the lifespan as revealed by a massive Internet-based sample. Proceedings of the National Academy of Sciences of the United States of America PMID: 22733748


Images: Philip Chapman-Bell/Flickr; Jay Rishel/Flickr

Math Shows Today's Writers Are Less Influenced by the Past

When Charles Dickens wrote It was the of, it was the of, the immortal first words in A Tale of Two Cities, he can't have imagined that 21st-century computer scientists would parse his prepositions and pronouns as part of vast literary data sets. But today's researchers are studying the unimportant words in books to find important literary trends. With the meaty words taken out, language becomes a numbers game.

To see how literary styles evolve over time--a science dubbed "stylometry"--researchers led by James Hughes at Dartmouth College turned to Project Gutenberg. The site contains the full text of more than 38,000 out-of-copyright books. Researchers began their mining expedition by digging out every author who wrote after 1550, had a known date of birth and (when relevant) death, and had at least 5 English-language books digitized.

These criteria gave the researchers a set of 537 authors with 7,733 published works. But they weren't interested in every word of those books. Nouns and adjectives were out: No Kareninas or Lolitas, nothing nice or bad or beautiful, no roads or homes or people. Most verbs were out, except for forms of the utilitarian to be. No one could speak or walk or Fly, good Fleance!


It may seem that the researchers were stripping all the information-containing words out of the sentences, and in fact that was their goal: "Content-free" words were all they wanted. The 307-word vocabulary that remained from the books was mostly prepositions, conjunctions, and articles.

This linguistic filler, the little stitches that hold together the good stuff, is known to contain a kind of authorial fingerprint. We may not think much about these words when we're writing or speaking, but scientists can use them to define our style.

Hughes and his team used computer analysis to score each author's similarity to every other author. They found that before the late 18th century, authors's stylistic similarity didn't depend on how close to each other they lived. (Each author was represented by a single year, the midpoint between his or her birth and death.) During this time period, authors who lived in the same generation didn't influence each other's styles much more than authors who lived hundreds of years away.

But from the late 18th century to today, it was a different story. Stylistically, authors were more similar to their contemporaries than to other writers. By the late 19th century, writers closely matched the style of other writers who lived at the same time (at least according to the computers tallying up their non-content words). This influence dropped off outside of 30 years. In other words, authors who lived more than three decades away each other may as well have lived centuries away, for all the similarity between their writing.

Looking at more recent books, that window of influence seems to become even tighter. Among authors from the first half of the 20th century, the similarity of style drops off beyond just 23 years.

Over time, authors have become more and more influenced by the other authors writing at the same time. The researchers say this may simply be due to the number of books published. In the early part of their dataset, there were few enough books around that a studious person could read, well, most of them. But as more and more books were published, contemporary books made up a larger share of what was available to read. Authors have filled more and more shelves in their libraries with books by their peers--and this has made them more likely to echo each other's styles.

Because Project Gutenberg relies on public-domain material, there weren't very many authors after the mid-20th century included in this study. Looking forward, "You would expect a continued diminishing of influence," says Daniel Rockmore, the paper's senior author. Contemporary books take up an ever greater portion of what's available to read. In addition to the huge number of books published each year (more than 288,000 in the United States in 2009), there are now e-books and e-readers and Japanese Twitter novels.

A century from now, we may be able to look back and see that today's authors had an ever-condensing frame of influence. Of course, by then literary styles might only last a week. Most books will be forgotten, but every author will be a revolutionary.

James M. Hughes, Nicholas J. Foti, David C. Krakauer, & Daniel N. Rockmore (2012). Quantitative patterns of stylistic influence in the evolution of literature PNAS : 10.1073/pnas.1115407109


Image: Library of Congress from ep_jhu/Flickr

Space Census Finds Extra Penguins, Poop

Playing what might have been the world's most tedious game of Where's Waldo?, scientists used photos taken from space to count all the emperor penguins in Antarctica. They found more than a hundred thousand birds that hadn't been spotted before. The news may affect the penguins' fate in a warming world. Besides, what's a better surprise than extra penguins?

Researchers from several institutions, including the British Antarctic Survey in Cambridge, undertook the emperor penguin space census. They thought previous penguin counts might not be accurate. For one thing, the last estimate of the Antarctic penguin population is almost 20 years old. For another, humans can't easily travel very far from their Antarctic research bases to seek out half-frozen bird huddles. So penguin colonies that are farther out in no man's land might have never been spotted by people.

Thanks to emperor penguins' habit of clumping together in giant colonies during breeding season--and their convenient lack of camouflage against the snow--the researchers knew high-resolution satellite photos should reveal the penguins. They used images from all around Antarctica's coastline, where penguin colonies camp out. Forty-six colonies appeared, including several that hadn't been counted before.

A penguin colony on the Antarctic coastline, spotted from above.

After zooming in on each colony and sharpening the images, the researchers used computers to count the penguins one by one. The challenge was for the computer to decide which dark pixels represent penguins, rather than shadows on the snow--or penguin poop. Author Peter Fretwell explains that in this method, "you 'train' the computer to recognize the pixels that are penguin, guano, snow or shadow by giving it sample pixels. The computer then goes away and splits the whole image into each pixel type."

Zooming in on a penguin colony and sharpening the image. I think I found the guano.

As long as the images have a high enough quality, Fretwell says, this technique is "usually quite accurate." Where the satellite pictures were more shadowy, penguin counts would be a little less certain. For some of the colonies, though, researchers were able to check their numbers against estimates others had made from the ground or from aerial photography.

And then there were the missing penguins. All the satellite images were taken during the breeding season, when emperor penguins congregate to create adorable new baby penguins. The new parents take turns babysitting: While one penguin takes care of the chick, the other goes out to sea and swallows lots of fish to regurgitate later. While the chicks are small, they spend most of their time balancing on top of their parents' feet to keep warm. Once the chicks are old enough to walk around on their own, both parents may leave to forage.

So for every individual counted in a satellite photo, the authors assumed there was a hidden chick and a second adult at sea hunting for food. (They were only interested in counting breeding adults, not the chicks, most of which will die.) Later in the season, some of the penguin pixels may have been kids instead of adults. But since a young penguin standing on the ice probably has two parents away foraging, the researchers figured that pixel still stood for two adult penguins.

The final count was about 595,000 adult emperor penguins in all of Antarctica. That's roughly the (human) population of Milwaukee. It's also substantially higher than the last estimate, which put the population between 270,000 and 350,000 adult birds.

The census could easily have overestimated or underestimated the true number of penguins. But, Peter Fretwell says, "The main thing is that this gives us an initial benchmark from which we can monitor emperor penguin numbers in the long term."

As climate change tightens its grip on every part of the globe--all the way to the poles--penguins will certainly see some changes around them. The sea ice along the coastlines they inhabit will disappear; shifting food webs may make their prey scarcer; and severe storms might become more frequent. Knowing how many emperor penguins are there now, and where to find their colonies, will help scientists monitor how the species is coping with the changes. We might even be able to keep them from becoming harder to find than Waldo.

Fretwell, P., LaRue, M., Morin, P., Kooyman, G., Wienecke, B., Ratcliffe, N., Fox, A., Fleming, A., Porter, C., & Trathan, P. (2012). An Emperor Penguin Population Estimate: The First Global, Synoptic Survey of a Species from Space PLoS ONE, 7 (4) DOI: 10.1371/journal.pone.0033751 


Image: Close-up penguins from Hannes Grobe/AWI/Wikimedia Commons; satellite images from Fretwell et al.


Note for British readers: You may know Waldo as Wally.