brdgt | Science Tuesday - Puzzles! Puzzles! Puzzles!

CALCULATIONS The scribe of the Rhind Mathematical Papyrus, an Egyptian document more than 3,600 years old, introduces the roughly 85 problems by saying that he is presenting the “correct method of reckoning, for grasping the meaning of things and knowing everything that is, obscurities and all secrets.”

Math Puzzles’ Oldest Ancestors Took Form on Egyptian Papyrus
By PAM BELLUCK, The New York Times, December 6, 2010

“As I was going to St. Ives
I met a man with seven wives. ...”
You may know this singsong quiz,

But what you might not know is this:
That it began with ancient Egypt’s
Early math-filled manuscripts.

It’s true. That very British-sounding St. Ives conundrum (the one where the seven wives each have seven sacks containing seven cats who each have seven kits, and you have to figure out how many are going to St. Ives) has a decidedly archaic antecedent.

An Egyptian document more than 3,600 years old, the Rhind Mathematical Papyrus, contains a puzzle of sevens that bears an uncanny likeness to the St. Ives riddle. It has mice and barley, not wives and sacks, but the gist is similar. Seven houses have seven cats that each eat seven mice that each eat seven grains of barley. Each barley grain would have produced seven hekat of grain. (A hekat was a unit of volume, roughly 1.3 gallons.)

The goal: to determine how many things are described. The answer: 19,607.

The Rhind papyrus, which dates to 1650 B.C., is one of several precocious papyri and other artifacts displaying Egyptian mathematical ingenuity. There is the Moscow Mathematical Papyrus (held at the Pushkin State Museum of Fine Arts in Moscow), the Egyptian Mathematical Leather Roll (which along with the Rhind papyrus is housed at the British Museum) and the Akhmim Wooden Tablets (at the Museum of Egyptian Antiquities in Cairo).

They include methods of measuring a ship’s mast and rudder, calculating the volume of cylinders and truncated pyramids, dividing grain quantities into fractions and verifying how much bread to exchange for beer. They even compute a circle’s area using an early approximation of pi. (They use 256/81, about 3.16, instead of pi’s value of 3.14159....)

It all goes to show that making puzzles is “the most ancient of all instincts,” said Marcel Danesi, a puzzle expert and anthropology professor at the University of Toronto, who calls documents like the Rhind papyrus “the first puzzle books in history.”

Dr. Danesi says people of all eras and cultures gravitate toward puzzles because puzzles have solutions.

“Other philosophical puzzles of life do not,” he continued. “When you do get it you go, ‘Aha, there it is, damn it,’ and it gives you some relief.”

But the Egyptian puzzles were not just recreational diversions seeking the comforting illusion of competence. They were serious about their mission. In the Rhind papyrus, its scribe, known as Ahmes, introduces the roughly 85 problems by saying that he is presenting the “correct method of reckoning, for grasping the meaning of things and knowing everything that is, obscurities and all secrets.”

And the documents were practical guides to navigating a maturing civilization and an expanding economy.

“Egypt was going from a centralized, structured world to partially being decentralized,” said Milo Gardner, an amateur decoder of Egyptian mathematical texts who has written extensively about them. “They had an economic system that was run by absentee landowners and paid people in units of grain, and in order to make it fair had to have exact weights and measures. They were trying to figure out a way to evenly divide the hekat so they could use it as a unit of currency.”

So the Akhmim tablets, nearly 4,000 years old, contain lists of servants’ names, along with a series of computations concerning how a hekat of grain can be divided by 3, 7, 10, 11 and 13.

The Egyptian Mathematical Leather Roll, also from about 1650 B.C., is generally considered a kind of practice test for students to learn how to convert fractions into sums of other fractions.

The Rhind papyrus contains geometry problems that compute the slopes of pyramids and the volume of various-shaped granaries. And the Moscow papyrus, from about 1850 B.C., has about 25 problems, including ways to measure ships’ parts and find the surface area of a hemisphere and the area of triangles. Especially interesting are problems that calculate how efficient a laborer was by how many logs he carried or how many sandals he could make and decorate. Or the problems that involve a pefsu, a unit measuring the strength or weakness of beer or bread based on how much grain is used to make it.

One problem calculates whether it’s right to exchange 100 loaves of 20-pefsu bread for 10 jugs of 4-pefsu malt-date beer. After a series of steps, the papyrus proclaims, according to one translation: “Behold! The beer quantity is found to be correct.”

The problems in these ancient texts are not difficult by modern mathematical standards. The challenge for scholars has come in deciphering what the problems are saying and checking their accuracy. Some of the numerical equivalents are written in a symbolic system called the Eye of Horus, based on a drawing representing the eye of the sky god Horus, depicted as a falcon. Sections of the falcon’s eye are used to represent fractions: one-half, one-quarter and so on, up to one sixty-fourth.

Scholars have found a few errors in the problems, and Ahmes even wrote an incorrect number in his St. Ives problem. But over all, the equations are considered remarkably accurate.

“The practical answers are solved,” Mr. Gardner said. “What is unsolved about them is the actual thinking in the scribe’s head. We don’t know exactly how he thought of it.”

On a Hunt for What Makes Gamers Keep Gaming
By JOHN TIERNEY, The New York Times, December 6, 2010

By the age of 21, the typical American has spent 10,000 hours playing computer games, and endured a smaller but much drearier chunk of time listening to sermons about this sinful habit. Why, the experts wail, are so many people wasting their lives solving meaningless puzzles in virtual worlds?

Now some other experts — ones who have actually played these games — are asking more interesting questions. Why are these virtual worlds so much more absorbing than school and work? How could these gamers’ labors be used to solve real-world puzzles? Why can’t life be more like a video game?

“Gamers are engaged, focused, and happy,” says Edward Castronova, a professor of telecommunications at Indiana University who has studied and designed online games. “How many employers wish they could say that about even a tenth of their work force?

“Many activities in games are not very different from work activities. Look at information on a screen, discern immediate objectives, choose what to click and drag.”

Jane McGonigal, a game designer and researcher at the Institute for the Future, sums up the new argument in her coming book, “Reality Is Broken: Why Games Make Us Better and How They Can Change the World.” It’s a manifesto urging designers to aim high — why not a Nobel Prize? — with games that solve scientific problems and promote happiness in daily life.

In the past, puzzles and games were sometimes considered useful instructional tools. The emperor Charlemagne hired a scholar to compile “Problems to Sharpen the Young,” a collection of puzzles like the old one about ferrying animals across a river (without leaving the hungry fox on the same bank as the defenseless goat). The British credited their victory over Napoleon to the games played on the fields of Eton.

But once puzzles and gaming went digital, once the industry’s revenues rivaled Hollywood’s, once children and adults became so absorbed that they forsook even television, then the activity was routinely denounced as “escapism” and an “addiction.” Meanwhile, a few researchers were more interested in understanding why players were becoming so absorbed and focused. They seemed to be achieving the state of “flow” that psychologists had used to describe master musicians and champion athletes, but the gamers were getting there right away instead of having to train for years.

One game-design consultant, Nicole Lazzaro, the president of XEODesign, recorded the facial expressions of players and interviewed them along with their friends and relatives to identify the crucial ingredients of a good game. One ingredient is “hard fun,” which Ms. Lazzaro defines as overcoming obstacles in pursuit of a goal. That’s the same appeal of old-fashioned puzzles, but the video games provide something new: instantaneous feedback and continual encouragement, both from the computer and from the other players.

Players get steady rewards for little achievements as they amass points and progress to higher levels, with the challenges becoming harder as their skill increases.

Even though they fail over and over, they remain motivated to keep going until they succeed and experience what game researchers call “fiero.” The term (Italian for “proud”) describes the feeling that makes a gamer lift both arms above the head in triumph.

It’s not a gesture you see often in classrooms or offices or on the street, but game designers like Dr. McGonigal are working on that. She has designed Cruel 2 B Kind, a game in which players advance by being nice to strangers in public places, and which has been played in more than 50 cities on four continents.

She and her husband are among the avid players of Chorewars, an online game in which they earn real rewards (like the privilege of choosing the music for their next car ride) by doing chores at their apartment in San Francisco. Cleaning the bathroom is worth so many points that she has sometimes hid the toilet brush to prevent him from getting too far ahead.

Other people, working through a “microvolunteering” Web site called Sparked, are using a smartphone app undertake quests for nonprofit groups like First Aid Corps, which is compiling a worldwide map of the locations of defibrillators available for cardiac emergencies. Instead of looking for magical healing potions in virtual worlds, these players scour buildings for defibrillators that haven’t been cataloged yet. If that defibrillator later helps save someone’s life, the player’s online glory increases (along with the sense of fiero).

To properly apply gaming techniques to school and work and other institutions, there are certain core principles to keep in mind, says Tom Chatfield, a British journalist and the author of “Fun Inc.: Why Gaming Will Dominate the Twenty-First Century.” These include using an “experience system” (like an avatar or a profile that levels up), creating a variety of short-term and long-term goals, and rewarding effort continually while also providing occasional unexpected rewards.

“One of the most profound transformations we can learn from games,” he says, “is how to turn the sense that someone has ‘failed’ into the sense that they ‘haven’t succeeded yet.’”

Some schools are starting to borrow gamers’ system of quests and rewards, and the principles could be applied to lots of enterprises, especially colossal collaborations online. By one estimate, Dr. McGonigal notes, creating Wikipedia took eight years and 100 million hours of work, but that’s only half the number of hours spent in a single week by people playing World of Warcraft.

“Whoever figures out how to effectively engage them first for real work is going to reap enormous benefits,” Dr. McGonigal predicts.

Researchers like Dr. Castronova have already benefited by tracking the economic transactions and social behavior in online games. Now that Facebook and smartphones have enabled virtual communities to be created fairly cheaply, Dr. Castronova is hoping to build a prototype that could be adapted by researchers studying a variety of real-world problems.

“Social media like video games are the only research tool we’ve ever had that lets us do controlled experiments on large-scale problems like global warming, terrorism and pandemics,” Dr. Castronova says. “Not everything in virtual environments maps onto real behavior, but a heck of a lot does. Rules like ‘buy low, sell high’ and ‘tall people are sexier’ play out exactly the same way, whether the environment is virtual or real.”

Dr. Castronova envisions creating financial games to study how bubbles and panics occur, or virtual cities to see how they respond to disasters.

“One reason that policy keeps screwing up — think Katrina — is because it never gets tested,” he says. “In the real world, you can’t create five versions of New Orleans and throw five hurricanes at them to test different logistics. But you can do that in virtual environments.”

Well, you can do it as long as there enough players in that virtual New Orleans who are having enough fun to keep serving as unpaid lab rats. Researchers will need the skills exhibited by Tom Sawyer when he persuaded his friends it would be a joyous privilege to whitewash a fence.

Tom discovered, as Twain explained, “that Work consists of whatever a body is obliged to do, and that Play consists of whatever a body is not obliged to do.” The ultimate challenge, when trying to extract work from the World of Warcraft questers and other players, will be persuading them that it’s still just a game.

Tracing the Spark of Creative Problem-Solving
By BENEDICT CAREY, The New York Times, December 6, 2010

The puzzles look easy, and mostly they are. Given three words — “trip,” “house” and “goal,” for example — find a fourth that will complete a compound word with each. A minute or so of mental trolling (housekeeper, goalkeeper, trip?) is all it usually takes.

But who wants to troll?

Let lightning strike. Let the clues suddenly coalesce in the brain — “field!” — as they do so often for young children solving a riddle. As they must have done, for that matter, in the minds of those early humans who outfoxed nature well before the advent of deduction, abstraction or SAT prep courses. Puzzle-solving is such an ancient, universal practice, scholars say, precisely because it depends on creative insight, on the primitive spark that ignited the first campfires.

And now, modern neuroscientists are beginning to tap its source.

In a just completed study, researchers at Northwestern University found that people were more likely to solve word puzzles with sudden insight when they were amused, having just seen a short comedy routine.

“What we think is happening,” said Mark Beeman, a neuroscientist who conducted the study with Karuna Subramaniam, a graduate student, “is that the humor, this positive mood, is lowering the brain’s threshold for detecting weaker or more remote connections” to solve puzzles.

This and other recent research suggest that the appeal of puzzles goes far deeper than the dopamine-reward rush of finding a solution. The very idea of doing a crossword or a Sudoku puzzle typically shifts the brain into an open, playful state that is itself a pleasing escape, captivating to people as different as Bill Clinton, a puzzle addict, and the famous amnesiac Henry Molaison, or H.M., whose damaged brain craved crosswords.

And that escape is all the more tantalizing for being incomplete. Unlike the cryptic social and professional mazes of real life, puzzles are reassuringly soluble; but like any serious problem, they require more than mere intellect to crack.

“It’s imagination, it’s inference, it’s guessing; and much of it is happening subconsciously,” said Marcel Danesi, a professor of anthropology at the University of Toronto and the author of “The Puzzle Instinct: The Meaning of Puzzles in Human Life.”

“It’s all about you, using your own mind, without any method or schema, to restore order from chaos,” Dr. Danesi said. “And once you have, you can sit back and say, ‘Hey, the rest of my life may be a disaster, but at least I have a solution.’ ”

For almost a century scientists have used puzzles to study what they call insight thinking, the leaps of understanding that seem to come out of the blue, without the incremental drudgery of analysis.

In one classic experiment, the German psychologist Karl Duncker presented people with a candle, a box of thumbtacks and the assignment of attaching the candle to a wall. About a quarter of the subjects in some studies thought to tack the box to the wall as a support — some immediately, and others after a few failed efforts to tack wax to drywall.

The creative leap may well be informed by subconscious cues. In another well-known experiment, psychologists challenged people to tie together two cords; the cords hung from the ceiling of a large room, too far apart to be grabbed at the same time.

A small percentage of people solved it without any help, by tying something like a pair of pliers to one cord and swinging it like a pendulum so that it could be caught while they held the other cord. In some experiments researchers gave hints to those who were stumped — for instance, by bumping into one of the strings so that it swung. Many of those who then solved the problem said they had no recollection of the hint, though it very likely registered subconsciously.

All along, researchers debated the definitions of insight and analysis, and some have doubted that the two are any more than sides of the same coin. Yet in an authoritative review of the research, the psychologists Jonathan W. Schooler and Joseph Melcher concluded that the abilities most strongly correlated with insight problem-solving “were not significantly correlated” with solving analytical problems.

Either way, creative problem-solving usually requires both analysis and sudden out-of-the-box insight.

“You really end up toggling between the two, but I think that they are truly different brain states,” said Adam Anderson, a psychologist at the University of Toronto.

At least, that is what brain-imaging studies are beginning to show. At first, such studies did little more than confirm that the process was happening as expected: brain areas that register reward spiked in activity when people came up with a solution, for instance..

Yet the “Aha!” moment of seeing a solution is only one step along a pathway. In a series of recent studies, Dr. Beeman at Northwestern and John Kounios, a psychologist at Drexel University, have imaged people’s brains as they prepare to tackle a puzzle but before they’ve seen it. Those whose brains show a particular signature of preparatory activity, one that is strongly correlated with positive moods, turn out to be more likely to solve the puzzles with sudden insight than with trial and error (the clues can be solved either way).

This signature includes strong activation in a brain area called the anterior cingulate cortex. Previous research has found that cells in this area are active when people widen or narrow their attention — say, when they filter out distractions to concentrate on a difficult task, like listening for a voice in a noisy room. In this case of insight puzzle-solving, the brain seems to widen its attention, in effect making itself more open to distraction, to weaker connections..

“At this point we have strong circumstantial evidence that this resting state predicts how you solve problems later on,” Dr. Kounios said, “and that it may in fact vary by individual.”

The punch line is that a good joke can move the brain toward just this kind of state. In their humor study, Dr. Beeman and Dr. Subramaniam had college students solve word-association puzzles after watching a short video of a stand-up routine by Robin Williams. The students solved more of the puzzles over all, and significantly more by sudden insight, compared with when they’d seen a scary or boring video beforehand.

This diffuse brain state is not only an intellectual one, open to looser connections between words and concepts. In a study published last year, researchers at the University of Toronto found that the visual areas in people in positive moods picked up more background detail, even when they were instructed to block out distracting information during a computer task.

The findings fit with dozens of experiments linking positive moods to better creative problem-solving. “The implication is that positive mood engages this broad, diffuse attentional state that is both perceptual and visual,” said Dr. Anderson. “You’re not only thinking more broadly, you’re literally seeing more. The two systems are working in parallel.”

The idea that a distracted brain can be a more insightful one is still a work in progress. So, for that matter, is the notion that puzzle-solving helps the brain in any way to navigate the labyrinth of soured relationships, uncertain career options or hard choices that so often define the world outside.

But at the very least, acing the Saturday crossword or some mind-bending Sudoku suggests that some of the tools for the job are intact. And as any puzzle-head can attest, that buoyant, open state of mind isn’t a bad one to try on for size once in a while. Whether you’re working a puzzle or not.

An 11-Letter Word for Perfectionist? Starts With C
By CORNELIA DEAN, The New York Times, December 6, 2010

PROVIDENCE, R.I. — Natan Last is making a crossword puzzle.

“The theme,” he says as he opens his laptop, “is Dr. Seuss books” — in particular “Yertle the Turtle,” “Green Eggs and Ham” and “Horton Hears a Who,” whose 15-letter titles will fit exactly across the blank grid he summons onto his screen. He writes one title across near the top, another at the middle and the third near the bottom.

“Now we have to put in the black squares,” he says. By the conventions of crossword making, or “constructing,” the design must be symmetrical. That is, it must look the same upside down as it does right side up.

The trick with black squares is to put them under letters that often end words, like T’s and S’s, says Joey Weissbrot, like Mr. Last a member of the Brown University Puzzling Association (the ambiguity is deliberate). He and some other members of the group have gathered with Mr. Last in a student lounge to collaborate.

A junior at Brown and a creative writing major from Brooklyn, Mr. Last has been making crossword puzzles since he was in high school, and he was, for a time, the youngest constructor ever to have a puzzle in The New York Times. Eventually, The Times’s puzzle editor, Will Shortz, took him on as an intern. His crosswords were “extraordinary,” Mr. Shortz said in an interview, especially for someone so young.

“Crosswords have this reputation of being for older people,” Mr. Shortz went on. “That’s just not true anymore.”

There are similar groups at places like Yale, Harvard, Princeton and Texas Christian University. But Mr. Shortz says Brown’s is the largest, and at Mr. Last’s suggestion he gave it the task of producing a week’s worth of puzzles in September. (Disclosure: This reporter is a Brown alumna and an emerita member of its board.)

Constructing puzzles is “mathematical,” said another kibitzer, Aimee Lucido, a sophomore from Chicago who had her first puzzle in The Times during the Brown week. “You can do it for hours and kind of have your mind go away. But it’s creative — you are making something.”

Like about a third of the puzzling students, Ms. Lucido is a computer science major. “A very large percentage of crossword puzzle constructors are into computers or math as professions,” Mr. Shortz said. He thinks that is because “crossword making involves having this huge amount of data and synthesizing it into a grid.”

But constructing puzzles is like writing, too. “You want the perfect word,” he said, “le mot juste.”

David Kwong agrees. Mr. Kwong, who in his day job develops projects for DreamWorks Animation, is another constructor. Solvers “are drawing from their knowledge base and trying to figure out the gimmick,” he said. “The constructor is pushing the envelope and trying to come up with a new, clever way to create something within the constraints.”

These constraints, which the Brown group and many other constructors embrace, are the rules of The New York Times, requirements that Mr. Shortz, who is also the “puzzle master” at National Public Radio, says evolved like a kind of common law.

Among them are grid size (usually 15 by 15 for a daily paper, 21 by 21 for a Sunday puzzle), minimum word length (three letters) and a ban on “unchecked letters” (“Every square has to be part of two answers, across and down,” Mr. Shortz said).

And the answers must be actual words. “You cannot make stuff up,” Mr. Shortz said. “You would be surprised how many submissions I get like that.”

On the other hand, sometimes the fun is breaking the rules. Mr. Kwong said he and his fellow constructor Kevan Choset, a lawyer in New York City, are proud of a puzzle they had in The Times that he described as an homage to the Fold-In feature in Mad Magazine. Once the solvers filled in the grid, “they had to fold the puzzle over to find the hidden words,” Mr. Kwong said. “It was a fine example of pushing the envelope.”

Another time, he said, they designed a puzzle around the theme “think outside the box.” It ran on April Fool’s Day, and it involved writing the world “think” in the margin, outside the grid.

Mr. Last’s puzzle is conventional. He has his theme words and his grid and he is getting suggestions from the other puzzlers — Ms. Lucido; Mr. Weissbrot, a senior classics major from Edgemont, N.Y.; Jonah Kagan, a sophomore computer science major from Los Angeles; and Zoe Wheeler, a third-year English major from Easton, Conn.

They are considering what to put in a space calling for a nine-letter word. Like many constructors, Mr. Last uses a computer program — in his case, Crossword Compiler — which has a database of words. For one nine-letter spot, the computer suggests “cablegram.” But as is often the case with accomplished constructors, the students reject it.

“I don’t know what that is,” Mr. Kagan says. Instead, they choose a pop singer in their own age group: Katy Perry. “She’s all the rage, and the letters work perfectly,” Mr. Last says.

In another space, though, they settle on the phrase “in cahoots.” It is old-fashioned, Mr. Kagan concedes, “but it’s hilariously old-fashioned.” In still another place the computer suggests “frogman.” The students decide on “wingman” instead. “It’s kind of a cool word,” Mr. Last says.

Mr. Shortz says that even the best constructors use such databases, and that their widespread use has improved crossword quality. But they modify the programs by adding their own words, sometimes by the tens of thousands.

The puzzling students collaborate on such a list, Mr. Kagan said. “It’s really nice to have this thing that everyone is working to make better.”

Now they have a spot for a five-letter word beginning with “qu.” Someone suggests queen, but it won’t work. “Try quail,” Ms. Lucido suggests. She is thinking about “quail man,” a character she remembers from a television program she watched as a child. “As you put words in, it’s fun to think how you would clue them,” she says.

For Ms. Lucido, who found herself signing autographs on campus after her puzzle appeared, another fun part is “gridding,” or filling in the corners. “It’s kind of a perfectionist’s dream — or nightmare,” she said.

These “fill” words “can be anything,” Mr. Weissbrot said. “You just try to make them as interesting as possible. It’s no fun to solve a corner that has a bunch of three-letter abbreviations.” They also strive to avoid words like “olla” (a pot used by Pueblo Indians), familiar only in the crossword world.

There are also crossword perennials like the four-letter town in Oklahoma (Enid) or Iowa (Ames). “Short words that are vowel-heavy are very useful for puzzle makers,” Mr. Shortz said.

Another is Asta, the terrier in the “Thin Man” movies. Even though the films are more than 60 years old, Mr. Shortz has no intention of banning the dog. The films, and the Dashiell Hammett novel they are based on, “are still part of our culture,” he said.

On the other hand, he is eager to rid the puzzles of items like SLA, which is not only an abbreviation but an abbreviation for the Symbionese Liberation Army, a violent leftist group that has been out of the news for decades. He would ban it and similar items, he said, “but sometimes you have a fantastic puzzle, and it hinges on that answer. So you say, ‘O.K., I’ll allow it once more.’ ”

Puzzlers disagree about whether it is acceptable to use reference works to solve puzzles. As a solver, Mr. Kwong said, “I never look things up.”

“You want to get to that ‘Aha!’ moment,” he said. “It allows you to feel smart as a solver and recognize the cleverness that went into constructing the piece.”

But Mr. Shortz said: “It’s your puzzle. Do what you want.”

After all, crossword addicts are “my favorite people,” he said, and he knows what draws them. “By solving puzzles we make order out of chaos and bring things to a conclusion. Which is nice.”

Science Tuesday - Puzzles! Puzzles! Puzzles!

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