An investing strategy based on the frequency of certain words Google searches, it turns out, might provide sizable profits. Image via Flickr user velorowdy

Google, as many researchers know well, is more than a search engine—it’s a remarkably comprehensive barometer of public opinion and the state of the world at any given time. By using Google Trends, which tracks the frequency particular search terms are entered into Google over time, scientists have found seasonal patterns, for example, in searches for information about mental illnesses and detected a link between searching behavior and a country’s GDP.

A number of people have also had the idea to use these trends to try achieving a more basic desire: making money. Several studies in recent years have looked at the number of times investors searched for particular stock names and symbols and created relatively successful investing strategies based on this data.

A new study published today in Scientific Reports by a team of British researchers, though, harnesses Google Trends data to produce investing strategies in a more nuanced way. Instead of looking at the frequency that the names of stocks or companies were searched, they analyzed a broad range of 98 commonly used words—everything from “unemployment” to “marriage” to “car” to “water”—and simulated investing strategies based on week-by-week changes in the frequencies of each of these words as search terms by American internet users.

A listing of the 98 words used in the study, from most effective at predicting market declines (debt) to least effective (ring). Image via Scientific Reports/Preis et. al.

The changes in the frequency of some of these words, it turns out, are very useful predictors of whether the market as a whole—in this case, the Dow Jones Industrial Average—will go down or up (the Dow is a broad index commonly considered a benchmark of the overall performance of the U.S. stock market).

The strategy was relatively straightforward: The system tracked whether a word such as “debt” increased in search frequency or decreased in search frequency from one week to the next. If the term was suddenly searched much less frequently, the investment simulation bought all the stocks of the Dow on the first Monday afterward, then sold all the stocks one week later, essentially betting that the overall market would rise in value.

If a term such as “debt” was suddenly searched much more frequently, the simulation did the opposite: It bought a “short” position in the Dow, selling all its stocks on the first Monday and then buying them all a week later. The concept of a “short” position like this might seem a bit confusing to some, but the basic thing to remember is that it’s the exact opposite of conventionally buying a stock—if you have a “short” position, you make money when the stock goes down in price, and lose money when it goes up. So for any given term, the system predicted that more frequent searches meant the market as a whole would decline, and less frequent searched meant it would rise.

During the period of time studied (2004-2011), making investment choices based on a few of these words in particular would have yielded overall profits several times higher than a conservative investment strategy of simply buying and holding the stocks of the Dow for the entire time. For example, basing a strategy solely on the search frequency of the word “debt,” which turned out to be the single most profitable term in the study, would have generated a profit of 326% over the seven years studied—compared to a profit of just 16% if you owned all the stocks of the Dow for the whole period.

So if you systematically bought a “short” position in the market every time the word “debt” suddenly started getting searched more often, you’d have made a ton of money over the seven years studied. But what about other words? The system simulated how this strategy would have performed for each of 98 words chosen, listed in the chart at right from most useful at predicting the movement of the markets (debt) to least useful (ring). As seen in the chart, for some of these terms the frequency that we type them into Google seems to serve as a very effective early-warning system for declines in the market.

Stock market declines typically reflect investors’ overall belief that, at any given time, it’s better to sell stock than buy it, and they often happen suddenly, when investors move in a herd to a new position—so the researchers speculate that rises in the terms’ frequencies in search convey a nascent feeling of concern about the market, before it’s expressed via actual transactions. All these searches might also reflect countless investors in an information-gathering phase, seeking to find out as much as they possibly can about an industry or a stock before selling it.

Even beyond the practical investment strategies that this type of analysis might generate, simply looking through the words provides a striking—and oftentimes confusing—window into the collective American psyche. It’s seemingly obvious why a sudden increase in the amount of people searching for the word “debt” might signal overall negative feelings about the market, and would likely precede a drop in stock values, and why “fun” might precede increases in the market. But why do searches for the words “color” and “restaurant” predict declines nearly as accurately as “debt”? Why do “labor” and “train” also predict stock market rises?

The gooey confections can be used to measure the speed of light and demonstrate relationships between the volume of a gas and its pressure and temperature. Photo by Flickr user John-Morgan

If the Easter Bunny comes to your house this weekend, you may find yourself with a plethora of marshmallows and Peeps. What to do with them all? Aside from simply eating them, cooking with them, or unleashing your artistic side by making dioramas, consider using them….for science!

Marshmallows, it turns out, are must-have pieces of equipment for at-home science experiments. Sure, you can use them test your kids’ self control through the the field of psychology’s notorious marshmallow test and its ever-more complex iterations. But if you’d rather not torture your kids by leaving tantalizingly in reach a marshmallow they’re ordered not to have, consider trying these easy science projects:

Marshmallows in a vacuum

The relationship between the volume of a gas and its pressure can be demonstrated at home with a simple set up. Photo by Mohi Kumar

No, not that kind of vacuum, despite the intriguing possibilities conjured by this phrase. You’ll need:

• A glass jar with a lid
• A mechanism to pump some of the air out of the jar
• Marshmallows

The Physics Hypertextbook recommends using a kitchen vacuum pump for this experiment. Cutting a small hole in the jar’s lid and squeezing a wine preserver’s vacuum pump into it also works.

Place a few marshmallows in the jar, seal it, and then pump the air out:

What’s going on? Marshmallows are basically a foam spun out of sugar, water, air, and gelatin. The sugar makes them sweet, the water and sugar combo makes them sticky and the gelatin makes them stretchy. But the air–which actually makes up most of the confection’s volume–makes marshmallows the tastiest way to encapsulate a gas in a solid. As you pump air out of the jar, the air inside the marshmallow expands and the marshmallow puffs up. Release the seal, and the marshmallows return to their normal size.

Congratulations! You’ve just demonstrated Boyle’s Law, which states that when the temperature doesn’t change, that the relationship between pressure (which is decreased by pumping air out of the jar) and volume of any set amount of gas (the marshmallow) is inversely proportional. In other words, decreasing one necessitates an increase of the other.

If you can’t eat ‘em, nuke ‘em!

If you’ve ever roasted a marshmallow over a campfire, you’ll know where this next demonstration is going. You’ll need:

• A microwave
• A microwavable plate
• A standard-sized marshmallow (avoid minis or jumbos; the former will fry and the latter may make an enormous mess!)

Place the marshmallow on one of its flat sides in the center of a plate. Then microwave the marshmallow for, say, 45 seconds on high.

It’s alive! This time, rather than changing the pressure surrounding the marshmallow, you’re changing the temperature. As the microwave bakes the marshmallow, the water in the marshmallow heats up and warms the air. When air becomes hot, it expands, forcing the marshmallow to puff up. The confection’s water also softens the sugars, causing it to ooze, as seen in the video above (created by YouTube user bbbpwns).

The relationship between temperature and volume is representative of Charles’ Law, which holds that any set amount of gas will expand when heated–increasing the temperature of a gas necessitates an increase in the gas’ volume.

Trying this with Peeps makes for a slightly alarming outcome, showcased by YouTube user UBrocks:

If you flashed back to the Stay Puft Marshmallow Man, alas–the monster marshmallow you pulled from your microwave doesn’t last–it will cool and deflate into a glob of ooze. But before it cools completely, the ooze is quite malleable and can be sculpted into shapes. But careful! The marshmallow remnants are like naplam–they’ll stick to you and burn. After it cools a bit, brush some oil on your palms before you mold anything, else your sculpture will stay glued to your hands.

 A gooey way to calculate the speed of light

For this demonstration you need a bit of background knowledge as you start out. The speed of a wave can be calculated by multiplying the wavelength (the distance from crest to crest) with the frequency (the number of crest-to-crest cycles that repeat in a stretch of time). Light is a wave, and its speed can be calculated the same way without fancy equipment. You’ll need:

A child measures the distance between melted patches after a layer of marshmallows was microwaved. Photo by Mohi Kumar

• A microwave with the turntable removed
• A  glass casserole dish or baking tray
• Mini marshmallows
• A ruler
• A calculator

Take the baking tray and pack one layer of marshmallows along the bottom, lined up like tiny puffy soldiers.  Make sure the turntable is removed from the microwave–this allows microwaves to move through the glass and the marshmallows in a standing wave pattern. Cook for a few minutes on low, watching the marshmallows carefully. With the turntable removed, the microwave doesn’t heat evenly–you’ll notice melted patches forming in your marshmallow field.

As soon as you see a few such patches, remove the dish and measure the distance between two that form a line parallel to the microwave’s door–these mark the locations of highest amplitudes within the standing wave. Multiply this by two to get the full wavelength of the microwaves that passed through your marshmallows (if you look at the geometry of a standing wave, your initial measurement only gave you half the wavelength). Convert this into meters.

Multiplying this result by frequency of the microwave, found in the microwave’s manual or in a label inside the device, gives ~299,000,000 meters per second–roughly speed of light! Catch a video of this here.

Fans celebrate Pi Day (3.14) with π pie. Photo by Flickr user pauladamsmith

March 14, when written as 3.14, is the first three numbers of pi (π). To commemorate the (completely artificial) confluence of the world’s most famous and never-ending mathematical constant with the way we can write the date, math enthusiasts around the country embrace their inner nerdiness by celebrating π, the ratio of the circumference of a circle and its diameter.

The date–which also happens to be Einstein’s birthday–inspires celebrations every year. Today. the Massachusetts Institute of Technology is posting password-protected decision letters on its admissions office site–would-be attendees can view whether they gained admittance at 6:28 pm (approximately equal to 2π, or the ratio of a circle’s circumference to its radius). Not to be outdone, Princeton’s celebrations of pi span an entire week, complete with a pie eating contest, an Einstein look-alike contest and a π-themed video contest (videos extolling pi and Einstein’s birthday must be less than 3.14 minutes; the winner will be announced at 3:14 today and will receive–you guessed it–$314.15).

Just why are people crazy about pi? The number–three followed by a ceaseless string of numbers after the decimal point, all randomly distributed–is the world’s most famous irrational number, meaning that it cannot be expressed as through the division of two whole numbers. In fact, it is a transcendental number, a term which boils down the idea that it isn’t the square root, cube root or nth root of any rational number. And this irrationality and transcendental nature of pi appeals, perhaps because pi’s continuous flow of numbers reflects the unending circle it helps to trace.

Pi has held an almost mystical quality to humans throughout time. Its unspoken presence can be felt in the circular ruins of Stonehenge, in the vaulted ceilings of domed Roman temples, in the celestial spheres of Plato and Ptolemy. It has inspired centuries of mathematical puzzles and some of humanity’s most iconic artwork. People spend years of their lives attempting to memorize its digits–they hold contests to see who knows the most numbers after the decimal, write poems–”piems,” if you will–where the number of letters in each word represents the next digit of pi, compose haikus (pikus)…the list goes on and on like pi itself.

Here are some notable moments in the history of pi:

1900-1650 BC: A Babylonian tablet gives a value of 3.125 for pi, which isn’t bad! In another document, the Rhind Mathematical Papyrus, an ancient Egyptian scribe writes, in 1650 BC “Cut off 1/9 of a diameter and construct a square upon the remainder; this has the same area as the circle” This implies that pi is 3.16049, “which is also fairly accurate,” according to David Wilson of Rutgers University’s math department.

800-200 BC: Passages in the Bible describe a ceremonial pool in the Temple of Solomon: “He made the Sea of cast metal, circular in shape, measuring ten cubits from rim to rim and five cubits high. It took a line of thirty cubits to measure around it” (I Kings 7:23-26). This puts pi at a mere 3.

Archimedes’ method of approximating pi involved sandwiching a circle in two other shapes. Image via Wikipedia/Leszek Krupinski

250 BC: Archimedes of Syracuse approximates the area of a circle by using the Pythagorean Theorem to find the areas of two shapes–a 96-sided polygon inscribed within the circle and an equally faceted polygon within which the circle was circumscribed. The areas of the 96-sided shapes sandwiched the area of circle, giving Archimedes upper and lower bounds for the circle’s extent. Though he knew that he had not found the exact value of pi, he was able to approximate it to between 3 1/7 and 3 10/71.

Late 1300s: Indian mathematician and astronomer Madhava of Sangamagrama first posits the idea that pi could be represented as the sum of terms in an infinite sequence–for example, 4 – 4/3 + 4/5 – 4/7 + 4/9…His work helped inspire branch of mathematics that examines the results of mathematical operations performed over and over on a never-ending stretch of numbers.

1706: Welsh mathematician William Jones began to use π as a the symbol for the ratio of the circumference of a circle to its diameter. Famed Swiss mathematician Leonhard Euler adopted this usage in 1737, helping to popularize it through his works.

1873: Amateur English mathematician William Shanks calculates pi out to 707 digits–his number was written on the wall of a circular room–appropriately named the Pi Room–in the Palais de la Découverte, a French science museum. But his number was only correct to the 527th digit–in 1946, the error was finally caught, and in 1949, the number was corrected.

1897: Lawmakers in Indiana almost pass a bill that erroneously labels the value of pi to 3.2. Cajoled by an amateur mathematician Edwin Goodwin, the Indiana General Assembly introduced House Bill 246, which introduced “a new mathematical truth” for sole use by the state. The “truth” was an attempt to square the circle–a puzzle which requires that a circle and square of the same area be constructed using only a geometrical compass and a straightedge. The bill unanimously passed the house, but the senate and hence the state was spared from embarrassment by C.A. Waldo, a Purdue mathematics professor who coincidentally happened to be in the State House that day. “Shown the bill and offered an introduction to the genius whose theory it was, Waldo declined, saying he already knew enough crazy people,” Tony Long of Wired wrote. Waldo gave the senators a math lesson, and the bill died.

1988: Larry Shaw of San Francisco’s Exploratorium inaugurates the first Pi Day celebration. This year, even as it prepares for its grand re-opening in April, the museum holds its 25th annual Pi Day extravaganza.

2005: Chao Lu, then a graduate student in China, becomes the Guinness record holder for reciting digits of pi–he recited the number to 67,980 digits. The feat took him 24 hours and 4 minutes (contest rules required that no more than 15 seconds could pass between any two numbers).

2009: Pi Day becomes official! Democratic Congressman Bart Gordon of Tennessee’s 6th congressional district, along with 15 co-sponsors, introduced HR 224, which “supports the designation of a Pi Day and its celebration around the world, recognizes the continuing importance of National Science Foundation math and science education programs, and encourages schools and educators to observe the day with appropriate activities that teach students about Pi and engage them about the study of mathematics.” The resolution was approved by the House of Representatives on March 12 of that year, proving that a love of pi is non-partisan.

How are you celebrating Pi Day?

Photo by Mohi Kumar

Today as you are slogging through the tasks marked on your calendar, you might notice the date: 12/12/12. This will be the last date with the same number for day, month and last two digits of the year until New Year’s Day, 2101 (01/01/01)–89 years from now.

Many are celebrating the date with weddings (the truly hard core are start their ceremonies at 12:00 pm, presumably so that they’d be mid-vow at at 12:12), concerts–such as this benefit for victims of Superstorm Sandy–even mass meditations. The Astronomical Society of the Pacific, based in San Francisco, has actually declared 12/12/12 “Anti-Doomsday Day,” the antidote to purported Mayan prognostications that the world will end on 12/21/12. Belgian monks have released the holy grail of beers–Westvleteren 12–for public sale today.

But even if you’re not doing something grand to commemorate the last such date in most of our lifetimes, you might find that a closer look at the date itself is intriguing from a mathematical point of view. As Aziz Inan, a professor of electrical engineering at the University of Portland whose hobby includes looking at number patterns in dates, describes (PDF) among other things:

• 12 = 3 x 4 (notice the numbers here are the consecutive counting numbers)
• 12 = 3 x 4, and 3 + 4 = 7; the date 12/12/12 happens to be the 347th day of 2012

On 12/12/12, there will be 12 days until Christmas. Twelve is also significant to society, the Astronomical Society of the Pacific reminds us. Aside from 12 inches in a foot, there are “contemporary calendars (12 months in the year), chronology (12 hours of day and night), traditional zodiac (12 astrological signs), Greek mythology (12 Olympic gods and goddesses), holiday folklore (12 days of Christmas), Shakespeare (Twelfth Night), and of course in our culinary world (dozen eggs, case of wine)…More importantly, in astronomy, Mars is 12 light minutes from the Sun, the average temperature of the Earth is 12 degrees Celsius, and Jupiter takes 12 years to orbit the Sun.”

The first 12 years of the next century will see 12 more dates with repeating numbers–01/01/01, 02/02/02, etc.–but other dates with numerical patterns are in our future. Here are a few categories:

Cheating but repeating: Every decade of this century will experience at least one date where all the numbers are the same–2/2/22, 3/3/33. 4/4/44, etc. The next decade will also have  2/22/22. Future dates out of reach for us–take 2/22/2222–may be truer representations of repetitive numbers in dates–imagine having that birthday!

Number palindromes: Palindromes–a number that reads the same forwards and backwards–are more common than repeats. This year hosted 2-10-2012. If you write dates in the “Gregorian little-endian” style of day/month/year, then 2012 had two: 21/02/2012 (in February) and 2/10/2012 (in October). The next palindrome date will be next year on 3/10/2013 (in March or October, depending on how you read the date). One-hundred and nine years from today, 12/12/2121 will also be a palindrome date. Inan has identified 75 palindrome dates this century–you can see the first 30 on a list he compiled. Of course, if you only use the last two digits of the year, then this past February (in the month/day/year way of noting dates)  was full of them:  2/10/12, 2/11/12, 2/13/12, etc.

Perfect squares: Some dates, like March 3, 2009 (3/3/09) are unique in that their numbers form perfect squares and their roots (as in 3 x 3 = 9). Other such dates are 4/4/16, 5/5/25, etc. But in some cases, if you take out the punctuation separating the dates, the resulting number is a perfect square. Take April 1, 2009, written as 4/01/2009 or 4012009–the number is a perfect square, with a root of 2003 (2003 x 2003 = 4012009). Other dates, when written the same way are reverse perfect squares, as Inan coined, when written from right to left. One such date December 21, 2010–when reversed it is 01022121, which happens to be the perfect square of 1011. Only two more such dates will occur this century.

Still other categories abound. Dates that are the product of three consecutive prime numbers (PDF), such as July 26, 2011, are an example; the date, when written as 7262011, equals 191 x 193 x 197. One date that is a simple sequence of consecutive numbers–1/23/45–will pop up every century. And my personal favorite, pi date (3/14/15), is only about two years away!

What other mathematical patterns in dates tickle your fancy?

A detailed glass anatomical model could be the perfect gift for the science nerd on your list, if you can stomach the $25,000 price tag. Photo by Garry McLeod via Wired

We all have science nerds in our lives (if you’re reading this blog, in fact, you probably are one yourself). But when the wintertime gift-giving holidays roll around, picking out gifts for this crowd can be more difficult than for others. A sweater just won’t cut it. With this in mind, here some fascinating (if sometimes impractical) gift ideas for science nerds:

Glass anatomical models: as detailed by Wired, master glassblower Gary Farlow and his team of artists make exquisitely detailed full-scale anatomical models of the human body’s vascular systems (above), from the arteries of the brain to the vessels that feed our internal organs. These stunning creations aren’t just for show—designed with the help of cardiologists, the see-through systems are used for training medical students. You might want to reserve them as gifts for the extra-special bio-nerds on your list, though, as a full-body model costs up to $25,000.

The Portabee 3D Printer. Image via Portabee

3-D Printers: Once restricted to professionals, 3-D printers are rapidly coming down enough in price to enter the consumer market in earnest. Much like a normal printer takes digital images and puts them on a piece of paper, a 3-D printer can convert plans for 3-D objects and carve them into plastic or other materials. They are beloved by engineers, inventors and tinkerers of all types. At the low end of the market is the Printbot jr., a $399 machine that requires some self-assembly, and the $480 Portabee 3D Printer, billed as the world’s first portable 3-D printing device.

One of Andy Aaron’s handcrafted adding machines. Image via Aaron

Retro Adding Machines: The age of the artisan calculator is upon us. As he desribes on his website, Andy Aaron makes fully functional Victorian-inspired adding machines, using old-fashioned tools like switches, cranks and levers, all mounted in a handsome wood casing. The handcrafted devices each take roughly a year to produce—and all the ones posted on Aaron’s website are already marked “SOLD”—so you might went to get in touch with him pronto if you want to buy one this holiday season.

Leafsnap, an iPhone app, can identify a tree species simply based on the shape of its leaves. Image via Leafsnap

Electronic Field Guides: In the past, nature lovers roamed forests and countrysides with a trusty field guide at hand to help identify plant and wildlife species. Now all you need is your smart phone. Leafsnap is one of the first in a series of field guide apps being developed by researchers from a group of institutions (including the Smithsonian) that automatically identify a plant species based on a picture you take of a leaf. Even better, it’s entirely free.

This slice of Martian rock can be yours for $1100. Image from MeteoriteMarket.com

Martian Meteorites: As Curisoity explores Mars, you can buy yourself a small piece of it. MeteoriteMarket.com sells a variety of meteorites, including pieces of Martian Shergottite rock that crashed into the Oman desert and were discovered in 1999. While the many of the smallest pieces are already long gone, a handful remain, ranging from $1067 to $14,500 in price.

See More Holiday Gift Guides from Smithsonian.com »

Image by Flickr user quinn.anya

Nature, for all of its free-wheeling weeds and lightning strikes, is also full of biological regularity: the rows of an alligator’s teeth, the stripes on a zebrafish, the spacing of a chicken’s feathers. How do these patterns arise?

Sixty years ago, with nothing but numbers, logic and some basic biological know-how, mathematician Alan Turing (best known for his pioneering work on artificial intelligence) came up with an explanation. He proposed that two chemicals—an “activator” and an “inhibitor”—work together, something like a pencil and eraser. The activator’s expression would do something—say, make a stripe—and the inhibitor would shut off the activator. This repeats, and voilà, stripe after stripe after stripe.

On Sunday, researchers reported the first experimental evidence that Turing’s theory is correct, by studying the eight evenly spaced ridges that form on the roof of a mouse’s mouth. (People, by the way, have four such ridges on each side, which help us feel and taste food.)

The scientists discovered that in mouse embryos, a molecule called FGF, or fibroblast growth factor, acts as a ridge activator, and SHH, or sonic hedgehog, acts as an inhibitor. When the researchers turned off FGF, the mice formed faint traces of the ridges that are normally made. Conversely, when they turned off SHH, the ridges morphed into one big mound. Changing the expression of one of these partners influenced the behavior of the other—just as Turing’s equations predicted.

Tragically, Turing would never know the importance of his contributions to developmental biology. The British government convicted him of homosexual acts in 1952 (for which it recently apologized), and punished him with chemical castration. Turing took his own life in 1954. This June is the 100th anniversary of his birth.

Studies show most football coaches make poor decisions on fourth down. Does Bill Belichick have a secret advantage? Photo by flickr user Keith Allison

Read our other posts about the history of football, what to bring to your Super Bowl party, the innovations of television advertising and much more.

This Super Bowl Sunday, as you watch grizzled coaches pace the sideline and bark at players, feel free to play armchair quarterback—or even head coach. Despite the hours they spend scouting players, analyzing game tape and drawing up complex tactical schemes, a pair of recent scientific studies indicates that many football coaches are no better at making some in-game decisions than you or I would be.

A 2006 paper by David Romer (pdf), a University of California at Berkeley economist, started things off by looking at a choice frequently encountered by coaches on fourth down: kick a field goal or try for a touchdown? Using data from more than 700 NFL games, Romer calculated the average chance of winning generated by each choice at different positions on the field. He then compared the data to the actual choices made by NFL coaches.

The conclusion: most avoid risk to an irrational extent, often opting to kick a field goal when going for a touchdown would provide a better chance of winning. Why would coaches—with their salaries and job security determined by on-field success—depart from the best possible choice? Romer speculates:

Perhaps the decision makers are systematically imperfect maximizers. Many skills are more important to running a football team than a command of mathematical and statistical tools…thus the decision makers may want to maximize their teams’ chances of winning, but rely on experience and intuition rather than formal analysis.

Another possible interpretation: for job security, coaches may prefer closer losses, coming after seemingly safe decision-making, to blowouts. A 23-0 loss may get a coach fired faster than a 23-6 score, which gives coaches incentive to kicking meaningless field goals rather than going for touchdowns.

Soon after the Romer study, Indiana University scientist Chuck Bower and partners from the business world went one step further. Using a similar dataset of actual NFL games, they built ZEUS: a powerful computer program that can analyze in-game situations on the fly and provide high-volume data analysis to coaches in real time. Bower said:

ZEUS is a valuable addition to a coaching staff’s tools, and one that can provide that elusive edge over the competition. The ZEUS engine is powerful enough to simulate the equivalent of every game played in the history of the NFL in less than a second. ZEUS can objectively assess crucial play-calling decisions with startling accuracy.

Comparing live data from the game with the historical track record of the NFL, ZEUS can indicate the choice that leads to a better chance of winning for a number of situations: not just what to do on fourth down, but whether to accept or decline penalties, attempt onside kicks, or try for two-point conversions.

In designing ZEUS, Bowers’ team drew upon many of the principles used in building computer models for other games—such as backgammon or chess—and applied them to football. “While the physical nature of the game is very different, the situational nature is strikingly similar. A football coach is constantly making decisions with respect to multiple variables: score, field position, down, yards to a first down, etc.,” said Bowers, an expert backgammon player.

NFL head coaches are a notoriously secretive bunch when it comes to strategy, so if anyone is currently using ZEUS, we’d likely not hear about it. But ZEUS’ own analysis indicates that one coach in particular might be using the cutting-edge program: New England Patriots coach Bill Belichick, set to coach in his 5th Super Bowl on Sunday.

The evidence? Belichick is famous for his unconventional decision-making, often opting to go for an aggressive play on fourth down when most coaches would punt or kick a field goal. The New York Times “Fifth Down” blog has used ZEUS to evaluate real-world decisions on a number of occasions. And when ZEUS was used to analyze a particularly controversial fourth down call made by Belichick—at the end of a crucial 2010 game against the Indianapolis Colts, he opted to go for it on his own 28-yard line, an unusually aggressive choice—ZEUS surprised many by saying he had, statistically, made the right call. The analysis indicated that, overall, it gave him team the best chance of winning.

Of course, statistical projections are not guarantees. In that case, the decision didn’t work out, and the Patriots lost the game. But if Belichick does have ZEUS on his sideline, it might give him that much better odds of being the winning coach on Sunday.

The first Death Star from Star Wars (via Wookieepedia)

Obi-Wan: That’s no moon. It’s a space station.

That space station was the Empire’s first Death Star in Star Wars: A New Hope. Obi-Wan and company had just bounced through a debris field, the remnants of the planet Alderaan. Such an act of destruction would seem impossible to us–it seemed so to many of the movie’s characters until it happened. But perhaps not, say three students at the University of Leicester in England who last year published a study on the subject in their university’s undergraduate physics and astronomy journal.

The study’s authors start off by making some simple assumptions: The planet being fired upon doesn’t have some sort of protection, like a shield generator. And it’s about the size of Earth but solid through and through (Earth isn’t solid, but the planet’s layers would have significantly complicated the math here). They then calculate the planet’s gravitational binding energy, which is the amount of energy required to pull apart an object. Using the mass and radius of the planet, they calculate that destruction of the object would require 2.25 x 10³² joules. (One joule is equal to the amount of energy required to lift an apple one meter. 10³² joules is a lot of apples.)

The energy output of the Death Star isn’t given directly in the movie, but the space station was said to have had a “hypermatter” reactor that had the energy output of several main-sequence stars. For an example of a main-sequence star, the authors look to the Sun, which puts out 3 x 10²⁶ joules per second, and they conclude that the Death Star could “easily afford to output [the energy required for an Earth-like planet's destruction] due to to its tremendous power source.”

It would be a different story, though, if the planet scheduled for destruction had been more like Jupiter than Earth. The gravitational binding energy of Jupiter is 1,000 times that of the Earth-like planet in the study. “To destroy a planet like Jupiter [the space station] would probably have to divert all remaining power from all essential systems and life support, which is not necessarily possible.”

Of course, that assumes that the Emperor wouldn’t be willing to sacrifice a space station full of people to wipe out his enemies. And considering that he was just fine with wiping out whole planets, I’m not sure I’d take that bet.

Sofia Kovalevskaya, Emmy Noether and Ada Lovelace are just three of the many famous female mathematicians you should know. Images courtesy of Wikicommons

If you haven’t yet read my story “Ten Historic Female Scientists You Should Know,” please check it out. It’s not a complete list, I know, but that’s what happens when you can pick only ten women to highlight—you start making arbitrary decisions (no living scientists, no mathematicians) and interesting stories get left out. To make up a bit for that, and in honor of Ada Lovelace Day, here are five more brilliant and dedicated women I left off the list:

Hypatia (ca. 350 or 370 – 415 or 416)

No one can know who was the first female mathematician, but Hypatia was certainly one of the earliest. She was the daughter of Theon, the last known member of the famed library of Alexandria, and followed his footsteps in the study of math and astronomy. She collaborated with her father on commentaries of classical mathematical works, translating them and incorporating explanatory notes, as well as creating commentaries of her own and teaching a succession of students from her home. Hypatia was also a philosopher, a follower of Neoplatonism, a belief system in which everything emanates from the One, and crowds listened to her public lectures about Plato and Aristotle. Her popularity was her downfall, however. She became a convenient scapegoat in a political battle between her friend Orestes, the governor of Alexandria, and the city’s archbishop, Cyril, and was killed by a mob of Christian zealots.

Sophie Germain (1776 – 1831)

When Paris exploded with revolution, young Sophie Germain retreated to her father’s study and began reading. After learning about the death of Archimedes, she began a lifelong study of mathematics and geometry, even teaching herself Latin and Greek so that she could read classic works. Unable to study at the École Polytechnique because she was female, Germain obtained lecture notes and submitted papers to Joseph Lagrange, a faculty member, under a false name. When he learned she was a woman, he became a mentor and Germain soon began corresponding with other prominent mathematicians at the time. Her work was hampered by her lack of formal training and access to resources that male mathematicians had at the time. But she became the first woman to win a prize from the French Academy of Sciences, for work on a theory of elasticity, and her proof of Fermat’s Last Theorem, though unsuccessful, was used as a foundation for work on the subject well into the twentieth century.

Ada Lovelace (1815 – 1852)

Augusta Ada Byron (later Countess of Lovelace) never knew her father, the poet Lord Byron, who left England due to a scandal shortly after her birth. Her overprotective mother, wanting to daughter to grown up as unemotional—and unlike her father—as possible, encouraged her study of science and mathematics. As an adult, Lovelace began to correspond with the inventor and mathematician Charles Babbage, who asked her to translate an Italian mathematician’s memoir analyzing his Analytical Engine (a machine that would perform simple mathematical calculations and be programmed with punchcards and is considered one of the first computers). Lovelace went beyond completing a simple translation, however, and wrote her own set of notes about the machine and even included a method for calculating a sequence of Bernoulli numbers; this is now acknowledged as the world’s first computer program.

Sofia Kovalevskaya (1850 – 1891)

Because Russian women could not attend university, Sofia Vasilyevna contracted a marriage with a young paleontologist, Vladimir Kovalevsky, and they moved to Germany. There she could not attend university lectures, but she was tutored privately and eventually received a doctorate after writing treatises on partial differential equations, Abelian integrals and Saturn’s rings. Following her husband’s death, Kovalevskaya was appointed lecturer in mathematics at the University of Stockholm and later became the first woman in that region of Europe to receive a full professorship. She continued to make great strides in mathematics, winning the Prix Bordin from the French Academy of Sciences in 1888 for an essay on the rotation of a solid body as well as a prize from the Swedish Academy of Sciences the next year.

Emmy Noether (1882 – 1935)

In 1935, Albert Einstein wrote a letter to the New York Times, lauding the recently deceased Emmy Noether as “the most significant creative mathematical genius thus far produced since the higher education of women began.” Noether had overcome many hurdles before she could collaborate with the famed physicist. She grew up in Germany and had her mathematics education delayed because of rules against women matriculating at universities. After she received her PhD, for a dissertation on a branch of abstract algebra, she was unable to obtain a university position for many years, eventually receiving the title of “unofficial associate professor” at the University of Göttingen, only to lose that in 1933 because she was Jewish. And so she moved to America and became a lecturer and researcher at Bryn Mawr College and the Institute for Advanced Study in Princeton, New Jersey. There she developed many of the mathematical foundations for Einstein’s general theory of relativity and made significant advances in the field of algebra.

A chocolate peanut butter pie for Pi Day (photo, and pie, by Sarah Zielinski)

Today is March 14, or 3.14, the day we celebrate the mathematical constant pi (π). Pi, the ratio of a circle’s circumference to its diameter, is an irrational number, meaning that it can’t be expressed as a simple fraction of two integers. It is also a transcendental number, which means it is not algebraic. The celebrated 3.14 is just the beginning of pi—it continues into infinity, and that may be one of the reasons people find it so fascinating. So in honor of Pi Day, here are some suggestions for how to celebrate:

1 ) Read about the long history of pi.

2 ) Memorize as many digits of pi as you can (here’s pi to a million digits). A Japanese man in 2005 memorized pi to 83,431 digits.

3 ) See how far you can calculate pi. Computer programmer Fabrice Bellard calculated pi to 2.7 trillion digits using his home computer.

4 ) Watch the movie Pi, a 1998 thriller about a paranoid mathematician.

5 ) Make a pi-themed pie (I went for chocolate peanut butter pie, but any flavor is appropriate).

6 ) Celebrate with music: Learn the song, “Pi, Pi, Mathematical Pi,” set to the tune of “American Pie”; listen to the Pi Rap; or sing Pi Day carols.

Whoever builds a better light bulb could win up to $10 million (photo courtesy of flickr user djaquay)

Last week, a neurologist at Beth Israel Deaconess Medical Center in Boston won $1 million from Prize4Life for his discovery of a reliable way to monitor progression of amyotrophic lateral sclerosis (ALS), also known as Lou Gehrig’s disease. Prize4Life, which also has an ongoing competition for development of a treatment for ALS, is just one of several organizations that are trying to promote the development of solutions to sometimes longstanding problems with crowdsourcing and the lure of a big prize. Here are some ways you can pad that bank account—if you’re smart enough:

Millennium Prize Problems: In 2000, the Clay Mathematics Institute announced that they would award $1 million to anyone who solved one of seven math problems: the Birch and Swinnerton-Dyer Conjecture, the Hodge Conjecture, the Navier-Stokes Equation, the P vs. NP problem, the Poincaré Conjecture, the Yang-Mills and Mass Gap and the Riemann Hypothesis, which has been on mathematicians’ wish list since 1900. Russian mathematician Grigoriy Perelman received a Millennium Prize last year for resolving the Poincaré Conjecture, the only problem on the list solved so far, but he turned down the prize money.

NASA Centennial Challenges: The space agency has already given away millions in competitions, including competitions over the development of better space suit gloves and reusable rocket-powered vehicles. Current challenges range from the development of super-efficient, “green” aircraft to the demonstration of a solar-powered rover that can operate at night. NASA’s budget plans include $10 million per year for future competitions.

Bright Tomorrow Lighting Prize (aka, L-Prize): If you can build a better light bulb, you might be able to win this Department of Energy-sponsored competition, which was developed to spur manufacturers to create high-quality, high-efficiency products. At stake are a $5 million and a $10 million prize along with promises from electric companies across the country to promote the winning designs.

Life Grand Challenges: Life Technologies, a biotech company, has announced the first four of seven $1 million challenges intended “to accelerate innovative solutions to technical life science challenges.” They’re starting with challenges to increase the capacity, speed and accuracy of DNA sequencing and to sequence the genome from a single cancer cell.

X Prizes: There are three current competitions: The Wendy Schmidt Oil Cleanup X Challenge will give $1.4 million to the team that demonstrates the best way to recover oil from the surface of the sea. The Archon X Prize for Genomics will award $10 million to the person who develops a method to sequence 100 human genomes in 10 days at a cost of less than $10,000 per genome. And the Google Lunar X Prize will give a jackpot $30 million to whoever manages to send a robot to the moon, have it travel 500 meters and then send video back to Earth.

A diagram showing partitions for the integers 1 through 8 (via wikimedia commons)

You’re familiar with partition numbers, even if you don’t recognize the term; even kindergartners know them. The partition of a number is all the ways that you can use integers to add up to that number. Start with 2. There is only one way to get there: 1 + 1. The number 3 has 2 partitions: 2 + 1 and 1 + 1 + 1. Four has 5 partitions: 3 + 1, 2 + 2, 2 + 1 + 1 and 1 + 1 + 1 + 1. And so forth. But partition numbers get unwieldy pretty quickly. By the time you get to 100, there are more than 190,000,000 partitions. We’re well beyond elementary school math.

Mathematicians have been searching for the past couple of centuries for an easy way to calculate partition values. In the 18th century, Leonhard Euler developed a method that worked for the first 200 partition numbers. Solutions proposed in the early 20th century for larger partition numbers proved to be inexact or impossible to use. And the search continued.

The most recent mathematician to tackle the problem was Ken Ono at Emory University, who had a eureka moment while on a walk through the north Georgia woods with his post-doc Zach Kent. “We were standing on some huge rocks, where we could see out over this valley and hear the falls, when we realized partition numbers are fractal,” Ono says. “We both just started laughing.”

Fractals are a kind of geometric shape that looks incredibly complex but is actually composed of repeating patterns. Fractals are common in nature—snowflakes, broccoli, blood vessels—and as a mathematical concept they’ve been hauled into use for everything from seismology to music.

Ono and his team realized that these repeating patterns can also be found in partition numbers. “The sequences are all eventually periodic, and they repeat themselves over and over at precise intervals,” Ono says. That realization led them to an equation (all math leads to equations, it sometimes seems) that lets them calculate the number of partitions for any number.

The results of their studies will soon be published; a more detailed analysis is available at The Language of Bad Physics.

On the episode I watched, Chris Budd, a mathematician at the University of Bath, presented his theory, “there is nothing random about chaos.” I’m still floored that such a thing could exist on TV (and wish they would show it here in the U.S.). Here’s how the segment went:

The current fuel economy sticker found on U.S. vehicles (credit: EPA)

Today, if you go to buy a new car, you’ll find a sticker like the one on the right giving you a bunch of data on fuel economy: the miles per gallon you’ll get on the highway and in the city and the estimated annual fuel cost (based on 15,000 miles driven over a year and gas costing $2.80 per gallon). You’ll also see a little diagram that rates and compares that vehicle’s fuel economy with others in its class.

The EPA has now proposed changing the fuel economy sticker, this time adding information about how much greenhouse gases and other pollutants are emitted by the vehicle and how that compares to others in its class. They also propose adding another measure of gas mileage, this time presenting the number in terms of gallons of gas used per 100 miles.

It’s the last bit of information that is potentially the most useful. That’s because measuring fuel economy in MPG is rather misleading. Jennifer Ouelette explains in The Calculus Diaries:

One of the newly proposed labels for fuel economy (credit: EPA)

Why doesn’t everyone ditch their current gas-guzzling cars for a Prius or similar hybrid? The answer might surprise you. It turns out that many of us assume that saving gas (and therefore money) corresponds linearly with miles per gallon. But according to a June 20, 2008, article in Science by Richard Larrick and Jack Soll at Duke University’s Fuqua School of Business, the gas used per mile is actually inversely proportional to miles per gallon. They call this the MPG illusion.

If you do the math, this becomes immediately obvious. A car that gets 10 MPG uses 10 gallons every 100 miles. A car that gets 20 MPG uses 5 gallons per 100 miles. An MPG of 30 equals 3.3 gallons per 100 miles. And 40 MPG is only 2.5 gallons per 100 miles. Each improvement in 10 MPG does not result in the same improvement in gallons per 100 miles. And it’s that number that matters in terms of money saved.

That’s why the MPG illusion can also been seen when looking at estimated annual fuel costs, which is probably the easiest number to relate to on the sticker. We all understand money coming out of our pockets. But it’s good to see the addition of the new numbers, to move people away from thinking of their vehicle in terms of MPG. And perhaps in a few years, after everyone is familiar with calculating fuel economy in this new way, we could scrap MPG all together. It’s an easy way to keep track of your car’s health and your driving habits when you own the car, but, as we can see from the math, it’s not very useful when buying one.

The Calculus Diaries, by Jennifer Ouellette

It doesn’t have to be that way, though, as Jennifer Ouellette demonstrates in her new book The Calculus Diaries: How Math Can Help You Lose Weight, Win in Vegas, and Survive a Zombie Apocalypse. There are plenty of opportunities in the world around us to find interesting examples of math, and especially calculus. Ouellette explains how to use calculus to analyze your odds of winning at craps and why your best option is simply not to play. She examines the Thermodynamics Diet, in which you can use calculus (or at least your own judgment) to optimize your diet and exercise regime so that you burn more calories than you consume. She links cholera, the black plague and zombies. (Okay, I’ll admit that last one falls into the fictional category that troubled me so much in school. But she links it to disease epidemiology. And beside, zombies are way more fun than Houdini tricks, at least in my world.)

The book has plenty of math and science history, and plain history itself—William the Conqueror makes an appearance—along with references to pop culture (the Mythbusters) and literature (the Aeneid). There’s a trove of material here for math teachers hoping to catch the attention of non-math students. Historical problems in math and physics show up regularly as do more recent analyses by modern scientists (there’s an actual study that goes with the zombie discussion).

The appendix includes many of the equations and graphs discussed in the text. However, I found that inadequate as I read through the book. What I really wanted was a workbook that would guide me along through the problems and scenarios that Ouellette posed in her writing. But that’s what surprised me: the book made me want to do the math, to work through the equations with a pencil and calculator, to graph out the curves and see for myself how all these things fit together.

I’m not sure I would have pursued math any more than I did if the teachers had made it this interesting in class. But perhaps I wouldn’t have slept through quite so many hours of it.