Strange Numbers

February 19, 2008

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A new report warns that U.S. grade-school students lag behind those in other developed countries in science and math. How do we get this young crop of engineers and scientists more excited by math? One way is to help them see the fun and strange ways math is used in real-world applications.

Topping the list of higher education and training in the World Economic Forum's recent global competitiveness rankings were Finland; Sweden; Denmark; Taiwan, China; and the United States.

Yet the world is moving from a competitiveness model based on cheap manpower to one based on cheap brainpower.

In total, China, India and Russia each year produce 14 million university students, as many as the U.S., according to global business school IMD's recent Competitiveness Roadmap 2007-2050. These students quickly become young professionals eager for success, who are relatively affordable and highly motivated.

The National Science Board's new Science and Engineering Indicators 2008 report, released last month, warns that U.S. grade school students continue to lag behind those in other developed countries in science and math.

How do we get children more excited in math and science? By helping them to see the fun and interesting ways in which math is used for diverse and unexpected real-world applications.

Here are a few.

Psychology: Mathematical Cognition Mathematical cognition — the brain's development, acquisition and application of mathematical skills — is a very important field in psychology. It benefits scientists and doctors studying the brain, and it helps educators develop better teaching methods for mathematics. In addition, its study is crucial to the development of "smart" computers, neural networks, fuzzy logic, robots and artificial intelligence.

Mathematics and psychology are linked in two other major ways: Psychologists investigate people's feelings and attitudes regarding mathematics; and they use mathematics, particularly statistics, as a professional tool to quantify and analyze their scientific findings.

Politics: Polling Exit polls of voters, along with questionnaires aimed to elicit citizen concerns, give statisticians plenty to work with in determining how to craft messages that incumbents and challengers use to drum up support for their candidacies. To win a race, campaigners ask a small number of people some questions and figure out what potential voters are thinking based upon the answers of the few. This educated guessing, called extrapolation, is employed in just about every political and public interest area today. A thorough understanding of statistics enables candidates and campaigners to evaluate how valid their conclusions are, to better allocate their limited resources, to address potential problems ahead of time, and to test speeches and slogans before they go public.

Sports: Draft Track and High-Altitude Soccer Airflow around cars on a NASCAR track is important to the outcome of the race, and now fans can see this previously invisible aspect on television. "Draft Track" on ESPN uses a special algorithm to calculate the drafting around cars, then shows viewers how the air changes as cars change positions. It's the NASCAR equivalent of the glowing puck in hockey, only it demonstrates how drivers strategically use air resistance to their advantage. (VIDEO)

In May 2007, football's governing body, the Fédération Internationale de Football Association (FIFA), banned international matches from being played at more than 2,500 meters above sea level. So Patrick McSharry, a research fellow at the University of Oxford, set out to assess the effect of altitude on match results. In analyzing the scores and results of 1,460 international football matches played at different altitudes in 10 countries in South America spanning over 100 years, McSharry used four variables — probability of a win, goals scored and conceded, and altitude difference between home and away team venues — to calculate the effect of altitude and to control for differences in team ability. He found that altitude difference had a significant negative impact on performance: Each additional 1,000 meters of altitude difference increased the goal difference by about half of a goal.

Entertainment: Movies and Music Advancements in computer-generated imagery (CGI) have redefined the movie industry. What used to be the realm of special effects artists using miniatures is now the domain of computer animators using vector-based mathematical rules and computations. Since 1995, when Toy Story became the first feature-length 3D CGI film, old classics like Star Wars have been re-released with new CGI enhancements and immediate classics like the Lord of the Rings trilogy have taken the technology to new heights. Effects that used to take days for computers to calculate now take minutes, making it possible for artists to create more detailed and intricate formulas and visual wonders.

Earlier this month, a mathematician won a Grammy award for restoring the only known recording of a live Woody Guthrie performance — a bootleg someone made in 1949 using a wire recorder. Guthrie's daughter, who had never heard her father perform in front of a live audience, oversaw the restoration by a University of New Hampshire math professor and other audio-restoration specialists. (Check out the before and after clips.)

Transportation: GPS and Roller Coasters A Global Positioning System (GPS) such as those inside of cars takes readings from three or more satellites over 12,000 miles high. Calculating the distance to each satellite (i.e., triangulation) allows the device to figure out where you are in three dimensions. GPS mapping software can then overlay this information on a map to show your location, including elevation. Its uses are far-reaching, including safety, security and convenience.

More "entertainment" than "transportation" perhaps, but amusement parks keep upping the ante, building faster and more complex roller coasters. But the fundamental principles at work remain the same. Roller coasters are driven almost entirely by basic inertial, gravitational and centripetal forces, all manipulated in the service of a great ride. The scientific concepts and mathematical equations that enable these rides equal the difference not only between constrained falls for kids and white-knuckle thrills for coaster enthusiasts, but also between life and death. (VIDEO)

Little Green Dudes: Alien Hunting and Crop Circles The SETI@home — "Search for Extra-Terrestrial Intelligence" — project has been searching for radio signals from alien civilizations for eight years now. Based at the University of California-Berkeley's Space Sciences Laboratory, SETI@home recruits regular people to crunch big calculations by dividing them into smaller problems and then sending them to be solved on home computers. Volunteers download special software that turns home computers into a part of a large computer network that distributes small pieces of big problems to all participants. The SETI@home software was recently upgraded to deal with new data, which amounts to 100 terabytes (100,000 gigabytes) per year — about the amount of data stored in the U.S. Library of Congress.

Explanations of crop circles range from the bizarre and the unnatural to the merely fantastic. To some people, the crop deformations represent the handiwork of extraterrestrial visitors. Others attribute the formations to crafty tradesmen or pranksters bent on a bit of mischief. To a few, the phenomenon suggests the action of numerate whirlwinds, microwave-generated ball lightning or some other peculiar atmospheric phenomenon. Whatever the case, whoever is making them knows quite a bit of geometry. "Crop circles" is not a wholly accurate term in the realm of geometric forms, as these crop deformations have also appeared in the shape of hexagons and triangles and other much more complicated patterns of geometric theorems.

Some of our future engineers are now in grade school, and they're losing interest and aptitude in math and science. It'd be nice if learning to reason logically were enough to interest them in these subjects (I've found logical reasoning sometimes proves useful...). But it may take white-knuckle rides, sports, Hobbits and E.T.s to get them interested initially.

Resources

Why MathCounts by Kevin Glennon MathCounts.org

Global Competitiveness Index 2007-2008 World Economic Forum, 2007

The Competitiveness Roadmap: 2007-2050 by Stéphane Garelli IMD World Competitiveness Yearbook, 2007

Science and Engineering Indicators 2008 National Science Board, January 2008

Mathematics and Psychology The World of Mathematics (Thomson Corp.), 2006

ESPN Draft Track Technology Will Allow NASCAR Fans to 'See the Air' ESPN, July 24, 2007

High Altitude Soccer Teams Have Significant Advantage Over Lowland Teams ScienceDaily.com, Jan. 4, 2008

The Grammy in Mathematics by Julie J. Rehmeyer Science News Online, Feb. 9, 2008

How Roller Coasters Work by Tom Harris HowStuffWorks.com

SETI@home Looking for More Volunteers by Robert Sanders UC-Berkeley News, Jan. 2, 2008

The Geometry of Crop Circles CoolMath.com

Theorems in Wheat Fields by Ivars Peterson Science News Online, June 28, 2003

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