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Mathematical software makes physics students miss the point
Technology
NEXT time you see something flapping in the breeze on an overhead power line, squint a little harder. It may not be an old pair of sneakers or a plastic bag. It could be a miniature aircraft in disguise, stealing power from the line to recharge its batteries. The US Air Force Research Lab (AFRL) in Dayton, Ohio, has come up with this bizarre idea in order to keep surveillance planes in the air for much longer than is possible today. Very small spy planes known as micro air vehicles (MAVs), with a wingspan of around 1 metre, already exist. They can be carried in a soldier’s backpack, assembled on the battlefield and hand-launched towards areas of interest, from where they are supposed to beam back photos. The trouble is that the planes run out of power after about 45 minutes.
When it’s time to sit back and think again
SOFTWARE designed to help physicists tackle complicated mathematics seems to be encouraging students to focus on the wrong aspects of scientific problems. Interested in how students use computer programs to solve problems, 22 | NewScientist | 5 January 2008
UIP/AMBLIN ENTERTAINMENT/AQUARIUS
The Pentagon’s new line in powered flight
Now the AFRL is developing an electric-powered MAV that can “harvest” energy by attaching itself to a power line. The hope is to design one that keeps going for days or even weeks. To avoid arousing suspicion when recharging, the spy plane will need to collapse its wings and hang limp on the cable, looking like a piece of wind-blown detritus. The Pentagon’s Defense Advanced Research Projects Agency (DARPA) has already developed much of the morphing technology to do this, including telescopic wings that can be folded
physicists Thomas Bing and Edward Redish of the University of Maryland, College Park, analysed videos of teams of students as they worked on their assignments. Among other tools, the students used Mathematica, a program that crunches not only numbers but also symbols, enabling it to do algebra and calculus. By solving equations that might take days to solve with a pencil and paper, Mathematica frees up researchers to explore larger questions and to explore more problems. But this comes at a cost, Bing and Redish warn. Using Mathematica for physics involves two stages: choosing a strategy for solving the problem, and then implementing that strategy by
But during tests, AFRL researchers found that this technique limited the amount of power harvested to microwatts – not nearly enough to fly an MAV. Landing on the cable is likely to provide more power, and the AFRL will now have to prove that the idea is viable. It has succeeded in landing two out of the six MAV designs it tested on power lines, but has yet to devise an efficient latching mechanism. It hopes to come up with ideas and test them for latching this year. Even if this is successful, challenges abound, says Zac Richardson, a power line engineer with National Grid in the UK. He points out that if the MAV –Spy plane in disguise?– touched a pair of 11-kilovolt local power lines at the same time the short circuit would disconnect away and “sliding skins” made of the very power the plane seeks. carbon composite, which allow On a 400-kilovolt inter-city power the fuselage to change shape. line, it risks “fizzing and banging The AFRL’s most immediate and giving its position away challenge is working out how to anyway”. The sparks could also get an MAV flying at 40 knots to interfere with the plane’s wireless latch onto a power line without communications system and destroying itself or the line. prevent it from beaming back Originally it had hoped that footage in real time. by flying close to a line “Even kites falling across power electromagnetic induction lines cause breakdowns,” says would provide enough power. Ian Fells, an expert in electricity transmission based at Newcastle “It is an utterly bizarre University in the UK. “It’s an idea to try to land a utterly bizarre idea to try to land a plane on one.” Paul Marks ● plane on a power line”
typing in a few lines of computer code. Although the second stage can require formidable mathematical ability, it is the first that trains a student in physics. The researchers found that Mathematica encourages students to focus on the second, programming stage, at the expense of the first (www.arxiv.org/abs/0712.1187). “Mathematica affects the kind of reasoning they use,” says Bing. “They focus on computational aspects of the problem, while suppressing the connection with the physics.” During an assignment in which students used Mathematica to solve a problem in quantum theory, their first answer was infinity. This was obviously wrong, but instead of
going back to check whether they had chosen a sensible strategy, they repeatedly came up with new ways to program the same strategy, and failed to solve the problem. Students might get trapped in this “sticky mindset” even when doing the calculation by hand, but Mathematica’s speed at doing calculations makes it more likely, Bing and Redish say. This is a common problem, according to researchers who study the psychology of how people interact with computational devices. “We often see,” says Elspeth McKay of the RMIT University in Melbourne, Australia, “that automated thinking tools tend to block people’s capacity to see or know the broader context of the problem they face.” Mark Buchanan ● www.newscientist.com
NEXT time you see something flapping in the breeze on an overhead power line, squint a little harder. It may not be an old pair of sneakers or a plastic bag. It could be a miniature aircraft in disguise, stealing power from the line to recharge its batteries. The US Air Force Research Lab (AFRL) in Dayton, Ohio, has come up with this bizarre idea in order to keep surveillance planes in the air for much longer than is possible today. Very small spy planes known as micro air vehicles (MAVs), with a wingspan of around 1 metre, already exist. They can be carried in a soldier’s backpack, assembled on the battlefield and hand-launched towards areas of interest, from where they are supposed to beam back photos. The trouble is that the planes run out of power after about 45 minutes.
When it’s time to sit back and think again
SOFTWARE designed to help physicists tackle complicated mathematics seems to be encouraging students to focus on the wrong aspects of scientific problems. Interested in how students use computer programs to solve problems, 22 | NewScientist | 5 January 2008
UIP/AMBLIN ENTERTAINMENT/AQUARIUS
The Pentagon’s new line in powered flight
Now the AFRL is developing an electric-powered MAV that can “harvest” energy by attaching itself to a power line. The hope is to design one that keeps going for days or even weeks. To avoid arousing suspicion when recharging, the spy plane will need to collapse its wings and hang limp on the cable, looking like a piece of wind-blown detritus. The Pentagon’s Defense Advanced Research Projects Agency (DARPA) has already developed much of the morphing technology to do this, including telescopic wings that can be folded
physicists Thomas Bing and Edward Redish of the University of Maryland, College Park, analysed videos of teams of students as they worked on their assignments. Among other tools, the students used Mathematica, a program that crunches not only numbers but also symbols, enabling it to do algebra and calculus. By solving equations that might take days to solve with a pencil and paper, Mathematica frees up researchers to explore larger questions and to explore more problems. But this comes at a cost, Bing and Redish warn. Using Mathematica for physics involves two stages: choosing a strategy for solving the problem, and then implementing that strategy by
But during tests, AFRL researchers found that this technique limited the amount of power harvested to microwatts – not nearly enough to fly an MAV. Landing on the cable is likely to provide more power, and the AFRL will now have to prove that the idea is viable. It has succeeded in landing two out of the six MAV designs it tested on power lines, but has yet to devise an efficient latching mechanism. It hopes to come up with ideas and test them for latching this year. Even if this is successful, challenges abound, says Zac Richardson, a power line engineer with National Grid in the UK. He points out that if the MAV –Spy plane in disguise?– touched a pair of 11-kilovolt local power lines at the same time the short circuit would disconnect away and “sliding skins” made of the very power the plane seeks. carbon composite, which allow On a 400-kilovolt inter-city power the fuselage to change shape. line, it risks “fizzing and banging The AFRL’s most immediate and giving its position away challenge is working out how to anyway”. The sparks could also get an MAV flying at 40 knots to interfere with the plane’s wireless latch onto a power line without communications system and destroying itself or the line. prevent it from beaming back Originally it had hoped that footage in real time. by flying close to a line “Even kites falling across power electromagnetic induction lines cause breakdowns,” says would provide enough power. Ian Fells, an expert in electricity transmission based at Newcastle “It is an utterly bizarre University in the UK. “It’s an idea to try to land a utterly bizarre idea to try to land a plane on one.” Paul Marks ● plane on a power line”
typing in a few lines of computer code. Although the second stage can require formidable mathematical ability, it is the first that trains a student in physics. The researchers found that Mathematica encourages students to focus on the second, programming stage, at the expense of the first (www.arxiv.org/abs/0712.1187). “Mathematica affects the kind of reasoning they use,” says Bing. “They focus on computational aspects of the problem, while suppressing the connection with the physics.” During an assignment in which students used Mathematica to solve a problem in quantum theory, their first answer was infinity. This was obviously wrong, but instead of
going back to check whether they had chosen a sensible strategy, they repeatedly came up with new ways to program the same strategy, and failed to solve the problem. Students might get trapped in this “sticky mindset” even when doing the calculation by hand, but Mathematica’s speed at doing calculations makes it more likely, Bing and Redish say. This is a common problem, according to researchers who study the psychology of how people interact with computational devices. “We often see,” says Elspeth McKay of the RMIT University in Melbourne, Australia, “that automated thinking tools tend to block people’s capacity to see or know the broader context of the problem they face.” Mark Buchanan ● www.newscientist.com