If two airliners are headed straight at each other, one standard emergency maneuver is for both of them to turn right and then curve back to their original course, almost as though they were driving opposite ways on a rotary in the sky.
But if the airliners are headed toward each other at a 45-degree angle, that maneuver can cause a collision, rather than avoid one.
That's one reason the aviation industry is working on upgrading its collision avoidance systems, and it's also a reason why the work of Carnegie Mellon University's Andre Platzer is gaining more recognition.
Dr. Platzer, a 30-year-old computer science professor, is named in today's edition of Popular Science as one of its "Brilliant 10," which the magazine calls "some of the nation's most promising young researchers."
He is being recognized for his development of software for checking the reliability of computer control systems like the ones that maneuver aircraft, oversee train safety or distribute electricity on power grids.
These are all examples of "hybrid systems" -- computer programs that make decisions in the face of constantly changing variables, whether it's the speed and position of other planes in the sky or the separation distance and wetness of the tracks for two speeding bullet trains.
These computer systems not only do vitally important jobs, but have become so complex that it is impossible to test every conceivable scenario that they might face.
"You can build very, very complicated systems today, but they are so complicated that you can no longer understand them. The more components that work together, the more tricky it is to follow their operation," he said.
"What my software does is to analyze these systems to find out if they really work."
His algorithms, embedded in a program called KeYmaera, enabled him, for instance, to determine how two intersecting planes could collide while trying to get out of each other's way, and to devise new escape maneuvers that avoid that problem.
Dr. Platzer grew up near Hamburg, Germany, and had some success when he was younger as a ballroom dance competitor, before mathematics and computers captured his passion.
After getting his master's degree in Germany, he was accepted into eight or nine Ph.D. programs, he said, and he then had to think long and hard about what he wanted to specialize in for his dissertation.
He decided that hybrid systems would be his focus, and that led him to Carnegie Mellon, where Professor Edmund Clarke is world-renowned for developing techniques for checking the reliability of computer control systems.
One area that may benefit soon from Dr. Platzer's software is train control in Europe, where passenger trains now hit 200 mph and are being designed to go even faster.
As more of these trains are built and their speed goes up, he said, the biggest challenge is making sure that no train runs into the rear of another one. That requires integrating automated sensors that track the positions of trains with the controls that can apply emergency braking.
While that might seem to be an "elementary school physics problem," Dr. Platzer said, "in reality it depends on the slope of a track, the mass of a train and the slippery conditions caused by the weather, and you have to take all these things into account."
One other big advantage of programs like KeYmaera: They can save truckloads of money.
"One of the major problems in the aviation and car industry," he said, "is they don't want their systems to fail and yet they have a serious issue with making sure everything works well. I've seen statistics that the cost of debugging their software systems is more than 50 percent of the total cost" of the software.
By cutting down on the number of debugging tests that are needed, KeYmaera can save these companies a lot of money.
He said he is proud to get the Brilliant 10 accolade not only because it recognizes his achievement, but because it might entice more students into his field.
"I think people understand how important it is to insure that all these computerized systems work correctly, but it's also kind of a terribly intimidating and difficult-to-understand field, so hopefully more people will now dare to go down this road."
Mark Roth can be reached at email@example.com or at 412-263-1130.