Weird Science: Stretching the Mind at Caltech : Education: In Prof. Tom Tombrello’s physics class, the focus is not on arriving at the correct answer. That’s because, in some cases, there are no correct answers.


Imagine a planet of warring rocks, paper and scissors, based on the popular hand game. Decide initial populations and birthrates of each species, and then figure out how each population evolves as they attack each other.

Hint: There is no right answer.

Each fall quarter, Caltech Prof. Tom Tombrello comes up with such brain-twisting questions as a way to screen freshmen applicants for his coveted Physics 11 course at the Pasadena university.

The class teaches students to nurture the creative side of the mind--not just the analytical part--and drop the high school habit of trying to kill a problem with math alone.


“The creative process is not something that one gets to in some linear fashion,” said Tombrello, 58, in his warm North Texas drawl. “The really good scientists saw the world in a different way, and in seeing it in a different way, worked real wonders in science.”

In the fall, interested students pick up their screening question. In December, Tombrello will pick five or so students from a field of about 30 for the winter quarter class, based on their responses to two screening questions. Meanwhile, the current Physics 11 students, who are now sophomores, are meeting for the class’s third and final quarter.

Physics 11 is a teen-age think tank, with no grades, no absolute answers and no pressure to produce anything but thought. Sometimes, students will attack a problem for weeks and never come up with an answer--but in the process, they learn to defy ‘X + Y = Z’ thinking.

One Physics 11 student described the class as “paradise,” replete with undergraduate luxuries such as paid research projects and shared office space in a complex within earshot of their professor.


Tombrello, a respected researcher and 30-year Caltech professor, good-naturedly admits that he believes the Physics 11 students are smarter than he is. Smarts are easy to come by at a place like Caltech, but these students are brains with killer instincts to boot, he said.

“I don’t think that I can give them the knack if they don’t have it,” Tombrello said. “But I can sharpen up their ability to use that knack.”


Each student gets a $3,600 stipend to work on individual research projects, funded by an anonymous donor, Caltech and the National Science Foundation.

Tombrello teaches the class in the center lounge of the small office complex, where a secretary keeps the coffee pot on and freshly baked cookies on hand. The students share offices in the facility, a converted warehouse with worn couches, rocking chairs and well-thumbed science magazines. On some mornings, Tombrello finds students plopped on the couch after all-night work sessions, the blackboards full of scribblings and waste baskets overflowing with empty pizza boxes.

Students work on individual research projects, meeting once a week to discuss their progress. In class, they also take on smaller problems, like the ones used to screen applicants.

Last quarter, Tombrello grabbed a jar of M & Ms, shook it and asked students to explain why the peanut ones rose above the plain ones. The students do not get to skip the math; they have to produce equations on the blackboard, figuring out the effects of mass, size and shape. Afterward, Tombrello told them the question has no known answer that works out mathematically.

“I think that the most frightening thing a professor can do is take an extremely bright group of students and ask them something the professor doesn’t know the answer to,” said physics professor David Goodstein, Caltech’s vice provost. “I wouldn’t have the courage to do it.”

The idea of the course is to cut to the chase, the way great thinkers do.


Take physicist Enrico Fermi, who died in 1954. In New Mexico, he and other scientists gathered in the desert to watch tests for the first atomic bomb. While other scientists observed their sensitive calibration instruments, Fermi tore up a piece of paper and threw the bits on the ground. After the blast, Fermi was quickly able to calculate the force of the blast, simply by noting how the bits of paper had moved.


Or consider Richard P. Feynman, a Caltech physicist who died in 1988. To explain how the space shuttle Challenger exploded in 1986, Feynman dropped a synthetic rubber O-ring in a glass of ice water and showed how it stiffened. And then Feynman summed up the problem: Cold weather probably affected the seals on the shuttle’s rocket boosters.

“Are we finding young Dick Feynmans?” mused Tombrello, who was awarded Caltech’s first Feynman prize, established last year to recognize creativity in teaching. “We hope so. That’s the point. Find the ones who really will make the world different, or see the world in an interesting and different way, which is just the essence of creativity.”

Tombrello’s approach is rare, said Yale physics professor Allan Bromley, who served as science adviser to former President George Bush.

“He’s not at all afraid to shoot sacred cows,” said Bromley, who once hired Tombrello as an assistant professor at Yale. “The kind of person who challenges students to really think and develop the spirit of innovation that all too frequently tends to get muffled in traditional course structures.”

Physics 11 student Dave Bacon is studying the mystery of the sliding boulders on a dry lake bed in Death Valley. Scientists note that the large rocks--weighing up to 600 pounds--change position, although no one has ever seen them move. In a paper he co-authored, Bacon, 19, came up with a likely explanation of why 30 of 31 rocks move (the stationary 31st remains a mystery).


His theory is that wind gusts help move the rocks, at times when the lake bed is slick from rain or other moisture. Bacon, who is submitting his paper to scientific journals, backs up the theory with mathematical equations on wind velocity and friction.


The literature and physics major said the class taught him to think with a twist.

“Before, maybe you’d look at it and say, ‘I have these tools (and) I can apply them,” Bacon said. “But this type of problem, you can’t really do that. You have to say, ‘What hasn’t been tried? What’s new?’ Once you think of something new, you use those tools to do the grunge work.”

Bacon is taking on a second project--the puzzle of the booming sand dunes. For decades, scientists have been trying to figure out why certain sand dunes in the Mojave Desert make humming noises when sand is displaced by a kick, breeze or other force.

In the Middle East, which has its own noisy sand dunes, legend has it that the sound comes from the bells of churches swallowed whole by the ghostly mounds. Bacon is focusing on individual sand grains in the booming 700-foot-tall Mojave dunes--are they smoother or rougher, for instance, than the grains in non-booming dunes?

In another project, Ben Siron, 19, is trying to figure out why sand dunes near the Salton Sea are moving and why they “give birth” to tiny, faster-moving sand dunes. The dunes, which are a few hundred feet long and 30 feet high, move several feet a year, and sometimes head on a collision course with a road or canal. Siron’s research focuses on the direction of the wind, the amount of sand in the area and the ruggedness of the terrain.


Outside class, even late bloomers to physics are starting to question the hows and whys of life at every turn. Physics 11 student Sebastian Maurer had only one high school physics course. Now, at home, the 19-year-old will absent-mindedly twirl a ring on his pen, and then try to predict the oscillation frequency. Or he will put a fan in front of his TV and study how the picture wavers. Then, he tries to calculate how fast the fan is spinning.

“Look around and say, ‘What kind of fun can I have now?’ ” said Maurer, working barefoot in his office one day. “Through this class, I learned I can solve problems--not just to solve a math problem in a textbook, but ones that have bearing on nature around us.”


Before class one recent afternoon, students swapped logic problems just for fun, their voices raised as they tried to talk over each other’s ideas, their minds working faster than their mouths. Tombrello jumped into the fray, tossing out a twist on the traditional tick-tack-toe game, in which players are allowed to switch their “X” or “O” position with an opponent’s, in lieu of making a new move.

It is not easy selecting students who will fill the handful of available slots for the Physics 11 class, so Tombrello must give his full attention to dreaming up the tricky screening questions.

“What you want to pick is something slightly outrageous and stated in an incomplete way, so their imagination can take hold,” he said.

One of this year’s two screening questions, which students must return by Oct. 24: An interstellar expedition is on a centuries-long, one-way voyage to a planetary system for colonization. They have exhausted their stored food and are limited to the food resources they can produce. So students must figure out a plan of strategic cannibalism, or whom to eat first, so that the group ends up at its destination with an optimal population.

Tombrello’s students help pick their successors. The students are usually more demanding than he is, dismissing applicants who have good ideas but do not back them up with math. Some freshmen turn in responses as long as 30 pages backed with computer programs.


In one of last year’s screening questions, students looked at an imaginary world based on Tombrello’s wording of a 1940s song. He used: “Mares eat oats and does eat oaks and little lambs eat ivy.” The question: Assume a small, equal number of each type of animal and type of vegetation; assuming that all compete for space, describe the evolution of the ecosystem.


One student came up with “The Oak Catastrophe” theory. Say the oaks dropped acorns with a long germination period. Meanwhile, the animals eat up all the food. Then, there’s nothing to eat, so they die too. But the acorns are time bombs. They grow, and there is nothing to eat them. And they become so big that their shade kills any other plants that grow.

Clever, Tombrello said, but the student made one big mistake: She did not back up her theory with math. She did not get in.

The ones who do get in, Tombrello said, are “potential superstars” at a place that has had 22 Nobel Prize-winning alumni and faculty.

“Life isn’t problem-solving, right?” said student Connie Chang, 19. “Life is the process of searching for the answer.”