This article was published in Scientific American’s former blog network and reflects the views of the author, not necessarily those of Scientific American
I look out on the sea of earnest nut-brown faces and maroon robes and smile. The young monk called Sonam has asked a good question: “If space is empty, how can it be expanding?”
We’re in a classroom at the Namgyal Institute of Tibetology, on a hilltop in Gangtok, the capital of the province of Sikkim in northern India. It’s a forested sanctuary with fluttering prayer flags, removed from the cacophony of the town. Getting here was a seemingly endless journey involving five flights over two days, ending in a six-hour drive over mountain roads that were often washed out by monsoon rains and strewn with boulders.
I’m teaching in a program started by the Dalai Lama almost 20 years ago. He knew that the Tibetan monastic tradition had not changed for centuries, and he worried that his monks wouldn’t be prepared for the 21st-century world unless they were learning math and science. Science for Monks started bringing out Western teachers to address this need. I’ve been coming to India for a decade, and it’s rejuvenating as a professor to work with students who are so humble in their approach and so committed to learning.
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“We use galaxies as markers of spacetime,” I tell Sonam. “Our only tools for understanding empty space are the objects it contains and the way light travels through it.”
I’m not entirely satisfied with this answer, but monks with an eighth-grade level of math are not able to handle the rigor of general relativity. So, we use models and analogies to tether physical concepts. Equipment is rudimentary. The classroom is strewn with balloons and batteries, paperclips and magnets.
We get a lot of mileage out of balls of dough. Each monk gets a golf-ball–sized lump and has to divide it into an Earth and a moon, then give them the correct separation. Many don’t make the moon small enough relative to the Earth and most put the Earth and moon too close together. Hoots of laughter are directed at the few monks who have the moon larger than the Earth.
Warm-up complete, they work in small groups to make a scale model of the solar system. Each group gets a kilogram of dough. They divide it into 10 equal lumps. Six combine to form Jupiter, and three combine to form Saturn. The last is divided into 10 lumps. Two combine to make Uranus, and two combine to make Neptune. The last is divided into 10 lumps. And on it goes. The remainder lump is divided into 10 twice more before the monks can make Mercury and Pluto, both dough balls no larger than the head of a pin.
Learning is active. Once the monks have finished their solar system, we’ll walk through the institute grounds to place the planets at their appropriate distances from the meter-wide sun back in the classroom. Then they’ll act out motions of the terrestrial planets. More mirth as the moon scurries to orbit the Earth while the Earth circumnavigates the Sun. In few days, we’ll turn the classroom into a scale model of the solar neighborhood. Then into a model of the Local Group of nearby galaxies.
Sometimes no equipment is needed. In one afternoon session, the monks assume a meditative state. I lead them on a guided visualization of the Milky Way, and on through gulfs of time and space towards the big bang. The monks report on their experiences. There’s a poignant moment as a cherubic-faced monk called Tenzin describes returning to the Earth at the end of the visualization. He hovers above the Himalayas, looking down at his Tibetan home, before reluctantly returning to his body in the classroom.
Dislocation is a leitmotif of my students. They’re stateless, and many are resigned to never seeing their families or their homeland. At breakfast, one of the teaching assistants, Kalten, describes crossing the ice fields from Tibet with a group of his relatives when he was 11. Chinese soldiers patrolled the bridges, so they had to swim the swollen rivers, and several in the group nearly perished. They were caught by Nepalese soldiers near the border and thrown in jail. His older brothers were beaten.
After the payment of bribes and several more weeks of arduous travel they made it to safety in India. Sikkim is the northeastern finger of India, with Bhutan to the east, Nepal to the west and China to the north. It’s a place of great beauty and substantial geopolitical tension.
Back at the hotel, I look over my notes and gather materials for the next day’s class. I go out to eat and navigate Gangtok’s warren of narrow streets, dodging potholes and speeding taxis and ducking under tangles of naked electrical wires. On the way back, I’m drenched by torrential rain. It comes down in sheets, the drops congealing into berry-sized globs. Later at night, the rain eases and the apocalyptic dogs emerge, their howls rendering my earplugs useless. My bed is planks covered by a hard pad. The time difference from Arizona is 12 hours and I lie awake, immersed in unfamiliar smells and sounds.
The senior monk in the group, a local named Kenpo, tosses handfuls of poker chips into the air. After they fall, the young monks smooth them out, so their distribution is close to random. Tables and chairs have been pushed to the edges of the room. Each chip represents a galaxy in the early universe. After a primer in Newtonian gravity, the monks pass over the several thousand chips, moving each slightly in response to the gravity of its neighbors. Squatting on their haunches, they give each chip and each situation careful consideration. They do it again, and again, repeatedly, seven times in total. The experiment is a poor person’s version of a computer simulation of the formation of structure in the universe.
In our consideration of space, we’ve neglected time. So, I divide the monks into groups, and each group gets a set of 40 images of events in the history of the universe. They range from the microwave background and the first galaxies and the formation of the Earth and moon to biological events like the appearance of stromatolites and lizards and apes to cultural landmarks like the building of the Pyramids and the development of the car and the cell phone and the internet. Each group is going to make a timeline on the floor of the classroom.
It gets loud in the classroom. The monks use their debating skills to critique, often without mercy, the timelines of neighboring groups. The air is filled with shouts and laughter and hand slaps. Human scrums form as they press forward to make their points. For any teacher, this rowdy activity is the mother lode of learning.
As the workshop draws to a close, they’ve learned a lot, but so have I. Modern cosmology is a sophisticated edifice based on a century of observations, but it’s intriguing that many aspects have been anticipated by Asian traditions, such as the idea of multiple universes and innumerable habitable worlds. Nothing I’ve said is discordant with their Buddhist training. This is salutary to someone who lives in a Western culture where science and religion often seem to be at odds.
The final day of the workshop is festive. I’ve brought out a realistic mask and have a serviceable German accent, so Einstein makes an appearance in class to mop up unanswered questions about gravity. We watch fly-through films of cosmological simulations and eat popcorn. Certificates are awarded. The Western teachers are given gifts and draped with silk ceremonial scarfs.
Nature managed the feat of starting with nothing, then creating empty space and filling it with matter and energy. But we’ve managed a small feat too, here on the edge of the roof of the world. We’ve taken an empty classroom and filled it with lightness and the simple pleasure of learning.