On Friday, Oct. 2, physicist Brian Greene addressed a packed Galileo Hall in the kick-off lecture of this year’s Dr. Bruce J. Nelson Distinguished Speaker Series, “The Power and Beauty of Mathematics.”Greene is a Professor of Mathematics and Physics at Columbia University. He wrote The Fabric of the Cosmos, Icarus at the End of Time, and the bestselling book The Elegant Universe. He has also appeared on a number of television shows, including “The Late Night with Conan O’Brien” and “The Late Show with David Letterman.”Before the talk, students and faculty alike waited in a line that stretched almost to Hoch-Shanahan Dining Hall. Practically every seat was taken in the three adjacent auditoriums that make up Galileo Hall; many had to stand.
Harvey Mudd President Maria Klawe introduced Brian Greene and the Dr. Bruce J. Nelson Distinguished Speaker Series, commemorating the life of Bruce Nelson HM ’74.She also recognized Robert M. Bell HM ’72 as being part of the BellKor team that recently won a $1 million prize from Netflix for designing an algorithm to predict movies that customers would like better than Cinematch, Netflix’s current software. Bell flew from New Jersey in order to attend the lecture.Greene began his lecture on string theory by connecting his own interest in the “joy and beauty of mathematics” to how mathematics can “extend our understanding of the universe.”In particular, he said mathematics may have the answer to one of the most significant problems in science today: the lack of a unified theory that could describe everything in the physical universe.“At the moment there is no experimental evidence, and string theory remains a wholly mathematical undertaking, but we hope that we might be onto that unified theory with the strange new world of string theory,” Greene said.The Newtonian theory of gravity works with macro-scale objects, Greene explained, and the same goes for quantum mechanics and small particles, but neither works well for describing both situations.By inventing calculus and coming up with equations to describe gravity, Isaac Newton set humanity down a powerful path in which math was seen as a tool, a powerful, economical language to describe reality.But when Albert Einstein came along, he realized that Newton’s equations could not be right.Newton’s Principia Matematica simply did not describe how gravity worked. “What is the mechanism behind gravity?” Einstein asked, and came up with his theory of general relativity, in which space-time warps and curves, thus exerting the force of gravity.But when Einstein’s theory was applied to the world of small things, it stopped working. A new body of knowledge, quantum mechanics, was developed in order to explain events like quantum tunneling, in which electrons have a small probability of penetrating impenetrable walls.This theory should apply to the larger world, Greene said, but uncertainty becomes so small that it can be ignored. As you explore the world of the atom and the electron, on the other hand, uncertainty becomes significant, and particles start to behave unpredictably and chaotically.This disparity between relativity and quantum mechanics becomes particularly significant when thinking about the first few seconds of the Big Bang, when a huge amount of mass was crammed into a very small volume.“We need to make gravity and quantum mechanics compatible,” Greene said. “Because only then will we even begin to be able to understand how our universe began.”String theory, he said, can provide a mathematics that applies under all circumstances.Making it clear that he was transitioning from known theory to unsupported hypothetical, Greene then began his explanation of a new set of mathematics that postulates the existence of 10 dimensions and suggested that particles are made up of string-like constituents that vibrate at different frequencies.“The universe can be seen as a dancing, cosmic symphony of strings,” he said.At a micro-level, strings spread space apart and reconcile some of the chaos that occurs. They establish the smallest possible length and the highest possible energy, providing a regulator that does not violate symmetry.Unfortunately, the mathematics behind strings does not make sense or work out in three dimensions.Luckily, Greene has a solution: “There are 10!”“Dimensions can be big and easy to see,” he continued. “Or they can escape notice by being small and difficult to detect. We think that there are additional curled-up dimensions that humans just cannot perceive.”Mathematically, string theory is based upon the rich, manifold geometry that describes the so-called ‘Calabi-Yau manifolds.’“The other dimensions of string theory may hold the key to explaining the parameters of the universe,” Greene said. “String theory could provide an answer, as a harmonic analysis of the Calabi-Yau shapes should give us those same parameters, if we find the right ones. The only problem is that there are 10500 possibilities.”As time ran out, Greene briefly touched on the possibility of multiple universes, each with its own shapes and universal parameters—called “inflationary cosmology”—before ending on a less theoretical note.“As soon as the Large Hadron Collider in Switzerland is fixed,” he said, “we hope to collide protons at high speeds. If debris, namely gravitron particles, are nowhere to be found afterwards, then this could mean that they were ejected into the other dimensions of string theory.”Students, faculty and other members of the audience gave Greene a hearty round of applause, while Harvey Mudd President Klawe remarked, “That was awesome!”Sam Lind PO ‘11 said, “Brian Greene’s talk was both interesting and funny—he definitely kept me engaged for the whole time. It was very similar to the PBS special on string theory, though, and Greene didn’t give a very satisfying explanation of the math behind it all. I wanted to see the equations!”
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