A student reflects on matrix multiplication


Stanford and Peking University students enjoying good spirits at the SCPKU.

A matrix with m rows and n columns looks like a rectangle filled with tiny boxes: m times n boxes, to be exact. But after visiting the Stanford Center at Peking University (SCPKU) for three months, my mental matrix of the world looked more like a weird trapezoid. New acquaintances added rows and their unique perspectives added columns. My brain drew lines from geography to economics to politics, but the lines were on crumpled paper. Ah and don't forget history. So multiply the rectangle by time t and out comes a 3D trapezoid.

How do we mentally travel through odd shapes with any sense and efficiency? China Studies in Beijing classes at the SCPKU sharpened our tools for the endeavor. On day one, Thomas Fingar emphasized that the goal of a foreign policy class is not to remember a list of facts, but to build a personal matrix of relations and to learn tricks for traversing the matrix. Jean Oi demonstrated how people's ideals can constrain the goals of business and political leaders. Scott Rozelle showed how economic developments in China changed real lives. Clarity reduces the dimensions we care about. Sometimes we need to melt and reshape the whole matrix. Other times we just need to prune a few rows and columns. We have the algorithms, technologies, "intelligences." Our tools, both natural and artificial, can be useful for navigating political spheres and leading to action.

But tools are not all we have. Other people's matrices sometimes slam into our own. Warping it, filling it. At Peking University (PKU), I met students with different stories and missions. One student transfers industrial expertise from China to Southeast Asia. Another connects Stanford and PKU students to openly discuss US-China relations. I also collaborated with PKU researchers. The scientists are fast learners and deeply curious. The clinicians are hard working and harder feeling. They all faithfully give their time and spirit. Despite the different bases of our matrices, language in particular, we could cooperate and together build a fuller model of the world.

What was the visiting graduate student's place in all of this? As a psychologist, I study humans and their brains. The brain itself is a messy matrix. Figuratively, a life history of data to curate; literally, cells that code spacetime. Maybe the psychology and geometry of every other brain is not so foreign from each of our own. Our science can keep digging deeper and tilling truer in search of common ground. We can build an empirical basis for humans to flourish together.

Sometimes, after long times, a complex matrix can instead be depicted as a fractal. Like flakes of snow. Each one is unique, starting with the same properties of H2O but morphing through many phases. Maybe with study and reflection we will look back at both China studies and brain studies and, rather than see a messy matrix, find a fractal. Hopefully such a model can also be useful to guide our way forward.

About the author Josiah Leong: Awarded a SCPKU Predoctoral fellowship for research from August to November 2018. He is a doctoral candidate in psychology and his research is about how brain creates emotions and makes decisions. During his visit, he started a neuroimaging study with the Peking psychology department and taught neuroimaging data analyses to addiction researchers at the Peking Sixth Hospital. He also engaged with researchers in anthropology, history, and political science, and he audited courses from the China Studies in Beijing overseas program. These experiences clarified his vision for how psychological science can guide the policies that govern everyday life. He has seen how scientific collaboration builds communities across borders, and he remains optimistic that the practice of science can lead people to question their assumptions and reshape their matrices, so to speak.