I spent two years in graduate school working toward a Masters in Computer Science, with a focus in theory, while also serving as a teaching assistant

The Tetris Proof. I spent two years in graduate school… | by Mark M Liu | Medium

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2022-09-21 04:30:05

I spent two years in graduate school working toward a Masters in Computer Science, with a focus in theory, while also serving as a teaching assistant for EECS 376, Foundations of Computer Science. I often joke to friends that the material taught in class had little practical value, which has more than a grain of truth; theoretical computer science is usually far-removed from my daily life as a software engineer. In fact, some of my professors advised me against specializing in theory, recommending more lucrative specialties like Artificial Intelligence or Security. Even upon graduating, I felt uncertain of my choice until one memorable incident showed me I definitely made the right decision.

A few years ago, I was living in an apartment with a group of friends, all of us on the geekier side. One day, a roommate came back and, barely able to contain his excitement, informed us that he had just purchased a set of Tetris piece magnets. Upon hearing the news, we decided to arrange them on the refrigerator immediately. Tearing open the package, we saw that the Tetris pieces were laid out in neat rows on a single sheet, each row containing 7 copies of the same tetromino. As you may remember, there are exactly 7 tetrominoes, making a total of 49 total magnets.

We rushed to move the magnets from the packaging to their new home on the fridge, enjoying the crisp snap of each magnet to the cold surface. At first, we placed them at random with no particular pattern. Then, following our instincts, we began arranging them tightly so that they hugged one another; there are few things more satisfying than tidying up (unfortunately, this does not seem to apply to my room). Somehow, wordlessly, we understood this was the right way to play with our new toy, and began creating the most compact, neatly aligned set of pieces possible. As the clump grew, someone asked if we could arrange the pieces into a square. Quickly doing the math, I pointed out that, since each tetromino has an area of 4 units, they covered a total area of 7x7x4, a perfect square. Delighted by our serendipitous situation, we began to construct a 14x14 square.

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