"The latter is rare in general when analysing puzzles in this way, so the monominoes case was pretty exciting," he adds. We wanted to understand which mixtures make puzzles that are hard for computers to solve, and thus probably difficult for humans, and which are actually easy for computers to solve - though that doesn't mean they're necessarily easy for humans." "Some puzzles use one clue type, while others use a mixture of clue types. "In general, we wanted to try to delineate the boundary between computationally easy and computationally hard aspects of The Witness' puzzles," Demaine says. So, who witnesses The Witness? As it turns out, it is remarkably difficult to tell - and that's why it's so academically enticing.ĭemaine's team often studies games in order to search for efficient algorithms, and to analyse computationally-intractable problems as a means of tracing innovative solutions that are often derived out of left-field. In the case of The Witness, the lower-case witness has to do with the ways in which puzzles are actually solved - it's about which strategy is successful, and what path(s) through a grid represents that. If you're especially interested, I've embedded a video of a class taught using a supercollaborative model below.ĭemaine was one of the main authors of a 2018 paper called Who witnesses The Witness?, which provides an exemplary case of supercollaborative research while simultaneously extrapolating what makes The Witness a game worth studying for doctoral mathematicians and computer scientists: primarily, its difficulty.įor those unacquainted with the term "witness" in a maths context, it's a specific value subbed into an existential statement - basically, it is an entity used to differentiate between something existing, something existing in at least one case, and something existing given certain conditions. It is, quite literally, supercollaborative, in that positive and effective teamwork takes precedence over individual input. To do this, Demaine uses a highly collaborative style of research called supercollaboration.Īccording to Demaine's site - linked above - supercollaboration is an innovative research method where researchers solve complex problems without concern over authorship or ego. The Witness' rules are mapped by symbols on its chessboard grids, and although they look quite simple, there's a lot more going on than meets the eye - so much so that some study what exactly makes The Witness' problems difficult at a doctoral level.Įrik Demaine, a professor in computer science at MIT, primarily focuses on research and teaching, and often combines the two by tasking students with solving open problems in groups. On the other, it is widely lauded for its mathematical complexity. On one hand, it is heralded as a champion of pretentiousness. The Witness is a curious, persnickety game. "Each clue type ended up offering a whole interesting problem to study."
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