How do we estimate the difficulty of performing a new task, a task we’ve never tried before such as making a sculpture, a birthday cake, or building a tower with LEGO blocks? Estimating difficulty helps us appreciate others’ accomplishments, and plays a critical role in deciding whether to undertake new tasks ourselves. Here we give a computational account of how humans judge the difficulty of a range of physical construction tasks, whererby the goal is to go from an inital configuration (e.g. blocks scattered on the floor) to a target configuration (e.g. a block tower). Our model takes into account two key aspects that influence construction difficulty: physical effort and physical risk. Physical effort captures the minimal raw work needed to transport all objects to their final positions and is computed using a hybrid task-and-motion planner. Physical risk corresponds to the precision with which objects must be transported for success, and is computed using noisy physics simulations; it reflects the costs (e.g., attention, coordination and fine motor movements) needed to ensure precise motion. We show that the full effort-risk model captures human estimates of difficulty and construction time better than either component alone, and that difficulty judgments are selectively sensitive to effort and risk in a task-dependent manner.
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