Sources of uncertainty in intuitive physics Kevin A Smith (k2smith@ucsd.edu) and Edward Vul (evul@ucsd.edu) University of California, San Diego Department of Psychology, 9500 Gilman Dr. La Jolla, CA 92093 USA Abstract arises because initial measurements of the location and velocity of objects is imperfect; this initial noise propagates through the model. Uncertainty about dynamics reflects noise in the physical model itself. Real object movement and collisions are perfectly deterministic only in an idealized system; in the world, objects can deviate from their ideal path because of multiple, unknowable interactions with the environment (e.g., a ball rolling across gravel will not move in a straight line). Stochastic dynamics could thus reflect such environmental uncertainty. Our goal is to disentangle the influence of initial noisy percepts and noisy physics on human predictions of object dynamics. We compared human behavior in a simple physical prediction task to a stochastic physics model with parameters reflecting the different types of uncertainty. Recent work suggests that people predict how objects interact in a manner consistent with Newtonian physics, but with additional uncertainty. However, the sources of uncertainty have not been examined. Here we measure perceptual noise in initial conditions and stochasticity in the physical model used to make predictions. Participants predicted the trajectory of a moving object through occluded motion and bounces, and we compared their behavior to an ideal observer model. We found that human judgments cannot be captured by simple heuristics, and must incorporate noisy dynamics. Moreover, these judgments are biased in a way consistent with a prior expectation on object destinations, suggesting that people use simple expectations about outcomes to compensate for uncertainty about their physical models. Keywords: intuitive physics, uncertainty, probabilistic inference stochastic simulation, Stochastic Physics Model Introduction We designed a model to replicate stochastic physics in a simple environment: a ball bouncing around a two- dimensional box. We based this model on idealized mechanics, but also incorporated the two sources of uncertainty: we added noise to the initial position and velocity to capture perceptual uncertainty, while dynamic uncertainty was captured by jitter in object movement over time, and variability in bounce angles. Predicting how the world will unfold is key to our survival and ability to function on a daily basis. When we throw a ball, cross a busy street, or catch a pen about to fall off of a desk, we must foresee the future physical state of the world to plan our actions. The cognitive mechanisms that help us make these predictions have been termed ‘intuitive physics’ models. Although human performance in physical prediction tasks tends to approximate real-world (Newtonian) physics, it does not match exactly: people make systematic prediction errors. While this has been taken as evidence that human models of intuitive physics are non-Newtonian (e.g., McCloskey, 1983), more recently human behavior has been explained by intuitive Newtonian physics models under uncertainty. On this account, human predictions deviate from Newtonian mechanics because of stochastic error – uncertainty about the initial positions or velocity of objects propagates through the non-linear physical model and causes variability and bias in final judgments. For instance, human predictions about the stability of a tower of blocks or the most likely direction for that tower to fall are consistent with a purely Newtonian model of physics with a small amount of uncertainty in the initial positions of the constituent blocks (Hamrick, Battaglia, & Tenenbaum, 2011). Similar models of physics with perceptual noise have been used to explain relative mass judgments in collisions (Sanborn, Mansinghka, & Griffiths, 2009) and infants’ expectations for object movement (Teglas et al., 2011). There are numerous ways in which uncertainty can be introduced into intuitive physical reasoning. We broadly classify these into two categories: perceptual uncertainty and uncertainty about dynamics. Perceptual uncertainty Uncertainty Parameters The model was based on a simple two-dimensional physics engine customized to add our sources of uncertainty. As physical uncertainty goes to zero, this model reduces to laws from idealized mechanics: the ball would continue to move in a straight line at a constant velocity until it hit a wall, at which point it would bounce elastically and with angle of incidence equal to the angle of exit. Uncertainty was captured using four parameters, two for the perceptual error, and two for the stochastic error: Perceptual Uncertainty At the start of the simulation, the ball’s position and velocity were based on where the ball would be in a perfectly deterministic simulation, but with noise added. Position was perturbed by isotropic two- dimensional Gaussian noise parameterized by standard deviation, ! p . Noise in velocity direction was captured in a von Mises (circular normal) distribution on direction of motion, parameterized by concentration (inverse variance) v . We did not consider uncertainty in the speed of the ball, as this would only affect the timing of the ball’s movement but not its destination, which is the prediction we aim to capture.
['Kevin A. Smith', 'Edward Vul']
Sources of uncertainty in intuitive physics.