Probabilistic internal physics models guide judgments about object dynamics

Internal physics models guide probabilistic judgments about object dynamics Jessica Hamrick (jhamrick@mit.edu) , Peter Battaglia (pbatt@mit.edu) , Joshua B. Tenenbaum (jbt@mit.edu) Department of Brain and Cognitive Sciences, MIT. Cambridge, MA 02139 Abstract Many human activities require precise judgments about the physical properties and dynamics of multiple objects. Clas- sic work suggests that people’s intuitive models of physics are relatively poor and error-prone, based on highly simplified heuristics that apply only in special cases or incorrect general principles (e.g., impetus instead of momentum). These con- clusions seem at odds with the breadth and sophistication of naive physical reasoning in real-world situations. Our work measures the boundaries of people’s physical reasoning and tests the richness of intuitive physics knowledge in more com- plex scenes. We asked participants to make quantitative judg- ments about stability and other physical properties of virtual 3D towers. We found their judgments correlated highly with a model observer that uses simulations based on realistic phys- ical dynamics and sampling-based approximate probabilistic inference to efficiently and accurately estimate these proper- ties. Several alternative heuristic accounts provide substan- tially worse fits. Keywords: intuitive physics, dynamics, per- ception, model Introduction Intuitive physics is a core domain of common-sense reason- ing, developing early in infancy and central in adult thought (Baillargeon, 2007). Yet, despite decades of research, there is no consensus on certain basic questions: What kinds of inter- nal models of the physical world do human minds build? How rich and physically accurate are they? How is intuitive phys- ical knowledge represented or used to guide physical judg- ments? The kinds of judgments we consider are those necessary to navigate, interact with, and constructively modify real-world physical environments. Consider the towers of blocks shown in Fig. 1. How stable are these configurations, or how likely are they to fall? If they fall, in what direction will the blocks scatter? Where could a block be added or removed from the tower to significantly alter the configuration’s stability? Peo- ple make such judgments with relative ease, yet the literature on intuitive physics has little to say about how they do so. Classic research focused on the limits of human physical reasoning. One line of work argued that people’s understand- ing of simple object trajectories moving under inertial dynam- ics was biased away from the true Newtonian dynamics, to- wards a more “Aristotelian” or “impetus” kinematic theory (Caramazza, McCloskey, & Green, 1981; McCloskey, 1983), yet no precise model of an intuitive impetus theory was de- veloped. Studies of how people judge relative masses in two- body collisions concluded that humans are limited to mak- ing physical judgments based on simple heuristics, or become confused in tasks requiring attention to more than one dimen- sion of a dynamic scene (Todd & Jr., 1982; Gilden & Proffitt, 1989a, 1989b, 1994). Neither the impetus accounts nor the simple one-dimensional heuristic accounts attempted to ex- plain how people might reason about complex scenes such as A. B. C. Figure 1: Three towers of varying height and stability. Each tower (A, B, C) corresponds to a colored point in Fig. 3. A is clearly unstable, C clearly stable, while B (matched in height to C) is less obvious. Fig. 1, or gave any basis to think people might reason about them with a high degree of accuracy. Here we argue for a different view. We hypothesize that humans can make physical judgments using an internal gen- erative model that approximates the principles of Newtonian mechanics applied to three-dimensional solid bodies. They use this model to forward-simulate future outcomes given be- liefs about the world state, and make judgments based on the outcomes of these simulations. We believe that only by posit- ing such rich internal models can we explain how people are able to perform complex everyday tasks like constructing and predicting properties of stacks of objects, balancing or stabi- lizing precariously arranged objects, or intercepting or avoid- ing multiple moving, interacting objects. The physical laws of the internal models we propose are es- sentially deterministic, but people’s judgments are probabilis- tic. Capturing that probabilistic structure is crucial for pre- dicting human judgments precisely and explaining how intu- itive physical reasoning successfully guides adaptive behav- ior, decision-making and planning in the world. We can in- corporate uncertainty in several ways. Objects’ positions and velocities and their key physical properties (e.g., mass, coeffi- cients of friction) may only be inferred with limited precision from perceptual input. People may also be uncertain about the underlying physical dynamics, or may consider the action of unobserved or unknown exogenous forces on the objects in the scene (e.g., a gust of wind, or someone bumping into the table). We can represent these sources of uncertainty in terms of probability distributions over the values of state vari- ables, parameters or latent forces in the deterministic physi- cal model. By representing these distributions approximately in terms of small sets of samples, uncertainty can be propa- gated through the model’s physical dynamics using only ana- log mental simulations. Thus a resource-bounded observer