Physical predictions over time

Physical predictions over time Kevin A Smith (k2smith@ucsd.edu), 1 Eyal Dechter (edechter@mit.edu), 2 Joshua B Tenenbaum (jbt@mit.edu), 2 Edward Vul (evul@ucsd.edu) 1 1. University of California, San Diego, Department of Psychology, La Jolla, CA 92093 2. MIT, Department of Brain and Cognitive Sciences, Cambridge, MA 02139 Abstract In order to interact with the world, people must be able to predict how it will unfold in the future, and these predictions must be updated regularly in light of new information. Here we study how the mind updates these predictions over time. Participants were asked to make ongoing predictions about the destination of a simulated ball moving on a 2D bumper table. We modeled these decisions by assuming people simulate the world forward under uncertainty. This model fit participants’ behavior well overall, suggesting that people continuously update their physical simulations to inform their decisions. In some specific scenarios participants’ behavior is not fit well by the simulation based model in a manner suggesting that in certain cases people may be using qualitative, rather than simulation-based, physical reasoning. Keywords: intuitive physics; forward simulation Introduction Changing lanes while driving seems like a simple and ordinary task – millions of people do it everyday. But to do so safely requires sophisticated predictions. Drivers must judge where their own car and those around it will be during the lane change, and, crucially, they must update these predictions with new information: if a car in the adjacent lane accelerates, a driver may abort her lane change to avoid a collision. This scenario demonstrates how people typically plan their actions: prediction is updated as new information is gathered. Research spanning decades has investigated how people predict future object movement while objects are hidden (Faisal & Wolpert, 2009; Rosenbaum, 1975; Runeson, 1975; Smith & Vul, 2013; Teglas et al., 2011), but in most natural cases, observers continue to see objects while updating their predictions. In this study we investigate how people change their instantaneous predictions about objects over time: are ongoing predictions the result of online simulation? Recent research provides evidence that people use ‘Noisy Newtonian’ models of physics to simulate the world (Sanborn, Mansinghka, & Griffiths, 2013): peoples’ internal physical models are based on correct assumptions about physics, but uncertainties in object position, movement, and latent variables can cause biases and variability in prediction. This framework has been used to predict peoples’ judgments about the stability of a tower of blocks (Hamrick, Battaglia, & Tenenbaum, 2011), the movement of hidden objects (Smith & Vul, 2013), and even judgments about physical causality (Gerstenberg, Goodman, Lagnado, & Tenenbaum, 2012). These works, however, solicited predictions at single instances in time. In this paper, we investigate whether a model that assumes faithful physics under uncertainty is also consistent with how peoples’ predictions evolve over time. We show that people’s decisions are often consistent with online forward simulation, but we also find that people can use qualitative reasoning about the world (e.g., Forbus, 1994) when this is more informative than simulations. Experiment We asked participants to play a game in which they make predictions about the path of a ball bouncing around a computerized table. The ball can reach one of two targets on the table, and participants earn points for predicting which target it reaches first. Crucially, they make this prediction continuously throughout the trial, earning points while predicting the correct target but losing points while predicting the incorrect target. In this way, we could capture how uncertainty (decisions whether to choose a target) and choices (which target) evolved over the course of each trial. Methods Sixty-six UC San Diego undergraduates participated in this experiment for course credit. 1 On each trial, participants saw a ball moving around a ‘table’ on the computer screen that contained blocks and both a red and a green target. The ball bounced perfectly elastically off of the edge of the table and blocks, ending when the ball reached one of the two targets. While the trial progressed, participants were asked to predict whether the ball would hit the red target or the green target first, indicating their guess by holding down either the ‘z’ or the ‘m’ key (each key counterbalanced for red and green between participants). If they were unsure, participants could press neither key, and if their prediction changed mid- trial, they were encouraged to switch keys. Holding down a key would fill a bar of the associated color, and at the end of the trial, the score would be determined by the difference between the proportion of time the keys for each target were held down: After each trial, participants were notified of their score and could continue to the next trial by pressing the spacebar. Participants were each given the same 400 trials in a random order. Of these, 370 trials were randomly generated, and 30 were designed to consider various extreme scenarios. We excluded one participant for holding down a single key through the entirety of the second half of the experiment.