In a glance, we can perceive whether a stack of dishes will topple, a branch will support a child's weight, a grocery bag is poorly packed and liable to tear or crush its contents, or a tool is firmly attached to a table or free to be lifted. Such rapid physical inferences are central to how people interact with the world and with each other, yet their computational underpinnings are poorly understood. We propose a model based on an "intuitive physics engine," a cognitive mechanism similar to computer engines that simulate rich physics in video games and graphics, but that uses approximate, probabilistic simulations to make robust and fast inferences in complex natural scenes where crucial information is unobserved. This single model fits data from five distinct psychophysical tasks, captures several illusions and biases, and explains core aspects of human mental models and common-sense reasoning that are instrumental to how humans understand their everyday world.T o see is, famously, "to know what is where by looking" (ref. 1, p. 3). However, to see is also to know what will happen and what can be done and to detect not only objects and their locations, but also their physical attributes, relationships, and affordances and their likely pasts and futures conditioned on how we might act. Consider how objects in a workshop scene ( Fig. 1 A and B) support one another and how they respond to various applied forces. We see that the table supports the tools and other items on its top surface: If the table were removed, these objects would fall. If the table were lifted from one side, they would slide toward the other side and drop off. The table also supports a tire leaning against its leg, but precariously: If bumped slightly, the tire might fall. Objects hanging from hooks on the wall can pivot about these supports or be easily lifted off; in contrast, the hooks themselves are rigidly attached.This physical scene understanding links perception with higher cognition: grounding abstract concepts in experience, talking about the world in language, realizing goals through actions, and detecting situations demanding special care (Fig. 1C). It is critical to the origins of intelligence: Researchers in developmental psychology, language, animal cognition, and artificial intelligence (2-6) consider the ability to intentionally manipulate physical systems, such as building a stable stack of blocks, as a most basic sign of humanlike common sense (Fig. 1D). It even gives rise to some of our most viscerally compelling games and art forms ( Fig. 1 E and F).Despite the centrality of these physical inferences, the computations underlying them in the mind and brain remain unknown. Early studies of intuitive physics focused on patterns of errors in explicit reasoning about simple one-body systems and were considered surprising because they suggested that human intuitions are fundamentally incompatible with Newtonian mechanics (7). Subsequent work (8, 9) has revised this interpretation, showing that when grounded in concrete dynamic...

Human observers localize events in the world by using sensory signals from multiple modalities. We evaluated two theories of spatial localization that predict how visual and auditory information are weighted when these signals specify different locations in space. According to one theory (visual capture), the signal that is typically most reliable dominates in a winner-take-all competition, whereas the other theory (maximum-likelihood estimation) proposes that perceptual judgments are based on a weighted average of the sensory signals in proportion to each signal's relative reliability. Our results indicate that both theories are partially correct, in that relative signal reliability significantly altered judgments of spatial location, but these judgments were also characterized by an overall bias to rely on visual over auditory information. These results have important implications for the development of cue integration and for neural plasticity in the adult brain that enables humans to optimally integrate multimodal information.

In a glance, we can perceive whether a stack of dishes will topple, a branch will support a child's weight, a grocery bag is poorly packed and liable to tear or crush its contents, or a tool is firmly attached to a table or free to be lifted. Such rapid physical inferences are central to how people interact with the world and with each other, yet their computational underpinnings are poorly understood. We propose a model based on an "intuitive physics engine," a cognitive mechanism similar to computer engines that simulate rich physics in video games and graphics, but that uses approximate, probabilistic simulations to make robust and fast inferences in complex natural scenes where crucial information is unobserved. This single model fits data from five distinct psychophysical tasks, captures several illusions and biases, and explains core aspects of human mental models and common-sense reasoning that are instrumental to how humans understand their everyday world.T o see is, famously, "to know what is where by looking" (ref. 1, p. 3). However, to see is also to know what will happen and what can be done and to detect not only objects and their locations, but also their physical attributes, relationships, and affordances and their likely pasts and futures conditioned on how we might act. Consider how objects in a workshop scene ( Fig. 1 A and B) support one another and how they respond to various applied forces. We see that the table supports the tools and other items on its top surface: If the table were removed, these objects would fall. If the table were lifted from one side, they would slide toward the other side and drop off. The table also supports a tire leaning against its leg, but precariously: If bumped slightly, the tire might fall. Objects hanging from hooks on the wall can pivot about these supports or be easily lifted off; in contrast, the hooks themselves are rigidly attached.This physical scene understanding links perception with higher cognition: grounding abstract concepts in experience, talking about the world in language, realizing goals through actions, and detecting situations demanding special care (Fig. 1C). It is critical to the origins of intelligence: Researchers in developmental psychology, language, animal cognition, and artificial intelligence (2-6) consider the ability to intentionally manipulate physical systems, such as building a stable stack of blocks, as a most basic sign of humanlike common sense (Fig. 1D). It even gives rise to some of our most viscerally compelling games and art forms ( Fig. 1 E and F).Despite the centrality of these physical inferences, the computations underlying them in the mind and brain remain unknown. Early studies of intuitive physics focused on patterns of errors in explicit reasoning about simple one-body systems and were considered surprising because they suggested that human intuitions are fundamentally incompatible with Newtonian mechanics (7). Subsequent work (8, 9) has revised this interpretation, showing that when grounded in concrete dynamic...

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The practice of mathematics involves discovering patterns and using these to formulate and prove conjectures, resulting in theorems. Since the 1960s, mathematicians have used computers to assist in the discovery of patterns and formulation of conjectures1, most famously in the Birch and Swinnerton-Dyer conjecture2, a Millennium Prize Problem3. Here we provide examples of new fundamental results in pure mathematics that have been discovered with the assistance of machine learning—demonstrating a method by which machine learning can aid mathematicians in discovering new conjectures and theorems. We propose a process of using machine learning to discover potential patterns and relations between mathematical objects, understanding them with attribution techniques and using these observations to guide intuition and propose conjectures. We outline this machine-learning-guided framework and demonstrate its successful application to current research questions in distinct areas of pure mathematics, in each case showing how it led to meaningful mathematical contributions on important open problems: a new connection between the algebraic and geometric structure of knots, and a candidate algorithm predicted by the combinatorial invariance conjecture for symmetric groups4. Our work may serve as a model for collaboration between the fields of mathematics and artificial intelligence (AI) that can achieve surprising results by leveraging the respective strengths of mathematicians and machine learning.