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Cited by 193Visual perception and processing mechanismsCategorization, perception, and languageDecision-Making and Behavioral Economics

Reconciling intuitive physics and Newtonian mechanics for colliding objects

Sanborn, Adam N., Mansinghka, Vikash K., Griffiths, Thomas L.·2013·Psychological Review
DOI 10.1037/a0031912
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Abstract

People have strong intuitions about the influence objects exert upon one another when they collide. Because people's judgments appear to deviate from Newtonian mechanics, psychologists have suggested that people depend on a variety of task-specific heuristics. This leaves open the question of how these heuristics could be chosen, and how to integrate them into a unified model that can explain human judgments across a wide range of physical reasoning tasks. We propose an alternative framework, in which people's judgments are based on optimal statistical inference over a Newtonian physical model that incorporates sensory noise and intrinsic uncertainty about the physical properties of the objects being viewed. This noisy Newton framework can be applied to a multitude of judgments, with people's answers determined by the uncertainty they have for physical variables and the constraints of Newtonian mechanics. We investigate a range of effects in mass judgments that have been taken as strong evidence for heuristic use and show that they are well explained by the interplay between Newtonian constraints and sensory uncertainty. We also consider an extended model that handles causality judgments, and obtain good quantitative agreement with human judgments across tasks that involve different judgment types with a single consistent set of parameters.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper proposes a “noisy Newton” framework in which people’s collision judgments are Bayesian inferences over Newtonian mechanics, corrupted by sensory noise and uncertainty about physical properties. It argues that mass-ratio biases and causal impressions previously taken as evidence for heuristics are well explained by this single rational framework.

Key findings

  • In a replication of Todd and Warren’s Experiment 1, lower coefficient of restitution reduced mass-judgment accuracy: repeated-measures ANOVA showed main effects of mass ratio, \(F(3,57)=133, p<.001\), and coefficient of restitution, \(F(2,38)=16.0, p<.001\), with a marginal interaction, \(F(6,114)=1.89, p=.08\).
  • The motor-object bias was replicated: points of subjective equality were \(0.91, 0.89, 0.59,\) and \(0.27\) for \(e=1, 0.9, 0.5,\) and \(0.1\), respectively; the \(e=0.5\) and \(e=0.1\) conditions were reliably biased away from \(m_a/m_b=1\). With both objects moving, PSEs were \(0.83, 0.81,\) and \(0.78\) for \(e=0.9, 0.5,\) and \(0.1\), all significantly biased.
  • The noisy Newton model fit mass judgments better than direct-perception and heuristic models: Experiment 1 NLL/AIC = \(696/1,398\) vs heuristic \(716/1,437\) and direct perception \(999/1,999\); Experiment 2 NLL/AIC = \(1,003/2,011\) vs heuristic \(1,258/2,522\) and direct perception \(1,462/2,927\).
  • For causality, real-or-random and physical-causality instructions produced very similar judgments (\(r=.998\)); the model matched 73% of trials, equal to a benchmark model. In a second causality experiment, real-or-random and pure-causality conditions correlated \(r=.98\), with a main effect of condition, \(F(1,28)=6.74, p<.05\), and the model matched 72% of trials vs 73% for the benchmark.

Methods

  • The noisy Newton model treats masses, coefficient of restitution, and initial velocities as hidden variables inferred from noisy observations of initial and final velocities, using Newtonian collision equations, Bayesian inference, Weber-like sensory noise, and priors such as lower masses and slower velocities being more likely.
  • Mass-judgment experiments replicated Todd and Warren (1982): Experiment 1 recruited 24 participants (4 discarded due to computer error); Experiment 2 recruited 22 participants. Both used 1 cm squares, mass ratios 1.25–3.0, and coefficients of restitution from 0.1 to 1.
  • Causality experiments each used 30 university-community participants split into two instruction conditions of 15; each participant saw 300 trials varying velocity ratio, gap, and time delay. Analyses included mixed-effects ANOVA, Pearson correlations, psychometric fitting, NLL/AIC model comparison, and parameter-robustness simulations.

Limitations

  • Stated: the authors cannot rule out that participants ignored instructions in one causality condition, and they cannot conclude from these results that causal impression depends only on physical hypotheses; other effects remain to be explained, such as higher velocities producing stronger causal impressions and time-dependent effects.
  • Stated: force judgments appear to be an exception, with people’s force judgments showing a more fundamental deviation from physical force.
  • Evident from the text: the framework assumes accurate Newtonian mechanics and specific prior/noise parameterizations; several extensions, including training and occlusion predictions, are discussed as future tests rather than directly tested here.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1037/a0031912

Cites

135 of 135 references verified0 citation errors · 0 not checkable

Statistics

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Claims the paper makes

0 of 93 cited sources checked · 0 supported · 0 flagged

  • Findingown data
    § Effect of Coefficient of Restitution

    Every parameter set showed the same ordering of accuracy of mass judgments by coefficient of restitution as the human data.

    “Every parameter set showed the same ordering of accuracy of mass judgments by coefficient of restitution as the human data.”
    Quote in the paperSubstantial claim
  • Findingown data
    § Effect of Coefficient of Restitution

    There is a main effect of coefficient of restitution on mass judgments.

    “and a main effect of coefficient of restitution, F ( 2 , 38 ) = 16 . 0 , p &lt; 0 . 001.”
    Quote in the paperSubstantial claim
  • Findingown data
    § Effect of Coefficient of Restitution

    The relative probability of the noisy Newton model compared to the direct perception and heuristic models is nearly one.

    “The relative probability of this model, compared to the direct perception and heuristic models using Akaike weights, is nearly one.”
    Quote in the paperSubstantial claim
  • Findingown data
    § Effect of Coefficient of Restitution

    There is a main effect of mass ratio on mass judgments.

    “A repeated-measures ANOVA showed a main effect of mass ratio, F ( 3 , 57 ) = 133 , p &lt; 0 . 001”
    Quote in the paperNot a substantial claim
  • Findingown data
    § Effect of Coefficient of Restitution

    The heuristic model predicts the difference in conditions (NLL=716, AIC=1437).

    “The heuristic model was developed to account for this result, and relying on the final speed to determine which object is lighter predicts the difference in conditions (NLL = 716 and AIC = 1,437).”
    Quote in the paperSubstantial claim
  • Classified as probably not a substantial claim. 48
  • May combine two claims. 58
  • The quote only partly states this claim. 2

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingown data
    § Effect of Coefficient of Restitution

    There is a marginally significant interaction between mass ratio and coefficient of restitution.

    “There was a marginally significant interaction between mass ratio and coefficient of restitution, F ( 6 , 114 ) = 1 . 89 , p = 0 . 08.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data
    § Effect of Coefficient of Restitution

    The noisy Newton model accounts for the difference in conditions (NLL=696, AIC=1398) and has a better quantitative fit than the heuristic model.

    “The noisy Newton model also accounts for this difference (NLL = 696 and AIC = 1,398) and with a better quantitative fit than the heuristic model, despite using parameters that chosen to produce qualitative results and not the best quantitative fit: The relative probability of this model, compared to the direct perception and heuristic models using Akaike weights, is nearly one.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Abstract

    We also consider an extended model that handles causality judgments, and obtain good quantitative agreement with human judgments across tasks that involve different judgment types with a single consistent set of parameters.

    “We also consider an extended model that handles causality judgments, and obtain good quantitative agreement with human judgments across tasks that involve different judgment types with a single consistent set of parameters.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Effect of Coefficient of Restitution

    The heuristic model produces a much better match to the human data than the direct perception model, and the separation in the predicted accuracy for the coefficient of restitution conditions matched human judgments both qualitatively and quantitatively.

    “The model produces a much better match to the human data than the direct perception model, and the separation in the predicted accuracy for the coefficient of restitution conditions matched human judgments both qualitatively and quantitatively.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning
    § Effect of Training

    The noisy Newton model predicts a reduced motor object bias for both experiments if training overwhelms the pre-experimental prior and only correct initial velocities are used.

    “If this is done, we find a reduced motor object bias predicted for both experiments, as shown in Figure 8B, because inference about the sum of initial velocities, ua + ub , which determine the decision boundary, is unbiased by the prior.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Motor Object Bias with Both Objects Moving

    The heuristic model predicts the same qualitative bias and provides a good quantitative fit.

    “The heuristic model predicts the same qualitative bias and provides a good quantitative fit.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Motor Object Bias with Both Objects Moving

    In robustness analysis, for all simulations the average subjective point of equality was biased, and for 71% of simulations the subjective point of equality for every coefficient of restitution condition was biased.

    “for all of the simulations the average subjective point of equality was biased and for 71% of simulations the subjective point of equality for every coefficient of restitution condition was biased.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Motor Object Bias: Faster Moving Object Appears Heavier

    In robustness analysis, for 94% of simulations the average subjective point of equality was biased, and for 65% of simulations the subjective point of equality for every coefficient of restitution condition was biased.

    “for 94% of the simulations the average subjective point of equality was biased and for 65% of simulations the subjective point of equality for every coefficient of restitution condition was biased.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Effect of Training

    In robustness analysis, for 82% of parameter sets in Experiment 1 and 65% in Experiment 2, the training task resulted in a smaller motor object bias for every coefficient of restitution condition.

    “for 82% of the parameter sets in Experiment 1 and 65% of the parameter sets in Experiment 2, the training task resulted in a smaller motor object bias for every coefficient of restitution condition.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Motor Object Bias: Faster Moving Object Appears Heavier

    The noisy Newton model produced the best quantitative fit (NLL = 1,003 and AIC = 2,011), with a relative probability nearly one compared to the direct perception and heuristic models using Akaike weights.

    “The noisy Newton model produced the best quantitative fit (NLL = 1,003 and AIC = 2,011): The relative probability of this model, compared to the direct perception and heuristic models using Akaike weights, is nearly one.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Motor Object Bias: Faster Moving Object Appears Heavier

    The ordering of the points of subjective equality for the heuristic model matched the empirical ordering, but otherwise the heuristic model was a poor match to the human data.

    “The ordering of the points of subjective equality for the heuristic model matched the empirical ordering, but otherwise the model was a poor match to the human data.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Dependence of Physical Causal Impression on Velocities

    If the initial velocity was twice as large as the final velocity or larger, the mean probability of collision judgments across participants was 0.14 higher than when the final velocity was twice as large as the initial velocity, a significant difference (t(29) = 2.62, p < 0.05).

    “If the initial velocity was twice as large as the final velocity or larger, the mean probability of collision judgments across participants was 0 . 14 higher compared to trials where the final velocity was twice as large as the initial velocity, a difference that was significant over participants, paired-sample t ( 29 ) = 2 . 62 , p &lt; 0 . 05.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Pure Causal Impressions from Probabilistic Inference

    The model predicted a broadly similar dependence of causality on variables for both instruction conditions, with a predicted asymmetry of 0.04.

    “First the two instruction conditions showed a broadly similar dependence of the impression of causality on the variables of the display, with a predicted asymmetry of 0.04.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data
    § Physical Causal Impressions from Probabilistic Inference

    There were main effects of gap, time delay, and velocity ratio on collision judgments, all F(1,28) > 30, p < 0.01.

    “There were main effects of gap, time delay, and velocity ratio, all F ( 1 , 28 ) &gt; 30, p &lt; 0 . 01.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Pure Causal Impressions from Probabilistic Inference

    The predictions were robust, with a velocity asymmetry for 55% of parameter sets and the real or random condition producing larger causality judgments for 93% of parameter sets.

    “The predictions were robust to different parameters, with a velocity asymmetry for 55% of the parameter sets and with the real or random condition producing larger causality judgments for 93% of the parameter sets tested.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Pure Causal Impressions from Probabilistic Inference

    In the pure causality experiment, the mixed effects ANOVA showed a main effect of condition (F(1,28) = 6.74, p < 0.05) and main effects of gap, time delay, and velocity ratio (all F(1,28) > 19, p < 0.001).

    “However, here the mixed effects ANOVA showed a main effect of condition, F ( 1 , 28 ) = 6 . 74, p &lt; 0 . 05 as well as main effects of gap, time delay, and velocity ratio, all F ( 1 , 28 ) &gt; 19, p &lt; 0 . 001.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Pure Causal Impressions from Probabilistic Inference

    In contrast to the first experiment, there were real differences between the real or random and pure causality conditions; the real or random instructions produced a stronger impression of causality than the pure causality instructions.

    “However, in contrast to the first experiment, here there were real differences between the real or random and the pure causality condition. For these types of trials, the real or random instructions produced a stronger impression of causality than the pure causality instructions.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Pure Causal Impressions from Probabilistic Inference

    The model produced differences between conditions similar to participants, with the real or random condition showing stronger impressions of causality than the pure causality condition.

    “More interestingly, the noisy Newton model produced differences between conditions quite similar to the differences found in the participants' responses, with the real or random condition showing stronger impressions of causality than the pure causality condition.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning
    § General Discussion

    Changes to the prior and changes to the likelihood predicted the effects of training and occlusion on the motor object bias, respectively.

    “changes to the prior and changes to the likelihood predicted the effects of training and occlusion on the motor object bias respectively.”
    Quote in the paperSubstantial claim

  • The quote only partly states this claim.

    Findingown data
    § Learning Newtonian Mechanics

    Predictions of the physical model with modified mass priors and 50 noisy samples per simulated participant are very similar to the predictions of the original model for both mass judgments and causality judgments.

    “The predictions for both mass judgments and causality judgments are very similar to the predictions of the original model (see Figures 5, 7, and 11 for comparison).”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingnone given
    § General Discussion

    Adding sensory noise to Newtonian mechanics predicted the effect of the coefficient of restitution on accuracy of mass judgments and the asymmetric effects of velocity ratio in causal impression.

    “adding sensory noise to Newtonian mechanics predicted the effect of the coefficient of restitution on accuracy of mass judgments and the asymmetric effects of velocity ratio in causal impression.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Heuristic model

    The best-fitting parameters for the heuristic model were a final speed ratio salience threshold of 1.58, a probability of using the final speed heuristic over the ricochet heuristic of 0.19, and a probability of unbiased guessing of 0.17.

    “We fit the parameters to the data and found that the best-fitting parameters were a final speed ratio salience threshold of 1 . 58, a probability of using the final speed heuristic over the ricochet heuristic of 0 . 19, and the probability of unbiased guessing was 0 . 17.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data
    § Appendix C: Explanation for Predictions of the Heuristic Model

    On the left-hand side of the discontinuity, the trials in the experiment all fall into the region in which |vb| ≥ |va|, but object a ricochets.

    “On the left-hand side of the discontinuity, the trials in our experiment all fall into the region in which | vb | ≥ | va | , but a ricochets.”
    Quote in the paperSubstantial claim

  • The quote only partly states this claim.

    Findingown data
    § Noisy Newton model

    The noisy Newton model implemented with a deterministic decision rule produced the same qualitative results as the probabilistic decision rule.

    “We found the same qualitative results for our model implemented with the deterministic decision rule.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Findingown data
    § Noisy Newton model

    The noisy Newton model's prior parameter s^2 was matched to human data in the mass judgment task using a value of 4, and kept fixed for the causality judgment task.

    “We matched this parameter to human data in the mass judgment task using a value of s 2 = 4, and kept it fixed for the causality judgment task.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: Lower masses are more likely than higher masses.
    • The authors state this as an assumption: Slower velocities are more likely than faster velocities.
    • The authors state this as an assumption: No external force is acting upon the system of two objects.

  • May combine two claims.

    Premisecitation
    § Collisions and Heuristics

    In Todd and Warren's second experiment, if the mass of the motor object was greater, participants responded accurately; however, if the mass of the projectile object was greater, participants often still reported that the motor object was heavier.

    “If the mass of the motor object was greater, participants responded accurately. However, if the mass of the projectile object was greater, participants often still reported that the motor object was heavier.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Todd & Warren, 1982

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Premisecitation
    § Abstract

    These deviations from a Newtonian account have been explained in terms of heuristics: looking for the object with the higher final speed and looking for the presence of a ricochet of one object off another, both of which are indications that this object is lighter.

    “These deviations from a Newtonian account have been explained in terms of heuristics: looking for the object with the higher final speed and looking for the presence of a ricochet of one object off another, both of which are indications that this object is lighter (Gilden &amp; Proffitt, 1989; Proffitt &amp; Gilden, 1989; Todd &amp; Warren, 1982).”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites Gilden & Proffitt, 1989

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    • cites Proffitt & Gilden, 1989

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    • cites Todd & Warren, 1982

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  • Classified as probably not a substantial claim. May combine two claims.

    Premisereasoning
    § Collisions and Heuristics

    Equation 3 does not involve e, and thus judgments should be invariant to changes in the coefficient of restitution.

    “Equation 3 does not involve e , and thus judgments should be invariant to changes in the coefficient of restitution.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Runeson, 1983

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    Premisecitation
    § Collisions and Heuristics

    Runeson showed that while the specific masses of objects were not determinable from observing the kinematic behavior of objects, the ratio of the masses was.

    “Runeson showed that while the specific masses of objects were not determinable from observing the kinematic behavior of objects, the ratio of the masses was.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Runeson, 1983

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    Premisecitation
    § Abstract

    People show sensitivity to irrelevant information, such as whether kinetic energy is conserved, as well as systematic biases, such as a strong bias toward believing that the object with higher initial speed is heavier.

    “However, people show sensitivity to irrelevant information, such as whether kinetic energy is conserved, as well as systematic biases, such as a strong bias toward believing that the object with higher initial speed is heavier (Andersson &amp; Runeson, 2008; A. Cohen &amp; Ross, 2009; Gilden &amp; Proffitt, 1989; Runeson &amp; Vedeler, 1993; Runeson et al., 2000; Todd &amp; Warren, 1982).”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites Andersson & Runeson, 2008

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    • cites A. Cohen & Ross, 2009

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    • cites Gilden & Proffitt, 1989

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  • May combine two claims.

    Premisecitation
    § Collisions and Heuristics

    In Michotte's Experiment 39, the causal impression of launching was strong when the projectile object traveled slower than the incoming motor object; in Experiment 40, the causal impression of launching was weak when the projectile object traveled faster.

    “In his Experiment 39, in which the projectile object traveled slower than the incoming motor object, the causal impression of launching was strong. But for his Experiment 40 in which the projectile object traveled faster than the incoming motor object, the causal impression of launching was weak.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Michotte, 1963

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Premisecitation
    § Collisions and Heuristics

    Instead people can only use restricted heuristics for judging mass, such as which object moves faster after a collision or which object ricochets.

    “Instead people can only use restricted heuristics for judging mass, such as which object moves faster after a collision or which object ricochets (A. Cohen, 2006; A. Cohen &amp; Ross, 2009; Gilden &amp; Proffitt, 1989; Proffitt &amp; Gilden, 1989; Runeson et al., 2000).”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites A. Cohen, 2006

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    • cites A. Cohen & Ross, 2009

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    • cites Gilden & Proffitt, 1989

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  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Collisions and Heuristics

    In the place of accurate perception of mass, it has been proposed that collisions between two objects present too complicated a problem for people to analyze correctly.

    “In the place of accurate perception of mass, it has been proposed that collisions between two objects present too complicated a problem for people to analyze correctly.”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites A. Cohen, 2006

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    • cites A. Cohen & Ross, 2009

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    • cites Gilden & Proffitt, 1989

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  • May combine two claims.

    Interpretationnone given
    § Combining Noisy Perception, Probabilistic Inference, and Newtonian Mechanics

    The noisy Newton framework does not necessarily require explicit or innate knowledge of physical constraints, but could be learned from a reasonably small number of examples.

    “Next, we demonstrate how the noisy Newton framework does not necessarily require explicit or innate knowledge of physical constraints, but could be learned from a reasonably small number of examples.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: People have an internal representation of physical constraints.
    • The authors state this as an assumption: People appropriately combine prior knowledge constrained by Newtonian mechanics with noisy sensory information to make inferences about the physical situation.

  • Classified as probably not a substantial claim.

    Interpretationnone given
    § Combining Noisy Perception, Probabilistic Inference, and Newtonian Mechanics

    The noisy Newton framework provides a model of how observed variables are generated based on states of the world.

    “The noisy Newton framework provides a model of how observed variables are generated based on states of the world, defining p ( O | S ) in Equation 4.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: People have an internal representation of physical constraints.
    • The authors state this as an assumption: People appropriately combine prior knowledge constrained by Newtonian mechanics with noisy sensory information to make inferences about the physical situation.

  • Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

    Interpretationreasoning
    § Combining Noisy Perception, Probabilistic Inference, and Newtonian Mechanics

    This combination of Newtonian physics and Bayesian inference can potentially be applied to any problem that requires making an inference from observed variables.

    “This combination of Newtonian physics and Bayesian inference can potentially be applied to any problem that requires making an inference from observed variables.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: People have an internal representation of physical constraints.
    • The authors state this as an assumption: People appropriately combine prior knowledge constrained by Newtonian mechanics with noisy sensory information to make inferences about the physical situation.

  • Classified as probably not a substantial claim.

    Interpretationreasoning
    § Combining Noisy Perception, Probabilistic Inference, and Newtonian Mechanics

    Here we propose that this approach can be extended to predicting people's judgments about physics.

    “Here we propose that this approach can be extended to predicting people's judgments about physics.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: People have an internal representation of physical constraints.
    • The authors state this as an assumption: People appropriately combine prior knowledge constrained by Newtonian mechanics with noisy sensory information to make inferences about the physical situation.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Combining Noisy Perception, Probabilistic Inference, and Newtonian Mechanics

    This idea was foreshadowed by Watanabe and Shimojo (2001) who proposed that people combining visual and auditory information to form a causal impression were solving the problem of 'inverse physics'.

    “This idea was foreshadowed by Watanabe and Shimojo (2001) who proposed that people combining visual and auditory information to form a causal impression were solving the problem of 'inverse physics' attempting to work out not just what object is generating the sensory information, but the physics governing the objects as well.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Watanabe and Shimojo, 2001

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  • May combine two claims.

    Premisecitation
    § Collisions and Heuristics

    Participants' point of subjective equality of the masses of the two objects was shifted: There was a bias towards believing that the initially moving object was heavier, which came to be known as the motor object bias.

    “Participants' point of subjective equality of the masses of the two objects was shifted: There was a bias towards believing that the initially moving object was heavier, which came to be known as the motor object bias .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Todd & Warren, 1982

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  • Probably not a substantial claim: may not pass S1 (asserted), S3 (load-bearing). May combine two claims.

    Premisecitation
    § Collisions and Heuristics

    It has been taken as strong evidence against KSD and more generally as evidence that people cannot accurately judge the relative mass of colliding objects.

    “It has been taken as strong evidence against KSD and more generally as evidence that people cannot accurately judge the relative mass of colliding objects (Gilden, 1991).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Gilden, 1991

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  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation
    § Combining Noisy Perception, Probabilistic Inference, and Newtonian Mechanics

    This approach, which here we call noisy Newton, was introduced in Sanborn, Mansinghka, and Griffiths (2009) and has been subsequently applied to other aspects of intuitive physics.

    “This approach, which here we call noisy Newton , was introduced in Sanborn, Mansinghka, and Griffiths (2009) and has been subsequently applied to other aspects of intuitive physics (Hamrick, Battaglia, &amp; Tenenbaum, 2011; Gerstenberg, Goodman, Lagnado, &amp; Tenenbaum, 2012; Smith &amp; Vul, 2012)”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites Sanborn, Mansinghka, and Griffiths, 2009

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    • cites Hamrick, Battaglia, & Tenenbaum, 2011

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    • cites Gerstenberg, Goodman, Lagnado, & Tenenbaum, 2012

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  • May combine two claims.

    Interpretationnone given
    § Motor Object Bias with Both Objects Moving

    The direct perception model predicts no bias, with the response proportion depending purely on the ratio of the masses.

    “The direct perception model again predicts no such bias, with the response proportion produced by the model depending purely on the ratio of the masses.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § Effect of Occlusion

    The occlusion predictions arise because inferred initial velocities are no longer constrained by observed values, allowing inferred values closer to the prior mode at zero; the smaller inferred sum ua + ub relative to va + vb causes a larger bias.

    “These predictions arise because the inferred initial velocities are no longer constrained by the observed values, allowing the inferred values to be closer to mode of the prior belief at zero. The smaller inferred sum of ua + ub relative to the inferred sum of va + vb , which is still constrained by observed values, causes a larger bias in the predicted choices.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Effect of Training

    Previous work has shown that the motor object bias is greatly reduced by training.

    “Previous work has shown that the motor object bias is greatly reduced by training (Jacobs et al., 2000; Runeson et al., 2000).”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites Jacobs et al., 2000

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    • cites Runeson et al., 2000

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    Premisecitation
    § Combining Noisy Perception, Probabilistic Inference, and Newtonian Mechanics

    The mapping between sensory information and interpretation is extremely complex.

    “Despite our apparent ease in interpreting the environment, the mapping between sensory information and interpretation is extremely complex.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Marr, 1982

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning
    § Motor Object Bias: Faster Moving Object Appears Heavier

    The prior distribution over initial velocities reduces the inferred sum of initial velocities, shifting the decision boundary that determines which object is judged heavier.

    “The prior distribution over initial velocities has reduced the inferred sum of initial velocities, and this shifts the decision boundary that determines the response of which object is heavier.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Premisecitation
    § Noisy Newton for Causal Inference

    The noisy Newton framework treats causal impression as inference about whether or not there is a causal relationship.

    “It treats causal impression as inference about whether or not there is a causal relationship.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites Griffiths & Tenenbaum, 2009

      Not checked in the free run.

    • cites Rips, 2011

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning
    § Comparison to Other Models of Causality

    The S&A model cannot predict a priori effects such as the asymmetry in response for high and low speed ratios and the influence of instructions.

    “but effects such as the asymmetry in response for high and low speed ratios and the influence of instructions cannot be predicted a priori by this model.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Interpretationnone given
    § Learning Newtonian Mechanics

    The learning process uses memories of people's experience with colliding objects in the world, which are guaranteed to be consistent with Newtonian mechanics, to stand in place of the noisy Newton model.

    “The idea is to use the memories of people's experience with colliding objects in the world - which are guaranteed to be consistent with Newtonian mechanics - to stand in place of the noisy Newton model.”
    Quote in the paperNot a substantial claim
    • Rests on an assumption: Newtonian mechanics is a good description of each stored collision event.

  • May combine two claims.

    Interpretationreasoning
    § Other Effects Using Colliding Objects

    A higher prior probability of tunneling rather than launching could produce the tunneling effect in the noisy Newton framework, so that when evidence is weak the prior bias toward objects missing each other would produce the causal impression of tunneling.

    “A higher prior probability of tunneling rather than launching could produce this effect in the noisy Newton framework, so that when the evidence is weak the prior bias toward objects missing each other would produce the causal impression of tunneling.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Interpretationreasoning
    § Learning Newtonian Mechanics

    Infants can judge whether displays are above or below threshold and are surprised if a series of below threshold events is followed by one above threshold.

    “Applying this implementation to the dishabituation experimental designs usually used in studies of causality with infants would mean that infants can judge whether displays are above or below threshold and are surprised if a series of below threshold events is followed by one above threshold.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationnone given
    § General Discussion

    The noisy Newton framework can be easily extended to a variety of judgments using different types of stimuli; all that is required is to characterize the sensory noise and how the stimuli should behave using Newtonian mechanics.

    “This framework can be easily extended to a variety of judgments using different types of stimuli all that is required is that we characterize the sensory noise as well as how the stimuli should behave using Newtonian mechanics.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationnone given
    § Other Effects Using Colliding Objects

    For displays that gave the causal impression of triggering, if an object activates its own motion in response to another object, its velocity should not depend on the speed of the first object.

    “However, for displays which gave the causal impression of triggering, if an object activates its own motion in response to the presence of another object, its velocity should not depend on the speed of the first object.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation
    § Other Effects Using Colliding Objects

    Participants do not report that the projectile object stopped the motor object, only that the motor object set the projectile object into motion.

    “A dissociation between force and causality is that participants do not report that the projectile object stopped the motor object, only that the motor object set the projectile object into motion (Michotte, 1963; White, 2006).”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites Michotte, 1963

      Not checked in the free run.

    • cites White, 2006

      Not checked in the free run.

  • May combine two claims.

    Interpretationown data
    § Other Effects Using Colliding Objects

    The noisy Newton framework is not limited to one type of judgment as the heuristic model is, but can predict both people's judgments of relative mass and impression of causality.

    “We have presented evidence that the noisy Newton framework is not limited to one type of judgment as the heuristic model is, but can predict both people's judgments of relative mass and impression of causality.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationreasoning
    § Learning Newtonian Mechanics

    Assuming events cluster together, latent clustering of this sort of statistical structure is a route toward predicting the infant dishabituation results.

    “Assuming these events do cluster together, latent clustering of this sort of statistical structure is a route toward predicting the infant dishabituation results.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: Events in the world cluster together.

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Interpretationnone given
    § Other Effects Using Colliding Objects

    The causality framework used is extensible to other causal impressions such as entraining and triggering, though they do not all correspond to simple Newtonian mechanics.

    “The causality framework we used is extensible to these other impressions, though they do not all correspond to simple Newtonian mechanics.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation
    § Other Effects Using Colliding Objects

    A sound played at or near the time of collision increased the causal impression, while a constant sound that disappeared only at the time of collision did not have an effect.

    “However, it was shown that a sound played at or near the time of collision increased the causal impression, while a constant sound that disappeared only at the time of collision did not have an effect.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Sekuler, Sekuler, and Lau (1997)

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationreasoning
    § Other Effects Using Colliding Objects

    The noisy Newton framework can explain causal capture by assuming participants use motion cues to group the display of four objects into two pairs of two objects.

    “We can hazard an explanation for this result from the noisy Newton framework as well, by assuming that participants use motion cues to group the display of four objects into two pairs of two objects”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: Participants use motion cues to group the display of four objects into two pairs of two objects.

  • May combine two claims.

    Interpretationcitation
    § Other Effects Using Colliding Objects

    Bounciness judgments could be modeled within the noisy Newton framework as estimates of the coefficient of restitution, but would have to account for how some physical variables appear more correlated with bounciness judgments and motor control than others.

    “Given this correlation, we could model bounciness judgments within the noisy Newton framework as estimates of the coefficient of restitution, but would have to account for how some physical variables appear more correlated with bounciness judgments and motor control than others”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites Siegler, Bardy, & Warren, 2010

      Not checked in the free run.

    • cites Warren et al., 1987

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Premisenone given
    § Other Effects Using Colliding Objects

    Causal impressions of triggering depend on an energy source within the stationary object, not just momentum transferred from the motor object.

    “Causal impressions of triggering depend on an energy source within the stationary object, not just momentum transferred from the motor object.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationreasoning
    § Other Effects Using Colliding Objects

    The noisy Newton framework can be extended to accommodate extra sources of information because observed variables are noisy, leaving room for additional variables to provide more information about the state.

    “The noisy Newton framework can also be extended to accommodate extra sources of information. Because we assume our observed variables are noisy, there is always room for additional variables to provide more information about what state generated the observed variables.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisereasoning
    § Learning Newtonian Mechanics

    The noisy Newton model differs from Friedman and Forbus (2009) because it represents variables quantitatively.

    “The noisy Newton model differs from this approach because it represents variables quantitatively.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Friedman and Forbus (2009)

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning
    § Other Effects Using Colliding Objects

    This overlap result is consistent with participants having a prior belief that colliding objects do not overlap too much, and this prior belief resulting in a reduction of perceived overlap when there is contextual evidence that a launching event occurred.

    “This is consistent with participants having a prior belief that colliding objects do not overlap too much, and this prior belief resulting in a reduction of the perceived overlap when there is contextual evidence that a launching event occurred.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation
    § Other Effects Using Colliding Objects

    Displays with partial or complete overlap alone gave the causal impression of tunneling; when an unambiguous launching event was presented nearby, participants underestimated the amount the objects overlapped.

    “Displays were presented in which one set of objects partially or completely overlapped and these displays alone gave the causal impression of tunneling. However, if an unambiguous launching event was also presented nearby, participants underestimated the amount that the objects overlapped.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Scholl & Nakayama, 2004

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Other Effects Using Colliding Objects

    Natsoulas (1960) found that the larger object of a pair was judged to be the heavier object more often, as would be expected from experience with the environment.

    “The influence of size on relative mass judgments was studied by Natsoulas (1960) who found that the larger object of a pair was judged to be the heavier object more often, as would be expected from our experience with the environment.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Natsoulas (1960)

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning
    § Other Effects Using Colliding Objects

    The prior bias toward tunneling is environmentally plausible because if there is reasonable uncertainty about the depth of the objects in the display and the objects are not too large, it is more likely that the objects miss each other rather than collide.

    “This prior bias is environmentally plausible because if there is reasonable uncertainty about the depth of the objects in the display and the objects are not too large, it is more likely that the objects miss each other rather than collide.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation
    § Other Effects Using Colliding Objects

    Scholl and Nakayama (2002) showed that two spatially and temporally neighboring events could influence one another; a tunneling event paired with a nearby launching event changes perception of tunneling to launching (causal capture).

    “Scholl and Nakayama (2002) showed how two spatially and temporally neighboring events could influence one another. A display may appear to be a tunneling event alone, but when paired with a nearby launching event, the perception of tunneling changes to one of launching.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Scholl and Nakayama (2002)

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S4 (based).

    Interpretationreasoning
    § Learning Newtonian Mechanics

    Learning that events in the world should be described as different hypotheses does not necessarily require innate knowledge; infants could form latent clusters of different types of objects, such as those that move mechanistically and those that move under their own power.

    “Learning that events in the world should be described as different hypotheses does not necessarily require innate knowledge, instead infants could form latent clusters of different types of objects, such as those that move mechanistically and those that move under their own power.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Premisecitation
    § Other Effects Using Colliding Objects

    White (2009) described how judgments people make about forces are divided into force and resistance, depending on which object is perceived to act upon the other.

    “Investigating people's judgment of force alone, White (2009) described how the judgments people make about forces are divided into force and resistance, depending on which object in perceived to act upon the other.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites White (2009)

      Not checked in the free run.

  • May combine two claims.

    Premisecitation
    § What Sort of Knowledge of Mechanics Do We Have?

    Participants predict that a ball dropped from a moving object will fall straight downwards, but when shown animated balls dropping from moving objects, they tend to pick the object moving forward as the correct option.

    “Likewise, while participants predict that a ball dropped from a moving object will fall straight downwards (McCloskey et al., 1983), when shown animated balls dropping from moving objects, they tend to pick the object moving forward as the correct option (Kaiser et al., 1992).”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites McCloskey et al., 1983

      Not checked in the free run.

    • cites Kaiser et al., 1992

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Future Directions

    Both Schlottmann and Anderson (1993) and Michotte (1963) found that collisions with delays of tens of milliseconds produced the best causal impressions.

    “Both Schlottmann and Anderson (1993) and Michotte (1963) found that collisions with delays of tens of milliseconds produced the best causal impressions.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites Schlottmann and Anderson (1993)

      Not checked in the free run.

    • cites Michotte (1963)

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S1 (asserted), S2 (checkable), S3 (load-bearing).

    Interpretationreasoning
    § Future Directions

    The combination of Newtonian physics and Bayesian inference underlying the framework will be useful in accounting for people's inferences in a wide range of settings.

    “Going beyond simple collisions, we anticipate that the combination of Newtonian physics and Bayesian inference that underlies our framework will be useful in accounting for people's inferences in a wide range of settings.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing). May combine two claims.

    Interpretationreasoning
    § Future Directions

    People have to make inferences about properties of objects based on observed behavior as a basic component of planning and executing motor actions, suggesting that the scope of noisy Newtonian models must be wider than simple collisions.

    “People have to make inferences about the properties of objects based on the observed behavior of those objects as a basic component of planning and executing motor actions, suggesting that the scope of noisy Newtonian models must be wider than just the simple collisions that we have focused on in this paper.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § What Sort of Knowledge of Mechanics Do We Have?

    Researchers have proposed that our understanding of mechanics reflects formal pre-Newtonian systems of ideas, such as Aristotelian or medieval impetus theories.

    “Researchers have proposed that our understanding of mechanics reflects formal pre-Newtonian systems of ideas, such as Aristotelian (diSessa, 1982; Shanon, 1976) or medieval impetus theories (Hubbard &amp; Ruppel, 2002; Kozhevnikov &amp; Hegarty, 2001; McCloskey, 1983) of mechanics.”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites diSessa, 1982

      Not checked in the free run.

    • cites Shanon, 1976

      Not checked in the free run.

    • cites Hubbard & Ruppel, 2002

      Not checked in the free run.

  • Classified as probably not a substantial claim. May combine two claims.

    Premisenone given
    § Future Directions

    The classical approximation used in the implementation for causality impressions assumed that the duration of contact between objects was zero, while the forces that act between objects are not instantaneous.

    “The classical approximation that we used in our implementation for causality impressions assumed that the duration of contact between objects was zero, while the forces that act between objects are not instantaneous.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Future Directions

    One explanation is that people derive causal impressions when events occur together in iconic memory.

    “One explanation is that people derive causal impressions when events occur together in iconic memory (White, 1988).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites White, 1988

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S1 (asserted), S3 (load-bearing).

    Premisecitation
    § What Sort of Knowledge of Mechanics Do We Have?

    A proposed explanation for biases and how they change with observing animations is that people can only reason about one-dimensional quantities.

    “A proposed explanation for our biases and how they change with observing animations is that people can only reason about one-dimensional quantities (Proffitt &amp; Gilden, 1989).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Proffitt & Gilden, 1989

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S4 (based).

    Interpretationreasoning
    § What Sort of Knowledge of Mechanics Do We Have?

    We could have local knowledge of Newtonian mechanics that corresponds to our perceptual variables, but not be able to project it onto other representations of the problem.

    “However, we could also have local knowledge of Newtonian mechanics that corresponds to our perceptual variables, but not be able to project it onto other representations of the problem.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Interpretationcitation
    § Other Effects Using Colliding Objects

    The split of force into two roles could be due to a dissociation of the common meaning of force from the meaning used by physicists, but the difference in strengths is a more fundamental deviation of force judgments from physical force.

    “The split of force into two roles could be due to a dissociation of the common meaning of force from the meaning used by physicists (Talmy, 1988), but the difference in strengths is a more fundamental deviation of force judgments from physical force (White, 2006).”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites Talmy, 1988

      Not checked in the free run.

    • cites White, 2006

      Not checked in the free run.

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation
    § Future Directions

    Contact durations very commonly experienced by participants are on the order of tens of milliseconds: around 30 ms between a finger and a light switch and around 100-150 ms for a well-practiced keypress.

    “Contact durations that very commonly experienced by participants are on the order of tens of milliseconds: around 30 ms between a finger and a light switch (Maij, Grave, Brenner, &amp; Smeets, 2011) and around 100-150 ms for a well-practiced keypress (Kello, Beltz, Holden, &amp; Van Orden, 2007).”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites Maij, Grave, Brenner, & Smeets, 2011

      Not checked in the free run.

    • cites Kello, Beltz, Holden, & Van Orden, 2007

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Interpretationreasoning
    § What Sort of Knowledge of Mechanics Do We Have?

    This local knowledge could be innate or learned, but would predict that accuracy in these tasks would diminish as we distance ourselves from the variables with which we are familiar.

    “This knowledge could be innate or learned, but would predict that our accuracy in these tasks would diminish as we distance ourselves from the variables with which we are familiar.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S2 (checkable).

    Interpretationreasoning
    § What Sort of Knowledge of Mechanics Do We Have?

    To explain dissociations in reasoning in the noisy Newton framework may require placing limits on the generality of the prior information.

    “To explain these dissociations in reasoning in the noisy Newton framework may require us to place limits on the generality of the prior information.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Premisecitation
    § What Sort of Knowledge of Mechanics Do We Have?

    These proposals have had difficulty explaining how people's responses appear to reflect different systems of ideas depending on the particular problem.

    “However, these proposals have had difficulty explaining how people's responses appear to reflect different systems of ideas depending on the particular problem that they have been given (Ranney &amp; Thagard, 1988).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Ranney & Thagard, 1988

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Premisecitation
    § What Sort of Knowledge of Mechanics Do We Have?

    This echoes the weak KSD approach, in which people only have an accurate conception of Newtonian mechanics within situations that match our terrestrial experiences.

    “This echoes the weak KSD approach, in which people only have an accurate conception of Newtonian mechanics within situations that match our terrestrial experiences (Gilden, 1991; Warren et al., 1987).”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites Gilden, 1991

      Not checked in the free run.

    • cites Warren et al., 1987

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S1 (asserted), S3 (load-bearing).

    Interpretationreasoning
    § Future Directions

    The noisy Newton model can be extended to more realistic collisions by using detailed dynamical simulations to generate prior distributions, rather than only using the closed-form solution studied.

    “The noisy Newton model can be extended to more realistic collisions by using these simulators to generate the prior distributions, rather than only using the closed-form solution we have studied here.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation
    § What Sort of Knowledge of Mechanics Do We Have?

    People are poor at reasoning about a ball that has followed a curved path, but are much more accurate at reasoning about water that has passed through a curved hose or about videos of balls traveling through tubes.

    “While people are poor at reasoning about a ball that has followed a curved path (McCloskey et al., 1980), they are much more accurate at reasoning about water that has passed through a curved hose (Kaiser, Jonides, &amp; Alexander, 1986) or about videos of balls traveling through tubes (Kaiser, Proffitt, &amp; Anderson, 1985).”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites McCloskey et al., 1980

      Not checked in the free run.

    • cites Kaiser, Jonides, & Alexander, 1986

      Not checked in the free run.

    • cites Kaiser, Proffitt, & Anderson, 1985

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S1 (asserted), S3 (load-bearing).

    Interpretationreasoning
    § Future Directions

    An explanation using the noisy Newton framework would need to tie contact durations of tens of milliseconds to real-world stimuli that remain in contact that long.

    “An explanation using the noisy Newton framework would need to tie contact durations of tens of milliseconds to real-world stimuli that remain in contact that long.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning
    § Conclusions

    The rational model goes beyond heuristic accounts in providing a way to understand how people might derive such a model from experience, and hence be helped by training, make decisions if information is missing, and by providing a single framework in which analyses of relative mass judgments can be unified with experiments on perceptual causality and other judgments.

    “It also goes beyond these heuristic accounts in providing a way to understand how people might derive such a model from experience, and hence be helped by training, make decisions if information is missing, and by providing a single framework in which analyses of relative mass judgments can be unified with experiments on perceptual causality and other judgments as well.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Future Directions

    Others have recently presented results suggesting that people may be able to stochastically simulate physical events for more complex sets of objects, providing a forward model of physical causality.

    “Others have recently presented results suggesting that people may be able to stochastically simulate physical events for more complex sets of objects, providing a forward model of physical causality that could support inferences about unobserved variables in a way that is very similar to our noisy Newton framework (Gerstenberg et al., 2012; Hamrick et al., 2011; Smith &amp; Vul, 2012).”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites Gerstenberg et al., 2012

      Not checked in the free run.

    • cites Hamrick et al., 2011

      Not checked in the free run.

    • cites Smith & Vul, 2012

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductown data
    § Replication of Experiment 1 of Todd and Warren (1982)

    In the replication of Experiment 1 of Todd and Warren (1982), four participants were discarded due to a computer error.

    “Four participants were discarded due to a computer error.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationnone given
    § Appendix C: Explanation for Predictions of the Heuristic Model

    The final speed heuristic depends entirely on the magnitude of the ratio of the final velocities, while whether object a ricochets depends on the sign of the final velocity ratio.

    “The final speed heuristic depends entirely on the magnitude of the ratio of the final velocities, while whether object a ricochets depends on the sign of the final velocity ratio.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S2 (checkable), S4 (based). May combine two claims.

    Interpretationreasoning
    § Conclusions

    Over the course of cognitive development, people learn how to deftly interact with and reason about a physical world that is often well described in Newtonian terms, so our unconscious physical intuitions must be in some harmony with physical law.

    “On the other hand, over the course of cognitive development, people learn how to deftly interact with and reason about a physical world that is often well described in Newtonian terms, so our unconscious physical intuitions must be in some harmony with physical law.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning
    § Appendix C: Explanation for Predictions of the Heuristic Model

    The discrepancy between the heuristic model's prediction and the data for e = 0.1 cannot be removed by fitting parameters to individual participants and averaging, because it is due to a structural property of the heuristic model.

    “as it is due to a structural property of the heuristic model; the discrepancy cannot be removed by fitting parameters to individual participants and averaging.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductown data
    § Replication of Experiment 1 of Todd and Warren (1982)

    In the replication of Experiment 1 of Todd and Warren (1982), no feedback was given to participants during the experiment.

    “No feedback was given to participants during the experiment.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning
    § Appendix C: Explanation for Predictions of the Heuristic Model

    On the right-hand side of the discontinuity in the final velocity ratio, |vb| > |va|, indicating that ma > mb by the final speed heuristic.

    “On the right-hand side of the discontinuity, | vb | &gt; | va | , indicating that ma &gt; mb by the final speed heuristic.”
    Quote in the paperNot a substantial claim
96 of 96

  • The authors state this as an assumption.

    People have an internal representation of physical constraints.

    “we assume that people have an internal representation of physical constraints.”

  • The authors state this as an assumption.

    People appropriately combine prior knowledge constrained by Newtonian mechanics with noisy sensory information to make inferences about the physical situation.

    “We then assume that people appropriately combine this prior knowledge that is constrained by Newtonian mechanics with noisy information from the sensory system to make inferences about the physical situation.”

  • The authors state this as an assumption.

    The probability of any stimulus arising from random movement is equal.

    “As a simplification, we can assume that the probability of any stimulus arising from random movement is equal (though this depends on the scaling of the space)”

  • The authors state this as an assumption.

    The bodies are perfectly rigid, so the smallest gap between them is zero and the time delay between the motor object stopping and the projectile object beginning to move approaches zero; the prior distribution for both time delay and gap has all its mass on zero.

    “If the bodies are perfectly rigid, then the smallest gap between them will be zero and neither will deform during the collision. Also, for rigid objects the time delay between the motor object stopping and the projectile object beginning to move approaches zero (Stronge, 2000). We will thus take a distribution with its entire mass on zero as our prior distribution for both time delay and gap”

  • The authors state this as an assumption.

    The masses are equal in both conditions of the first causality experiment.

    “this is used to represent the assumption that the masses are equal, which participants in both conditions of this experiment were instructed to believe.”

  • The authors state this as an assumption.

    The noise for gap and time delay approximately follows Weber's law.

    “Here we parameterize the noise for gap and time delay in the same way we did for velocities, as approximately following Weber's law, as is consistent with psychophysical studies (Andrews &amp; Miller, 1977; Ekman, 1959).”

  • The authors state this as an assumption.

    The model assumes symmetric noise.

    “Despite assuming symmetric noise, the model produces asymmetries due to the assumption that collisions exhibit coefficients of restitution between zero and one.”

  • The authors state this as an assumption.

    The model assumes a prior distribution over the coefficient of restitution e that allows values less than 1.

    “As the model assumes a prior distribution over e that allows values less than 1 and noise in the velocity observations, it predicts a positive skew in the choice function.”

  • The authors state this as an assumption.

    The prior distribution over the sum of velocities has its mode at zero.

    “the motor object bias is due to having a prior distribution over the sum of velocities with the mode at zero.”

  • The authors state this as an assumption.

    People have an accurate conception of Newtonian mechanics.

    “For both mass judgments and causality judgments, the noisy Newton framework depends on an accurate conception of Newtonian mechanics. If this assumption is accepted”

  • The authors state this as an assumption.

    People can store a small number of past experiences with collisions.

    “First, we assume that people can store a small number of past experiences with collisions.”

  • The authors state this as an assumption.

    People can assess the perceptual similarity of a given collision with each stored memory, using a similarity function derived from perceptual noise.

    “Second, we assume that people can assess the perceptual similarity of a given collision with each of these stored memories, using a similarity function derived from perceptual noise.”

  • The authors state this as an assumption.

    The experiences chosen are drawn randomly and will be representative of the environmental prior.

    “by assuming the experiences chosen are drawn randomly they will be representative of the environmental prior.”

  • The authors state this as an assumption.

    Events in the world cluster together.

    “Assuming these events do cluster together”

  • The authors state this as an assumption.

    Participants use motion cues to group the display of four objects into two pairs of two objects.

    “by assuming that participants use motion cues to group the display of four objects into two pairs of two objects”

  • The paper relies on this without support.

    Newtonian mechanics is a good description of each stored collision event.

    “As Newtonian mechanics is a good description of each of these collisions”

  • The authors state this as an assumption.

    Observers perceive the true mass ratio, and this true mass ratio is corrupted by zero-median noise.

    “The direct perception model assumes that observers perceive the true mass ratio and that this true mass ratio is then corrupted by zero-median noise (Runeson, 1983; A. Cohen, 2006).”

  • The authors state this as an assumption.

    The mass ratio lies on a logarithmic scale and Gaussian noise with mean zero and variance s^2 is added to the logarithmic transform of the true mass ratio on each trial.

    “The mass ratio is assumed to lie on a logarithmic scale and Gaussian noise with mean zero and variance s 2 is added to the logarithmic transform of the true mass ratio on each trial.”

  • The authors state this as an assumption.

    Lower masses are more likely than higher masses.

    “the prior distributions on the masses reflects the assumption that lower masses are more likely than higher masses.”

  • The authors state this as an assumption.

    Slower velocities are more likely than faster velocities.

    “The priors we place on the true, noiseless initial velocities reflect the belief that slower velocities are more likely than faster velocities; this is a standard assumption in Bayesian models of velocity perception (Weiss et al., 2002; A. A. Stocker &amp; Simoncelli, 2006).”

  • The authors state this as an assumption.

    Object a begins on the left-hand side of the display and object b begins on the right-hand side of the display.

    “under the assumption that object a begins on the left-hand side of the display and object b begins on the right-hand side of the display”

  • The authors state this as an assumption.

    No external force is acting upon the system of two objects.

    “with the assumption that no external force is acting upon the system of two objects.”

  • The authors state this as an assumption.

    People probability match to their internal belief distribution.

    “making the assumption that people probability match to their internal belief distribution (Vulkan, 2000).”

  • The authors state this as an assumption.

    The prior probabilities of the two hypotheses (causal event vs random) were equal.

    “The prior probabilities of the two hypotheses were assumed to be equal”

  • The authors state this as an assumption.

    The prior on the coefficient of restitution gave equal weight to all possible values.

    “The prior on the coefficient of restitution gave equal weight to all possible values”

  • The authors state this as an assumption.

    The noiseless final velocities are given by Newtonian mechanics.

    “Given the initial velocities, the prior on the noiseless final velocities are the values given by Newtonian mechanics”
26 of 26

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Bayesian models of cognition have primarily flourished as explanations of the complex dependency of behavior on the environment in domains including intuitive physics, causal learning, perception, motor control, and language.

    “Bayesian models of cognition have primarily flourished as explanations of the complex dependency of behavior on the environment in domains including intuitive physics, causal learning, perception, motor control, and language [1-10]”

    From Bayesian Brains without Probabilities (2016) · cites this paper as [2]

Cites

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Authors
Sanborn, A. N., Mansinghka, V. K., & Griffiths, T. L.
Affiliations
  • University of Warwick (GB)
  • Massachusetts Institute of Technology (US)
  • University of California, Berkeley (US)
ORCID
Venue
Psychological Review
Publisher
American Psychological Association (APA)
Published
2013
Volume
120
Issue
2
Pages
411-437
ISSN
  • 0033-295X (ISSN-L)
  • 1939-1471
DOI
10.1037/a0031912
OpenAlex
W2040908702
Cited by
189
References
126
Citations by year
2026: 15 · 2025: 15 · 2024: 13 · 2023: 22 · 2022: 10 · 2021: 14 · 2020: 14 · 2019: 11 · 2018: 12 · 2017: 20 · 2016: 12 · 2015: 17 · 2014: 8 · 2013: 6
FWCI
8.01
Type
journal article
Language
en
Open access
closed
Locations
  • Psychological Review (publishedVersion)
  • PubMed (publishedVersion)
  • Warwick Research Archive Portal (University of Warwick) (acceptedVersion)
  • UWA Profiles and Research Repository (UWA) (submittedVersion)
Funders
  • National Science Foundation
  • Royal Society USA
  • Gatsby Charitable Foundation
  • Air Force Office of Scientific Research (FA-9550-07-1-0351, FA-9550-10-1-0232)
Topics
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Visual perception and processing mechanisms
  • Social Sciences › Psychology › Experimental and Cognitive Psychology › Categorization, perception, and language
  • Social Sciences › Decision Sciences › General Decision Sciences › Decision-Making and Behavioral Economics
Keywords
intuitive physics, classical mechanics, causal judgment, Bayesian inference, sensory noise, physical uncertainty, heuristics, physical reasoning, unified model
MeSH terms
Bayes Theorem, Child, Data Interpretation, Statistical, Humans, Infant, Judgment, Models, Psychological, Motion Perception, Perceptual Masking, Physics, Problem Solving, Psychophysics, Models, Statistical, Causality, Intuition, Mechanics, Uncertainty

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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-09.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-09.

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