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Smaller = denser, and the brain knows it: natural statistics of object density shape weight expectations.

Peters MA, Balzer J, Shams L - PLoS ONE (2015)

Bottom Line: Interestingly, this "smaller is denser" relationship does not hold for natural or unliftable objects, suggesting some ideal density range for objects designed to be lifted.These results indicate that the human brain represents the statistics of everyday objects and that this representation can be quantitatively abstracted and applied to novel objects.Finally, that the brain possesses and can use precise knowledge of the nonlinear association between size and weight carries important implications for implementation of forward models of motor control in artificial systems.

View Article: PubMed Central - PubMed

Affiliation: Department of Psychology, University of California Los Angeles, 1285 Franz Hall, Box 951563, Los Angeles, California, 90095-1563, United States of America.

ABSTRACT
If one nondescript object's volume is twice that of another, is it necessarily twice as heavy? As larger objects are typically heavier than smaller ones, one might assume humans use such heuristics in preparing to lift novel objects if other informative cues (e.g., material, previous lifts) are unavailable. However, it is also known that humans are sensitive to statistical properties of our environments, and that such sensitivity can bias perception. Here we asked whether statistical regularities in properties of liftable, everyday objects would bias human observers' predictions about objects' weight relationships. We developed state-of-the-art computer vision techniques to precisely measure the volume of everyday objects, and also measured their weight. We discovered that for liftable man-made objects, "twice as large" doesn't mean "twice as heavy": Smaller objects are typically denser, following a power function of volume. Interestingly, this "smaller is denser" relationship does not hold for natural or unliftable objects, suggesting some ideal density range for objects designed to be lifted. We then asked human observers to predict weight relationships between novel objects without lifting them; crucially, these weight predictions quantitatively match typical weight relationships shown by similarly-sized objects in everyday environments. These results indicate that the human brain represents the statistics of everyday objects and that this representation can be quantitatively abstracted and applied to novel objects. Finally, that the brain possesses and can use precise knowledge of the nonlinear association between size and weight carries important implications for implementation of forward models of motor control in artificial systems.

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Human observers’ data, by condition and object type.Participants’ reported PV ratios are consistently smaller than EW responses, indicating a belief that smaller objects are denser than larger ones. Consistent with previous studies, PV consistently underestimates true volume, leading to PV responses larger than the true volume ratio between the objects (gray vertical line). EW ratios are consistently larger than PV ratios, indicating that subjects believe smaller objects are denser than larger objects, over and above any mis-estimation of volume.
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pone.0119794.g003: Human observers’ data, by condition and object type.Participants’ reported PV ratios are consistently smaller than EW responses, indicating a belief that smaller objects are denser than larger ones. Consistent with previous studies, PV consistently underestimates true volume, leading to PV responses larger than the true volume ratio between the objects (gray vertical line). EW ratios are consistently larger than PV ratios, indicating that subjects believe smaller objects are denser than larger objects, over and above any mis-estimation of volume.

Mentions: Consistent with previous studies [29], PV ratios did not approach true volume ratios, indicating consistent underestimation of volume (two-tailed t-tests against 0: tBlobs = 4.766, p << .001; tGreebles = 5.4994, p << .001; tCubes = 5.1265, p << .001). We next conducted a 2 (condition: EW vs. PV) x 3 (object type: Blobs, Greebles, Cubes) x 6 (pair: A:B, A:C, A:D, B:C, B:D, C:D) mixed design ANOVA. This analysis revealed a main effect of condition (F(1,18) = 7.542, p = .013) and pair (F(5,90) = 334.179, p < .001), and an interaction between condition and pair (F(5,90) = 3.334, p = .008), but no other significant effects (p > 0.05). The main effect of condition indicates that participants in the EW group consistently reported larger ratios than did participants in the PV group; the direction of this effect indicates that observers believed the smaller objects to be denser than the larger objects—over and above the typical underestimations of volume—which qualitatively matches the statistics of the environment. The main effect of pair indicates that participants reported different EW and PV ratios for the pairs of objects, and the interaction indicates that the degree to which EW ratios were larger than PV ratios varies by pair (Figs. 3 and 4).


Smaller = denser, and the brain knows it: natural statistics of object density shape weight expectations.

Peters MA, Balzer J, Shams L - PLoS ONE (2015)

Human observers’ data, by condition and object type.Participants’ reported PV ratios are consistently smaller than EW responses, indicating a belief that smaller objects are denser than larger ones. Consistent with previous studies, PV consistently underestimates true volume, leading to PV responses larger than the true volume ratio between the objects (gray vertical line). EW ratios are consistently larger than PV ratios, indicating that subjects believe smaller objects are denser than larger objects, over and above any mis-estimation of volume.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4358826&req=5

pone.0119794.g003: Human observers’ data, by condition and object type.Participants’ reported PV ratios are consistently smaller than EW responses, indicating a belief that smaller objects are denser than larger ones. Consistent with previous studies, PV consistently underestimates true volume, leading to PV responses larger than the true volume ratio between the objects (gray vertical line). EW ratios are consistently larger than PV ratios, indicating that subjects believe smaller objects are denser than larger objects, over and above any mis-estimation of volume.
Mentions: Consistent with previous studies [29], PV ratios did not approach true volume ratios, indicating consistent underestimation of volume (two-tailed t-tests against 0: tBlobs = 4.766, p << .001; tGreebles = 5.4994, p << .001; tCubes = 5.1265, p << .001). We next conducted a 2 (condition: EW vs. PV) x 3 (object type: Blobs, Greebles, Cubes) x 6 (pair: A:B, A:C, A:D, B:C, B:D, C:D) mixed design ANOVA. This analysis revealed a main effect of condition (F(1,18) = 7.542, p = .013) and pair (F(5,90) = 334.179, p < .001), and an interaction between condition and pair (F(5,90) = 3.334, p = .008), but no other significant effects (p > 0.05). The main effect of condition indicates that participants in the EW group consistently reported larger ratios than did participants in the PV group; the direction of this effect indicates that observers believed the smaller objects to be denser than the larger objects—over and above the typical underestimations of volume—which qualitatively matches the statistics of the environment. The main effect of pair indicates that participants reported different EW and PV ratios for the pairs of objects, and the interaction indicates that the degree to which EW ratios were larger than PV ratios varies by pair (Figs. 3 and 4).

Bottom Line: Interestingly, this "smaller is denser" relationship does not hold for natural or unliftable objects, suggesting some ideal density range for objects designed to be lifted.These results indicate that the human brain represents the statistics of everyday objects and that this representation can be quantitatively abstracted and applied to novel objects.Finally, that the brain possesses and can use precise knowledge of the nonlinear association between size and weight carries important implications for implementation of forward models of motor control in artificial systems.

View Article: PubMed Central - PubMed

Affiliation: Department of Psychology, University of California Los Angeles, 1285 Franz Hall, Box 951563, Los Angeles, California, 90095-1563, United States of America.

ABSTRACT
If one nondescript object's volume is twice that of another, is it necessarily twice as heavy? As larger objects are typically heavier than smaller ones, one might assume humans use such heuristics in preparing to lift novel objects if other informative cues (e.g., material, previous lifts) are unavailable. However, it is also known that humans are sensitive to statistical properties of our environments, and that such sensitivity can bias perception. Here we asked whether statistical regularities in properties of liftable, everyday objects would bias human observers' predictions about objects' weight relationships. We developed state-of-the-art computer vision techniques to precisely measure the volume of everyday objects, and also measured their weight. We discovered that for liftable man-made objects, "twice as large" doesn't mean "twice as heavy": Smaller objects are typically denser, following a power function of volume. Interestingly, this "smaller is denser" relationship does not hold for natural or unliftable objects, suggesting some ideal density range for objects designed to be lifted. We then asked human observers to predict weight relationships between novel objects without lifting them; crucially, these weight predictions quantitatively match typical weight relationships shown by similarly-sized objects in everyday environments. These results indicate that the human brain represents the statistics of everyday objects and that this representation can be quantitatively abstracted and applied to novel objects. Finally, that the brain possesses and can use precise knowledge of the nonlinear association between size and weight carries important implications for implementation of forward models of motor control in artificial systems.

Show MeSH