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

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

Related In: Results  -  Collection

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pone.0119794.g001: Environmental data.‘Uniform distribution’ predictions (a) differ markedly from the observed power function relationship between volume and density (b). For ease of viewing, (c) displays the natural log-transformed scatterplot of the power function relationship between volume and density for man-made objects, showing a significant inverse correlation between log volume and log density.
Mentions: True volume and weight data was collected for 195 liftable, man-made, everyday objects, and used to calculate their density: d = w/V where d is density, w is weight, and V is volume. Technically, d = m/V, where m is mass; however, because w = m × a, where a is acceleration (in this case, acceleration is due to gravity, which is constant), and because weight and mass are used interchangeably in everyday discourse, weight is used as a functional equivalent to mass in this experiment. We used the property of density because it is defined as the very relationship we were interested in (that between volume and weight) and density estimation is often mentioned as a crucial factor in preparation for lifting objects [5]. In contrast to predictions of independence between volume and density (Fig. 1a), a power function relationship between volume and density was observed for the man-made object datasets (Dataset 1 in S1 Dataset and Dataset 2 in S2 Dataset and Dataset 3 in S3 Dataset) (Fig. 1b), so a log transform was computed to reveal the nature of the inverse correlation between volume and density for each of the three man-made object datasets (R1 = -.4673, p = .002; R2 = -.6290, p << .001; R3 = -.7917, p << .001), as well as the pooled man-made object data (R = -.5721, p << .001) (Fig. 1c). To compare directly between artificial and natural objects, the same calculation was also performed for a dataset of natural, liftable objects (Dataset 4 in S3 Dataset) (R4 = -.0048, p = .981), but revealed no significant relationship between volume and density (Fig. 2a and 2b). A final comparison between a randomly-selected subset (n = 28) of objects in Dataset 2 in S2 Dataset (liftable artificial object statistics garnered from online retailers) and a set of unliftable artificial objects with dimensions and weight data collected in the same manner (Dataset 5 in S2 Dataset) also revealed the persistence of the inverse correlation for the subset of liftable artificial objects (R2,subset = -.8390, p << .001) but not the unliftable ones (R5 = .0396, p = .8416) (Fig. 2c and 2d). Thus, these data revealed that, for liftable man-made objects, density is distributed not uniformly, but instead as a power function of volume: Smaller liftable artificial objects are denser than larger ones, and by more so the smaller they are. This relationship does not hold for natural objects or unliftable man-made objects. (See also S1 Fig. for non-log-transformed data.)

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.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.

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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