Smaller = Denser, and the Brain Knows It: Natural Statistics of Object Density Shape Weight Expectations

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.

The Size-Weight Illusion is not anti-Bayesian after all: a unifying Bayesian account

“…This joint probability of a density relationship and volume relationship p ( R , y ) is defined in line with previously reported data ( Peters, Balzer & Shams , 2015 ).…”

“…For the simulations, we set , , , , ρ R 2 = − 0.95, ρ R 3 = 0.95, p ( R 1 , y ) = 0.8, p ( R 2 , y ) = 0.15, and p ( R 3 , y ) = 0.05. These a priori probabilities p ( R , y ) for the three R relationships are qualitatively consistent with the everyday object data collected by Peters, Balzer & Shams ( 2015 ), with the change that in the real world objects are rarely the same density if they have different sizes. However, in SWI studies the material of the objects is visually similar, which artificially inflates the probability that they will have the same density.…”

“…It is thus hidden from immediate access for human observers, but has been repeatedly shown to be crucial in heaviness estimation ( Buckingham & Goodale , 2013 ; Cross & Rotkin , 1975 ; Ross & Di Lollo , 1970 ). It has also been shown that visual estimates of material affect predictions of an object’s weight ( Ellis & Lederman , 1998 ), and that visual size estimation alone can play a role in density estimation prior to lifting an object, such that smaller objects are judged to be denser than larger objects even when visual material is held constant ( Peters, Balzer & Shams , 2015 ). Other investigations have reported that well-learned material-density priors interact with sensorimotor memory of previous lifts in producing heaviness percepts ( Baugh et al , 2012 ), and that a single representation of typical object density based on visual size alone may underlie the SWI ( Buckingham et al , 2016 ; Buckingham & Goodale , 2013 ).…”

Object size can influence perceived weight independent of visual estimates of the volume of material

“…It has been suggested that density information, plays a role in the size-weight illusion 14 and it is suggested to be a result of the densities of the two differently sized objects being unexpectedly different 15 16 . Of course, in experiments usually one of the two objects is manipulated to achieve equal masses despite size variations.…”

The material-weight illusion is a Bayes-optimal percept under competing density priors

“…We use a joint prior over the density relationship R and volume estimation y , since usually in the daily environment they are highly correlated and the brain seems to be capable of utilizing this kind of natural statistic (Peters, Balzer & Shams, 2015) . We indeed used some version of a joint Gaussian prior in modeling SWI (Peters, Ma & Shams, 2016) ; however, in the MWI, since the density relationship is explicitly suggested by the visual material and not implicitly suggested by each object's size, we assume these are independent of each other.…”