Mass Is All That Matters in the Size–Weight Illusion Myrthe A. Plaisier1,2*, Jeroen B. J. Smeets2 1 Cognitive Neurosciences Department, Bielefeld University, Bielefeld, Germany, 2 Faculty of Human Movement Sciences, VU University, Amsterdam, The Netherlands Abstract An object in outer space is weightless due to the absence of gravity, but astronauts can still judge whether one object is heavier than another one by accelerating the object. How heavy an object feels depends on the exploration mode: an object is perceived as heavier when holding it against the pull of gravity than when accelerating it. At the same time, perceiving an object’s size influences the percept: small objects feel heavier than large objects with the same mass (size– weight illusion). Does this effect depend on perception of the pull of gravity? To answer this question, objects were suspended from a long wire and participants were asked to push an object and rate its heaviness. This way the contribution of gravitational forces on the percept was minimised. Our results show that weight is not at all necessary for the illusion because the size–weight illusion occurred without perception of weight. The magnitude of the illusion was independent of whether inertial or gravitational forces were perceived. We conclude that the size–weight illusion does not depend on prior knowledge about weights of object, but instead on a more general knowledge about the mass of objects, independent of the contribution of gravity. Consequently, the size–weight illusion will have the same magnitude on Earth as it should have on the Moon or even under conditions of weightlessness. Citation: Plaisier MA, Smeets JBJ (2012) Mass Is All That Matters in the Size–Weight Illusion. PLoS ONE 7(8): e42518. doi:10.1371/journal.pone.0042518 Editor: Friedemann Paul, Charite´ University Medicine Berlin, Germany Received November 9, 2011; Accepted July 10, 2012; Published August 9, 2012 Copyright: 2012 Plaisier, Smeets. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: Funding provided by VICI grant (MaGW 453-08-004) for JBJS from the Netherlands Organization for Scientific Research. Rubicon grant from NWO in collaboration with the Marie Curie Cofund (MAGW 446-10-012) for MAP. www.nwo.nl. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. * E-mail: myrthe.plaisier@uni-bielefeld.de Introduction The size-weight illusion is the well-known effect that large objects are perceived to be lighter than small objects of the same weight [1]. Although this illusion originally was discovered as a multi–sensory phenomenon in which the visually perceived size of an object influences its perceived weight, the illusion also occurs in the absence of vision if haptic size cues are available [2]. This shows that the illusion is not a multi-sensory one per se. It is based on a general effect of perceived size on perceived weight. In fact, showing an object before lifting, but not during lifting already triggers the illusion [3]. Similarly, there exists also a material– weight illusion [4,5]: objects that are perceived to be made out of a denser material are perceived to be lighter than objects with the same size and weight that appear to be made out of a less dense material. Apparently, our percept of how heavy an object feels is biased by prior knowledge about the general relationship between object properties and the weight of an object. This suggests that the size–weight illusion occurs because we have learned that there is a correlation between size and weight. This idea is supported by a study in which it was shown that the illusion can be reversed: repeatedly lifting a set of objects manufactured such that the smaller objects had more mass than the larger objects for several days reduced the illusion and finally reversed it [6]. Combining information sources, such as size and weight, is common in human perception. It has been shown that when judging the size of an object through vision and touch simultaneously, the two estimates are integrated in a statistically optimal fashion [7]. This means that the combined percept is more precise than either of the two percepts independently. In fact, one can even learn to integrate two unrelated perceptual signals such as stiffness and luminance [8]. Sometimes, several information sources are combined with prior assumptions. This can be modelled using Bayesian statistics [9]. In the case of the size– weight illusion a perceptual estimate of size is combined with an estimate of the weight together with a prior for large objects being heavier. The way these information sources are combined in the size–weight illusion is fundamentally different from the previous examples, as it makes the percept less accurate and can be regarded as anti-Bayesian [10]. A prior for larger objects being heavier would suggest that a larger lifting force is applied for lifting large objects than for lifting small objects [11]. It has been shown that initially larger lifting forces are applied when lifting large objects, but the difference in the applied forces disappears within a few lifts while the perceived weight difference remains constant [12,13]. This suggests that the illusion is not caused by applying more force when lifting a large object than when lifting a smaller object. Since the illusion is usually referred to as size-weight illusion, one would expect it to be related to the weight of an object. Note that weight is another word for the gravitational force acting upon an object, which is proportional to the (gravitational) mass of an object. The mass of an object can also be experienced without weight through inertial forces proportional to the (inertial) mass acting during acceleration of an object [14]. This is why the mass of an object can be judged in the absence of gravity, such as in outer–space. Since gravitational and inertial masses of an object are the same (Einstein’s equivalence principle), one might expect that the two types of mass appear to be the same for the perceptual system. Surprisingly, an object is perceived to be almost twice as heavy through perception of gravitational pull than through PLoS ONE | www.plosone.org 1 August 2012 | Volume 7 | Issue 8 | e42518