Since gravity affects the flight of moving objects, one area in which gravity has been given some attention is interceptive timing. Modeling in this area aims at adequately predicting human performance in a variety of catching tasks. Traditionally, the proposed models have strongly relied on information available directly from the optic flow, such as tau (Lee, 1976; Lee and Reddish, 1981) which signals the time to contact of an object under some visual conditions (constant velocity, head-on approach) and consists of combining the visual angle and its rate of expansion. Binocular optic information such as binocular disparity (Rushton and Wann, 1999; Gray and Regan, 2004) can also contribute to extract time-to-contact (TTC) information. As more and more evidence became available for the fact that physical prior information like known size (López-Moliner et al., 2007; López-Moliner and Keil, 2012) or object familiarity (Hosking and Crassini, 2010) seems to be used by the perceptual system to more accurately estimate TTC (that is the remaining time until an object reaches a predefined target such as the observer, a certain point on a screen, etc.), another physical variable came into focus: (earth) gravity. Gravitational biases have been reported for free falling targets (McIntyre et al., 2001; Zago et al., 2005, 2008, 2010, 2011) as well as for parabolic trajectories (Bosco et al., 2012; Diaz et al., 2013; Delle Monache et al., 2014; de la Malla and López-Moliner, 2015; Lacquaniti et al., 2015, validated a gravity based model for parabolic interception brought forward in Gómez and López-Moliner, 2013), objects on ramps (Mijatović et al., 2014), and even for objects that move horizontally (De Sá Teixeira et al., 2013; De Sá Teixeira, 2016). Interestingly, there seem to be certain constraints as to when computations can access the internal representation of gravity; when the so called “idiotropic vector” along the vertical body axis, for example, is not aligned with the direction of gravity, the contribution of the internal representation of gravity decreases (De Sá Teixeira, 2014; De Sá Teixeira and Hecht, 2014). In absence of physical gravity, on the contrary, the use of internally represented gravity information is not necessarily suspended (McIntyre et al., 2001).

In addition to this behavioral evidence, some studies have delivered brain imaging evidence to the case. One study measured brain activation of subjects viewing objects fall downwards with 1g acceleration and compared it to activation when viewing 1g upwards acceleration (that is, −1g). The previously mentioned performance advantages for +1g conditions were here accompanied by differential brain activation in insular cortex, temporoparietal junction, premotor and supplementary motor areas, middle cingulate cortex, postcentral gyrus, posterior thalamus, putamen and medial cerebellum (Indovina et al., 2005). This was replicated by Miller et al. (2008) to account for different variations such as context; and another study added 0g motion to the comparison and found similar differential activations between 1g and 0g and between 1g and −1g (Maffei et al., 2010). Furthermore, a causal role of the temporo-parietal junction was established through TMS: hyperpolarization of this area lead to a significant performance decrease when catching objects governed by 1g, but not for objects governed by −1g (Bosco et al., 2008). Similarly, a lesion study (Maffei et al., 2016) indicated that patients with brain damage in perisylvian areas performed significantly worse than healthy subjects at intercepting targets dropping with 1g, but not for targets moving upwards with 1g acceleration.

A second important vein of research at the intersection of gravity and cognition is motor planning and control. Hypogravity and hypergravity affect different motor parameters of catching, grasping and pointing. An increase in variability under earth-discrepant gravity conditions (Bock et al., 1992; Crevecoeur et al., 2010) as well as systematic biases such as pointing undershoot in microgravity and overshoot in hypergravity (Bringoux et al., 2012) points towards the attunement of the perceptuomotor system to earth gravity. Unlike TTC estimation mechanisms, motor commands have proven relatively adaptable to new gravity conditions: (Augurelle et al., 2003) provided evidence for the rapid development of an appropriate and constant grip force for microgravity and hypergravity phases in parabolic flight. Furthermore, the central pattern generator, a mechanism co-responsible for driving rhythmic movements such as walking, modifies issued motor commands for rhythmic arm movements according to the gravitational context (White et al., 2008). While instructions from the experiments partially overruled central pattern generator commands in microgravity, it generally adapted limb oscillations to the resonant frequency, that is the energetically optimal frequency for the gravitational environment. Finally, several studies indicate an optimal integration of gravity and other cues for example for single-joint arm movements (Gaveau et al., 2014) and for vertical pointing movements (Crevecoeur et al., 2009). The use of the internal model seems to be at least partially motivated by the goal of minimizing energy spent on movements (Gaveau et al., 2016). The human motor system hence adapts strongly to its dynamic environment and uses sensory input about gravity to plan movements accordingly.

Another set of computations to which gravity contributes crucially is the estimation of body orientation. Astronauts reported that while working on inclined surfaces in a lunar 0.166g environment they were sometimes overcome by the sensation that the ground was actually plain. Other astronauts speak of the so called inversion illusion in which, in zero-gravity, they occasionally have the impression of being turned upside-down with respect to their environment (Lackner and DiZio, 2000). These reports underline the common-sense notion that the direction of gravity is crucial for our perception of orientation and suggest that, when gravity cues grow weaker, the contributions of other sources of information have a higher impact on the final percept.

Apart from direction and strength of gravity, two additional factors influence the sense of verticality: visual cues from the environment, such as the orientation of the insides of a space shuttle, and the so called idiotropic vector which is aligned with the current body orientation (Harris et al., 2012). In the recent past, the contribution of gravity has been investigated to some extent. de Winkel et al. (2012) investigated verticality judgments in hypogravity and found that, under gravities as high as 0.57g, verticality was assigned according to visual cues such as the orientation of the environment, rather than according to the gravitational downwards pull. However, there was huge inter-subject variation: one subject judged verticality under gravities as low as 0.03g according to the direction of gravity instead of their body axis. Interestingly, this threshold correlated with age, with older subjects being less sensitive to the gravitational pull. In hypergravity on the contrary, verticality was consistently judged correctly. These results contrast with Harris et al. (2012) who could not find significant differences in body orientation estimates between 1g and a lunar gravity of 0.166g, while a previous study of the same group reported a significant difference between 1g and 0g (Dyde et al., 2009). However, this study did not report on inter-subject variability, so it is only partially in discordance with the high gravity perception thresholds reported for some of the participants from de Winkel et al. (2012). Whatever the exact gravitational threshold value for verticality judgments may be, the picture drawn by these studies is that gravity bears an important role in how we relate with our physical environment. Especially low gravities just below lunar gravity seem to be problematic, as orientation perception is impaired, but the gravitational downwards pull is still in place. In addition to other factors like the weight of the space suit and limited visual field (Harris et al., 2012), this may be an explanation for why astronauts are prone to falling over when walking or working on the moon surface. Several other sub-areas of body orientation perception have been investigated: participants consistently overestimate roll tilt in centrifuge-induced hypergravity (Clark et al., 2015); both the apparent horizon and the visual straight ahead are reported lower than under 1g conditions (Cian et al., 2014); and the discrepancy between perceived longitudinal axis and actual position was greater in weightlessness during parabolic flights than during control conditions on earth (Clément et al., 2007). Last but not least, gravity may play a fundamental role in multimodal sensory integration as an invariant reference frame (Scotto Di Cesare et al., 2014).

Furthermore, gravity has been suggested as a mediator between spatial and temporal cues (Lacquaniti et al., 2015): for example, participants judged more precisely the time that elapsed during the gravity-governed free fall of an object than for the same movement in upwards or horizontal directions (Moscatelli and Lacquaniti, 2011). What is more, biological motion is to a large extent dependent on the pendulum-like movements of the organism’s limbs, whose frequency and amplitude are in turn governed by gravity. Biological motion is therefore a good example of gravity being on the interface between time and space, a relationship that is also leveraged by the sensory system for the perception of biological movements. In a task where participants had to place a simulated moving animal in the depth of a given scene, they usually chose the depth that made the animal’s movement congruent with biological movements under earth gravity (Jokisch and Troje, 2003). Although physical differences between motion under moon gravity (0.166g) and speed matched motion under earth gravity (1g) are not very marked, Maffei et al. (2015) reported that observers could easily judge if a movement pattern was governed by moon gravity or by earth gravity. Additionally, certain areas (perisylvian areas, frontal and occipital cortex, hippocampus and putamen) were differentially activated when observing motion governed by earth gravity in comparison to motion governed by lunar gravity. Furthermore, both human and nonhuman vertebrates show a preference for right side up biologically moving stick figures over upside down stick figures shortly after birth (Vallortigara and Regolin, 2007; Simion et al., 2008). Since, conceptually, the difference between right side up and upside down condition can be reduced to gravity congruent and gravity incongruent motion (see Indovina et al., 2005 for a similar argument), a possible conclusion is that humans have an innate, gravity-mediated attention bias for spotting other animals. However, another experimental approach to the issue, namely a looking-time-surprise paradigm, provided evidence that 7 month olds expect dropping objects to accelerate and upwards moving objects to decelerate, while at 5 months they do not (Kim and Spelke, 1992). Simion et al. (2008) attributed this divergence in results to the fact that Kim and Spelke (1992) task involved predictions about moving objects, while their own task involved animate entities, for which babies have been shown to have an attention preference.

Furthermore, gravity effects have been discovered for many tasks involving spatial inferences and spatial reasoning. (Clément et al., 2008) showed that exposure to microgravity leads participants to perceive 3D cubes as taller, thinner and shallower than under earth gravity. In the same fashion, when asked to adjust a 3D cube for it to look “normal”, the result was a shorter, wider and deeper object. Another study (Villard et al., 2005) provided evidence that several optical illusions (such as the Reversed-T, Müller-Lyer, Ponzo and Hering illusions), which rely on the effects of linear perspective, were less likely to occur in 0g than in 1g. Other illusions, that are not connected to linear perspective (such as the Zöllner and Poggendorf illusions), however, were not impacted by microgravity. The authors attribute this difference to the idea that gravity mediates the role of linear perspective in 3D processing. Moreover, while on earth there is usually a preferred interpretation of ambiguous perspective figures (with one being perceived in 70% of the cases), this preference disappears after 3 months in space (with both being perceived about 50% of the time), with earth 70:30 homeostasis being reestablished within a week after reentry (Clément et al., 2015). Moreover, the perceived direction of gravity influenced judgments about the stability of objects that were on the verge of falling off a table (Barnett-Cowan et al., 2011). Finally, also the critical aperture, that is the smallest width of a door just wide enough to pass through, was judged lower in weightlessness during parabolic flights (Bourrelly et al., 2016). The overall evidence presented strongly supports the thesis that bodily felt gravity influences spatial reasoning. Further results suggest that even some other cognitive tasks, such as face recognition, may be impaired, while performance for others, like same-different judgments for abstract objects, are unaffected by microgravity (see Grabherr and Mast, 2010 for more details).

Results from these five fields—catching and TTC estimation, motor control, body orientation estimation, the perception of biological movements and spatial reasoning—suggest that our perceptual apparatus might be attuned to earth gravity even more strongly and in many more ways than previously thought. They also make a compelling case that there is no neat separation between visually and bodily perceived gravities and their computational applications in perceptual processes: primarily visual tasks, such as depth perception, are influenced by bodily gravity cues, and primarily bodily tasks, such as verticality and straight ahead judgments, are influenced by visual gravity cues, a phenomenon upon which Section “Gravity in a Bayesian Framework of Perception” is expanding.

Experiments conducted in space are the most ecological method in the study of gravity-based perception. Due to the obvious technical difficulties, (McIntyre et al., 2001) remains to the present day the only interception study conducted in space. Early during the Neurolab space shuttle mission—on Day 3, Astronauts performed an interception task with an object that was moving downwards towards their hand with relatively low, constant speeds (that is, governed by 0g) of 0.7, 1.7 and 2.7 m/s. While accuracy of the eventual catch was perfect due to task design (McIntyre et al., 2003), the participants initiated their hand movements consistently earlier with regards to TTC than under 1g conditions on Earth. Moreover, they displayed an abnormal pattern of forearm rotation: after the early onset, they reversed the rotation—potentially because they corrected their TTC expectations through online visual cues—and caught the ball at a lower forearm rotation angle than on earth.

The only parabolic flight study to test catching performance under non-earth gravity (Senot et al., 2012; see Section “Gravity Information in Vision Related Processing: What is It Useful and Used for?” for more details) found that in the weightlessness phases, subjects expected downwards moving targets to decelerate and upwards moving targets to accelerate. Apart from the conclusions that this experiment allows about the multisensory nature of gravity perception, it is striking that a perceived upwards gravity leads subjects to anticipate a concordant target movement. After all, previous studies indicate that subjects will nearly always use an internal model of earth gravity, that is, they will expect downwards moving objects to accelerate and upwards moving objects to decelerate, and there is contradicting evidence to the fact that this internal model remains intact even when bodily cues to the opposite are present (McIntyre et al., 2001). One possible explanation is that vestibular cues may lead subjects to believe that they are turned upside down, an interpretation which is, however, counter-evidence by the fact that when vestibular and other bodily gravity cues are weak, visual cues about body orientation tend to maintain the upper hand (see Section “Gravity in a Bayesian Framework of Perception”). The more likely explanation is that, as each period of weightlessness is preceded by a period of hypergravity, otolith receptors react to the sudden cease of hypergravity with signals that indicate an upwards gravity, as a consequence of which weightlessness after hypergravity is interpreted as upwards gravity. And in fact, the authors found evidence for corresponding otolith receptor responses (see Section “Adaptation to Catching Under Zero Gravity Conditions” for further details on this study).

3D environments in virtual reality remain, due to their favorable ratio of accessibility and ecologicality, the most important method in visual gravity perception. A series of studies (Zago et al., 2004, 2005; Zago and Lacquaniti, 2005b) established that humans expect objects that move downwards to accelerate with 1g gravity, even when their velocity is constant, as indicated by the observation that TTC for 0g targets was consistently underestimated. In the Punching Task design, participants had to punch a ball dropping behind a screen, whose location was indicated by a projection on the screen, in the moment it reached the lower edge of the screen. The semi-virtuality of the task can be seen as an asset, as it increases engagement of the participant and ecological validity. Further evidence comes from Senot et al. (2005) who found that, when acceleration and direction of the ball were congruent with earth gravity, error rates were lower than in incongruent trials. Interestingly, the overall lowest error rates were recorded for the constant speed condition. Big parts of the literature predict the gravity prior to be tapped in the case of free-falling target interception, which should result in larger interception errors for objects that move downwards with constant velocities. This inconsistency can, however, be explained by the fact that accelerating objects had a higher final velocity than those dropping at constant speed.

Then again, there is the simplest category of 2D tasks based on on-screen presentation. Here, results are seemingly contradictory: some studies report the use of a gravity prior, as for example Mijatović et al. (2014) who found that participants were judging time of arrival correctly for balls rolling down familiar geometrical shapes (an inclined plane) under 1g conditions, but overestimated time of arrival for −1g conditions, that is, when the ball was rolling up the plane. Similarly, Zago et al. (2010) found that performance for targets on a partially occluded, vertical trajectory was consistently better for 1g than for 0g or −1g; likewise, for partially occluded parabolic trajectories, arrival of the ball was spatially and temporally underestimated for 0g, judged correctly for 1g and overestimated for 2g (Bosco et al., 2012). Zago et al. (2004), on the contrary, reported that participants’ performance in TTC estimation for balls dropping on screen was a reasonable fit for the predictions of a first order model for TTC estimation that does not take into account gravity, while a second model including gravity did not match human performance in this task. To unify these results, it has been argued that in 2D presentation, the internal model of gravity is only accessed if pictorial cues are present to put motion into perspective or if parts of the trajectory are occluded (Zago et al., 2009).

Two caveats, brought on by Baurès et al. (2007), retain some relevance up to the present date. First of all, the study of gravity’s role in interception has often been limited to free falling objects. In the wake of this observation, some recent studies investigated parabolic and other trajectories: trajectories. Bosco et al. (2012) introduced a combination of weightlessness and hypergravity perturbances and occlusions in 1g trajectories and reported earth gravity biases for interception; (Delle Monache et al., 2014) used eye tracking in a similar design and showed predictive effects of an internal presentation of gravity. A paradigm based on an initial parabolic trajectory and several bounces in combination with eye tracking revealed that gaze movements were consistent with earth gravity based predictions of the ball’s position (Diaz et al., 2013). La Scaleia et al. (2015) reported a gravity bias for parabolic interception even when sensory information prior to initiation of the parabolic trajectory indicated an earth-discrepant gravity of 0.2g. And finally, a gravity based model for parabolic interception has been established (Gómez and López-Moliner, 2013) and partially validated (de la Malla and López-Moliner, 2015). Nonetheless, effects of earth-discrepant gravities, especially other than 0g, on naturalistic trajectories have yet to be studied more thoroughly.

Second, when studying an internal model of gravity one also has to take into account the confounding properties of air drag: effectively, it represents a progressive decrease in downward acceleration with increasing velocity with considerable effects on trajectories (d’Avella et al., 2011). While again Gómez and López-Moliner (2013) propose a way of integrating air resistance into their model of parabolic target interception, a relatively accurate and precise gravity prior (as brought forward by authors such as Lacquaniti and Zago) seems contradictory with effectively observed acceleration values of under 9.81 m/s². And in fact, Flavell (2014) suggests that the gravity prior may actually not be set at 1g exactly, but rather at a value between 1g and just below 1g. However, these findings are consistent with an alternative explanation based on the existence of two priors: one relatively inflexible gravity prior and an adaptable air drag prior with information about air resistance and drag coefficients of known objects. This second prior would add to the size prior put forward in López-Moliner et al. (2007). A separate representation of air drag has the additional advantage that it can be employed for both vertical and horizontal movement components, while an integrated gravity and air drag prior is only viable for free fall. While evidence for the existence of a friction prior for movement on surfaces has been presented (Hubbard, 1995; Amorim et al., 2015), the role of air resistance and drag-relevant features of objects in perception remain to be studied more systematically.

Notwithstanding these reservations, many different approaches—from 2D presentation up to experiments conducted in space—have revealed gravitational biases in a big range of computations, which supports the claim that gravity is represented in the brain and accessed in a variety of computations.

All the results presented in Section “Attunement to Earth Gravity: Interception Performance Under Earth-Discrepant Gravity Conditions” are based on performance by naive observers, that is, observers that had not received any training at all, nor in the tested gravity, nor in other earth-discrepant gravities. To our knowledge, there are two studies that have investigated to what extent experience in a 0g environment (McIntyre et al., 2001) or explicit training with earth-discrepant, visually perceived gravities (Zago et al., 2004, 2005) can normalize catching in gravities other than 1g. The McIntyre study was mentioned before as the one example in permanent weightlessness in space. In addition to testing in the beginning of the participants’ stay in space, the measures were taken again on the ninth and on the 15th day. No explicit training with the actual task was conducted, but training effects through experience with the general 0g environment can be assumed. And in fact, the result was a naturalization of catching movements: while hand movements, after 3 days just like after 9 and after 15 days, were consistently initiated too early with respect to TTC, they smoothened over time. However, after 15 days they still did not resemble the velocity profile for catching under earth conditions. While the smaller final velocity grants enough time for a slower, smoother interceptive movement, these results still suggest that, at least when both bodily and visual cues indicate a 0g environment, adaptation is possible. Nonetheless, it can be assumed to be a relatively slow process.

Unlike McIntyre, (Zago et al., 2005; Zago and Lacquaniti, 2005a) tested training effects in virtual reality, that is, only visual input served for perceptual adaptation while bodily cues were indicating 1g. They explored whether subjects in their punching design (see Section “Virtual Reality”) could learn to deal with 0g conditions, while at the same time tackling that question whether, in case of positive results, the internal 1g model was adapted or a second internal model for 0g was established. For this purpose, they used different protocols which interleaved 1g and 0g stimuli in different proportions of 0g stimuli (0%, 9%, 50%, 91% and 100%) over one (for the 50% protocol) or two training days (for the other protocols) while on the second day, the proportions of 0g and 1g stimuli was inversed (for example 91% on day 2 for the group that received the 9% protocol on day 1). A first important result is that, regardless of the protocol, performance for 0g improved very quickly, but then, after 5–6 trials, stagnated at an inferior rate in comparison to 1g interception. Also, performance and timing for 1g trials remained constant in every protocol; if the internal 1g model was adapted through training, then performance should worsen for 1g trials: TTC should be overestimated and movement initiation should be delayed. In the same manner, the adoption of a second, 0g model is rather unlikely as movement initiation trended asymptotically towards a value between naïve 0g catching performance and perfect 0g catching performance. Further analysis of the same data indicated that the observed data was, in principle, consistent with an intact 1g gravity representation. Instead the time threshold for movement initiation could have been lowered to the minimum made necessary by processing constraints; due to the uncertainty in the environment, the perceptual apparatus minimizes in this way the timespan for which it has to extrapolate the position of the ball using internal models of physical variables (such as velocity and gravity). And in fact, the plateau value for adaption to 0g interception was 123 m/s in the 50% protocol, which is consistent with previously observed visuo-motor delays for interception (Lacquaniti and Maioli, 1989a; Port et al., 1997).

However, the latter study has not gone uncriticized. Baurès et al. (2007) have pointed out several weak points of the experimental design. The most important disadvantage is a discrepancy in the admissible time window for successfully punching the target between the (virtual) ball displayed on the screen and the actual ball dropping behind the screen in the 0g condition. While both balls crossed the interceptive zone at the same time, they did so with different velocities. In the lowest initial velocity condition (0.7 m/s), the time subjects had to successfully punch the physical target was 24 ms, while the slower motion of the virtual target indicated a time window of 214 m/s. However, as pointed out in Zago et al. (2008), this discrepancy nearly disappeared in the highest initial velocity condition (4.5 m/s), while interception still happened too early. The effect observed by Zago et al. (2004, 2005) can thus not be reduced to different time windows. Baurès et al. (2007) furthermore point out a series of studies (Brenner et al., 1998; Brenner and Smeets, 2005) that suggests that interceptive movements adapt to the velocity of the target, so that different observed velocities during the trajectory influence interceptive movements. Zago et al. (2008) answered this criticism by referring to the fact that movement kinematics (movement speed, peak hand velocity) were constant across different initial velocities (Zago et al., 2005; Zago and Lacquaniti, 2005a). According to their interpretation, these movement parameters are evidence for an attunement to the kinematics of the ball falling behind the screen, thus lending support to the hypothesis of an internal model of gravity.

All in all, discrepancies between onscreen and real ball kinematics in Zago and Lacquaniti’s (2005a) 0g condition are a necessary consequence of the design, which could at least partially account for why participants’ performance in 0g tasks did not improve beyond a certain plateau. They can, however, in no way account for all evidence in favor of in internal model of gravity provided in this study.

Perceptual adaptation is generally necessary to deal with new environments and has, as an overarching topic, been treated thoroughly in the literature. One of the most promising frameworks to account for perceptual adaptation is Bayesian perception modeling. This application of Bayesian frameworks originated as a natural answer to the so called Inverse Problem: how does the perceptual system draw conclusions about the actual state of the world from ambiguous and noisy sensory information? This question has been formulated in terms of the concepts of “Encoding” (or “Representation”) and “Decoding” (or “Readout”; Gold and Ding, 2013). The Encoding of the information is what is reported by sensory organs and can be viewed in terms of neural activity in response to a stimulus. Through the process of Decoding, this neural activity is interpreted in order to derive a final percept to guide behavior. There are different strategies for decoding: for example, different sensorial inputs (e.g., information encoded by single neurons or populations of neurons) may be weighted according to their reliability and then combined. The modus operandi of Decoding in a Bayesian framework as the integration of a priori information, that is, information condensed from the subject’s previous experiences, with sensory information. The weighting of each is inversely related to the variance of the signal, that is, the lower the variance of a signal, the more precise it is, and the higher its weight for the a posteriori guess about the actual state of the world. The following expression is a formalization of this reasoning: (1)P (world|data)∝P (data/world)×P (world)

which reads as: the probability of the state of the world given the available sensory data (Posterior) corresponds to the probability of the data given a certain state of the world (Likelihood Term) multiplied by the Probability of the world being in a certain state (Prior).

Within this framework, perceptual adaptation can occur in two ways: changes to the likelihood or changes to the prior (Yamamoto et al., 2012). As the prior represents a history of past percepts, it is intuitive how adaptation on the level of the prior takes place: after finishing the processing of each percept, the prior is modified to reflect the difference between the posterior percept and the prior (Miyazaki et al., 2006) through a shift towards the posterior percept. Generally, the human perceptual system aims to minimize this difference, called “prediction error”, in order to prepare for future percepts (Friston, 2009, 2010), which is achieved through the integration of previous percepts in the prior. The adaptation of the prior provides the system with a more accurate representation of statistical properties of the world, allowing it to make more accurate sensory predictions and to minimize the prediction error. This mechanism accounts for attraction effects, that is for situations in which an adaptor shifts subsequent posterior percepts towards the adaptor. But not only the prior allows for changes, but also the likelihood can account for adaptation effects (Stocker and Simoncelli, 2006). In this case, the perceptual system focusses resources to cover the range of the adaptor in order to increase the reliability of sensory input within this range, thus shifting the posterior percept towards the likelihood. It has been suggested that in most cases both opposing mechanisms are at play, with statistical properties of the stimuli favoring one or the other (Yamamoto et al., 2012; Linares et al., 2016).

In a Bayesian framework, the likelihood function represents the signal provided by sensory organs. Unlike other sensory data such as luminosity or tone pitch, gravity is picked up by different sensory organs: vision, the vestibular system (otolith organs and semicircular canals), proprioception (receptors in muscles and tendons) and other sensory sources (e.g., for somatic cues from kidneys and the intestines); which under normal conditions are subsequently integrated into final percept of the gravity vector.

In the light of the existing empirical data it seems thus much more likely that gravity adaptation occurs at the level of the prior. However, previous studies indicating a slow or asymptotical adaptation do not support the notion of a standard prior that is easily changed with new, contradicting sensory input. While the gravity prior may be relatively plastic or not accessed at all for virtually/2D presented motion (Zago et al., 2004), this doesn’t hold for the more ecological case of real objects or objects presented in an immersive virtual reality environment. Under such circumstances, it resembles the so called strong priors such as the light-from-above or the bigger-is-heavier priors (Adams et al., 2004; Peters et al., 2016). These priors are representations of ubiquitous and persistent properties of the external world, such as the fact that light usually comes from above or that bigger objects are usually heavier, which have been present throughout the whole of humanity’s evolution and every individual human’s development. In Bayesian terms, our lifelong experience with these representations reduces the represented variance of this state of the world to a minimum, making it highly reliable. As a consequence, the weighting of such priors is so high that they easily overrule contrary sensory information represented by the likelihood. Figure 1 provides a visualization of this reasoning.

Nonetheless, evidence has been brought forward that other priors, such as the light-from-above prior or the bigger-is-heavier prior can at least to a certain degree be adapted through experience (Adams et al., 2004; Flanagan et al., 2008). One important difference between these priors and the earth gravity prior is, however, that the necessary sensory information (direction of light and weight/size) is readily available to the perceptual apparatus, while at least the visual system is highly insensitive to accelerations. The second difference is the multimodal nature of sensory gravity input: while the case of conflicts between visually and bodily perceived gravities still needs further empirical investigation, it is warranted to speculate that a full adaptation to gravities other than 1g can only occur when both visual and bodily sensory gravity input indicate the same earth-discrepant gravity value.

In the framework outlined above, the role of the internal representation of gravity, or gravity prior, is to aid the decoding process of encoded information by calibrating noisy or ambiguous visual information. In order to illustrate the potential role of assuming a gravity prior in the decoding process of sensory information, we simulate the process of inferring the horizontal velocity component of a parabolic trajectory, which is not directly sensed. This inference is carried out based on two optical variables, the elevation angle (γ) and its temporal rate of change (γ˙). The elevation angle is the angle between the observer’s straight ahead and his line of sight on the object. Its value at time t is determined by the following equation: (2)γ(t)=tan−1(gt2νh)

with g being the underlying gravity and v_h being the horizontal velocity which is, as air drag is neglected for the scope of this simulation, constant throughout the trajectory. Its temporal rate of change is, accordingly, the temporal derivative of this optical variable and indicates how the visual angle changes over the course of a trajectory. Its value at time t is determined by the following equation: (3)γ(t)=γ′(t)=2gνhg2t2+4νh2

Figures 2B,C show the development of these optic variables over the first 200 m/s of a trajectory. Note that the elevation angle (γ) refers to an angular value encoded on the retina of the observer and not to the angle at which the ball is launched relative to the horizontal plane. Note also that the object is approaching the observer frontally on a parabolic trajectory. In order to carry out the simulations, we used 56 different parabolic trajectories (Figure 2A) resulting from combining eight horizontal velocities (from 3 m/s to 10 m/s) and seven gravity values (6.874, 7.856, 8.838, 9.820, 10.802, 11.784 and 12.766 m/s²). We defined corresponding tuning curves for γ and γ˙ that would encompass all possible values of these two optical variables for the time that we considered (0.2 s after motion onset). Figure 3A shows part of the range of the tuning curves (gray solid lines) that we used to encode γ˙. The covered range was from 0 rad to 1.0 rad for the elevation angle (γ) and from 0.1 rad/s to 2.2 rad/s for its temporal rate of change (γ˙). Within these ranges, there were 11 and 15 peaks for γ and γ˙, respectively and the standard deviation of the Gaussian curves was 0.1 in both cases.

We simulated 1000 trials in which the system was exposed to 1g and, in any one trial, we randomly selected one trajectory with one horizontal velocity and a gravity of 1g. After encoding γ and γ˙ for the sampled trajectory, we proceeded to recover the most likely value for the two optical variables (see below). Once the likely values for γ and γ˙ were estimated through Maximum Likelihood estimate (MLE), we selected all potential trajectories (including all gravities) that matched these values and compared the corresponding selected horizontal velocities with the one used in the encoding to compute the fraction of correct responses. We obtain two possible responses in each trial: one in which we did not take into account the gravity prior with MLE as sole decoding method, and the other in which the MLE was combined with the prior. In order to simulate a strong prior, we used a rather low standard deviation of 0.5 m/s²; unfortunately, there is no literature available about the precision with which the gravity prior is represented.