Mental Imagery of Free Fall: We do not see acceleration, but a constant speed

Mental Imagery of Free Fall: Does a Falling Apple Accelerate in Our Minds? Daniel Bratzke and Rolf Ulrich. Timing & Time Perception, Jan 27 2021. https://doi.org/10.1163/22134468-bja10022

Abstract: The present study examined whether people’s mental imagery of falling objects includes the acceleration due to the earth’s gravitational force. To investigate this question, we used two different tasks, a height estimation and a fall-time estimation task. In the height estimation task, participants were presented with different free-fall times and had to indicate the corresponding heights from which the object fell to the ground. In the fall-time estimation task, participants had to produce the fall time associated with free falls from different heights. In contrast to the law of free fall, our results are more consistent with a linear than with an accelerated relationship between height and fall time. Thus, the present results suggest that mental imagery of an object’s free fall does not represent the gravitational acceleration due to gravity.

Keywords: Intuitive physics; mental imagery; time perception

4. Discussion

In the present study, we investigated whether people’s mental imagery of free fall (of an object) represents the acceleration due to gravity. Irrespective of the estimation task (i.e., whether participants estimated heights or fall times), the results were more consistent with a linear than with an accelerated relationship between height and fall time. This suggests that the mental imagery of an object’s free fall does not represent the acceleration due to gravity and thus resembles the Aristotelian rather than the Newtonian model of kinematic phenomena.

The present results are in line with the previous results by Gravano et al. (2017), who showed that the mental imagery of throwing a ball against the ceiling and catching it on the rebound was compatible with microgravity, irrespective of whether participants imagined the ball’s motion under terrestrial or space conditions. They explained their results by assuming that participants used a visual mode of imagery, which does not represent the gravitational acceleration because visual processing of accelerating/decelerating motion is rather poor (e.g., Werkhoven et al., 1992). A related possibility why people do not represent the gravitational acceleration is that the Aristotelian model is an appropriate approximation of the largest parts of many free falls. Namely, under conditions of air resistance, falling objects rapidly attain a constant level of speed. Thus the initial phase of acceleration is too short to be carefully observed without instruments (see e.g., Rovelli, 2015). For example, the terminal velocity of an apple (m =0.15 kg, d =7 cm) would be V∞=35.70 m/s. However, 75% of this terminal velocity is attained already after 3.54 s or 53.70 m. According to this explanation, the mental representation of free fall does not include gravitational acceleration because the change of speed during the acceleration phase cannot be perceived. As a consequence, constant velocity is attributed to all phases of free fall.

As already mentioned in the Introduction, a study by Huber and Krist (2004) reported fall-time estimates that are consistent with an acceleration of imagined free fall. In their study, participants saw a ball rolling off a horizontal surface and had to estimate the time until the ball fell onto a marked landing point. Importantly, the fall of the ball was hidden from the participants’ view by an occluding curtain so that they had to imagine the fall of the ball. In a production task, participants started the motion of the ball and had to indicate the point in time when the ball hit the ground. In a judgment task, participants had to judge the flight time by using a circular rating scale. In both tasks, the height and the distance to the landing point were manipulated. The produced flight times showed a pattern that matched the normative rule very well. In the judgment task, however, the judgments deviated from the predicted pattern. The authors explained this dissociation between produced and judged flight times by arguing that only in the production task (but not in the judgment task) mental imagery was based on a timing-responsive representation (e.g., Schwartz & Black, 1999) of free fall, which helped to predict the point in time when the ball hit the ground.

One could argue that the production tasks used in Huber and Krist (2004) and the present study were comparable so that one should have expected accelerated functions also in the present study. There was, however, one possibly crucial difference between the two tasks. In the production task of Huber and Krist, the participants saw the ball moving on the horizontal surface until it was occluded, which was not the case for the apple in the current study (and also not in the judgment task of Huber and Krist). The perception of this initial movement of the ball might be crucial to activate dynamic mental imagery (see also Huber & Krist, 2004). Thus, it remains unclear whether participants would represent the acceleration in the free-fall scenario of the present study if one provided a similar initial motion cue as in the study of Huber and Krist.

A related issue regarding the present study is whether participants actually imagined the free fall. Although they were instructed to do so, they could have followed the simple rule: the higher the height the longer the fall time and vice versa. Such a strategy would be virtually indistinguishable from mental imagery of a linear relationship between the two variables. Additionally, one could argue that the height estimation task used in the present study was not optimal for inducing mental imagery because participants had to indicate the height from which the apple fell. Possibly, mental imagery would have been easier or more natural in a scenario where the apple falls from a fixed height and participants indicate the height the apple reaches at the end of the free fall (even though this scenario can also be considered somewhat unnatural as the apple would not simply stop falling before it reaches the ground). In fact, two participants were excluded from data analyses because they apparently understood the task in the latter way. We used the former scenario because we wanted to make the height estimation task as similar to the fall-time estimation task as possible. In future studies, the assessment of eye movements could potentially shed some light on the involvement of mental imagery in free-fall scenarios like the present one (for a discussion of the relationship between eye movements and mental imagery, see Huber & Krist, 2004).

In conclusion, the present study suggests that the intuitive physics of free fall as assessed by estimates of height and fall time during mental imagery of an object’s free fall does not represent the gravitational acceleration. A plausible explanation for this result is that the change of speed during the rather short acceleration phase of free fall cannot be visually detected and hence people (incorrectly) attribute constant speed to all phases of free fall. Nevertheless, future studies may provide an answer to the question of whether people are capable of imaging the acceleration of falling objects when initial motion cues are available.