(A) Main phases of the experiments. Left. An inventory was constructed by arranging abstract shapes into horizontal and vertical pairs. True pairs behaved as objects: their shapes always appeared together, and in the same relative spatial configuration, and were hard to pull apart physically. Pseudo pairs served as controls: they had consistent visual statistics but were as easy to pull apart as two separate objects (indicated by the small separation between their shapes). Colouring and separation for illustration only, participants saw all shapes in grey-scale during exposure and testing, with no gaps between them, so that no visual cues separated the pairs of a compound scene (as shown on screens in the center and right panels). Center. During the exposure phase, participants experienced a sequence of visual scenes showing compound objects consisting of several pairs. The way the image displayed on the screen was constructed from the inventory is shown above each screen in colour for illustration. In the first experiment (top), participants observed compound scenes each constructed from three true pairs of the inventory. In the second experiment (bottom), on each trial, a compound scene consisting of two pairs (true or pseudo) was displayed and participants were required to pull the scenes apart in one of two directions as shown. A bimanual robotic interface (Howard et al., 2009) was used so that participants experienced the force at which the object broke apart (breakage force shown in red) but, crucially, visual feedback did not reveal the identity of true and pseudo pairs (see Materials and methods). Thus, only haptic information distinguished the true and pseudo pairs as the force required depended on the underlying structure of the scene. Right. In both experiments, participants finally performed two tests. First, in the haptic pulling test (bottom), participants were asked to pull with the minimal force which they thought would break apart a scene, composed of true or pseudo pairs (in both directions). We measured this force by ‘clamping’ the scene so that no haptic feedback was provided about the actual breakage force (black clamps at the corners of the scene). Crucially, the visual display also did not reveal the identity of true and pseudo pairs. Second, in the visual familiarity test (top), participants were asked to select which of two scenes presented sequentially appeared more familiar. One scene contained a true pair and the other a chimeric pseudo pair. Selecting the true pair counted as a correct response, but no feedback was given to participants as to the correctness of their choices. (B) Timeline of events in haptic exposure and test trials (displayed force traces are from representative single trials). Left. Haptic statistical exposure trials had scenes consisting of combinations of true and pseudo pairs of the inventory (top). After a fixed amount of time, the scene was masked (black square covering the scene), then pulling was initiated (‘pull’ instruction was played), and the scene was unmasked and shown as separated once the pulling force (green arrows and curve) exceeded the breakage force (orange line). Right. In the haptic pulling test, participants were asked to generate a pulling force which they thought would be just sufficient to break the scene apart (ideally the breakage force corresponding to the scene, orange dashed line). The scenes were constructed using the pairs of the inventory without any visible boundary between them and held together by virtual clamps at the corners of the scene (top). Pulling was initiated (‘pull’ instruction), and once the participant’s pulling force (green arrows and curve) exceeded a 5 N threshold (dashed black line), three beeps were played at 1 s intervals (notes). The clamps remained on until the end of the trial (top), so the scene never actually separated, and after the third beep (at which the pulling force was measured) participants were asked to ‘relax’. See Materials and methods for details of the variant used in the haptic exposure task.