Learning by imitation is fundamental to human behavior, but not all observed actions are equally easy to imitate. To understand why some actions are more difficult to imitate than others, we examined how higher-order relationships among the components of a stimulus model influenced the fidelity with which an action could be observed and then reproduced. With static contours, perception and short-term memory are strongly influenced by contour geometry, particularly by the presence and distribution of curvature extrema. To determine whether analogous relationships among subcomponents of a seen action would be important in encoding the action for subsequent reproduction, we manipulated actions' spatio-temporal geometry. In three experiments, we measured imitation fidelity for sequences of randomly directed, linked motions of a disc. The geometry of the disc's motion path strongly affected the accuracy of subsequent imitation: When the disc moved along a trajectory whose components were fairly consistent in their directions, imitation was strikingly better than when with irregular, jagged trajectories. A second experiment showed that this effect depended not upon co-variation in stimulus models' spatial extent, but rather on the relationship between successive movement directions. In a final, learning experiment, subjects had multiple opportunities to view and reproduce each model. The effect of the model's geometry persisted throughout the learning process, suggesting that it does not depend upon variables such as familiarity or expectancy but is somehow inherent to the pattern generated by the disc's motion. Our findings suggest that when analyzing seen actions, the brain privileges regular, consistent curvatures, grouping components that form a coherent shape into a unified “chunk.” Inconsistencies among the directional components of a motion sequence cause the sequence to be chunked into additional components, which increases the load on working memory, undermining the fidelity with which the sequence can be imitated.

*θ*

_{1}, the orientation of

*S*

_{1}, the first segment, was chosen randomly from a uniform distribution of orientations:

*S*

_{2}to

*S*

_{5}, each segment's orientation is given by

*θ*is chosen randomly from a uniform distribution. The orientation difference between segments

*S*

_{1}and

*S*

_{2}establishes a local CW or CCW trend in the trajectory. For each subsequent segment

*S*

_{n}(

*n*= 3, 4, 5), we designate with a binary variable

*κ*

_{n−2}whether that segment's orientation conforms to the trend set by the previous two segments (segment is

*curvature-consistent*) or violates the trend (segment is

*curvature-inconsistent*). For the third segment, then

*κ*

_{n}= 1 represents consistency with the previous CW or CCW trend and

*κ*

_{n}= −1 represents a violation of the trend. Similarly,

*K*= {

*κ*

_{1},

*κ*

_{2},

*κ*

_{3}}, indicating the degree to which the disc's motion changes its course from CW to CCW and vice versa, with {1, 1, 1} defining an enclosed pattern and {−1, −1, −1} a constant “zig-zag.” For convenience, from this point on we shall use only the sign of

*K,*so that models will be classified as +++, −+−, −−−, etc. It is important to emphasize that for each value of

*K,*there exist many possible models;

*K*defines the general relationship between segments but does not explicitly constrain their orientations, so on each trial a completely novel sequence was presented. Figure 1B shows sample stimulus models for each one of the eight (2

^{3}) possible stimulus types.

*convexity*vs.

*concavity*(e.g., Barenholtz, Cohen, Feldman, & Singh, 2003; Bertamini, 2001) or

*positive extrema*vs.

*negative*

*extrema*(e.g., Feldman & Singh, 2005; Richards et al., 1986) to describe the direction of curvature with respect to the interior of the object or the figure. As none of our stimulus trajectories formed a closed contour, the trajectories' “interior” is only weakly defined. Therefore, we shall use the terms

*curvature consistency*and

*curvature inconsistency*to describe changes from CW to CCW motion (or vice versa). Thus, a segment that conforms to the trend (CW or CCW) established by the two preceding segments will be referred to as a

*consistent*segment, whereas an

*inconsistent*segment will describe a segment violating the previous CW or CCW relationship.

*p*< 0

*.*0001, two-way ANOVA). In the more consistent patterns, such as +++ and −++, the primacy effect is almost completely absent, whereas curves corresponding to the more inconsistent patterns, like −−− and +−−, are more reminiscent of the serial position curves ubiquitously reported in the serial recall literature (e.g., Agam et al., 2005, 2007; Avons, 1998; Crowder, 1970; Drewnowski, 1980; Drewnowski & Murdock, 1980; Haberlandt, Lawrence, Krohn, Bower, & Thomas, 2005). To gauge the overall effect of curvature inconsistencies on performance, we sorted the stimulus types into groups comprising sequences with no inconsistent segments (+++), one inconsistent segments (++−, +−+, −++), two inconsistent segments (+−−, −+−, −−+), and three inconsistent segments (−−−). As can be appreciated from Figure 2B, the number of curvature inconsistencies strongly affects imitation accuracy (

*p*< 0

*.*0015, one-way ANOVA).

*K*. For example, note how the inconsistency between the fourth and fifth segments in ++− sequences leads to a fundamentally different curve than +++ sequences, where the fifth segment is consistent with all previous segments (

*p*< 0

*.*002, two-way ANOVA).

*κ*

_{1}was 1, i.e., models where the third segment was consistent with the first two segments, to models with

*κ*

_{1}= −1, where the third segment was inconsistent. Similarly, we created two other data sets, based on the values of

*κ*

_{2}and

*κ*

_{3}. Figure 3 shows serial position curves for the two groups in each data set. Two interesting points arise from the figure: First, just as imitation accuracy is usually better for earlier segments than later ones (the

*Primacy*effect), performance seems to be more robust to curvature inconsistencies when they occur early: Whether the third segments is consistent with the direction of the first two (left panel) makes little difference to the shape of the serial position curve (

*p*> 0

*.*6, two-way ANOVA) and only weakly affects the mean orientation error across all segments (

*p*< 0

*.*1, paired

*t*-test). Conversely, inconsistencies in the fourth (middle panel) and fifth (right panel) segments result in a significant change in the shape of the serial position curve (

*p*< 0

*.*02,

*p*< 0

*.*001, respectively) and in an increase in overall error (

*p*< 0

*.*04 for both). The second observation is that the serial position curves tend to diverge at the point at which inconsistency arises. For example, in the middle panel of Figure 3, where data are sorted according to

*κ*

_{2}, the curves differ the most at the middle position, whereas differences in

*κ*

_{3}(right panel) modulate the final portion of the curves.

*vice*

*versa*. We found that consistency in that domain was a crucial factor in subjects' ability to remember and imitate the sequences. However, variation in curvature consistency produces other correlated spatial consequences: When the disc moves steadily along a CW or CCW contour, for example, it is likely to remain within a relatively restricted region of space; we can describe such a trajectory as

*compact*. A “zig-zag” pattern, on the other hand would generate a more spread out trajectory, which can be described as

*extended*. To quantify these differences, we examined 1,000 randomly generated models of each class. Table 1 shows for each model class the mean and standard deviation of the distance, in degrees of visual angle, from a model's starting point to the most distant point anywhere else in the trajectory. As expected, models of class +++ were the most compact, and models of class −−− were the most extended. This difference in models' spatial extent could lead to differences in the utilization of visual resources for perceptually encoding and remembering models of different types. Also, eye movements would be more frequent when models were more spread out, possibly impairing spatial memory (Postle, Idzikowski, Della Sala, Logie, & Baddeley, 2006). This made it imperative to evaluate the possibility that models' size, rather than their internal structure, produced the effects observed in Experiment 1. Therefore, in Experiment 2, we explicitly controlled the spatial extent of stimulus models.

Model type | Maximum distance | Standard deviation |
---|---|---|

+++ | 2.88 | 0.70 |

++− | 3.32 | 0.80 |

+−+ | 3.97 | 0.82 |

+−− | 3.99 | 0.95 |

−++ | 3.95 | 0.69 |

−+− | 4.50 | 0.77 |

−−+ | 4.31 | 0.85 |

−−− | 4.77 | 0.84 |

*S*

_{1}and

*S*

_{2}, were generated according to the previously described quasi-random rules:

*d*between each point along segment

*S*

_{ n}and points along segments

*S*

_{1},…,

*S*

_{ n−2}was forced to be within certain lower and upper limits. Those limits, expressed as multiples of segment length,

*l,*differed between the three experimental conditions. In the

*Compact*condition,

*Intermediate*condition,

*Extended*condition,

*SD*0.47), 4.37 (0.64), and 5.79 (0.82), for Compact, Intermediate, and Extended type models, respectively. The three model classes span about the same range of distances as that covered by the model classes in Experiment 1 and therefore comprise an appropriate control for possible influences of spatial extent. Stimulus types were randomly interleaved and appeared at equal probability. Each subject performed 360 trials in the course of two sessions.

*p*> 0

*.*85, one-way ANOVA), nor was there an interaction between condition and serial position (

*p*> 0

*.*45, two-way ANOVA). This suggests that the outcome of Experiment 1 was not due to differences in models' spatial extent.

*κ*

_{2}(

*p*< 0.002, two-way ANOVA) and for the second (

*p*< 0.004) and third (

*p*< 0.05) presentations when

*κ*

_{3}was used as a criterion. The persistence of the differences in the curves indicates that the deleterious effects of curvature inconsistency are at least partially resistant to familiarity with the motion sequence.

*vice*

*versa,*a curvature extremum is present, and the subject is “forced” to create a new shape entity in his or her mind, thereby increasing the amount of information that must be kept in memory for successful imitation. In other words, continuous curvature facilitates integration of component segments into a single unit in memory because they can be represented as a single shape; curvature inconsistency calls for a multiple-part representation. As visual working memory is extremely limited in capacity (Olsson & Poom, 2005; Todd & Marois, 2004; Vogel & Machizawa, 2004; Vogel, Woodman, & Luck, 2001), it should not be surprising that even a single partition entails a cost in imitation performance. This hypothesis is supported by the fact that imitation error increases around the position where the presumed partition took place, namely, the point at which curvature becomes inconsistent (Figure 3).

*p*), with

*p*being the probability of a change in the tangent direction on a smooth curve. This “surprisal” measure, in turn, is proportional to the negative cosine of the angle created by successive points along the contour. This way, curvature extrema maximize shape information. Particularly, negative extrema carry the most information, as they are less likely to occur in a closed shape than positive extrema. Feldman and Singh point, then, to two factors governing the information content along a contour: the magnitude of the turning angle and its sign. In our case, angle magnitude cannot account for the differences in performance between stimulus types, as discussed earlier in this section. However, the robust effect of the sign of the turning angle may be a direct consequence of the subjects' treatment the motion path as defining a shape, with inconsistent turns leading to higher “surprisal” and more information to be encoded. Integrating over these negative turning points should then lead to increased error, which is exactly the pattern seen in Figure 2B.