**5.2 Results**

The learning data mirrored that found previously, with more rapid learning for visual than haptic presentation but with terminal levels reaching nearly 100% in all learning conditions. As a consequence, the multidimensional spaces derived from similarity ratings following learning were based on comparable and near-errorless performance.

For each of the six conditions, the objects were multidimensionally scaled in dimensions 1-6. The three dimensional solutions were selected for further analysis because stress levels were low (none exceeded .05), of comparable value, and were the highest dimensionality that could be visually inspected. Three analyses were performed: (a) computation of the structural ratio (Homa, Rhodes, & Chambliss, 1979) for 15 objects as well as overall for each condition; (b) a comparison of the structural similarity among the six conditions; and (c) computation of each object to the centroid of its learning exemplars. The first measure tells us how structured each space was and whether the psychological structure mirrored objective structure. The second measure tells us whether the various scalings produced similar or different representations. The third measure assesses whether the prototype for each category was positioned away from or near the centroid of each category

The structural ratio was calculated for each of the 15 objects in a given condition by calculating the mean distance of that item to members of the same category, relative to the mean distance to objects from the other two categories. The mean of these 15 ratios for a given condition defined the mean structural ratio and represented level of conceptual structure, with smaller values indicating greater structure and values approaching 1.00 indicating a random structure. Figure 9 shows the mean structural ratio for each of the six conditions.

The structural ratios (SRs) ranged from (poorest) the space determined from visual inspection of the objects following no learning (SR = .414) to haptic inspection following systematic learning (SR = .223). In general, the structural ratios decreased with degree of learning, with the weakest structure associated with no learning (SR = .381), greatest structure with systematic learning (SR = .297), and intermediate structure with random learning (SR = .332). Overall, the haptic conceptual spaces were more structured than were the visual spaces (.301 vs. .381). To assess the similarity among the six conditions,

Haptic Concepts 19

Fig. 10. Three dimensional MDS space following systematic learning in the haptic modality

There exists ample evidence that vision and touch activate common neurological sites (Amedi *et al*., 2001; Ernst & Banks, 2002) and that objects experienced visually or haptically can, with fair success, be recognized in the alternate modality (Klatzky, Lederman, & Metzger, 1985; Pensky *et al*., 2008). However, almost nothing is known about the transfer of *categorical* information between these modalities. That is, can it be demonstrated that abstract categories, learned in one modality, maintain their categorical identity in an alternate modality? The answer, at least for the forms used here and considering only the

We purposely selected fairly complex three dimensional objects that were comprised of continuous distortions from three prototypes that, informally at least, appeared to preclude simple naming of objects or even features. The major results of the three experiments that explored the learning, transfer, and retention of concepts acquired visually, haptically, or combined can be summarized: (a) Visual learning of categories, as expected, was more rapid than haptic learning, but haptic learning reached the same errorless criterion after only four study blocks; (b) When categories were learned in one modality, the classification of novel forms on a transfer test was virtually perfect, even when presented in the alternate modality; (c) The interposition of a week's delay had a statistically significant but minimal effect on

**6. General discussion** 

classification accuracy.

visual and haptic modalities, is clearly yes.

correlations were computed among the six conditions, using as input the individual structural ratios for each object. These 15 correlations were positive and high, ranging from r = + .817 to r = + .981; the average correlation was r = +.924. A sample space – in this case, the MDS space following systematic learning in the haptic modality - is shown in Figure 10. What is clear is that the three haptic categories are clearly defined. Comparison with the original space (Figure 1) clearly reveals that the category prototype (P1, P2, P3) has become centered within each category rather than occupying the location at the extreme points of the two transformational paths.
