6. Continuum of haptic space

Abstract

The structure of haptic has first received serious attention in 1937 by Blumenfeld. Haptic space, as used in this chapter and indeed also by Blumenfeld, involves around us which we can reach by touch from a fixed position. How this is related to through which we navigate is an interesting question but not topic of this chapter. Inspired by earlier experimental results in visual domain, Blumenfeld measured so-called alley curves. Subjects had to pull two threads, that were fixed symmetrically on both sides of median plane, towards themselves such that threads felt as parallel to each other and to median plane. Depending on distance to median plane, resulting lines either were diverging, parallel, or converging. Rightly so, Blumenfeld concluded from these results that haptic was not Euclidean; that is, lines that are parallel in haptic are usually not parallel in Euclidean or physical space. Moreover, since deviations from physical were apparently systematic and not just random, it became possible to talk about structure of haptic space. Although Blumenfeld discussed his findings in terms of parallelity laws and speculated about underlying cause for deformation, he did not give a formal description of his results. Surprisingly, unlike in visual domain, his interesting haptic experiments did not really get a follow-up. Just a few studies concerning haptic space were published (e.g., Worchel, 1951; Bambring, 1976; Lederman, Klatzky & Barber, 1985), but none of these studies directly addressed way haptic space is deformed with respect to Euclidean space. To our knowledge, our research is first serious attempt to study and describe structure of haptic space. One of questions that had to be answered was whether it is justifiable to speak of the structure of haptic space at all. For this question to be answered affirmatively, haptic should possess a number of properties, most important being that measured spatial relations (such as, for example, parallelity) are reproducible and that from a set of measurements predictions can be made for spatial relations at other locations by interpolation or even extrapolation. This latter property assumes that haptic space is continuous and would indicate that there is indeed an underlying structure. Once it has been established that haptic is structured, another question is to find how it is structured, or in other words, find a formal description of structure. These two questions cannot be answered independently, and our strategy has been to collect a large amount of data in a number of different experiments all investigating haptic spatial relations. What follows is a bird's eye view over these experiments.