Continuum of haptic space

Abstract

The structure of haptic space has first received serious attention in 1937 by Blumenfeld. Haptic space, as used in this chapter and indeed also by Blumenfeld, involves the space around us which we can reach by touch from a fixed position. How this space is related to the space through which we navigate is an interesting question but not the topic of this chapter. Inspired by earlier experimental results in the visual domain, Blumenfeld measured the so-called "alley curves". Subjects had to pull two threads, that were fixed symmetrically on both sides of the median plane, towards themselves such that the threads felt as parallel to each other and to the median plane. Depending on the distance to the median plane, the resulting lines either were diverging, parallel, or converging. Rightly so, Blumenfeld concluded from these results that haptic space was not Euclidean; that is, lines that are parallel in haptic space are usually not parallel in Euclidean or physical space. Moreover, since the deviations from physical space were apparently systematic and not just random, it became possible to talk about the structure of haptic space. Although Blumenfeld discussed his findings in terms of the "parallelity laws" and speculated about the underlying cause for the deformation, he did not give a formal description of his results. Surprisingly, unlike in the 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 the way haptic space is deformed with respect to Euclidean space. To our knowledge, our research is the first serious attempt to study and describe the structure of haptic space. One of the 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 space should possess a number of properties, the 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 space is structured, another question is to find how it is structured, or in other words, find a formal description of the 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.