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
... read more
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.
show less