Flexibility of Motor Control 343displacements of the physical target so that it remains in a
constant egocentric direction; with this procedure, systematic
pointing errors are masked by random errors and are not
noticed by the subjects (Howard, 1968).
Prism adaptation implies some kind of change of the in-
ternal model of the motor transformation. What is the nature
of this change? A first point to note is that it is generalized
and not restricted to the particular movement performed dur-
ing prism exposure. Instead, an exposure period with a single
visual target results in negative aftereffects not only for this
particular target, but for a range of targets in different direc-
tions, and when prismatic displacement is different for tar-
gets in different directions, aftereffects reveal a kind of linear
interpolation for targets in between (Bedford, 1989). Beyond
the generalization across the work space, the aftereffect is not
even restricted to pointing at visual targets. In many cases it
is approximately the sum of two components, a propriocep-
tive aftereffect and a visual aftereffect (Hay & Pick, 1966),
with the relative size of the two components depending on
exposure conditions (e.g., Kelso, Cook, Olson, & Epstein,
1975). A test of the proprioceptive aftereffect is pointing
straight ahead, whereas a test for the visual aftereffect is to
align a visual stimulus with the straight-ahead position. Thus,
what is changed is not the specific relation between visual
and proprioceptive direction, but rather the directional mean-
ing of visual and/or proprioceptive signals.
Some findings suggest that the adaptation during prism
exposure does not involve a modification of a single internal
model of the motor transformation, but some kind of addi-
tion, so that the original model remains in existence. On the
one hand, negative aftereffects decay even when participants
remain in darkness (e.g., Dewar, 1971); on the other hand,
even when participants are confronted with the normal visual
world between experimental sessions, long-term effects of
prismatic adaptation can be observed as soon as they are
brought back to the experimental setup (McGonigle & Flook,
1978). In addition, with repeated alternations of periods with
and without lateral displacement, or with different lateral dis-
placements, aftereffects tend to disappear, and switching be-
tween different visuo-motor transformations becomes almost
instantaneous (e.g., Kravitz, 1972; Welch, 1971). These and
other results (cf. Welch, Bridgeman, Anand, & Browman,
1993) strongly suggest that multiple models of visuo-motor
transformations can be learned and, when required by
the task, selectively be put to use, although little is known
about the nature of the cues that mediate the retrieval of
stored internal models.
In a certain way, the situation when wearing laterally dis-
placing prisms is similar to a situation that has become quite
common during the last one or two decades, namely the
operation of a computer mouse with concurrent movements
of a cursor on a laterally displaced monitor. Although in the
first case there are aftereffects, we encounter no difficulties in
operating the mouse with different lateral displacements of
the screen. There seem to be mainly two reasons for this dif-
ference: First, movements performed with the computer
mouse are parameterized in terms of (allocentric) distances,
whereas movements produced in experiments with laterally
displacing prisms are parameterized in terms of (egocentric)
locations. Second, and perhaps of less importance, is that
with the computer mouse proprioceptive and visual informa-
tion indicate different egocentric directions of different
objects, the hand and the cursor, while in prism-adaptation
studies they refer to the same object, the hand. Object iden-
tity is a factor that affects the size of negative aftereffects
(Welch, 1972).
Visuo-motor transformations can also be changed such
that the relations between (allocentric) visual distances
and/or directions and (hand-centered) movement amplitudes
and/or directions are modified. The basic findings seem to
parallel those obtained in prism-adaptation studies to a re-
markable degree. For example, aftereffects occur and multi-
ple models of visuo-motor transformations can be learned
and selectively accessed when appropriate (Cunningham &
Welch, 1994). When a certain internal model has been
learned, there seems to follow a kind of labile period in which
the learning of a new transformation results in a modification
of the model, but after a period of consolidation the learning
of a new transformation results in the development of a new
model rather than the overriding of the old one (Krakauer,
Ghilardi, & Ghez, 1999). With sufficient delays between
learning periods, it seems that repeated alternation between
different transformations is not needed to acquire multiple in-
ternal models.
When discussing visual feedback, I have pointed to the
limitations in acquiring internal models of additional trans-
formations of one’s own movements. Whereas adjustments to
changes of visuo-motor gains require only one or a few dis-
crete movements (Young, 1969), adjustments to new rela-
tions between the directions of hand movements and cursor
motions require more trials (e.g., Krakauer et al., 1999). Ad-
justments to nonlinear transformations require even longer
experience, and for too complex transformations internal
models can no longer be developed. Although the mastery of
added transformations is typically not associated with their
awareness (who could tell the gain factor of his or her com-
puter mouse?), the difficulty of such transformations is
affected by higher level cognitive processes. This is nicely
illustrated by a little-known study of Merz, Kalveram, and
Huber (1981), and additional evidence from reaction-time