Reciprocal aiming: a window into continuous versus discrete movements
Laure Fernandez
Institute of Human Sciences E.J. Marey (UMR 6233)
University of the Mediterranean, Marseille, France
Our daily activities incessantly require that we control both the speed and the accuracy
our movements via which we interact with the environment. As we all know, moving fast
goes at the cost of accuracy and vice versa, which was first documented by Woodworth early
as 1899 [1]. The most renowned formalization of this so-called speed-accuracy trade-off is
known as Fitts’ law [2], which states that movement time is a linear function of task
difficulty, i.e., MT = a + b ID, where MT denotes movement time, a and b are constants, and
ID (index of difficulty) equals log2(2A/W), where A and W represent target amplitude and
width, respectively.
The changes in MT result from changes in the movement patterns, which is most
readily observed in the case of reciprocal aiming [3; 4]. In fact, previous studies have shown
that the particular kinematic patterns associated with different levels of task difficulty were
captured by a unique behavioural dynamics [5]. These patterns span the full range from
seemingly concatenated discrete movements, with a clear separation between a deceleration
towards the current target and an acceleration towards the next, to fully continuous
movements, with a single, fused deceleration/acceleration peak at each movement extremity.
Thus, with the appearance of discrete and continuous (rhythmic) movements, the reciprocal
aiming task provides a promising window into movement categorization.
According to the ecological approach to perception and action, an agent is considered
as a constituent part of an environment-agent system; movement is thus understood as
emerging from the interaction between the agent’s dynamics and those pertaining to the
environment. The agent-environment coupling is thought to be informational (from the
environment to the agent) as well as mechanical (from the agent to the environment). These
couplings provide the conditions for the emergence of task-specific behavioral dynamics.
Identifying how information impacts the particular characteristics of the behavioral dynamics
in each specific case is a key challenge for the ecological psychologist. In the present
presentation, I will first present our studies on the influence of information on the
characteristics of the behavioral dynamics in the case of (reciprocal) aiming.
Next, I will focus on the distinction between discrete and reciprocal movements, and
discuss the question whether they constitute two distinct movements classes. In fact, the
question whether a single control principle underlies the execution of discrete and rhythmic
movements has appeared hard to resolve, not in the least so because it has long time been
pursued mainly along empirical lines while evading the fundamental question how to
demarcate distinct movement classes. Unambiguous classification requires identification of
class-defining invariance. Dynamical systems theory offers such a classification principle
based on phase flow topologies, which identify all behavioral possibilities within a class [6].
Using a novel technique to reconstruct phase flows from kinematic data, we recently found
evidence that movements at low IDs were associated with limit-cycle dynamics (the
‘rhythmic’ mechanism) while those at high IDs were associated with fixed-point dynamics
(the ‘discrete’ mechanism) [7]. Moreover, we also showed that ID-MT relation, which has for
more than five decades been held to be invariantly linear, in fact contains a discontinuity due
to the transition between the discrete and rhythmic mechanism.
References:
1. Woodworth, R. S. (1899). The accuracy of voluntary movement. Psychological Review, 3, 1-106.
2. Fitts, P. M. (1954). The information capacity of the human motor system in controlling the
amplitude of movement. Journal of Experimental Psychology: Human Perception and
Performance, 47, 381-391.
3. Fernandez, L. & Bootsma, R.J. (2008). Non linear gaining in precision aiming: Making Fitts’ task a
bit easier. Acta Psychologica, 129, 217-227.
4. Guiard, Y. (1993). On Fitts’ and Hooke’s laws: Simple harmonic movement in upper-limb
cyclical aiming. Acta Psychologica, 82, 139-159.
5. Mottet, D., & Bootsma, R.J. (1999). The dynamics of goal-directed rhythmical aiming. Biological
Cybernetics, 80, 235-245.
6. Huys, R., Studenka, B. E., Rheaume, N. L., Zelaznik, H. N. & Jirsa, V. K. (2008). Distinct timing
mechanisms produce discrete and continuous movements. PLoS Comput Biol, 4, e1000061.
7. Huys, R., Fernandez, L., Bootsma, R.J., & Jirsa, V.K. (2010). Fitts’ law is not continuous in reciprocal
aiming. Proceedings of The Royal Society B.