The Reciprocal Nature of Fitts’ Law in Space and Time

Abstract

Human movement takes place in both space and time so that measures of movement accuracy in space are made with respect to time, and vice-versa providing a foundation to the proposal of the complementarity of spatial and temporal error in aiming movements. We examined this hypothesis in both the standard Fitts and Peterson discrete movement speed-accuracy protocol that requires moving to stop within a fixed spatial target (distance (D) with target bandwidth (W_D) in an emergent movement time (T) and, also in the reciprocal and novel space-time protocol introduced here that required moving for a fixed temporal target goal T with bandwidth of W_T with an emergent D. Experiment 1 examined a range of D conditions (45, 100, 180, 280, and 405 mm with bandwidth W_D ±5 mm) within the Fitts’ Law discrete spatial accuracy protocol to provide compatible spacetime boundary conditions for the reciprocal spacetime protocol in Experiment 2 that examined the effect of target time (T − 250, 460, 670, and 880 ms each with bandwidth W_T ±50 ms) on the emergent D. The findings showed that the spatial and temporal error profiles in Experiment 2 were consistent with exchanging D and T in Fitts’ Law Equation. This provides evidence for the reciprocal nature of the spacetime error functions in Fitts’ type movement aiming protocols and is compatible with the reciprocal profiles of spatial and temporal errors in other classes of movement aiming tasks.

Keywords:

• discrete movement
• speed and accuracy tradeoff
• movement time
• temporal constraint

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the authors.

Notes

1 The label movement speed and accuracy has historically been used to capture the research theme of this paper (Crossman & Goodeve, 1963; Woodworth, 1899). However, the term speed is typically invoked in a way that represents both the velocity and time duration of the movement event. Time is the interval over which change occurs but it does not alone define or equate to movement speed or velocity. Speed is velocity without specification of movement direction and is a scalar quantity equal to the magnitude of the velocity vector. Velocity is defined as the time rate of change of position. As we show in the results of Experiment 2 the confounding of time and speed/velocity can lead to erroneous inferences about the movement speed and accuracy relation.

2 A reciprocal relationship is one in which two variables can mutually influence one another; that is each can be both a cause and effect (APA Dictionary of Psychology).

3 In Newton’s (1687) framework, time is independent from the three dimensions of space so that the passage of time is absolute for all observers no matter their place and motion in the world. Some two centuries and more later and the development of Einstein’s (1905) theory of relativity, Minkowski (1923) articulated the contrasting view that “henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality”. The spacetime framework holds that time is not separate from space leading to time as relative in a four-dimensional spacetime manifold that is curved by the existence of matter and energy. Nevertheless, the fact that the differences in the experimental consequences of the relative and absolute frameworks are so infinitesimally small and imperceptible to humans in earth bound activities, has contributed to the Newtonian laws of motion preserving their centrality to the theory and practice of the biomechanics of motor control. Lee (1980) has shown that the spacetime framework provides some novel ways to conceptualize the roles of space and time in the control of human movement. The focus here is the relative and potential reciprocal nature of the spatial and temporal outcome of discrete aiming movements in the Fitts’ Law experimental protocol.

4 We have included the successful trials in analysis of the DVs of Expt 1 and Expt 2. The general trend for successful and unsuccessful trials was essentially the same but variability was lower with successful trials only as one would expect through reducing the outliers.

Additional information

Funding

This research was supported by Ministry of Science and Technology of Taiwan Grant MOST 109-2410-H-030-062.