A Direct-Learning Approach to Acquiring a Bimanual Tapping Skill

ABSTRACT

The theory of direct learning (D. M. Jacobs & C. F. Michaels, 2007) has proven useful in understanding improvement in perception and exploratory action. Here the authors assess its usefulness for understanding the learning of a motor skill, bimanual tapping at a difficult phase relation. Twenty participants attempted to learn to tap with 2 index fingers at 2 Hz with a phase lag of 90° (i.e., with a right-right period of 500 ms and a right-left period of 125 ms). There were 30 trials, each with 50 tapping cycles. Computer-screen feedback informed of errors in both period and phase for each pair of taps. Participants differed dramatically in their success. Learning was assessed by identifying the succession of attractors capturing tapping over the experiment. A few participants’ attractors migrated from antiphase to 90° with an appropriate period; others became attracted to a fixed right-left interval, rather than phase, with or without attraction to period. Changes in attractor loci were explained with mixed success by direct learning, inviting elaboration of the theory. The transition to interval attractors was understood as a change in intention, and was remarkable for its indifference to typical bimanual interactions.

Keywords:

• bimanual tapping
• coordination dynamics
• learning

Notes

1. Also included in preliminary fitting was a double-phase relation—the appearance of attraction to both 90° and 270° or other symmetrical phases, but since no such attractors were found, double-phase was not included among the final fitting options.

2. The degree to which pairs are constrained by period or interval is the reciprocal of the degree to which taps are constrained by period, so does not constitute an additional dimension.

3. Newer statistical tools are being employed by Kelty-Stephen and his colleagues that are able to test the significance of some of the changes expected in direct learning:growth curve analyses of the consequences of feedback (e.g., Stephen, Arzamarski, & Michaels, 2010) and multifractal scaling techniques to investigate the interactions of processes operating on the different time scales of perception, calibration, and learning (Kelty-Stephens, Palatinus, Saltzman, & Dixon, 2013).

4. It may seem that this vector field should be radially symmetric about 500, π/2, but remember that the feedback error on both period and phase was shown in ms, and the angle-to-ms error conversion depends on period.

5. The horizontal screen error for an observed Period P is P – 500, and the vertical error for observed (RL) interval I is I – P/4. The squared radial error, then, is (P – 500)² + (I – P/4)², which is obviously minimized at P = 500 and I = 125. However, if I is “stuck” at P/2 (i.e., in an antiphase regime), the squared distance between the feedback cross and center of the target circle is (P – 500)² + (P/2 – P/4)², the minimum of which occurs at P = 470.6.

6. Some authors have forwarded a more ecological take by emphasizing higher-order information that guides change. For example, Fowler and Turvey (1978) hypothesized Δ(ΔError). Their approach is consistent with aspects of direct learning, but differs in being a one-dimensional variable, and therefore not specific to needed changes in multidimensional space.