Referee 1's review (John Spencer):

Overall, I liked this manuscript. It is well-written and generally clear. It also makes an important point, albeit a point that has been established by other empirical findings (e.g., we already know that latency, motion duration, and button press force are related to learning and cognitive processing). Still, I think the point is worth making in multiple outlets. And the novelty of using the Wii controller here adds some intrigue. I have several comments to make this a better manuscript. These comments are listed below.

1. I think the setup of this manuscript needs to go a bit farther in acknowledging that the issue of how cognition and action are coordinated has been a longstanding issue in the motor control literature. For instance, there’s a large literature looking at how people plan actions to particular locations in space that are cued by abstract stimuli. David Rosenbaum has done a great deal of work on this front. More recently, Erlhagen and Schöner provided a theoretical framework for thinking about these issues (see “A dynamic field theory of movement preparation”, Psych Review, 2002). I recognize that the task used here is paired associate learning—an important element of novelty. That said, the task used—moving a cursor to a target location in space based on some abstract rule—has been around for a very long time, and folks outside of the “embodied cognition” camp largely cited in this paper have done some serious thinking about how to connect the motor system up with the cognitive system.

2. Issue #1 also raises a theme that I think should be raised in the Discussion. In several places, the authors talk about demonstrating that cognition-action are linked or that processes at multiple time scales are linked. Frankly, I think we already know both points, but, again, I’m sympathetic to the need to make these points repeatedly. That said, at some point, we need to move beyond demonstration toward a formal understanding of how all of this works, that is, precisely how cognition and action can be integrated or precisely how multiple time scales can be integrated. The lack of correlation between cognitive performance and x-flips as well as some of the acceleration measures underscores this point (e.g., can an “embodied” view explain why some motor control measures are linked to cognitive performance while others are not? Can this view predict which measures should be linked a priori?) I’d like to see some pointers to these issue (and I refer to the aforementioned work by Erlhagen and Schöner as one example of movement toward a formal account of these links; there’s also relevant work on integrating processes at multiple time scales by Karl Newell which should be cited; and here’s a paper by Schutte and Spencer that seems directly related to trajectory control and learning:

Schutte, A.R. & Spencer, J.P. (2007). Planning ‘discrete’ movements using a continuous system: Insights from a dynamic field theory of movement preparation. Motor Control, 11, 166-208.

3. Results p. 8: “centered trial number”—please explain what this is.

4. This paper needs clearer figure captions. In particular, in Figure 4, what are the dots? Also, the figure numbers are off somewhere. There’s a reference to Figure 4 that I think it referring to Figure 3. There’s also a reference to a Figure 6, but no such figure in the file.

5. The first paragraph on p. 9 is dense. Needs some clarity.

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N.B. These are the comments made by the referee when reviewing an earlier version of this paper. Prior to publication the manuscript has been revised in light of these comments and to address other editorial requirements.