A comment on "Measuring fractality" by Stadnitski (2012)

Non-linear Amplification of Variability Through Interaction Across Scales Supports Greater Accuracy in Manual Aiming: Evidence From a Multifractal Analysis With Comparisons to Linear Surrogates in the Fitts Task

Movement coordination depends on directing our limbs to the right place and in the right time. Movement science can study this central requirement in the Fitts task that asks participants to touch each of two targets in alternation, as accurately and as fast as they can. The Fitts task is an experimental attempt to focus on how the movement system balances its attention to speed and to accuracy. This balance in the Fitts task exhibits a hierarchical organization according to which finer details (e.g., kinematics of single sweeps from one target to the other) change with relatively broader constraints of task parameters (e.g., distance between targets and width of targets). The present work seeks to test the hypothesis that this hierarchical organization of movement coordination reflects a multifractal tensegrity in which non-linear interactions across scale support stability. We collected movement series data during a easy variant of the Fitts task to apply just such a multifractal analysis with surrogate comparison to allow clearer test of non-linear interactions across scale. Furthermore, we test the role of visual feedback both in potential and in fact, i.e., by manipulating both whether experimenters instructed participants that they might potentially have to close their eyes during the task and whether participants actually closed their eyes halfway through the task. We predict that (1) non-linear interactions across scales in hand movement series will produce variability that will actually stabilize aiming in the Fitts task, reducing standard deviation of target contacts; (2) non-linear interactions across scales in head sway will stabilize aiming following the actual closing eyes; and (3) non-linear interactions across scales in head sway and in hand movements will interact to support stabilizing effects of expectation about closing eyes. In sum, this work attempts to make the case that the multifractal-tensegrity hypothesis supports more accurate aiming behavior in the Fitts task.