# Human Cognitive and Motor Abilities in the Aging Workforce: An Information-Based Model
## 3 A Review of Experimental Tests of Motor-Cognitive Abilities from Information Theory Perspective
### Tests of Motor Abilities  
Using information theory, the amount of information processed during a task that requires movement of the subject can also be expressed in bit unit, similarly to the abovementioned cognitive tasks. Let us consider a subject executing a reaching task within a time interval called movement time. During the movement, the subject processes an amount of information [56] expressed by the \"Shannon formulation\" of the [PERSON]'s Index Difficulty (ID) parameter [22]; based on the theorem 17 of [PERSON] [21], ID can be expressed as follows:  
\[\text{ID}=\text{log}_{2}\bigg{(}\frac{\text{D}}{\text{W}}+1\bigg{)}\left[\text{ bit}\right] \tag{6}\]  
where D is the distance from the hand's starting point to the center of the target and W is the width of the target measured along the line connecting the two motion's endpoints. In the Purdue Pegboard Test (PPT) participants are asked to pick up pegs from a bowl by their right hand, left hand, and then by both hands (three runs) and place them in one of the 25 vertical holes of a plate. During the test, after each pick and place movement, the operator is required to move his/her arm back to the bowl and grab another peg. The test score is measured as the number of pegs the subject places within 30 s [57; 58]. The test evaluates manual dexterity. The more pegs the subject can place correctly in 30 s (one run), the higher his manual dexterity is. Based on the relationship given by [PERSON] [56], a linear dependency between the movement time (MT-time needed by the operator to perform the task) and the information volume to be processed (I\({}_{\text{m}}\)-bit) is adopted:  
\[\text{MT}=\text{T}_{\text{p,m}}\times\text{I}_{\text{m}}\ [\text{s}] \tag{7}\]  
where, T\({}_{\text{p,m}}\) (s/bit) is the time needed to process one bit of information and I\({}_{\text{m}}\) is the information volume to be processed during the motor task. Based on models from information theory, the time required to perform a task with 0-bit information content must be 0, yielding a null Y-intercept for the Fitts' law (as in Equation (7)), which is the working assumption used in the regressions performed in the next section. Equation (7) is applied to the PPT to quantify the amount of information of a test run. The diameter of the holes is 0.25 cm, the distance between two contiguous centers equals five times the diameter of the holes, the distance between the bowl that contains the pegs and the center of the first hole is 3.37 cm, and the MT (as the duration of the entire PPT test) is 30 s. The center of the bowl and every hole of the board are aligned. Under these test conditions, the movement time (MT) of the test run is obtained by adopting Equation (7) where I\({}_{\text{m}}\) is calculated as:  
\[\text{I}_{\text{m}}=\text{I}_{\text{m,ID}}+\text{I}_{\text{m,MTM}}=\sum_{\text {i}=1}^{\text{n}}\text{log}_{2}\bigg{(}\frac{\text{D}_{\text{i}}}{\text{W}}+ 1\bigg{)}+\text{I}_{\text{m,MTM}}\ [\text{bit}]. \tag{8a}\]  
The first term, I\({}_{\text{m,ID}}\), is the index of difficulty that quantifies the information volume associated with the n reaching movements, i.e., the number of pegs placed by the subject in the board within MT; D\({}_{\text{i}}\) is the distance from the starting point (bowl with all the pegs) to the i-th target (hole), and W is the width of the target (constant holes diameter). The second term, I\({}_{\text{m,MTM}}\), is the amount of information associated with translating, picking and placing movements not considered in I\({}_{\text{m,ID}}\). I\({}_{\text{m,MTM}}\) is obtained by the Method-Time Measurement (MTM) standard time as follows:  
\[\text{I}_{\text{m,MTM}}=\frac{\text{MTM}}{\text{T}_{\text{p,m}}^{*}}\ [\text{bit}] \tag{8b}\]  
where MTM is equal to the sum of Method-Time Measurement standard times of all n translating, picking, and placing movements of the hand, and T\({}_{\text{p,m}}^{*}\) is an average (on age and sex) value of the motor processing time.