The intentional spring: a strategy for modeling systems that learn to perform intentional acts

Area of Science:

• Motor Learning
• Cognitive Science
• Mathematical Modeling

Background:

• Motor task learning involves internalizing an instructor's skills and intentions.
• The formal description of this internalization process is not well-established.
• Understanding this dynamic is crucial for effective skill acquisition.

Purpose of the Study:

• To formally describe the process of motor task learning by instruction.
• To develop a mathematical strategy for dynamically learning instructor intentions and skills.
• To model the transfer of task goals from instructor to learner.

Main Methods:

• Generalizing Hooke's law to a coupled instructor-spring-learner system.
• Utilizing dual Volterra functions to model anticipatory and hereditary influences.
• Employing mathematical operators (self-adjoint) for boundary conditions and Hilbert-Schmidt/Green's functions for analysis.

Main Results:

• A mathematical framework was developed to describe the internalization of extrinsic constraints into intrinsic ones during motor learning.
• The model quantifies the instructor's forcing function, encompassing both informing and controlling influences.
• The study demonstrates how task goals (boundary conditions) are transferred and absorbed between systems.

Conclusions:

• The proposed mathematical strategy offers a formal description of motor skill acquisition through instruction.
• The model provides insights into the dynamic interplay between instructor guidance and learner internalization.
• This work bridges concepts in motor control, cognitive psychology, and applied mathematics.