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The Quest for Lognormality in a Curved Gaussian Space-Time : An On-line Handwriting Generation Journey

Handwriting is a very complex neuromotor skill requiring the interaction of many cognitive processes. It normally aims at producing a message to be memorized as an ink trace left on a writing medium. At the core of this ability stands the control of neuromuscular networks by the Central Nervous System, each of these being made up of a large number of neural and muscular coupled sub-systems. According to Kinematic Theory of rapid human movements, the trajectory of a pen tip can be seen as a time superimposition of strokes, each one being described by a lognormal function and considered as the basic unit of handwriting. This paradigm, which relies on the Central Limit Theorem, has not only been experimentally confirmed in numerous predictive and physiologically significant tests but it has also been shown to be the ideal mathematical description for the impulse response of a neuromucular system. This demonstration suggests that lognormal velocity patterns, which are the results of an asymptotic convergence, can be interpreted as reflecting the behavior of subjects who are in perfect control of their movements, here after referred to as lognormal writers. To illustrate this definition, we present various software tools and psychophysical tests used to investigate these ideal behaviors. We emphasize how the lognormal parameters extracted during various tasks can be used to analyze some underlying psychophysical processes associated with their realization, pointing out successful strategies for accomplishing a given task. To investigate the convergence toward lognormality, we report a few original projects conducted by our team and our collaborators. On the one hand, we focus on handwriting learning, to illustrate for example how kindergarten children moves toward lognormality as they become more fluent writers. On the other hand, we exemplify how aging phenomena affect handwriting by pointing out the increasing departure from the ideal lognormal behavior as the control of the fine motricity begins to decline. We particularly focus on investigations dealing with brain strokes, Parkinson and Alzheimer diseases to point out how the lognormal parameter sets obtained from the model could also be used as a metric to characterize some disabilities and their evolution with time.