Title: Complexity of human response delay in intermittent control: The case of virtual stick balancing,
Abstract: Response delay is an inherent and essential part of human actions. In the
context of human balance control, the response delay is traditionally modeled
using the formalism of delay-differential equations, which adopts the
approximation of fixed delay. However, experimental studies revealing
substantial variability, adaptive anticipation, and non-stationary dynamics of
response delay provide evidence against this approximation. In this paper, we
call for development of principally new mathematical formalism describing human
response delay. To support this, we present the experimental data from a simple
virtual stick balancing task. Our results demonstrate that human response delay
is a widely distributed random variable with complex properties, which can
exhibit oscillatory and adaptive dynamics characterized by long-range
correlations. Given this, we argue that the fixed-delay approximation ignores
essential properties of human response, and conclude with possible directions
for future developments of new mathematical notions describing human control.