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.
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