  High-dimensional computational challenges are frequently explained via the
curse of dimensionality, i.e., increasing the number of dimensions leads to
exponentially growing computational complexity. In this commentary, we argue
that thinking on a different level helps to understand, why we face the curse
of dimensionality. We introduce as a guiding principle the curse of
instability, which triggers the classical curse of dimensionality. Furthermore,
we claim that the curse of instability is a strong indicator for analytical
difficulties and multiscale complexity. Finally, we suggest some practical
conclusions for the analysis of mathematical models and formulate several
conjectures.
