  Multi-fractal patterns occur widely in nature. In developing new algorithms
to determine multi-fractal spectra of experimental data I am lead to the
conclusion that generalised dimensions $D_q$ of order $q\leq0$, including the
Hausdorff dimension, are effectively \emph{irrelevant}. The reason is that
these dimensions are extraordinarily sensitive to regions of low density in the
multi-fractal data. Instead, one should concentrate attention on generalised
dimensions $D_q$ for $q\geq 1$, and of these the information dimension $D_1$
seems the most robustly estimated from a finite amount of data.
