  Extensive confusion exists and persists in the literature on dynamical
systems theory, cosmology, and other fields over spectra of fractal dimensions.
Entirely different generating functions have been treated as if they should
yield identical spectra, or scaling exponents. An uncritical implicit
assumption of universality of scaling exponents is made, even though there is
no good theoretical reason to expect scaling exponents to be universal away
from criticality. Expectations based on the unphysical and empirically
inapplicable zero length scale limit (which would require infinite precision in
data analysis) are often taken for granted. A source of confusing together
different generating functions can be traced back to the Hentschel-Procaccia
conjecture, which I prove to be wrong for the case of data analysis in the only
applicable limit, that of finite precision. The two different definitions of
'multifractal' stated by Mandelbrot and by Halsey et are compared and
contrasted.
