  We characterize the algorithmic dimensions (i.e., the lower and upper
asymptotic densities of information) of infinite binary sequences in terms of
the inability of learning functions having an algorithmic constraint to detect
patterns in them. Our pattern detection criterion is a quantitative extension
of the criterion that Zaffora Blando used to characterize the algorithmically
random (i.e., Martin-L\"of random) sequences. Our proof uses Lutz's and
Mayordomo's respective characterizations of algorithmic dimension in terms of
gales and Kolmogorov complexity.
