  We introduce a numerical scale to quantify to which extent a planar continuum
is not locally connected. For a locally connected continuum, the numerical
scale is zero; for a continuum like the topologist's sine curve, the scale is
one; for an indecomposable continuum, it is infinite. Among others, we shall
pose a new problem that may be of some interest: can we estimate the scale from
above for the Mandelbrot set $\mathcal{M}$ ?
