Left: HIPPARCOS inverse-parallax histogram for all 113 942 stars from van Leeuwen (2007) with ϖ >  0 mas (3803 objects fall outside the plotted range). Right: distribution of the first significant digit of the inverse parallaxes, referred to as “distances” by Alexopoulos & Leontsinis (2014), together with the theoretical prediction of Benford’s law; compare with Fig. 3b in Alexopoulos & Leontsinis (2014). The data have vertical error bars to reflect Poisson statistics, but the error bars are much smaller than the symbol sizes.