(A): To explore this possibility, the fraction discriminated vs percent mixture overlap is plotted here. This is analogous to Figure 2, except plotting fraction discriminated directly (as in Figure 4—figure supplement 1), instead of fraction significantly discriminable. The threshold (50%) and the procedure for computing mixture overlap at that threshold are as in Figure 2A. Derived from data in (Bushdid et al., 2014) as for Figure 2. (B): The thick red line shows the critical distance d that would result from the data in (Bushdid et al., 2014) for a range of ‘fraction discriminated’ thresholds between 100% (perfect discrimination), and 33.3% (chance discrimination). The curve was obtained by regression on plots like that in Figure 4—figure supplement 2, by analogy to Figure 2 and (Bushdid et al., 2014). Note that d exhibits a nearly constant-slope relationship with threshold, meaning the data are not defined by a characteristic length scale, much like in Figure 4—figure supplement 1C. The thick black curve shows the relationship between z and the chosen threshold. This relationship was obtained directly from d, using Equation 1, as in (Bushdid et al., 2014). The thin red lines correspond to the same calculation for d but using data for only a single subject (one per line), showing similar sensitivity to the choice of threshold. The absence of a robust d for any individual subject argues that the group data are not simply explained by averaging across a population with well-defined, but diverse values of d. Note that very modest and reasonable alternative choices for the threshold result in extremely disparate estimates. The vertical axis is bounded by the smallest and largest possible number of discriminable stimuli allowed by the framework. The dashed lines are a visual guide to specific (threshold, z) pairs. (C): Box and whisker plots showing the median and inter-quartile range for z when restricting the analysis to individual subjects. Note that the worst performing subjects under one threshold can discriminate many more stimuli than the best performing subjects under a slightly more liberal threshold (compare best subject using a 60% threshold vs worst subject using a 40% threshold). Therefore, it is impossible to report with any confidence the number of discriminable stimuli using this approach. In the main text, we show that the actual framework used in (Bushdid et al., 2014) is nominally employed to make a more principled choice of threshold; however it merely cloaks the arbitrariness of the threshold choice, but does not eliminate it.