Abstract: Geometry is typically associated with simultaneous processing of the relationship between objects, while probability is typically associated with the sequential processing of events.   I will  discuss some of our preliminary work on combining these subjects in two contexts: (i) characterizing geometry probabilistically using a relatively simple invariant measure with the ability to explain some seemingly surprising behavioral results that show that we can distinguish between large and small objects, or animate and inanimate objects; (ii)  characterizing probability geometrically, couched in terms of a perceptual test of randomness.