Two experiments were directed at the comparison between two perspectives on the perception of size achieved by probing the gap between two occluded distal surfaces by means of a hand-held rod. One perspective was the classical size-distance invariance hypothesis developed for the problem of visual size perception with a central role for perceived distance; the other was the hypothesis that the extended haptic perception of gap size is specific to a physical invariant lambda of the dynamics of probing. Experiment 1 examined the relation between hepatically perceived gap size and haptically perceived gap distance. No causal connection between the two was found, and all the variance in perceived size was accounted for by lambda. Experiment 2 manipulated the rotational inertia of the probe. Its effect was different for the two perceptions of size and distance, underscoring their independence. The indifference of perceived size to perceived distance was discussed in reference to identifying invariants for both the haptic and the visual perception of size at a distance.