The length of a piece of string: Where the whole is more than the sum of its constituent parts

Determination of the magnitude or size of objects is crucial in many activities of daily living. Here we provide psychophysical evidence across multiple experiments that judgements for accumulated length of fragmented lines are non-veridical, with a larger number of fragments leading to a larger reduction in perceived size. The reported reduction in the size of fragmented stimuli is not a result of stimulus bias or frequency of observations and reflects an inherent perceptual bias. We have extended the findings to real objects in laboratory conditions. Whilst the discrimination threshold for two intact lines remained similar to those reported previously, the reduction in perceived length with fragmentation persisted. Finally, we gathered behavioral data on a real-life task of matching the length of a strand of cooked spaghetti using spaghetti pieces of varying sizes. Participants used progressively larger amounts of spaghetti to match reference length when selecting from smaller cut pieces. The reduction in the perceived magnitude of small segments remained evident when participants decided on the portion size of cooked spaghetti. The converging evidence from multiple investigations demonstrates the robustness of the observed reduction in perceived size with fragmentation.