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Phoenix666 writes:

But what, exactly, is a number? A group of Chinese researchers tackled this deep philosophical question from a neurological perspective in a study reported in the Proceedings of the National Academy of Sciences. They sought to verify the invariant nature of numerosity perception in an experiment that included fMRI scanning to establish the brain structures activated in number sense.

Proceeding from the obvious assumption that numerosity is invariant to specific features like size, orientation, shape and color, they designed a test that included a number of dots within an enclosed space. To test the invariant effect of connection, they used arbitrary and irregular line segments connecting dots; there were three conditions: zero, one, and two connected pairs of dots were included in the test patterns. Subjects were shown these patterns adjacent to reference patterns that contained 12 dots unconnected by line segments. They were asked to indicate solely through visual perception which pattern contained more dots.

The researchers found that connecting dots in the patterns led to a robust result of underestimation. The researchers tested another topological invariant, the inside/outside relationship, by enclosing pairs of dots within ovals and irregular oval-like shapes. Interestingly, the results demonstrated that underestimation also occurred in this condition, and that it depended directly on the number of enclosed dot pairs in the pattern.

Original Submission