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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.
(Score: 2) by buswolley on Monday October 12 2015, @04:05PM
There are a few problems with the summary, namely that the summary fails to even reference previous work in this area, which is quite substantial...at least behaviorally.
There are a number of subfields of number sense, but I'll just bring up one straightforward past research question. Suppose I were to show briefly show you 10 acorns spread loosely on the ground over a square foot, or briefly show you 10 acorns in a 6 square inch pile. Will we perceive those piles to have equivalent number of acorns? Or say I show you 20 small acorns, packed tightly, or 10 xtra large acorns, packed tightly, such that either pile takes up the same area. Will you reliably perceive theme as different in frequency? How about one pile of 10 acorns and one pile of 11 acorns for less than a second. Will you perceive that one pile is larger, or will it take 12 or 13 or 14 acorns in the larger pile before we notice a difference in magnitude. Does our accuracy change and strategies change as the number of items increase? I might do something different when estimating whether there are more eggs in a basket than when estimating whether one pile of sand contains more sand than another....probably because in the former we perceive it as a collection of individual objects (i.e. how many), while in the latter we probably perceive it as a unitized object (i.e. how much).
These kinds of questions are not based on ill-defined concepts, if you think in terms of skill.
subicular junctures