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The "counting low numbers of things instantly" thing has a name: Subitizing. It's quite the fascinating topic.

https://en.wikipedia.org/wiki/Subitizing

Also, it's apparently not restricted to counting:

> A 2006 study demonstrated that subitizing and counting are not restricted to visual perception, but also extend to tactile perception, when observers had to name the number of stimulated fingertips.[7] A 2008 study also demonstrated subitizing and counting in auditory perception.[8] Even though the existence of subitizing in tactile perception has been questioned,[9] this effect has been replicated many times and can be therefore considered as robust.[10][11][12] The subitizing effect has also been obtained in tactile perception with congenitally blind adults.[13] Together, these findings support the idea that subitizing is a general perceptual mechanism extending to auditory and tactile processing.



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