Counting and the Mind

Here is an interesting fact taken verbatim from the book “A Passion for Mathematics” by Clifford A Pickover.


I quickly toss a number of marbles onto a pillow. You may stare at them for an instant to determine how many marbles are on the pillow. Obviously, if I were to toss just two marbles, you could easily determine that two marbles sit on the pillow. What is the largest number of marbles you can quantify, at a glance, without having to individually count them?


Seven. In 1949, Kaufman, Lord, Reese, and Volkmann flashed random patterns of dots on a screen. When subjects looked at patterns containing up to five or six dots, the subjects made no errors. The performance on these small numbers of dots was so different from the subjects’ performance with more dots that the observation methods were given special names. Below seven, the subjects were said to subitize; above seven, they were said to estimate. For more information, see E. L. Kaufman, M. W. Lord, T. W. Reese, and J. Volkmann, “The Discrimination of Visual Number,” American Journal of Psychology 62 (1949): 498–525. Also see George Miller, “The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information,” The Psychological Review 63 (1956): 81–97.

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