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I wonder if experiments in perceptual or cognitive psychology have been performed following these considerations:

Standard experiment: Present small numbers of simple items to a test subject, for the sake of specifity and simplicity as equal dots distributed inside a box:

enter image description here enter image description here

I guess experiments testing which number of dots test subjects are able to tell without consciously counting have been performed, and that the mean number is something like $7$ (the "magic number"). (The maximal number any test person was able to tell without consciously counting would be very interesting, too.)

I also guess that the magic number depends on the degree of evenness of the distribution of the dots (per test subject and on average).

But the magic number will depend also on the speeds of the dots. (The cases above assumed resting dots.) Two cases are to be distinguished:

  1. Not the dots, but their entirety rotates (around the center of the containing box) with angular velocity $v_1$.

  2. Each dot moves independently and behaves like a billiard ball reflected at the borders of the box

    1. with collision among dots

    2. without collision among dots, in this case

      1. all with the same speed $v_2$

      2. with slightly different speeds

      3. with very different speeds

All these cases give experimental setups and one might try to determine "magic numbers" depending e.g. on $v_1$ (in case 1) or $v_2$ (in case 2.2.1).

This is case 2.1:

enter image description here

But what interests me even more is the question up to which number people can actually count (not see at a glance) when asked to tell the number of some moving dots. This number will be greater than the magic numbers above - but how great? Check it out:

enter image description here enter image description here

Can anyone give a link to results related to the experimental setups I tried to describe? (Please forgive me, I'm not a learned psychologist or cognitive scientist, so my talk about experiments and so on may sound amateurish.)

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