Can humans detect true randomness?

Now we are embarking upon a more audacious adventure: Can the human mind consciously distinguish genuine randomness from pseudo randomness? Genuine randomness is fundamentally governed by uncertainty in the quantum mechanical laws. It can be generated by timing successive pairs of radioactive decays. Pseudo randomness, on the other hand, is an imitator of the true randomness generated by a deterministic process (e.g. a computer algorithm).

This question has invited numerous suspicions and doubts, and yet we are curious to see how far the mind can stretch. To test this, we are using a simple visual display of dots. (see the graph to the right) Each dot can be either blue or green and the decision represents a random binary outcome. Now I tell you that half of the screen is generated by genuine random numbers, and the other half is by pseudo random numbers. It could be either a horizontal division (which means that one of the upper and lower halves is genuine randomness), or a vertical division (which means that one of the left and right halves is genuine randomness). Your job is to tell me which orientation the division is.

So which orientation is it in this graph? If you are one of the few geniuses, you'll say it's horizontal division, with the lower half being the genuine randomness, the upper half being the pseudo randomness (indeed, that's correct). We are hoping to find the bunch that can succeed in this task.