can humans generate a purely random number sequence?

nope, individually; but a minimum of seven individuals can

Central to the study of psychophysics is the idea of numbers by individuals. While individuals have an inherent sense of number (which starts with the natural numbers, and base 10 by the number of fingers), certain ideas about numbers and number arrangements have only been acquired through education.

An example of such is the idea of random numbers. One encounters such sequences in statistical mechanics, in a simple model called the random walk, and the very idea is used to derive the profound principle of central limit theorem. But of the many possible distributions that are classified as "random" (uniform, Poisson, Gaussian), what exactly does the mind imagine it to be? The biases and the "misconceptions" of the mind when it comes to the idea of random number generation (RNG) is discussed in various papers, and one of the recent investigations have been conducted by a team of IPL Complex Systems Researchers composed of I. Crisologo, A. Longjas, E. Legara and C. Monterola. Their results are published in Pisika, the journal of the Philippine Society of Physics [1].

Not really random

The team studied the number combinations generated by human samples under three different conditions: that without a guide and those with guides printed on a flashboard: one board is unbiased (all numbers appear at equal frequencies) and the other is biased to a particular number (the number 2 appears more often).

In judging whether the generated sequence is random or not, the team used the fact that in a purely random sequence, the probability of finding a number followed by another is uniform or equally probable. For example, a "1" to be followed by a "2" is equally likely as it is being followed by a "3" or a "4" or any other number. Note that this does not exclude the possibility of finding a number followed by the same number: "1" followed by "9" is as likely as "1" followed by "1".

This the human mind does not seem to realize.

The research found out that humans generate a series with preference for different number series and bias against repetition of similar numbers. This behavior seems universal for all people involved and for all numbers studied.

Randomize

Appending the series of non-random sequences generated by individuals obviously will not correct the problem; i.e. the resulting sequence will still fail the randomness test. The researchers instead try to stitch the series: given N number of generated sequences of numbers {x}, they formed a stitched sequence of {X} where the first component is from the first series, the second component is from the second series, and so on.

This time, they find that the resulting sequence is random, based on the same criterion used for the appended sequence. The probability of finding all number series (this number followed by this number) are roughly the same.

Biasing the biased?

Guiding the person generating the series has its effects, the study notes. When the board shown the participants are biased to a certain number, that number not only appears more often in the resulting sequence, the probability of it appearing in series (i.e. it appears immediately after the same number) is significantly higher.

This result is counter-intuitive. Biasing, in effect, will drive the sequence to be more random.

Psychophysic(ist)s

The group investigates psychophysical phenomena, defined as the quantitative study of the way the mind perceives things.

Crisologo, the first author, is the youngest of the group, an undergraduate student of the University of the Philippines. The other members are faculty members of the National Institute of Physics of the same University.

1. I. Crisologo, A. Longjas, E. Legara and C. Monterola (2008). A procedure for generating a random number sequence using at least seven individuals. Pisika 2(1).