Scaling in cognition

Conscious activity is generally consistent with a deterministic mode of action, however some activities demand randomness. The goal of this study was to find whether mind can produce randomness. We asked various human subjects, aged between 21 and 57, to produce sequences of random integers. The non-repetition of the terms in the series was the "algorithm" generally used by all the subjects. The series were analyzed by using spectral analysis (SA), detrended fluctuation analysis (DFA), information (I₂) and approximate entropy (AE) and correlation dimension analysis (CDA). SA of the series revealed 1/f^β (-0.4 < β < 1) types of spectra. The α scaling exponent resulting from DFA ranged between 0.2 and 1.1. The maximum of the distribution of α was centered at about 0.62. This is equivalent to a quarter power law in spectral terms. A significant percentage of subjects were able to produce random series. I₂ of mental series revealed short-range correlation for pairs of successive numbers in the series. The correlation decreased gradually and it disappeared at a delay step of about 7 which is the characteristic number of short memory. AE had a minimum value at α = 1 and a maximum value at α = 0.5 for mental and random series, respectively. CDA showed no presence of attractors in the series, therefore none of the randomness produced by the subjects was of deterministic origin. A comparison of the scaling exponents revealed that the mental series have a certain long-range characteristic which is common to the human language as evident in the literature writings.