Random Item Generation tasks (RIG) are commonly used to assess high cognitive abilities such as inhibition or sustained attention. They also draw upon our approximate sense of complexity. A detrimental effect of aging on pseudo-random productions has been demonstrated for some tasks, but little is as yet known about the developmental curve of cognitive complexity over the lifespan. We investigate the complexity trajectory across the lifespan of human responses to five common RIG tasks, using a large sample (n = 3429). Our main finding is that the developmental curve of the estimated algorithmic complexity of responses is similar to what may be expected of a measure of higher cognitive abilities, with a performance peak around 25 and a decline starting around 60, suggesting that RIG tasks yield good estimates of such cognitive abilities. Our study illustrates that very short strings of, i.e., 10 items, are sufficient to have their complexity reliably estimated and to allow the documentation of an age-dependent decline in the approximate sense of complexity.

It has been unclear how this ability evolves over a person’s lifetime and it had not been possible to be assessed with previous classical tools for statistical randomness. To better understand how age impacts behavior, we have assessed more than 3,400 people aged 4 to 91 years old. Each participant performed a series of online tasks that assessed their ability to behave randomly. The five tasks included listing the hypothetical results of a series of 12 coin flips so that they would “look random to somebody else,” guessing which card would appear when selected from a randomly shuffled deck, and listing the hypothetical results of 10 rolls of a die. We analyzed the participants’ choices according to their algorithmic randomness, which is based on the idea that patterns that are more random are harder to encode in a short computer program. After controlling for characteristics such as gender, language, and education. We have found that age was the only factor that affected the ability to behave randomly. This ability peaked at age 25, on average, and declined from then on. We also demonstrate that a relatively short list of choices, say 10 hypothetical coin flips, can be used to reliably gauge randomness of human behavior. A similar approach could be then used to study potential connections between the ability to behave randomly, cognitive decline, neurodegenerative diseases and abilities such as human creativity.

Copyright: © 2017 Gauvrit et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Introduction

Knowledge forming the content of several academic fields, including mathematics, follows from precocious core knowledge [1–3], and then follows a specific developmental course along the lifespan [4]. Numerosity (our approximate implicit sense of quantity) has been a privileged target of recent research, because numbers form one of the main pillars of elementary mathematical knowledge [5], but the study of randomness perception and statistical reasoning has also yielded striking results in the field of probability: adults with no formal education [6] as well as 8 to 12 month-old children [7, 8] have the wherewithal for simple implicit probabilistic reasoning. One of the toughest problems when it comes to Bayesian reasoning, however, is the detection of randomness, i.e., the ability to decide whether an observed sequence of events originates from a random source as opposed to produced by a deterministic origin [9].

Formally, the algorithmic (Kolmogorov-Chaitin) complexity of a string is the length of the shortest program that, running on a universal Turing machine (an abstract general-purpose computer), produces the string and halts. The algorithmic complexity of a string is a measure of how likely it is to have been produced deterministically by a computer program rather than by chance. In this way, a random string is a string that cannot be compressed by any means, neither statistically or algorithmically, that is a string for which no computer program shorter than the string itself exists. Humans, adults and infants [10, 11], have a keen ability to detect structure, both of statistic and algorithmic nature (e.g. 0101… and 1234…) that only algorithmic complexity can intrinsically capture (as opposed to e.g. entropy rate).

Within the field of study devoted to our sense of complexity, the task of randomly arranging a set of alternatives is of special interest, as it poses almost insurmountable problems to any cognitive system. The complexity of a subject-produced pseudorandom sequence may serve as a direct measure of cognitive functioning, one that is surprisingly resistant to practice effects [12] and largely independent of the kind of alternatives to be randomized, e.g., dots [13], digits [14], words [15], tones [16] or heads-or-tails [17]. Although random item generation (RIG) tasks usually demand vocalization of selections, motor versions have comparable validity and reliability [18, 19]. RIG tasks are believed to tap our approximate sense of complexity (ASC), while also drawing heavily on focused attention, sustained attention, updating and inhibition [20, 21]. Indeed to produce a random sequence of symbols, one has to avoid any routine and inhibit prepotent responses. The ability to inhibit such responses is a sign of efficient cognitive processing, notably a flexibility assumed to be mediated by the prefrontal cortex.

Instructions may require responding at various speeds [22], or else the generation of responses may be unpaced [27]. Participants are sometimes asked to guess a forthcoming symbol in a series (“implicit randomization”, [51]), or vaguely instructed to “create a random-looking string” [23]. The consensus is that, beyond their diversity, all RIG tasks rely heavily on an ASC, akin to a probabilistic core knowledge [24, 25].

Theoretical accounts of the reasons why RIG tasks are relevant tests of prefrontal functions are profuse, but pieces of experimental evidence are sparse. Sparse empirical factors indirectly validate the status of RIG tasks as measures of controlled processing, such as the detrimental effect of cognitive load or sleep deprivation [26] or the fact that they have proved useful in the monitoring of several neuropsychological disorders [27–31].

As a rule, the development of cognitive abilities across the lifespan follows an inverse U-shaped curve, with differences in the age at which the peak is reached [4, 32]. The decrease rate following the peak also differs from one case to another, moving between two extremes. “Fluid” components tend to decrease at a steady pace until stabilization, while “crystalized” components tend to remain high after the peak, significantly decreasing only in or beyond the 60s [33]. Other evolutions may be thought of as a combination of these two extremes.

Two studies have addressed the evolution of complexity in adulthood, but with limited age ranges and, more importantly, limited ‘complexity’ measures. The first [22] compared young and older adults’ responses and found a slight decrease in several indices of randomness. The second [15] found a detrimental effect of aging on inhibition processes, but also an increase of the cycling bias (a tendency to postpone the re-use of an item until all possible items have been used once), which tends to make the participants’ productions more uniform. In both studies, authors used controversial indices of complexity that only capture particular statistical aspects, such as repetition rate or first-order entropy. Such measures have proved some usefulness in gauging the diversity and type of long sequences (with e.g., thousands of data points) such as those appearing in the study of physiological complexity in [34–36], but are inadequate when in comes to short strings (e.g., of less than a few tens of symbols), such as the strings typically examined in the study of behavioral complexity. Moreover, such indexes are only capable of detecting statistical properties. Authors have called upon algorithmic complexity to overcome these difficulties [37, 38]. However, because algorithmic complexity is uncomputable, it was believed to have no practical interest or application. In the last years, however, methods were introduced related to algorithmic complexity that are particularly suitable for short strings [39, 40], and native n-dimensional data [41]. These methods are based on a massive computation to find short computer programs producing short strings and have been made publicly available [42] and have been successfully applied in a range of different applications [41, 43, 44].

The main objective of the present study is to provide the first fine-grained description of the evolution over the lifespan of the (algorithmic) complexity of human pseudo-random productions. Secondary objectives are to demonstrate that, across a variety of different tasks of random generation, the novel measure of behavioral complexity does not rely on the collection of tediously long response sequences as hitherto required. The playful instructions to produce brief response sequences by randomizing a given set of alternatives are suitable for children and elderly people alike, can be applied in work with various patient groups and are convenient for individual testing as well as Internet-based data collection.

Participants with ages ranging from 4 to 91 performed a series of RIG tasks online. Completion time (CT) serves as an index of speed in a repeated multiple choice framework. An estimate of the algorithmic complexity of (normalized) responses was used to assess randomization performance (e.g., response quality). The testing hypothesis is that the different RIG tasks are correlated, since they all rely on similar core cognitive mechanisms, despite their differences. To ensure a broad range of RIG measurements, five different RIG tasks were selected from the most commonly used in psychology.

The experiment is some sort of reversed Turing test where humans are asked to produce configurations of high algorithmic randomness that are then compared to the occurrence of what computers can produce by chance according to the theory of algorithmic probability [39, 40].