Eye position predicts what number you have in mind

Abstract

Despite the apparent simplicity of picking numbers at random, it is virtually impossible to produce a sequence of truly random numbers. Although numbers seem to pop-up spontaneously in one's mind, their choice is invariably influenced by previously generated numbers [1Knoch D. Brugger P. Regard M. Suppressing versus releasing a habit: frequency-dependent effects of prefrontal transcranial magnetic stimulation.Cerebr. Cortex. 2005; 15: 885-887Crossref PubMed Scopus (49) Google Scholar]. Here, we demonstrate how the eyes and their position give an insight into the nature of the systematic choices made by the brain's ‘random number generator’. By measuring a person's vertical and horizontal eye position, we were able to predict with reliable confidence the size of the next number — before it was spoken. Specifically, a leftward and downward change in eye position announced that the next number would be smaller than the last. Correspondingly, if the eyes changed position to the right and upward, it forecast that the next number would be larger. Apart from supporting the old wisdom that it is often the eyes that betray the mind, the findings highlight the intricate links between supposedly abstract thought processes, the body's actions and the world around us. Despite the apparent simplicity of picking numbers at random, it is virtually impossible to produce a sequence of truly random numbers. Although numbers seem to pop-up spontaneously in one's mind, their choice is invariably influenced by previously generated numbers [1Knoch D. Brugger P. Regard M. Suppressing versus releasing a habit: frequency-dependent effects of prefrontal transcranial magnetic stimulation.Cerebr. Cortex. 2005; 15: 885-887Crossref PubMed Scopus (49) Google Scholar]. Here, we demonstrate how the eyes and their position give an insight into the nature of the systematic choices made by the brain's ‘random number generator’. By measuring a person's vertical and horizontal eye position, we were able to predict with reliable confidence the size of the next number — before it was spoken. Specifically, a leftward and downward change in eye position announced that the next number would be smaller than the last. Correspondingly, if the eyes changed position to the right and upward, it forecast that the next number would be larger. Apart from supporting the old wisdom that it is often the eyes that betray the mind, the findings highlight the intricate links between supposedly abstract thought processes, the body's actions and the world around us. Sitting in a dark room, twelve right-handed men acted as random number generators. Paced by an electronic metronome (1 Hz) they named 40 numbers between 1 and 30 in a sequence ‘as random as possible’. Each participant's eye position was measured with dual search coils (Skalar, Delft, The Netherlands, see [2Ferman L. Collewijn H. Jansen T.C. Vandenberg A.V. Human gaze stability in the horizontal vertical and torsional direction during voluntary head movements, evaluated with a three-dimensional scleral induction coil technique.Vision Res. 1987; 27: 811-828Crossref PubMed Scopus (206) Google Scholar]) as they sat within a 1.4 m diameter coil frame, which generated three orthogonal magnetic field. The voltages induced on the coils were proportional to the orientation of the coil relative to the magnetic field and the signals were sampled at 1000 Hz and a 16 bit resolution. The subjects' spoken responses were recorded and synchronized with eye position. Saccades and blink artifacts were detected and removed with an interactive computer program on the basis of velocity and noise criteria. For each number, we computed the average horizontal and vertical eye position during the 500 msec interval before it was named. On the basis of consistent research showing that small numbers are associated with the left and upper parts of space and large numbers with the right and lower [3Hubbard E.M. Piazza M. Pinel P. Dehaene S. Interactions between number and space in parietal cortex.Nat. Rev. Neurosci. 2005; 6: 435-448Crossref PubMed Scopus (837) Google Scholar, 4Schwarz W. Keus I.M. Moving the eyes along the mental number line: Comparing SNARC effects with saccadic and manual responses.Percept. Psychophys. 2004; 66: 651-664Crossref PubMed Scopus (190) Google Scholar], we predicted that selecting a number smaller than the last would be anticipated by leftward (downward) changes in eye position. Similarly, shifts to a larger number would be accompanied by rightward (upward) changes in eye position. Our results show that both horizontal and vertical changes in eye position predicted the direction of the change in number magnitude well above the chance level of 50% (Figure 1A ; horizontal mean: 61.6%, SE 2.6: t(11) = 4.47, p < 0.001; vertical mean 65.7% SE 1.6: t(11) = 9.73, p < 0.0001). To assess whether the size of the change in eye position predicted the size of the change in number, we performed a repeated-measures regression analysis for each individual participant [5Lorch Jr., R.F. Myers J.L. Regression analyses of repeated measures data in cognitive research.J. Exp. Psych.: Learn. Mem. Cognit. 1990; 16: 149-157Crossref PubMed Scopus (623) Google Scholar]. Numerical distance (number ‘n + 1’ minus number ‘n’) was the dependent variable, and the corresponding changes of the horizontal and vertical eye position were used as predictors. Crucially, the individual regression weights for changes in horizontal (mean = 0.126, SE = 0.03, t(11) = 3.95, p < 0.002) and vertical eye position (mean = 0.127, SE = 0.03, t(11) = 4.68, p < 0.001) were significantly different from 0 (one-sample t-test). A large change in eye position therefore predicted a marked change in number size, whereas a small change indicated that the next random number would be of comparable magnitude (Figure 1B,C). To a substantial degree, changes in eye position allow us to predict a number that is in a person's mind before it is named. Not only does the direction of the change in eye position indicate whether a smaller or larger number is picked, but also the degree of change reliably reflects the size of the numerical shift. Our data are correlative, and the intriguing question remains: Does merely thinking of a number cause a change in eye position? Alternatively, does the direction of an ocular shift constrain the selection of numbers? In any case, our findings substantiate earlier claims for an analogical representation of numbers [3Hubbard E.M. Piazza M. Pinel P. Dehaene S. Interactions between number and space in parietal cortex.Nat. Rev. Neurosci. 2005; 6: 435-448Crossref PubMed Scopus (837) Google Scholar]. The results also suggest, however, that the notion of a left-to-right oriented mental number line might be an oversimplification. In many individuals (Figure 1A) the mental representation of numbers may be better described in a diagonal fashion (left bottom to right top, see also [4Schwarz W. Keus I.M. Moving the eyes along the mental number line: Comparing SNARC effects with saccadic and manual responses.Percept. Psychophys. 2004; 66: 651-664Crossref PubMed Scopus (190) Google Scholar]). An influential theory — the ‘theory of magnitude’; see [6Walsh V. A theory of magnitude: Common cortical metrics of time, space and quantity.Trends Cogn. Sci. 2003; 7: 483-488Abstract Full Text Full Text PDF PubMed Scopus (1207) Google Scholar]) considers coordinate information in ‘number space’ to be just one instance of magnitudes within a single metric system unifying size information of a broad range of units, from spatial extension to temporal duration. It is postulated that this general magnitude system is mediated by inferior parietal structures of the brain and that it encodes information used in actions [6Walsh V. A theory of magnitude: Common cortical metrics of time, space and quantity.Trends Cogn. Sci. 2003; 7: 483-488Abstract Full Text Full Text PDF PubMed Scopus (1207) Google Scholar]. This hypothesis successfully predicted interactions between numbers and goal-directed hand movements. Exposure to small or large numbers has, for example, been shown to modify grip aperture (small, large) in grasping behaviour [7Andres M.C.A. Davare M. Pesenti M. Olivier E. Seron X. Number magnitude and grip aperture interaction.Neuroreport. 2004; 15: 2773-2777PubMed Google Scholar, 8Lindemann O. Abolafia J.M. Girardi G. Bekkering H. Getting a grip on numbers: Numerical magnitude priming in object grasping.J. Exp. Psychol. Hum. Percept. Perform. 2007; 33: 1400-1409Crossref PubMed Scopus (104) Google Scholar]. Our results are therefore particularly interesting because they demonstrate links between numbers, magnitude and movement in a task where no action planning was required — especially as they relate to a task-irrelevant oculo-motor system. Our study is also noteworthy because it demonstrates that simply thinking of random numbers is accompanied by systematic changes in eye position. Lateral eye movements have previously been linked specifically to the computation of mental arithmetic problems, such as addition and subtraction [9Knops A. Thirion B. Hubbard E.M. Michel V. Dehaene S. Recruitment of an area involved in eye movements during mental arithmetic.Science. 2009; 324: 1583-1585Crossref PubMed Scopus (261) Google Scholar]. Although we have not directly investigated the neural mechanisms which link random number generation to eye position, it is interesting to speculate about these mechanisms. One possibility is that abstract cognitive tasks, such as random number generation, automatically adopt spatial strategies based on the exploitation of neural mechanisms which evolved primarily for navigating and interacting with the real world. In conclusion, a close look at the eyes may not only reveal what is in a person's mind, but also illustrate how abstract thoughts are grounded in basic sensory-motor processes [10Barsalou L.W. Grounded cognition.Annu. Rev. Psychol. 2008; 59: 617-645Crossref PubMed Scopus (3306) Google Scholar]. This study was supported by the Swiss National Science Foundation and the Betty and David Koetser Stiftung. We thank Caroline Schwarz for editorial assistance.