Research Interests Prof. W. Schwarz

We are exposed to a world full of numbers, and without our ability to rapidly estimate, count, and discriminate numerical magnitudes our species would very likely be extinct. Numerical information as given by digits or number words is symbolic: it relies on learned conventions which must be held in, and retrieved from, long-term memory. My interest in these cognitive processes stems from the classical work of Moyer & Landauer (1967), in which they introduced their concept of a 'mental number line', a cognitive analog representation not unlike the representation of physical space.

In [Schwarz & Stein (1998)], we studied the time course of digit comparison processes by varying the relative onset of two to-be-compared digits, and accounted for the temporal dynamics in this task in terms of a diffusion model, which also handles numerical distance and speed-accuracy effects [Schwarz in Fischer & Laming, (1994)]. Related more recent work is [Reike & Schwarz (2016)]; in Schwarz & Eiselt (2012) we studied numerical distance effects in visual search and in Schwarz & Eiselt (2009) we studied numerical distance effects in temporal order judgments (TOJs).  The paper [Schwarz (2001)] looks at sequential trial-to-trial repetition benefits in repeating the number's format (eg, digit 4 vs. number word 'FOUR') and/or it's numerical value; also see Schwarz & Reike (2017). In [Schwarz & Ischebeck (2003)], we were interested the number-size congruency effects that arise when (eg) a numerically large (that is, large within a range of 1-9) digit such as 8 is printed in a small physical font, and accounted for many quantitative details of this effect on response speed and accuracy in terms of a diffusion 'coalescence' model. The same effect is studied in [Schwarz & Heinze (1998)] by means of event-related potentials (ERPs), which allow for an online-measurement of the temporal genesis and the electrophysiological signature of the number-size congruency effect.  Related more recent work is [Reike & Schwarz (2017) and Schwarz & Reike (2017)].

In [Schwarz & Keus (2004)], we explore the SNARC effect first reported by Dehäne et al. (1993): humans are faster to respond to small digits with the left hand, and to large digits with the right hand, even when the numerical magnitude of the digits is irrelevant for the task at hand (eg, parity judgment). We reasoned that this effect might simply reflect overlearned hand-specific associations of small/large digits with the left/right hand, as, eg, on most keyboards; alternatively, it might reflect a genuinely spatial number representation, independent of the activated effectors.

We thus studied this task using eye movements, and found that the SNARC effect obtains in an essentially identical form with saccadic responses, too. This finding clearly supports the second view; similar findings hold for pedal responses (Schwarz & Müller, 2006). Related more recent work is [Müller & Schwarz (2006, 2007)].