Existing random number generation studies demonstrate the presence of an embodied attentional bias in spontaneous number production corresponding to the horizontal Mental Number Line: Larger numbers are produced on right-hand turns and smaller numbers on left-hand turns (Loetscher et al.,, Curr. Biol., 18, R60). Furthermore, other concepts were also shown to rely on horizontal attentional displacement (Di Bono and Zorzi, 2013, Quart. J. Exp. Psychol., 66, 2348). In two experiments, we used a novel random word generation paradigm combined with two different ways to orient attention in horizontal space: Participants randomly generated words on left and right head turns (Experiment 1) or following left and right key presses (Experiment 2). In both studies, syllabically longer words were generated on right-hand head turns and following right key strokes. Importantly, variables related to semantic magnitude or cardinality (whether the generated words were plural-marked, referred to uncountable concepts, or were associated with largeness) were not affected by lateral manipulations. We discuss our data in terms of the ATOM (Walsh, 2015, The Oxford handbook of numerical cognition, 552) which suggests a general magnitude mechanism shared by different conceptual domains.