Purpose: We compare right-to-left and left-to-right orthographies to test the theory, derived from studying the latter, that small temporal asynchronies between the two eyes at the beginning and end of every fixation favor ocular prevalence for the left eye in the left hemifield and the right eye in the right hemifield. Ocular prevalence is the prioritizing of one eye's input in the conscious, fused binocular percept. Method: We analyze binocular eye-tracking data from the reading of multiline Arabic and Hebrew text by 28 Arabic (M = 28.7, SD = 7.2 years, 71% female) and 16 Hebrew (M = 30.1, SD = 7.9 years, 50% female) native speakers, respectively. Results: Critically, the complex pattern of asynchronies in Arabic and Hebrew resembles that reported for the left-to-right orthographies, English and Chinese, but with some particular differences that we attribute to left hemisphere specialization in word recognition. Conclusion: We conclude, first, that the oculomotor musculature plays an "embodied" role in the perception and cognition associated with reading. We further discuss how the evident hemispheric asymmetries in parafoveal lookahead may be reflected in the nature of the conventions of right-to-left scripts. We articulate the claim that the orthographic conventions of a language tend to reflect reading direction and hemispheric differences.