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Comparing continuous and discrete birthday coincidences : "Same-Day" versus "Within 24 Hours"
(2010)
In its classical form the famous birthday problem (Feller 1968; Mosteller 1987) addresses coincidences within a discrete sample space, looking at births that fall on the same calendar day. However, coincidence phenomena often arise in situations in which it is more natural to consider a continuous-time parameter. We first describe an elementary variant of the classical problem in continuous time, and then derive and illustrate close approximate relations that exist between the discrete and the continuous formulations.
As Chinese is written without orthographical word boundaries (i.e., spaces), it is unclear whether saccade targets are selected on the basis of characters or words and whether saccades are aimed at the beginning or the centre of words. Here, we report an experiment where 30 Chinese readers read 150 sentences while their eye movements were monitored. They exhibited a strong tendency to fixate at the word centre in single-fixation cases and at the word beginning in multiple-fixation cases. Different from spaced alphabetic script, initial fixations falling at the end of words were no more likely to be followed by a refixation than initial fixations at word centre. Further, single fixations were shorter than first fixations in two-fixation cases, which is opposite to what is found in Roman script. We propose that Chinese readers dynamically select the beginning or centre of words as saccade targets depending on failure or success with segmentation of parafoveal word boundaries.