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Ordinal Rules

Research on how people process numerical order carries implications for our basic theoretical understanding of what a number means and our practical understanding of the foundations upon which more sophisticated mathematics are built. Previous work has consistently shown that one’s sense of ordinality is linked to the count-list, leading to a general assumption that participants are strongly biased to see sequences of numbers that match the count-list (2-3-4, 5-6-7) as being in order. One relatively unexamined consequence of the link between ordinality and the count-list is a bias to see all non-count-list sequences as not in order (even when they actually are: 1-3-5, 2-4-6). Here, we disentangled these factors using a novel paradigm that manipulated the rules for determining whether numerical sequences are ‘in-order’. While we found strong biases to see ordered, non-count-list sequences as ‘not-in-order’ (single-digits: d=1.25, double-digits: d=1.50), we saw only weak biases to see count-list sequences as ‘in-order’ (single-digits: d=0.33, double-digits: d=0.19). Furthermore, the non-count-list bias provided a stronger and more consistent explanation for the reversal of the distance-effect (single-digits: d=0.42, double-digits: d=0.65), relative to the count-
list bias (single-digits: d=0.28, double-digits: d=0.22). These data provide evidence that over-reliance on the count-list in guiding our sense of numerical order may restrict our broader sense of what it means for numbers to be ordered, which in turn provides a novel explanation for a common phenomenon in numerical cognition. More broadly, this work helps describe how people think about one of the foundational principles of mathematics – numerical order.