The approximate number system represents magnitude and precision

Rational number representation by the approximate number system

The approximate number system (ANS) enables organisms to represent the approximate number of items in an observed collection, quickly and independently of natural language. Recently, it has been proposed that the ANS goes beyond representing natural numbers by extracting and representing rational numbers (Clarke & Beck, 2021a). Prior work demonstrates that adults and children discriminate ratios in an approximate and ratio-dependent manner, consistent with the hallmarks of the ANS. Here, we use a well-known "connectedness illusion" to provide evidence that these ratio-dependent ratio discriminations are (a) based on the perceived number of items in seen displays (and not just non-numerical confounds), (b) are not dependent on verbal working memory, or explicit counting routines, and (c) involve representations with a part-whole (or subset-superset) format, like a fraction, rather than a part-part format, like a ratio. These results vindicate key predictions of the hypothesis that the ANS represents rational numbers.

When eleven does not equal 11: Investigating exactness at a number's upper bound

The approximate number system (a) views number as an imprecise signal that (b) functions equivalently regardless of a number's initial presentation. These features do not readily account for exact readings when a task calls for them. While profiting from insights in areas neighboring the number cognition literature, we propose that linguistic-pragmatic and cultural pressures operate on a number's upper bound in order to provide exact readings. With respect to (a), Experimental Pragmatic findings indicate that numbers appear to be semantically lower-bounded (Eleven candidates are coming means at least eleven) but fluid at its upper-bound; exactly readings emerge as a consequence of an additional pragmatic process that solidifies the upper bound. With respect to (b), studies from cognitive anthropology underline how symbolic representations of number are distinct from written codes. Here, we investigate a novel hypothesis proposing that symbolic expressions of number (such as "11") explicitly provide exactly readings unlike verbal (oral and written) ones, which engender at least readings. We then employ a Numerical Magnitude Task (NMT), in which French-speaking participants determine whether a presented number is lesser or greater than a benchmark (12) in one of three presentation conditions: i) Symbolic/Hindu-Arabic (e.g. "11" via screen), ii) Oral (e.g. "/'on.zə/" via headphones), or; iii) spelled-out-in-Letters (e.g. "onze" via screen). Participants also carry out a Number Identification Task (NIT) so that each participant's recognition speed per number can be removed from their NMT times. We report that decision reaction times to "onze" take longer to process (and prompt more errors) than "treize" whereas "11" and "13" are comparable. One prediction was not supported: Decision times to the critical oral forms ("/'on.zə/" and "[tʁ̥ɛːzə̆]") were comparable, making these outcomes resonate with those in the Symbolic condition.