A hierarchical syntactic tree for numbers

Hierarchical representations of meaningful information are a unique property of human cognition and were studied extensively for language. Here, we show that meaning-carrying hierarchical representations exist in another, non-linguistic domain, namely multi-digit numbers. Participants heard 3- to 6-digit numbers and wrote down each number on paper with a digitizing pen. We recorded the inter-digit temporal gaps, which reflect the post-gap digit processing effort. The gaps followed a systematic hierarchical pattern: short gaps between decade and unit digits (also in the left triplet of 5- and 6-digit numbers), longer gaps between hundred and decade digits, and even longer inter-triplet gaps. We conclude that multi-digit numbers are represented hierarchically, e.g., a 6-digit number (123,456) as [1 & (2 & 3)] & [4 & (5 & 6)]. Critically, this hierarchical pattern was contingent on the stimuli being syntactically structured (‘twenty-three’) and was absent for unstructured stimuli (‘two, three’) – i.e., the hierarchical organization is not a general property of numbers but a unique property of their syntactic structure. We propose that the origin of this hierarchy is in a core syntactic representation of numbers, which can be likened to the internal hierarchical representation of sentences.