This paper investigates how people build interpretations of compound expressions in a novel formal system. In traditional arithmetic, interpretations are guided by an order of precedence convention (times and division precede addition and subtraction). This order is supported by alignment with the order of precedence. In the experiment described here, participants learned computation tables of two simple novel operators, and then were asked to discover a precedence order between them. The operators were presented with a physical spacing convention that either aligned with the precedence order, opposed it, or randomly opposed or aligned with the precedence order. Participants were more likely to reach a criterion of successful performance when the order of operations aligned with the precedence order, and did so more quickly than either other group. The results indicate that reasoners integrate salient perceptual cues with formal knowledge following particular conventions, even on novel systems.

# How space guides interpretation of a novel mathematical system

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