The mapping of number onto space is fundamental to measurement and mathematics. However, the mapping of young children, unschooled adults, and adults under attentional load shows strong compressive nonlinearities, thought to reflect intrinsic logarithmic encoding mechanisms, which are later "linearized" by education. Here we advance and test an alternative explanation: that the nonlinearity results from adaptive mechanisms incorporating the statistics of recent stimuli. This theory predicts that the response to the current trial should depend on the magnitude of the previous trial, whereas a static logarithmic nonlinearity predicts trialwise independence. We found a strong and highly significant relationship between numberline mapping of the current trial and the magnitude of the previous trial, in both adults and school children, with the current response influenced by up to 15% of the previous trial value. The dependency is sufficient to account for the shape of the numberline, without requiring logarithmic transform. We show that this dynamic strategy results in a reduction of reproduction error, and hence improvement in accuracy.numerical cognition | predictive coding | approximate number system | Weber-Fechner law | serial dependency H umans have a strong intuition of the spatial nature of numbers, usually (but not always) a horizontal "mental numberline," with numbers increasing from left to right (1-4). However, the nature of number mapping is not identical for all, but changes during development, starting from a nonlinear representation, well characterized as logarithmic (placing, for example, the number 10 near the midpoint of a 1-100 scale), then becoming more linear over the first years of schooling (3,5,6). Similarly, logarithmic-like numberlines have been demonstrated in indigenous Amazonian populations without formal mathematical schooling (4).Several recent studies have shown that under certain circumstances even the math-educated tend to reproduce numbers logarithmically. For example, we showed that depriving attentional resources leads to logarithmic-like numberline responses (7), consistent with the possibility that the native logarithmic encoding emerges when attention is deprived. Other studies have shown that the use of unfamiliar numerical format (such as exponential) can induce a switch from a linear to a logarithmic-like response, even in math-educated adults (7,8). Most recently, Dotan and Dehaene (9) have devised a clever technique to record the whole trajectory of the pointing response (across the face of a touchscreen), rather than just the endpoint: The response begins quite logarithmically, then corrects toward linear mapping by the time contact is made. All these studies have led many to interpret the logarithmic map as the direct reflection of the internal native number representation (4, 10-12) that becomes corrected over time by education but can emerge under special circumstances.Whereas the nonlinear numberline is consistent with intrinsic logarithmic processes, other explanat...