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Abstract The subjective number-space mapping and, especially, its evolution in young children has been the subject of intense controversy among different competing models. Many studies point out that: (i) young children's innate estimates follow a logarithmic mapping (Weber-Fechner law) and (ii) driven by education, children evolve into a linear mapping. In this paper we show, in consonance with other investigations, that innate numerical intuitions of young children are in fact a linear mapping, and not a logarithmic one. We found that young children extrapolate linearly from a reference point. The apparent logarithmic mapping is an artifact produced by placing a huge range of numbers within a small number line. We show how the appearance of the mapping can be modulated by changing the size and contour conditions of the number lines used in experiments.

Al hablar sobre los orígenes de la ciencia ficción y la literatura de anticipación, inmediatamente pensamos en los nombres de Herbert G. Wells o Julio Verne, prolíficos autores de finales del xix y fuente de inspiración de posteriores generaciones. Pocos incluyen a Edgar Allan Poe, autor de principios del mismo siglo y fuente de inspiración de los ya mencionados. Y es que si Verne y Wells fueron los padres de la ciencia ficción, sin duda Poe fue el abuelo.

The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map nonlinearity or other particulars. We derive exact results for their degree distribution and related quantities, recast them in the context of the renormalization group and find that its fixed points coincide with those of network entropy optimization. Furthermore, we show that the network entropy mimics the Lyapunov exponent of the map independently of its sign, hinting at a Pesin-like relation equally valid out of chaos.