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Daily experience suggests that we perceive distances near us linearly. However, the actual geometry of spatial representation in the brain is unknown. Here we report that neurons in the CA1 region of rat hippocampus that mediate spatial perception represent space according to a non-linear hyperbolic geometry. This geometry uses an exponential scale and yields greater positional information than a linear scale. We found that the size of the representation matches the optimal predictions for the number of CA1 neurons. The representations also dynamically expanded proportional to the logarithm of time that the animal spent exploring the environment, in correspondence with the maximal mutual information that can be received. The dynamic changes tracked even small variations due to changes in the running speed of the animal. These results demonstrate how neural circuits achieve efficient representations using dynamic hyperbolic geometry.

 

When conducting a science investigation in biology, chemistry, physics or earth science, students often need to obtain, organize, clean, and analyze the data in order to draw conclusions about a particular phenomenon. It can be difficult to develop lesson plans that provide detailed or explicit instructions about what students need to think about and do to develop a firm conceptual understanding, particularly regarding data analysis. This article demonstrates how computational thinking principles and data practices can be merged to develop more effective science investigation lesson plans. The data practices of creating, collecting, manipulating, visualizing, and analyzing data are merged with the computational thinking practices of decomposition, pattern recognition, abstraction, algorithmic thinking, and automation to create questions for teachers and students that help them think through the underlying processes that happen with data during high school science investigations. The questions can either be used to elaborate lesson plans or embedded into lesson plans for students to consider how they are using computational thinking during their data practices in science.