Biological Cybernetics

, Volume 108, Issue 5, pp 701–712 | Cite as

Neuroscience from a mathematical perspective: key concepts, scales and scaling hypothesis, universality

Original Paper
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Abstract

This article analyzes the question of whether neuroscience allows for mathematical descriptions and whether an interaction between experimental and theoretical neuroscience can be expected to benefit both of them. It is argued that a mathematization of natural phenomena never happens by itself. First, appropriate key concepts must be found that are intimately connected with the phenomena one wishes to describe and explain mathematically. Second, the scale on, and not beyond, which a specific description can hold must be specified. Different scales allow for different conceptual and mathematical descriptions. This is the scaling hypothesis. Third, can a mathematical description be universally valid and, if so, how? Here we put forth the argument that universals also exist in theoretical neuroscience, that evolution proves the rule, and that theoretical neuroscience is a domain with still lots of space for new developments initiated by an intensive interaction with experiment. Finally, major insight is provided by a careful analysis of the way in which particular brain structures respond to perceptual input and in so doing induce action in an animal’s surroundings.

Keywords

Postsynaptic Neuron Firing Time Command Neuron Presynaptic Spike Threshold Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Notes

Acknowledgments

It is the author’s great pleasure to thank Henk Broer (Groningen), Robert Miller (Otago), Georg Northoff (Ottawa), Almut Schüz (Tübingen), and Theo Wobbes (Nijmegen) for constructive feedback. He acknowledges financial support from the BMBF through the BCCN—Munich.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Physik Department T35 and BCCN – MunichTechnische Universität MünchenGarching bei MünchenGermany

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