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

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.

journal_name

Biol Cybern

journal_title

Biological cybernetics

authors

van Hemmen JL

doi

10.1007/s00422-014-0609-3

subject

Has Abstract

pub_date

2014-10-01 00:00:00

pages

701-12

issue

5

eissn

0340-1200

issn

1432-0770

journal_volume

108

pub_type

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