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Biophysics of ComputationInformation Processing in Single Neurons$
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Christof Koch

Print publication date: 1998

Print ISBN-13: 9780195104912

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195104912.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 23 October 2021

Computing with Neurons: A Summary

Computing with Neurons: A Summary

Chapter:
(p.469) 21 Computing with Neurons: A Summary
Source:
Biophysics of Computation
Author(s):

Christof Koch

Publisher:
Oxford University Press
DOI:10.1093/oso/9780195104912.003.0027

We now have arrived at the end of the book. The first 16 chapters dealt with linear and nonlinear cable theory, voltage-dependent ionic currents, the biophysical origin of spike initiation and propagation, the statistical properties of spike trains and neural coding, bursting, dendritic spines, synaptic transmission and plasticity, the types of interactions that can occur among synaptic inputs in a passive or active dendritic arbor, and the diffusion and buffering of calcium and other ions. We attempted to weave these disparate threads into a single tapestry in Chaps. 17-19, demonstrating how these elements interact within a single neuron. The penultimate chapter dealt with various unconventional biophysical and biochemical mechanisms that could instantiate computations at the molecular and the network levels. It is time to summarize. What have we learned about the way brains do or do not compute? The brain has frequently been compared to a universal Turing machine (for a very lucid account of this, see Hofstadter, 1979). A Turing machine is a mathematical abstraction meant to clarify what is meant by algorithm, computation, and computable. Think of it as a machine with a finite number of internal states and an infinite tape that can read messages composed with a finite alphabet, write an output, and store intermediate results as memory. A universal Turing machine is one that can mimic any arbitrary Turing machine. We are here not interested in the renewed debate as to whether or not the brain can, in principle, be treated as such a machine (Lucas, 1964; Penrose, 1989), but whether this is a useful way to conceptualize nervous systems in this manner. Because brains have limited precision, only finite amounts of memory and do not live forever, they cannot possibly be like “real” Turing machines. It is therefore more appropriate to ask: to what extent can brains be treated as finite state machines or automata! Such a machine only has finite computational and memory resources (Hopcroft and Ullman, 1979). The answer has to be an ambiguous “it depends.”

Keywords:   Apical dendrite, Bandpass filters, Computation, Finite state machines, Gain control, Information processing, Linearity, Power consumption, Shunting inhibition

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