13 Apr 2009

Argument from Noise 1 Abstract and Introduction, in Schonbein, "Cognition and the Power of Continuous Dynamical Systems"

by Corry Shores
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[Nick Bostrom & Anders Sandberg argue for digital computation instead of analog for simulating human cognition. They base their contention in part on the "argument from noise." The entries in this series summarize Schonbein's defense of that argument.]

Whit Schonbein

Cognition and the Power
of Continuous Dynamical Systems


We normally model cognition as a computational system. So far, these models have been based on discrete-state digital computation. Recently philosophers have argued that cognition is too 'subtle' and 'complex' to be modeled this way. Their alternate proposal uses continuous rather than discrete mathematics. Which is to say, they employ analog computation rather than digital. They contend analog neural networks are more powerful computers. Schonbein will discuss three arguments against this analog alternative. He will show that the first two are untenable. But the third one, based on the "argument from noise," is a successful objection. Noise decreases the computational power of analog neural networks. And, noise always interferes with our brain's ability to process information. Hence proponents of analog models must first show how we might construct continuous dynamic systems that are not hindered by noise.

1. Introduction

We still do not understand the nature of cognition. Some argue that it is computational. We have complex mental representations. These we assemble from basic parts. Some call them "mental words." We build-up larger sentences using a finite set of rules, called the "grammar." Cognition results when we manipulate these mental sentences in accordance with transformation rules.

Recently others have rejected this "classical" explanation. They think that there is more to cognition than these mechanical rule-based manipulations that our home computers perform. They instead see cognition as resulting from the activity of complex dynamical systems.

Schonbein is concerned with one claim put forth by these dynamical theories, namely, that dynamical systems are more powerful than classical computers. This position is based on the intuition that "systems defined in terms of continuous rather than discrete values – e.g., artificial neural networks with real-valued activations – offer more ‘ways of behaving’ than are provided by classical systems." (57-58)

According to Schonbein, we need more than this intuition to argue that continuous dynamical systems are more powerful computers. There is reason to think that digital computation is no less adequate.

First he explains the discrete nature of traditional computation. Then, he shows how the continuous nature of analog computers may allow them to be more powerful. In fact, analog artificial neural networks have proven more powerful than traditional digital computers.

Schonbein follows with three critiques of the analog proposal. The first two fail, but the third succeeds. Noise reduces the power of analog systems to the point where they can be matched by digital ones. An idealized analog system might be more powerful. But we have no way to conceive how they will be realized materially. Proponents of analog need to explain how their more powerful system can be constructed despite problems with noise.

However, Schonbein will not conclude that we need to adopt classical digital systems. For, "there are systems that are simultaneously computational and non-classical." (58c)

Schonbein, Whit. "Cognition and the Power of Continuous Dynamical Systems." Mind and Machines, Springer, (2005) 15: pp. 57-71.

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