Chaos theory and Turing’s oracle computer

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Michael Brooks, based on Emmett Redd & Steven Younger, Missouri State University

New Scientist, 19 July 2014

Summary and review of the above article

INTRODUCTION: The proposal for a computer based on a whole range of inputs between fully off and fully on, which could exceed the limitations of the Gödel theorem by operating in an unpredictable and chaotic manner, may throw light on consciousness in the brain.

Alan Turing appreciated that the universal computing machines that he pioneered would have inescapable limitations. However in 1938, he had floated the idea of an ‘oracle’ that would go beyond these limitations. Turing seems to have speculated on the possible connection between randomness in nature and creative intelligence.

In more modern times, most computer scientists have considered that an oracle machine would be impossible because of how energy and information flow in the physical universe. Nevertheless, Emmett Redd and Steven Younger at Missouri State University think that they may be able to devise such a computer.

The Gödel theorem

Normal computers perform much better than humans at addition, multiplication, and if ‘x’ then ‘y’ type logical decisions. However, such computers can encounter ‘undecidable problems’. In the same generation as Turing, the mathematician, Kurt Gödel demonstrated that any system of logical axioms would always generate unprovable statements. This was similar in concept to the ‘halting problem’, in which a computer can never tell in advance if any programme will find a solution or instead become stuck or trapped in a loop. The requirement for an oracle machine was in order to go beyond the limitations proposed by Gödel and by the halting problem.

Unpredictability and chaos

The idea that Redd and Younger have proposed is that of analogue inputs. In contrast to the digital ‘0’ and ‘1’, on or off, used by conventional computers, they suggest using a whole range of values between fully off and fully on. This was seen as introducing an element of unpredictability. Unpredictability is a feature of chaotic systems, in which tiny changes in the initial conditions can lead to major changes in the eventual outcome. It is suggested that the computing of a neural network could be sensitive to such small differences. It is hoped that this exploration of chaos and unpredictability could allow the development of a computer that goes beyond the limitation imposed by Gödel.

COMMENT: Neuroscience has demonstrated a rational system in the brain involving the dorsolateral prefrontal with processing analogous to that of conventional computers, as limited by the Gödel theorem. However, it has also demonstrated the existence of a subjectively conscious emotional system that evaluates the reward/punisher qualities of both inputs and future actions. The comparisons of different kinds of rewards that do not have common measures of value is not capable of being the subject of algorithms, which by their nature depend on values. Such a comparison may require an accessing of the same fundamental physical law that governs the behaviour of quanta. Such behaviour is not the result of algorithms based on values, but is a given property of the universe. The interaction between evaluative systems accessing a fundamental level, and the more rational parts of the brain may well be unpredictable, in much the same way as the proposed functioning of the Emmett and Redd computer.

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