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Roger Penrose's View

Roger Penrose [Pen90] comes into play by arguing that low-level quantum effects, which are thought to be incomputable, may be relevant at the level of consciousness. In short, this would render the brain and consciousness noncomputational and nonalgorithmic.
While most scientists can center their research around one area, such as Quantum physics at the lower level of scale, or astrology at the higher level of scale, Roger Penrose has made some remarkable breakthroughs in both fields^{4.1}.

Proponents of strong AI say the the mind can be simulated and can be ascribed as having thoughts and a mind. If the mind is a product of a mere calculations done by brain cells, this makes it transferable to any other Turing complete machine (other hardware). The hardware becomes an implementation that is irrelevant to the behavior of the system. Believers of strong AI also ascribe properties such as conscience and understanding to any such simulation. Penrose attacks this idea on the ground of dualism. Dualism is the view originating from Descartes view of separate body and mind. In this view, the mind is regarded as being distinctly non-material. Roughly speaking, strong AI says that the mind stays intact and can exist in any Universal Turing machine given enough capacity.

Penrose points out the far-reaching implications of the infamous stopping problem^{4.2}, which is applicable to universal Turing machines, and in consequence any algorithmic machine, which it's by definition equivalent to.

The same conclusion is drawn for mathematics in general. In order to unequivocally be able to decide the truth of any proposition, Hilbert created the challenge of once and for all creating a sound and consistent formal approach. If successful, anything that was provable would be calculable. Hilbert's approach hit a wall because of Kurt Gödel's incompleteness theorem^{4.3}: formalist axiom-based approaches can never be consistent or proved based on the formal system itself, stressing the importance for insight and perhaps mathematical intuition.

The fact that algorithmic operations are only a small and limited domain of mathematics, is a central point in Penrose's argument.

Time-reversibility (or symmetry) is allowed for any law of physics and does not create inconsistencies, except for quantum vector reduction `R'. This, according to Penrose, calls for a Quantum Gravitation Theory with this inconsistency and the direction of entropy addressed at its basis. Neither classical nor quantummechanics - in its current form - can physically explain the way we think.

Erik de Bruijn
2007-10-19