Mathematical physicist Roger Penrose has written controversial books on the connection between fundamental physics and human (or animal) consciousness. In The Emperor’s New Mind, he argues that known laws of physics are inadequate to explain the phenomenon of consciousness. Penrose proposes the characteristics this new physics may have and specifies the requirements for a bridge between classical and quantum mechanics (what he calls correct quantum gravity). He claims that the present computer is unable to have intelligence because it is an algorithmically deterministic system. He argues against the viewpoint that the rational processes of the mind are completely algorithmic and can thus be duplicated by a sufficiently complex computer. This contrasts with supporters of strong artificial intelligence, who contend that thought can be simulated algorithmically. He bases this on claims that consciousness transcends formal logic because things such as the insolubility of the halting problem and Gödel’s incompleteness theorem prevent an algorithmically based system of logic from reproducing such traits of human intelligence as mathematical insight. These claims were originally espoused by the philosopher John Lucas of Merton College, Oxford. The Penrose/Lucas argument about the implications of Gödel’s incompleteness theorem for computational theories of human intelligence has been widely criticized by mathematicians, computer scientists and philosophers, and the consensus among experts in these fields seems to be that the argument fails, though different authors may choose different aspects of the argument to attack.
Penrose uses a variant of Turing’s halting theorem to demonstrate that a system can be deterministic without being algorithmic. (E.g., imagine a system with only two states, ON and OFF. If the system’s state is ON if a given Turing machine halts, and OFF if the Turing machine does not halt, then the system’s state is completely determined by the Turing machine, however there is no algorithmic way to determine whether the Turing machine stops.) Penrose believes that such deterministic non-algorithmic processes may come in play in the quantum mechanical wave function reduction, and may be harnessed by the brain.
In 1994, Penrose followed up The Emperor’s New Mind with Shadows of the Mind, and in 1997 with The Large, the Small and the Human Mind, further updating and expanding his theories. Marvin Minsky, a leading proponent of artificial intelligence, responded that Penrose “tries to show, in chapter after chapter, that human thought cannot be based on any known scientific principle.” In contrast, Minsky argues that humans are, in fact, machines, whose functioning, although complex, is fully explainable by current physics. Minsky maintains that “one can carry that quest [for scientific explanation] too far by only seeking new basic principles instead of attacking the real detail. This is what I see in Penrose’s quest for a new basic principle of physics that will account for consciousness.”
Penrose and Stuart Hameroff have speculated that consciousness is the result of quantum gravity effects in microtubules, which they dubbed Orch-OR(orchestrated objective reduction). But Max Tegmark, in a paper in Physical Review E, calculated that the time scale of neuron firing and excitations in microtubules is slower than the decoherence time by a factor of at least 10,000,000,000. The reception of the paper is summed up by this statement in Tegmark’s support: “Physicists outside the fray, such as IBM’s John A. Smolin, say the calculations confirm what they had suspected all along. ‘We’re not working with a brain that’s near absolute zero. It’s reasonably unlikely that the brain evolved quantum behavior'”. Tegmark’s paper has been widely cited by critics of the Penrose-Hameroff position. It has been claimed by Hameroff to be based on a number of incorrect assumptions (see linked paper below from Hameroff, Scott Hagan and Jack Tuszyński), but Tegmark in turn has argued that the critique is invalid (see rejoinder link below). In particular, Hameroff points out the peculiarity that Tegmark’s formula for the decoherence time includes a factor of T2 in the numerator, meaning that higher temperatures would lead to longer decoherence times. Tegmark’s rejoinder keeps the factor of T2 for the decoherence time.
Phillip Tetlow, although himself supportive of Penrose’s views, acknowledges that Penrose’s ideas about the human thought process are not widely accepted in scientific circles, citing Minsky’s criticisms and quoting science journalist Charles Seife’s description of Penrose as “one of a handful of scientists” who believe that the nature of consciousness suggests a quantum process.
In spite of the many critics, new experimental results of imaging neuronal spikes and spike directivity data suggest a complex process of computation in neurons that may include electrical interactions on the quantum level  and reject naive spike timing models of neural coding.