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Theoretical physicist Roger Penrose and anaesthesiologist Stuart Hameroff collaborated to produce the theory known as "orchestrated objective reduction" (Orch-OR). Penrose and Hameroff initially developed their ideas separately and later collaborated to produce Orch-OR in the early 1990s. They reviewed and updated their theory in 2013. Penrose's argument stemmed from Gödel's incompleteness theorems. In his first book on consciousness, The Emperor's New Mind (1989), he argued that while a formal system cannot prove its own consistency, Gödel's unprovable results are provable by human mathematicians. Penrose took this to mean that human mathematicians are not formal proof systems and not running a computable algorithm. According to Bringsjord and Xiao, this line of reasoning is based on fallacious equivocation on the meaning of computation. In the same book, Penrose wrote: "One might speculate, however, that somewhere deep in the brain, cells are to be found of single quantum sensitivity. If this proves to be the case, then quantum mechanics will be significantly involved in brain activity." Penrose determined that wave function collapse was the only possible physical basis for a non-computable process. Dissatisfied with its randomness, he proposed a new form of wave function collapse that occurs in isolation and called it objective reduction. He suggested each quantum superposition has its own piece of spacetime curvature and that when these become separated by more than one Planck length, they become unstable and collapse. Penrose suggested that objective reduction represents neither randomness nor algorithmic processing but instead a non-computable influence in spacetime geometry from which mathematical understanding and, by later extension, consciousness derives. Hameroff provided a hypothesis that microtubules would be suitable hosts for quantum behavior. Microtubules are composed of tubulin protein dimer subunits. The dimers each have hydrophobic pockets that are 8 nm apart and may contain delocalized π electrons. Tubulins have other smaller non-polar regions that contain π-electron-rich indole rings separated by about 2 nm. Hameroff proposed that these electrons are close enough to become entangled. He originally suggested that the tubulin-subunit electrons would form a BoseEinstein condensate, but this was discredited. He then proposed a Frohlich condensate, a hypothetical coherent oscillation of dipolar molecules, but this too was experimentally discredited. For instance, the proposed predominance of A-lattice microtubules, more suitable for information processing, was falsified by Kikkawa et al., who showed that all in vivo microtubules have a B lattice and a seam. Orch-OR predicted that microtubule coherence reaches the synapses through dendritic lamellar bodies (DLBs), but De Zeeuw et al. proved this impossible by showing that DLBs are micrometers away from gap junctions. In 2014, Hameroff and Penrose claimed that the discovery of quantum vibrations in microtubules by Anirban Bandyopadhyay of the National Institute for Materials Science in Japan in March 2013 corroborates Orch-OR theory. Experiments that showed that anaesthetic drugs reduce how long microtubules can sustain suspected quantum excitations appear to support the quantum theory of consciousness. In April 2022, the results of two related experiments at the University of Alberta and Princeton University were announced at The Science of Consciousness conference, providing further evidence to support quantum processes operating within microtubules. In a study Stuart Hameroff was part of, Jack Tuszyński of the University of Alberta demonstrated that anesthetics hasten the duration of a process called delayed luminescence, in which microtubules and tubulins re-emit trapped light. Tuszyński suspects that the phenomenon has a quantum origin, with superradiance being investigated as one possibility. In the second experiment, Gregory D. Scholes and Aarat Kalra of Princeton University used lasers to excite molecules within tubulins, causing a prolonged excitation to diffuse through microtubules further than expected, which did not occur when repeated under anesthesia. However, diffusion results have to be interpreted carefully, since even classical diffusion can be very complex due to the wide range of length scales in the fluid filled extracellular space. Nevertheless, University of Oxford quantum physicist Vlatko Vedral told that this connection with consciousness is a really long shot. Also in 2022, a group of Italian physicists conducted several experiments that failed to provide evidence in support of a gravity-related quantum collapse model of consciousness, weakening the possibility of a quantum explanation for consciousness. Although these theories are stated in a scientific framework, it is difficult to separate them from scientists' personal opinions. The opinions are often based on intuition or subjective ideas about the nature of consciousness. For example, Penrose wrote:

[M]y own point of view asserts that you can't even simulate conscious activity. What's going on in conscious thinking is something you couldn't properly imitate at all by computer.... If something behaves as though it's conscious, do you say it is conscious? People argue endlessly about that. Some people would say, "Well, you've got to take the operational viewpoint; we don't know what consciousness is. How do you judge whether a person is conscious or not? Only by the way they act. You apply the same criterion to a computer or a computer-controlled robot." Other people would say, "No, you can't say it feels something merely because it behaves as though it feels something." My view is different from both those views. The robot wouldn't even behave convincingly as though it was conscious unless it really was—which I say it couldn't be, if it's entirely computationally controlled.

Penrose continues: