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Several other criticisms regarding biology have come to the fore over the years. Papers by Georgiev, D.<ref name="Georgiev2007"/><ref name="Georgiev2009a"/> point to a number of problems with Hameroff's proposals, including a lack of explanation for the probabilistic firing of axonal synapses, an error in the calculated number of the tubulin dimers per cortical neuron. Nevertheless Hameroff insisted on a 2013 interview that those falsifications are invalid, including the assertions made by this wikipedia article.<ref name="singularityinterview2013">{{Cite AV media
Several other criticisms regarding biology have come to the fore over the years. Papers by Georgiev, D.<ref name="Georgiev2007"/><ref name="Georgiev2009a"/> point to a number of problems with Hameroff's proposals, including a lack of explanation for the probabilistic firing of axonal synapses, an error in the calculated number of the tubulin dimers per cortical neuron. Nevertheless Hameroff insisted on a 2013 interview that those falsifications are invalid, including the assertions made by this wikipedia article.<ref name="singularityinterview2013">{{Cite AV media
|title=Stuart Hameroff on Singularity 1 on 1: Consciousness is More than Computation!
|title=Stuart Hameroff on Singularity 1 on 1: Consciousness is More than Computation!
|time=00:31:21
|time=00:30:59
|date=12 Sept 2013
|date=12 Sept 2013
|editor-first=Nikola
|editor-first=Nikola
|editor-last=Danaylov
|editor-last=Danaylov
|publisher=Singularity Weblog
|publisher=Singularity Weblog
|quote=They [the wikipedia article] talk about [...] some fairly minor things, all of which are wrong! [...] I dispute Wikipedia :-)
|quote=Consciousness is the most important thing there is!
|url=https://www.youtube.com/watch?v=YpUVot-4GPM
|url=https://www.youtube.com/watch?v=YpUVot-4GPM
|accessdate=25 March 2014
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Revision as of 10:18, 25 March 2014

Orchestrated objective reduction (Orch-OR) is a controversial but prospective 20-year-old theory of consciousness conceptualized by the theoretical physicist Sir Roger Penrose and anesthesiologist Stuart Hameroff, which claims that consciousness derives from deeper level, finer scale quantum activities inside the cells, most prevalent in the brain neurons. It combines approaches from the radically different angles of molecular biology, neuroscience, quantum physics, pharmacology, philosophy, quantum information theory, and aspects of quantum gravity.[1]

While mainstream theories assume consciousness to emerge from complex computations performed by communicating cerebral neurons through synapses,[2][3] Orch-OR posits that consciousness is based on non-computable quantum processing performed by qubits formed collectively on the microtubules of the cells, a process significantly amplified in the neurons.[4] The qubits are based on oscillating dipoles forming superimposed resonance rings in helical pathways throughout microtubule lattices. The oscillations are either electric, due to charge separation from London forces, or most favorably magnetic, due to electron spin—and possibly also due to nuclear spins (which can remain isolated for longer periods of time), and occur in gigahertz, megahertz and kilohertz frequency ranges. [1][5] The orchestration refers to the hypothetical process by which connective proteins, such as microtubule-associated proteins (MAPs), influence or orchestrate the state reduction of the qubits by modifying the spacetime-separation of their superimposed states.[6] The later is based on the Diósi-Penrose scheme for interpreting quantum mechanics, which postulates the existence of an objective threshold governing the collapse of quantum-states, related to the difference of the space-time curvature of these states in the fine scale structure of the universe.[7]

The basis of Orch-OR has been harshly criticized from its inception by mainstream mathematicians,[8][9][10] philosophers,[11][12][13][14][15][16] and scientists,[17][18][19][20][21] forcing the authors to revise and elaborate many of the peripheral assumptions of the theory, but the core ideas have withstood.[22] The criticism was mostly drawn on Penrose's interpretation of Gödel's theorem to assume the non-computability of consciousness, on the abductive reasoning linking that non-computability to quantum processes, and on the unsuitability of the brain to host the seemingly delicate quantum phenomena required by the theory, since it was considered too "warm, wet and noisy" to avoid decoherence.

The Penrose–Lucas argument

The Penrose–Lucas argument states that, because humans are capable of knowing the truth of Gödel-unprovable statements, human thought is necessarily non-computable.[23]

In 1931, mathematician and logician Kurt Gödel proved that any effectively generated theory capable of proving basic arithmetic cannot be both consistent and complete. Furthermore, he showed that any such theory also including a statement of its own consistency is inconsistent. A key element of the proof is the use of Gödel numbering to construct a "Gödel sentence" for the theory, which encodes a statement of its own incompleteness, e.g. "This theory can't assert the truth of this statement." This statement is either true but unprovable (incompleteness) or false and provable (inconsistency). An analogous statement has been used to show that humans are subject to the same limits as machines.[24]

However, in his first book on consciousness, The Emperor's New Mind (1989), Penrose made Gödel's theorem the basis of what quickly became an intensely controversial claim.[23] He argued that while a formal proof system cannot prove its own inconsistency, Gödel-unprovable results are provable by human mathematicians. He takes this disparity to mean that human mathematicians are not describable as formal proof systems, and are not therefore running a non-computable algorithm. Similar claims about the implications of Gödel's theorem were originally espoused by the philosopher John Lucas of Merton College, Oxford.

The inescapable conclusion seems to be: Mathematicians are not using a knowably sound calculation procedure in order to ascertain mathematical truth. We deduce that mathematical understanding – the means whereby mathematicians arrive at their conclusions with respect to mathematical truth – cannot be reduced to blind calculation!

— Roger Penrose[25]

Criticism of the Penrose–Lucas argument

The Penrose–Lucas argument about the implications of Gödel's incompleteness theorem for computational theories of human intelligence has been widely criticized by mathematicians,[8][9][10] computer scientists,[16] and philosophers,[11][12][13][14][15] and the consensus among experts in these fields is that the argument fails,[26][27][28] with different authors choosing different aspects of the argument to attack.[28][29]

Geoffery LaForte points out that in order to know the truth of an unprovable Gödel sentence, one must already know the formal system is consistent. Referencing Benacerraf, he then demonstrates that humans cannot prove that they are consistent,[8] and in all likelihood human brains are inconsistent. He comically points to contradictions from within Penrose's own writings as evidence. Similarly, Marvin Minsky argues that because humans can construe false ideas to be factual, human mathematical understanding need not be consistent, and consciousness may easily have a deterministic basis.[30]

Solomon Feferman, a professor of mathematics, logic and philosophy has made criticisms of Penrose's argument.[31] He faults detailed points in Penrose's second book, Shadows of the Mind. As a mathematician, he[clarification needed] argues that mathematicians do not progress by computer-like or mechanistic search through proofs, but by trial-and-error reasoning, insight and inspiration, and that machines cannot share this approach with humans. However, he thinks that Penrose goes too far in his arguments. Feferman points out that everyday mathematics, as used in science, can in practice be formalized. He also rejects Penrose's Platonism.

John Searle criticizes Penrose's appeal to Gödel as resting on the fallacy that all computational algorithms must be capable of mathematical description. As a counter-example, Searle cites the assignment of license plate numbers to specific vehicle identification numbers, in order to register a vehicle. According to Searle, no mathematical function can be used to connect a known VIN with its LPN, but the process of assignment is quite simple—namely, "first come, first served"—and can be performed entirely by a computer.[32]

Another critic, Charles Seife, has said, "Penrose, the Oxford mathematician famous for his work on tiling the plane with various shapes, is one of a handful of scientists who believe that the ephemeral nature of consciousness suggests a quantum process."[citation needed]

Objective reduction

Main article: Penrose interpretation

Motivation

If correct, the Penrose–Lucas argument creates a need to understand the physical basis of non-computational behaviour in the brain.[citation needed] Most physical laws are computable, and thus algorithmic. However, Penrose determined that wave function collapse was a prime candidate for a non-computable process.

In quantum mechanics, particles are treated differently from the macroscopic objects of classical mechanics. Particles are described not by position vectors, but by wave functions, which evolve according to the Schrödinger equation. Non-stationary wave functions are linear combinations of the eigenstates of the system, a phenomenon described by the superposition principle. When a quantum system interacts with a classical system—i.e. when an observable is measured—the system appears to collapse to a random eigenstate of that observable from a classical vantage point.

If collapse is truly random, then there is no process or algorithm that can deterministically predict its outcome. This provided Penrose with a candidate for the physical basis of the non-computable process that he hypothesized to exist in the brain. However, he disliked the random nature of environmentally-induced collapse, as randomness was not a promising basis for mathematical understanding. Penrose proposed that isolated systems may still undergo a new form of wave function collapse, which he calls objective reduction (OR).[citation needed]

Details

Penrose sought to reconcile general relativity and quantum theory using his own ideas about the possible structure of spacetime.[23][33] He suggested that at the Planck scale curved spacetime is not continuous, but discretized. Penrose postulates that each separated quantum superposition has its own piece of spacetime curvature, a blister in spacetime. Penrose suggests that gravity exerts a force on these spacetime blisters, which become unstable above the Planck scale of and collapse to just one of the possible states of the particle. The rough threshold for OR is given by Penrose's indeterminacy principle:

where:

  • is the time until OR occurs,
  • is the gravitational self-energy or the degree of spacetime separation given by the superpositioned mass, and
  • is the reduced Planck constant.

Thus, the greater the mass-energy of the object, the faster it will undergo OR, and vice versa. Atomic-level superpositions would require 10 million years to reach OR threshold, while an isolated 1 kilogram object would reach OR threshold in only 10−37s. However objects somewhere between these two scales could collapse on a timescale relevant to neural processing.[citation needed]

An essential feature of Penrose's theory is that the choice of states when objective reduction occurs is selected neither randomly, as are choices following wave function collapse, nor completely algorithmically. Rather, states are selected by a "non-computable" influence embedded in the Planck scale of spacetime geometry. Penrose claims that such information is Platonic, representing pure mathematical truth, aesthetic, and ethical values at the Planck scale. This relates to Penrose's ideas concerning the three worlds: physical, mental, and the Platonic mathematical world. In his theory, the Platonic world corresponds to the geometry of fundamental spacetime that is claimed to support non-computational thinking.[citation needed]

There is no evidence for Penrose's objective reduction, but the theory is considered testable, and plans exist to carry out a relevant experiment.[34]

In August 2013, Penrose and Hameroff reported that the experiments have been carried out by Bandyopadhyay et al., supporting Penrose's theory on six out of the twenty theses he puts forward and invalidating none of the others. They subsequently responded to further critiques from a number of sources, including a 2013 critique from an Australian group led by Reimers.[6][35][36]

The creation of the Orch-OR model

Penrose and Hameroff initially developed their ideas quite separately from one another, and it was only in the 1990s that they cooperated to produce the Orch-OR theory. Penrose came to the problem from the view point of mathematics and in particular Gödel's theorem, while Hameroff approached it from a career in cancer research and anesthesia that had given him an interest in brain structures. Specifically, when Penrose wrote his first consciousness book, The Emperor's New Mind in 1989, he lacked a detailed proposal for how such quantum processes could be implemented in the brain. Subsequently, Hameroff read The Emperor's New Mind and suggested to Penrose that certain structures within brain cells (neurons) were suitable candidate sites for quantum processing and ultimately for consciousness.[37][38] The Orch-OR theory arose from the cooperation of these two scientists, and was developed in Penrose's second consciousness book Shadows of the Mind (1994).[33]

Hameroff's contribution to the theory derived from studying brain cells. His interest centered on the cytoskeleton, which provides an internal supportive structure for neurons, and particularly on the microtubules,[38] which are the most important component of the cytoskeleton. As neuroscience has progressed, the role of the cytoskeleton and microtubules has assumed greater importance. In addition to providing structural support, microtubule functions include axoplasmic transport and control of the cell's movement, growth and shape.[38]

Microtubule condensates

Hameroff proposed that microtubules were suitable candidates for quantum processing.[38] Microtubules are made up of tubulin protein subunits. The tubulin protein dimers of the microtubules have hydrophobic pockets which might contain delocalized π electrons. Tubulin has other smaller non-polar regions, for example 8 tryptophans per tubulin, which contain π electron-rich indole rings distributed throughout tubulin with separations of roughly 2 nm. Hameroff claims that this is close enough for the tubulin π electrons to become quantum entangled.[39] During entanglement, particles' states become inseparably correlated.

Hameroff originally suggested the tubulin-subunit electrons would form a Bose–Einstein condensate,[40] but this was discredited.[citation needed] He then proposed a Frohlich condensate, a hypothetical coherent oscillation of dipolar molecules. However, this too has been experimentally discredited by Reimers et all.[41] Hameroff suggested that such condensate behavior would magnify nanoscopic quantum effects to have large scale influences in the brain.

Hameroff proposed that condensates in microtubules in one neuron can link with microtubule condensates in other neurons and glial cells via the gap junctions of electrical synapses.[42][43] Hameroff proposed that the gap between the cells is sufficiently small that quantum objects can tunnel across it, allowing them to extend across a large area of the brain. He further postulated that the action of this large-scale quantum activity is the source of 40 Hz gamma waves. Here, Hameroff built upon[44] the much less controversial theory that gap junctions are related to the gamma oscillation.[45]

Consequences

The Orch-OR theory combines the Penrose–Lucas argument with Hameroff's hypothesis on quantum processing in microtubules. Altogether, it proposes that when condensates in the brain undergo an objective reduction of their wave function, their collapse connects non-computational decision making to experiences embedded in the fundamental geometry of spacetime.

The theory further proposes that the microtubules both influence and are influenced by the conventional activity at the synapses between neurons. Further to this, Hameroff in 1998 made 8 probable assumptions and 20 testable predictions to back his proposal.[46] However, many of these proposals have been disproven (see "Criticism" section, below).

In January 2014 Hameroff and Penrose announced[citation needed] that a discovery of quantum vibrations in microtubules by Anirban Bandyopadhyay of the National Institute for Materials Science in Japan[47][48] confirms the hypothesis of Orch-OR theory.[49]

Criticism

Hameroff's theory is criticized at every level,[17][19] and considered to be a poor model of brain physiology.[19] Primarily, Hameroff requires tubulin electrons to form either a Bose–Einstein or Frohlich condensate, both of which have been experimentally disproven.[40][41]

Microtubule decoherence

Another objection to Hameroff's hypothesis is that any quantum coherent system in the brain would undergo wave function collapse due to environmental interaction long before it could ever influence neural processes. Max Tegmark determined the decoherence timescale of microtubule entanglement to be extremely rapid.[17] Tegmark developed a model for time to decoherence, and from this calculated that microtubule quantum states could exist, but would be sustained for only a femtoseconds (fs) timescale at brain temperatures, far too brief to be relevant to neural processing. Most physicists have sided with Tegmark's analysis and believe that quantum coherence does not play a major role in neurophysiology.[20][21][irrelevant citation]

In response to Tegmark, physicists Scott Hagan, Jack Tuszynski and Hameroff[50][51] claimed that Tegmark did not address the Orch-OR model, but instead a model of his own construction. This involved superpositions of quanta separated by 24 nm rather than the much smaller separations stipulated for Orch-OR. As a result, Hameroff's group claimed a decoherence time seven orders of magnitude greater than Tegmark's, although still far below 25 ms. Also, Hameroff's group suggested that the Debye layer of counterions could screen thermal fluctuations, and that the surrounding actin gel might enhance the ordering of water, further screening noise. Also, they suggest incoherent metabolic energy could further order water, and finally that the configuration of the microtubule lattice might be suitable for quantum error correction, a means of resisting quantum decoherence. In addition Hameroff also refers to the fact that quantum processes have been found to exist at normal temperatures. For example, Harvard researchers have been able to achieve quantum states lasting for 2 sec at room temperatures using pure diamonds.[52] In the past 6 years, evidence has accumulated that plants routinely use quantum coherent electron transport at ambient temperatures in photosynthesis.[53]

Cell biology

Hameroff proposed that microtubule coherence reaches the synapses via dendritic lamellar bodies (DLBs), where it could influence synaptic firing and be transmitted across the synaptic cleft to other neurons.[19][54] However De Zeeuw et al. proved this impossible,[55] by showing that DLBs are located micrometers away from gap junctions. Anirban Bandyopadhyay and his team speculate that this issue might be resolved if their notion of wirelessl transmission of information globally across the entire brain is proven,[56] yet Hameroff and Penrose doubt whether such a wireless transmission would be capable of transmitting superimposed quantum-states.[5]

Hameroff's 1998 hypothesis required that cortical dendrites contain primarily 'A' lattice microtubules,[46] but this was experimentally disproved by Kikkawa et al[57][58] who showed that all in vivo microtubules have a 'B' lattice and a seam. However, the recent research by Anirban Bandyopadhyay showed that microtubules can change their structure from B-lattice to A-lattice as part of the processing of information, and tubulin in microtubules exists in multiple states.[citation needed]

It also required gap junctions between neurons and glial cells,[46] yet Binmöller et al proved that these don't exist.[59]

Hameroff also speculated that visual photons instead of decohering in the retina are detected directly by the cones and rods, and subsequently connect with the retinal glia cells via gap junctions,[46] but this was falsified.[60]

Several other criticisms regarding biology have come to the fore over the years. Papers by Georgiev, D.[19][54] point to a number of problems with Hameroff's proposals, including a lack of explanation for the probabilistic firing of axonal synapses, an error in the calculated number of the tubulin dimers per cortical neuron. Nevertheless Hameroff insisted on a 2013 interview that those falsifications are invalid, including the assertions made by this wikipedia article.[61]

Other criticisms

In 2009, the debate focused around papers by Reimers et al.[41] and McKemmish et al.[18] and Hameroff's reply to these,[40] which is not regarded as being independently reviewed. The Reimers paper claimed that microtubules could only support 'weak' 8 MHz coherence, but that the Orch-OR proposals required a higher rate of coherence. Hameroff, however, claims that 8 MHz coherence is sufficient to support the Orch-OR proposal. McKemmish et al. makes two claims; firstly that aromatic molecules cannot switch states because they are delocalised. Hameroff, however, claims that he is referring to the behaviour of two or more electron clouds; secondly McKemmish shows that changes in tubulin conformation driven by GTP conversion would result in a prohibitive energy requirement. Against this, Hameroff claims that all that is required is switching in electron cloud dipole states produced by London forces.

See also

References

  1. ^ a b Hameroff, Stuart; Penrose, Roger (March 2014). "Reply to criticism of the 'Orch OR qubit' – 'Orchestrated objective reduction' is scientifically justified". Physics of Life Reviews. 11 (1). Elsevier: 94–100. doi:10.1016/j.plrev.2013.11.013. Retrieved 17 March 2014.
  2. ^ McCulloch, Warren; Pitts, Walter (12 January 1943). "A logical calculus of the ideas immanent in nervous activity". The bulletin of mathematical biophysics. 5 (4). Kluwer Academic Publishers: 115–133. doi:10.1007/BF02478259. Retrieved 17 march 2014. {{cite journal}}: Check date values in: |accessdate= (help)
  3. ^ HODGKIN; HUXLEY (1952). "A quantitative description of membrane current and its application to conduction and excitation in nerve". The Journal of Physiology. 117 (4). MEDLINE: 500–544. Retrieved 17 march 2014. {{cite journal}}: Check date values in: |accessdate= (help)
  4. ^ Chopra, Deepak (2014-03-18). "'Collision Course' in the Science of Consciousness: Grand Theories to Clash at Tucson Conference". The Huffington Post. United States: TheHuffingtonPost.com, Inc. Retrieved 2014-03-18. {{cite news}}: |archive-url= requires |archive-date= (help); Unknown parameter |deadurl= ignored (|url-status= suggested) (help)
  5. ^ a b Hameroff, Stuart; Penrose, Roger (March 2014). "Reply to seven commentaries on "Consciousness in the universe: Review of the 'Orch OR' theory"". Physics of Life Reviews. 11 (1). Elsevier: 104–112. doi:10.1016/j.plrev.2013.11.014. Retrieved 16 March 2014.
  6. ^ a b Hameroff, Stuart; Penrose, Roger (March 2014). "Consciousness in the universe: A review of the 'Orch OR' theory". Physics of Life Reviews. 11 (1). Elsevier: 39–78. doi:10.1016/j.plrev.2013.08.002. Retrieved 16 March 2014.
  7. ^ Natalie Wolchover (31 October 2013). "Physicists Eye Quantum-Gravity Interface". Quanta Magazine (Article). Simons Foundation. Retrieved 19 March 2014.
  8. ^ a b c LaForte, Geoffrey, Patrick J. Hayes, and Kenneth M. Ford 1998.Why Gödel's Theorem Cannot Refute Computationalism. Artificial Intelligence, 104:265–286.
  9. ^ a b Feferman, Solomon (1996). "Penrose's Gödelian argument". PSYCHE. 2: 21–32. CiteSeerx: 10.1.1.130.7027.
  10. ^ a b Krajewski, Stanislaw 2007. On Gödel's Theorem and Mechanism: Inconsistency or Unsoundness is Unavoidable in any Attempt to 'Out-Gödel' the Mechanist. Fundamenta Informaticae 81, 173–181. Reprinted in in Logic, Philosophy and Foundations of Mathematics and Computer Science:In Recognition of Professor Andrzej Grzegorczyk (2008), p. 173
  11. ^ a b http://consc.net/mindpapers/6.1b
  12. ^ a b http://users.ox.ac.uk/~jrlucas/Godel/referenc.html
  13. ^ a b Boolos, George, et al. 1990. An Open Peer Commentary on The Emperor's New Mind. Behavioral and Brain Sciences 13 (4) 655.
  14. ^ a b Davis, Martin 1993. How subtle is Gödel's theorem? More on Roger Penrose. Behavioral and Brain Sciences, 16, 611–612. Online version at Davis' faculty page at http://cs.nyu.edu/cs/faculty/davism/
  15. ^ a b Lewis, David K. 1969.Lucas against mechanism. Philosophy 44 231–233.
  16. ^ a b Putnam, Hilary 1995. Review of Shadows of the Mind. In Bulletin of the American Mathematical Society 32, 370–373 (also see Putnam's less technical criticisms in his New York Times review)
  17. ^ a b c Tegmark, Max (April 2000). "Importance of quantum decoherence in brain processes". Phys. Rev. E. 61 (4): 4194. doi:10.1103/PhysRevE.61.4194. Retrieved 18 November 2012.
  18. ^ a b McKemmish, L.K., Reimers, J.R., McKenzie, R.H., Mark, A.E., and Hush, N.S. (2009). "Penrose–Hameroff orchestrated objective-reduction proposal for human consciousness is not biologically feasible". Physical Review E. 80 (2): 021912–021916. Bibcode:2009PhRvE..80b1912M. doi:10.1103/PhysRevE.80.021912.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  19. ^ a b c d e Georgiev, D.D. (2007). "Falsifications of Hameroff–Penrose Orch OR model of consciousness and novel avenues for development of quantum mind theory". NeuroQuantology. 5 (1): 145–174.
  20. ^ a b Koch, Christof (30 March 2006). "Quantum mechanics in the brain". Nature. 440 (7084): 611. doi:10.1038/440611a. Retrieved 8 August 2013. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  21. ^ a b Hepp, K. (27 September 2012). "Coherence and decoherence in the brain". J. Math. Phys. 53 (9): 095222. doi:10.1063/1.4752474. Retrieved 8 August 2013.
  22. ^ "Discovery of Quantum Vibrations in "Microtubules" Inside Brain Neurons Corroborates Controversial 20-Year-Old Theory of Consciousness". elsevier.com (press release). Amsterdam: Elsevier. 16 January 2014. Retrieved 19-March-02014. {{cite web}}: Check date values in: |accessdate= (help)
  23. ^ a b c Penrose, Roger (1989). The Emperor's New Mind: Concerning Computers, Minds and The Laws of Physics. Oxford University Press. p. 480. ISBN 0-19-851973-7.
  24. ^ Hofstadter 1979, pp. 476–477, Russell & Norvig 2003, p. 950, Turing 1950 under "The Argument from Mathematics" where he writes "although it is established that there are limitations to the powers of any particular machine, it has only been stated, without sort of proof, that no such limitations apply to the human intellect."
  25. ^ Roger Penrose. Mathematical intelligence. In Jean Khalfa, editor, What is Intelligence?, chapter 5, pages 107–136. Cambridge University Press, Cambridge, United Kingdom, 1994.
  26. ^ Bringsford, S. and Xiao, H. 2000. A Refutation of Penrose's Gödelian Case Against Artificial Intelligence. Journal of Experimental and Theoretical Artificial Intelligence 12: 307–329. The authors write that it is "generally agreed" that Penrose "failed to destroy the computational conception of mind."
  27. ^ In an article at http://www.mth.kcl.ac.uk/~llandau/Homepage/Math/penrose.html L.J. Landau at the Mathematics Department of King's College London writes that "Penrose's argument, its basis and implications, is rejected by experts in the fields which it touches."
  28. ^ a b Princeton Philosophy professor John Burgess writes in On the Outside Looking In: A Caution about Conservativeness (published in Kurt Gödel: Essays for his Centennial, with the following comments found on pp. 131–132) that "the consensus view of logicians today seems to be that the Lucas–Penrose argument is fallacious, though as I have said elsewhere, there is at least this much to be said for Lucas and Penrose, that logicians are not unanimously agreed as to where precisely the fallacy in their argument lies. There are at least three points at which the argument may be attacked."
  29. ^ Dershowitz, Nachum 2005. The Four Sons of Penrose, in Proceedings of the Eleventh Conference on Logic Programming for Artificial Intelligence and Reasoning (LPAR; Jamaica), G. Sutcliffe and A. Voronkov, eds., Lecture Notes in Computer Science, vol. 3835, Springer-Verlag, Berlin, pp. 125–138.
  30. ^ Marvin Minsky. "Conscious Machines." Machinery of Consciousness, Proceedings, National Research Council of Canada, 75th Anniversary Symposium on Science in Society, June 1991.
  31. ^ Feferman, S. (1996). "Penrose's Gödelian argument" (PDF). Psyche. 2: 21–32.
  32. ^ Searle, John R. The Mystery of Consciousness. 1997. ISBN 0-940322-06-4. pp 85–86.
  33. ^ a b Penrose, Roger (1989). Shadows of the Mind: A Search for the Missing Science of Consciousness. Oxford University Press. p. 457. ISBN 0-19-853978-9.
  34. ^ Marshall, W., Simon, C., Penrose, R., and Bouwmeester, D. (2003). "Towards quantum superpositions of a mirror". Physical Review Letters. 91 (13): 130401. arXiv:quant-ph/0210001. Bibcode:2003PhRvL..91m0401M. doi:10.1103/PhysRevLett.91.130401. PMID 14525288.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  35. ^ "Discovery of quantum vibrations in microtubules inside brain neurons corroborates controversial 20-year-old theory of consciousness". KurzweilAI. 2014-01-16. Retrieved 2014-02-01.
  36. ^ "Penrose, Hameroff & Bandyopadhyay, Lecture: Microtubules and the great debate about consciousness (Lezing: Microtubuli & het grote debat over het bewustzijn)". Brakke Grond. 2014-01-16. Retrieved 2014-02-01.
  37. ^ Hameroff, S.R., and Watt, R.C. (1982). "Information processing in microtubules" (PDF). Journal of Theoretical Biology. 98 (4): 549–561. doi:10.1016/0022-5193(82)90137-0. PMID 6185798.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  38. ^ a b c d Hameroff, S.R. (1987). Ultimate Computing. Elsevier. ISBN 0-444-70283-0.
  39. ^ Hameroff, Stuart (2008). "That's life! The geometry of π electron resonance clouds". In Abbott, D; Davies, P; Pati, A (eds.). Quantum aspects of life (PDF). World Scientific. pp. 403–434. Retrieved Jan 21, 2010.
  40. ^ a b c Roger Penrose & Stuart Hameroff (2011). "Consciousness in the Universe: Neuroscience, Quantum Space-Time Geometry and Orch OR Theory". Journal of Cosmology. 14.
  41. ^ a b c Reimers, Jeffrey R. (17 March 2009). "Weak, strong, and coherent regimes of Fröhlich condensation and their applications to terahertz medicine and quantum consciousness". PNAS. 106 (11): 4219–4224. Bibcode:2009PNAS..106.4219R. doi:10.1073/pnas.0806273106. PMC 2657444. PMID 19251667. Retrieved 10 June 2013. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  42. ^ Hameroff, S.R. (2006). "The entwined mysteries of anesthesia and consciousness". Anesthesiology. 105 (2): 400–412. doi:10.1097/00000542-200608000-00024. PMID 16871075.
  43. ^ Hameroff, S. (2009). "The "conscious pilot"—dendritic synchrony moves through the brain to mediate consciousness". Journal of Biological Physics. 36 (1): 71–93. doi:10.1007/s10867-009-9148-x. PMC 2791805. PMID 19669425.
  44. ^ Specifically, he cites:
    • Buhl, D.L., Harris, K.D., Hormuzdi, S.G., Monyer, H., and Buzsaki, G. (2003). "Selective Impairment of Hippocampal Gamma Oscillations in Connexin-36 Knock-Out Mouse In Vivo". Journal of Neuroscience. 23 (3): 1013–1018. PMID 12574431.{{cite journal}}: CS1 maint: multiple names: authors list (link)
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