Orchestrated objective reduction

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The founders of the theory: Roger Penrose and Stuart Hameroff, respectively

Orchestrated objective reduction (Orch OR) is a controversial hypothesis that postulates that consciousness originates at the quantum level inside neurons, rather than the conventional view that it is a product of connections between neurons. The mechanism is held to be a quantum process called objective reduction that is orchestrated by cellular structures called microtubules. It is proposed that the theory may answer the hard problem of consciousness and provide a mechanism for free will.[1] The hypothesis was first put forward in the early 1990s by Nobel laureate for physics, Roger Penrose, and anaesthesiologist and psychologist Stuart Hameroff. The hypothesis combines approaches from molecular biology, neuroscience, pharmacology, philosophy, quantum information theory, and quantum gravity.[2][3]

While mainstream theories assert that consciousness emerges as the complexity of the computations performed by cerebral neurons increases,[4][5] Orch OR posits that consciousness is based on non-computable quantum processing performed by qubits formed collectively on cellular microtubules, a process significantly amplified in the neurons. The qubits are based on oscillating dipoles forming superposed resonance rings in helical pathways throughout lattices of microtubules. The oscillations are either electric, due to charge separation from London forces, or magnetic, due to electron spin—and possibly also due to nuclear spins (that can remain isolated for longer periods) that occur in gigahertz, megahertz and kilohertz frequency ranges.[2][6] Orchestration refers to the hypothetical process by which connective proteins, such as microtubule-associated proteins (MAPs), influence or orchestrate qubit state reduction by modifying the spacetime-separation of their superimposed states.[7] The latter is based on Penrose's objective-collapse theory for interpreting quantum mechanics, which postulates the existence of an objective threshold governing the collapse of quantum-states, related to the difference of the spacetime curvature of these states in the universe's fine-scale structure.[8]

Orchestrated objective reduction has been criticized from its inception by mathematicians, philosophers,[9][10][11][12] and scientists.[13][14][15] The criticism concentrated on three issues: Penrose's interpretation of Gödel's theorem; Penrose's abductive reasoning linking non-computability to quantum events; and the brain's unsuitability to host the quantum phenomena required by the theory, since it is considered too "warm, wet and noisy" to avoid decoherence.

Background[]

Further information: Penrose–Lucas argument
Logician Kurt Gödel

In 1931, mathematician and logician Kurt Gödel proved that any effectively generated theory capable of proving basic arithmetic cannot be both consistent and complete. In other words, a mathematically sound theory lacks the means to prove itself. An analogous statement has been used to show that humans are subject to the same limits as machines.[16] However, in his first book on consciousness, The Emperor's New Mind (1989), Roger Penrose argued that Gödel-unprovable results are provable by human mathematicians.[17] He takes this disparity to mean that human mathematicians are not describable as formal proof systems, and are therefore running a non-computable algorithm.

If correct, the Penrose–Lucas argument leaves the question of the physical basis of non-computable behaviour open. 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 objects of classical mechanics. Particles are described by wave functions that 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 no process or algorithm 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 called objective reduction (OR).[7]

Penrose sought to reconcile general relativity and quantum theory using his own ideas about the possible structure of spacetime.[17][18] He suggested that at the Planck scale curved spacetime is not continuous, but discrete. He further postulated 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. 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 10−37s. Objects somewhere between these two scales could collapse on a timescale relevant to neural processing.[7][additional citation(s) 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 algorithmically. Rather, states are selected by a "non-computable" influence embedded in the Planck scale of spacetime geometry. Penrose claimed 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: the physical, the mental, and the Platonic mathematical world.[7][additional citation(s) needed]

The Penrose–Lucas argument was criticized by mathematicians,[19][20][21] computer scientists,[12] and philosophers,[22][23][9][10][11] and the consensus among experts in these fields is that the argument fails,[24][25][26] with different authors attacking different aspects of the argument.[26][27] Minsky argued that because humans can believe false ideas to be true, human mathematical understanding need not be consistent and consciousness may easily have a deterministic basis.[28] Feferman argued that mathematicians do not progress by mechanistic search through proofs, but by trial-and-error reasoning, insight and inspiration, and that machines do not share this approach with humans.[20]

Orch OR[]

Penrose outlined a predecessor to Orch OR in The Emperor's New Mind, coming to the problem from a mathematical viewpoint and in particular Gödel's theorem, but lacked a detailed proposal for how quantum processes could be implemented in the brain. Stuart Hameroff separately worked in cancer research and anesthesia, which gave him an interest in brain processes. Hameroff read Penrose's book and suggested to him that microtubules within neurons were suitable candidate sites for quantum processing, and ultimately for consciousness.[29][30] Throughout the 1990s, the two collaborated on the Orch OR theory, which Penrose published in Shadows of the Mind (1994).[18]

Hameroff's contribution to the theory derived from his study of the neural cytoskeleton, and particularly on microtubules.[30] 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.[30]

Orch OR combines the Penrose–Lucas argument with Hameroff's hypothesis on quantum processing in microtubules. It proposes that when condensates in the brain undergo an objective wave function reduction, their collapse connects noncomputational decision-making to experiences embedded in spacetime's fundamental geometry. The theory further proposes that the microtubules both influence and are influenced by the conventional activity at the synapses between neurons.

Microtubule computation[]

A: An axon terminal releases neurotransmitters through a synapse and are received by microtubules in a neuron's dendritic spine.
B: Simulated microtubule tubulins switch states.[1]

Hameroff proposed that microtubules were suitable candidates for quantum processing.[30] Microtubules are made up of tubulin protein subunits. The tubulin protein dimers of the microtubules have hydrophobic pockets that may 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.[31] During entanglement, particle states become inseparably correlated.

Hameroff originally suggested in the fringe Journal of Cosmology that the tubulin-subunit electrons would form a Bose–Einstein condensate.[32] He then proposed a Frohlich condensate, a hypothetical coherent oscillation of dipolar molecules. However, this too was rejected by Reimers' group.[33] Hameroff then responded to Reimers. "Reimers et al have most definitely NOT shown that strong or coherent Frohlich condensation in microtubules is unfeasible. The model microtubule on which they base their Hamiltonian is not a microtubule structure, but a simple linear chain of oscillators." Hameroff reasoned that such condensate behavior would magnify nanoscopic quantum effects to have large scale influences in the brain.

Hameroff then 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.[34][35] 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, building upon the much less controversial theory that gap junctions are related to the gamma oscillation.[36]

Criticism[]

Orch OR has been criticized both by physicists[13][37][33][38][39] and neuroscientists[40][41][42] who consider it to be a poor model of brain physiology. Orch OR has also been criticized for lacking explanatory power; the philosopher Patricia Churchland wrote, "Pixie dust in the synapses is about as explanatorily powerful as quantum coherence in the microtubules."[43]

Decoherence in living organisms[]

In 2000 Max Tegmark claimed that any quantum coherent system in the brain would undergo effective wave function collapse due to environmental interaction long before it could influence neural processes (the "warm, wet and noisy" argument, as it was later came to be known).[13] He determined the decoherence timescale of microtubule entanglement at brain temperatures to be on the order of femtoseconds, far too brief for neural processing. Christof Koch and Klaus Hepp also agreed that quantum coherence does not play, or does not need to play any major role in neurophysiology.[14][15] Koch and Hepp concluded that "The empirical demonstration of slowly decoherent and controllable quantum bits in neurons connected by electrical or chemical synapses, or the discovery of an efficient quantum algorithm for computations performed by the brain, would do much to bring these speculations from the 'far-out' to the mere 'very unlikely'."[14]

In response to Tegmark's claims, Hagan, Tuszynski and Hameroff 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. Hameroff's group also 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. They also suggested that 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.[44][45]

In 2009, Reimers et al. and McKemmish et al., published critical assessments. Earlier versions of the theory had required tubulin-electrons to form either Bose–Einsteins or Frohlich condensates, and the Reimers group noted the lack of empirical evidence that such could occur. Additionally they calculated that microtubules could only support weak 8 MHz coherence. McKemmish et al. argued that aromatic molecules cannot switch states because they are delocalised; and that changes in tubulin protein-conformation driven by GTP conversion would result in a prohibitive energy requirement.[37][33][38]

Neuroscience[]

Further information: Neuroscience

Hameroff frequently writes: "A typical brain neuron has roughly 107 tubulins (Yu and Baas, 1994)", yet this is Hameroff's own invention, which should not be attributed to Yu and Baas.[46] Hameroff apparently misunderstood that Yu and Baas actually "reconstructed the microtubule (MT) arrays of a 56 μm axon from a cell that had undergone axon differentiation" and this reconstructed axon "contained 1430 MTs ... and the total MT length was 5750 μm."[46] A direct calculation shows that 107 tubulins (to be precise 9.3 × 106 tubulins) correspond to this MT length of 5750 μm inside the 56 μm axon.

Hameroff's 1998 hypothesis required that cortical dendrites contain primarily 'A' lattice microtubules,[47] but in 1994 Kikkawa et al. showed that all in vivo microtubules have a 'B' lattice and a seam.[48][49]

Orch OR also required gap junctions between neurons and glial cells,[47] yet Binmöller et. al. proved in 1992 that these don't exist in the adult brain.[50] In vitro research with primary neuronal cultures shows evidence for electrotonic (gap junction) coupling between immature neurons and astrocytes obtained from rat embryos extracted prematurely through Cesarean section;[51] however, the Orch OR claim is that mature neurons are electrotonically coupled to astrocytes in the adult brain. Therefore, Orch OR contradicts the well-documented electrotonic decoupling of neurons from astrocytes in the process of neuronal maturation, which is stated by Fróes et al. as follows: "junctional communication may provide metabolic and electrotonic interconnections between neuronal and astrocytic networks at early stages of neural development and such interactions are weakened as differentiation progresses."[51]

Other biology-based criticisms have been offered, including a lack of explanation for the probabilistic release of neurotransmitter from presynaptic axon terminals[52][53][54] and an error in the calculated number of the tubulin dimers per cortical neuron.[46]

In 2014, Penrose and Hameroff published responses to some criticisms and revisions to many of the theory's peripheral assumptions, while retaining the core hypothesis.[2][6]

See also[]

References[]

  1. ^ Jump up to: a b Hameroff, Stuart (2012). "How quantum brain biology can rescue conscious free will". Frontiers in Integrative Neuroscience. 6: 93. doi:10.3389/fnint.2012.00093. PMC 3470100. PMID 23091452.
  2. ^ Jump up to: a b c Hameroff, Stuart; Penrose, Roger (2014). "Reply to seven commentaries on "Consciousness in the universe: Review of the 'Orch OR' theory"". Physics of Life Reviews. 11 (1): 94–100. Bibcode:2014PhLRv..11...94H. doi:10.1016/j.plrev.2013.11.013.
  3. ^ Penrose, Roger (2014). "On the Gravitization of Quantum Mechanics 1: Quantum State Reduction". Foundations of Physics. 44 (5): 557–575. Bibcode:2014FoPh...44..557P. doi:10.1007/s10701-013-9770-0. S2CID 123379100.
  4. ^ McCulloch, Warren S.; Pitts, Walter (1943). "A logical calculus of the ideas immanent in nervous activity". Bulletin of Mathematical Biophysics. 5 (4): 115–133. doi:10.1007/bf02478259.
  5. ^ Hodgkin, Alan L.; Huxley, Andrew F. (1952). "A quantitative description of membrane current and its application to conduction and excitation in nerve". Journal of Physiology. 117 (4): 500–544. doi:10.1113/jphysiol.1952.sp004764. PMC 1392413. PMID 12991237.
  6. ^ Jump up to: a b Hameroff, Stuart; Penrose, Roger (2014). "Reply to criticism of the 'Orch OR qubit' – 'Orchestrated objective reduction' is scientifically justified". Physics of Life Reviews. 11 (1): 104–112. Bibcode:2014PhLRv..11..104H. doi:10.1016/j.plrev.2013.11.014.
  7. ^ Jump up to: a b c d Hameroff, Stuart; Penrose, Roger (2014). "Consciousness in the universe". Physics of Life Reviews. 11 (1): 39–78. Bibcode:2014PhLRv..11...39H. doi:10.1016/j.plrev.2013.08.002. PMID 24070914.
  8. ^ Natalie Wolchover (31 October 2013). "Physicists Eye Quantum-Gravity Interface". Quanta Magazine (Article). Simons Foundation. Retrieved 19 March 2014.
  9. ^ Jump up to: a b Boolos, George; et al. (1990). "An Open Peer Commentary on The Emperor's New Mind". Behavioral and Brain Sciences. 13 (4): 655. doi:10.1017/s0140525x00080687.
  10. ^ Jump up to: 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/
  11. ^ Jump up to: a b Lewis, David K. (1969). "Lucas against mechanism". Philosophy. 44 (169): 231–233. doi:10.1017/s0031819100024591.
  12. ^ Jump up to: 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)
  13. ^ Jump up to: a b c Tegmark, Max (2000). "Importance of quantum decoherence in brain processes". Physical Review E. 61 (4): 4194–4206. arXiv:quant-ph/9907009. Bibcode:2000PhRvE..61.4194T. doi:10.1103/PhysRevE.61.4194. PMID 11088215. S2CID 17140058.
  14. ^ Jump up to: a b c Koch, Christof; Hepp, Klaus (2006). "Quantum mechanics in the brain". Nature. 440 (7084): 611. Bibcode:2006Natur.440..611K. doi:10.1038/440611a. PMID 16572152. S2CID 5085015.
  15. ^ Jump up to: a b Hepp, K. (27 September 2012). "Coherence and decoherence in the brain". J. Math. Phys. 53 (9): 095222. Bibcode:2012JMP....53i5222H. doi:10.1063/1.4752474. Retrieved 8 August 2013.
  16. ^ 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."
  17. ^ Jump up to: a b Penrose, Roger (1989). The Emperor's New Mind: Concerning Computers, Minds and The Laws of Physics. Oxford University Press. p. 480. ISBN 978-0-19-851973-7.
  18. ^ Jump up to: a b Penrose, Roger (1989). Shadows of the Mind: A Search for the Missing Science of Consciousness. Oxford University Press. p. 457. ISBN 978-0-19-853978-0.
  19. ^ LaForte, Geoffrey, Patrick J. Hayes, and Kenneth M. Ford 1998.Why Gödel's Theorem Cannot Refute Computationalism. Artificial Intelligence, 104:265–286.
  20. ^ Jump up to: a b Feferman, Solomon (1996). "Penrose's Gödelian argument". Psyche. 2: 21–32. CiteSeerX 10.1.1.130.7027.
  21. ^ 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 Topics in Logic, Philosophy and Foundations of Mathematics and Computer Science:In Recognition of Professor Andrzej Grzegorczyk (2008), p. 173
  22. ^ "MindPapers: 6.1b. Godelian arguments". Consc.net. Retrieved 2014-07-28.
  23. ^ "References for Criticisms of the Gödelian Argument". Users.ox.ac.uk. 1999-07-10. Retrieved 2014-07-28.
  24. ^ Bringsjord, 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."
  25. ^ In an article at "King's College London - Department of Mathematics". Archived from the original on 2001-01-25. Retrieved 2010-10-22. 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."
  26. ^ Jump up to: 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."
  27. ^ Dershowitz, Nachum 2005. The Four Sons of Penrose, in Proceedings of the Eleventh Conference on Logic for Programming, 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.
  28. ^ Marvin Minsky. "Conscious Machines." Machinery of Consciousness, Proceedings, National Research Council of Canada, 75th Anniversary Symposium on Science in Society, June 1991.
  29. ^ Hameroff, S.R. & 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. Archived from the original (PDF) on 2006-01-07. Retrieved 2006-05-19.
  30. ^ Jump up to: a b c d Hameroff, S.R. (1987). Ultimate Computing. Elsevier. ISBN 978-0-444-70283-8.
  31. ^ Hameroff, Stuart (2008). "That's life! The geometry of π electron resonance clouds" (PDF). In Abbott, D; Davies, P; Pati, A (eds.). Quantum aspects of life. World Scientific. pp. 403–434. Retrieved Jan 21, 2010.
  32. ^ Roger Penrose & Stuart Hameroff (2011). "Consciousness in the Universe: Neuroscience, Quantum Space-Time Geometry and Orch OR Theory". Journal of Cosmology. 14. Archived from the original on February 7, 2014.
  33. ^ Jump up to: a b c Reimers, J. R.; McKemmish, L. K.; McKenzie, R. H.; Mark, A. E.; Hush, N. S. (2009). "Weak, strong, and coherent regimes of Frohlich condensation and their applications to terahertz medicine and quantum consciousness". Proceedings of the National Academy of Sciences. 106 (11): 4219–4224. Bibcode:2009PNAS..106.4219R. doi:10.1073/pnas.0806273106. PMC 2657444. PMID 19251667.
  34. ^ Hameroff, S.R. (2006). "The entwined mysteries of anesthesia and consciousness". Anesthesiology. 105 (2): 400–412. doi:10.1097/00000542-200608000-00024. PMID 16871075. S2CID 1655684.
  35. ^ 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.
  36. ^ Bennett, M.V.L. & Zukin, R.S. (2004). "Electrical Coupling and Neuronal Synchronization in the Mammalian Brain". Neuron. 41 (4): 495–511. doi:10.1016/S0896-6273(04)00043-1. PMID 14980200. S2CID 18566176.
  37. ^ Jump up to: a b McKemmish, Laura K.; Reimers, Jeffrey R.; McKenzie, Ross H.; Mark, Alan E.; Hush, Noel S. (2009). "Penrose-Hameroff orchestrated objective-reduction proposal for human consciousness is not biologically feasible" (PDF). Physical Review E. 80 (2): 021912. Bibcode:2009PhRvE..80b1912M. doi:10.1103/PhysRevE.80.021912. PMID 19792156.
  38. ^ Jump up to: a b Reimers, Jeffrey R.; McKemmish, Laura K.; McKenzie, Ross H.; Mark, Alan E.; Hush, Noel S. (2014). "The revised Penrose–Hameroff orchestrated objective-reduction proposal for human consciousness is not scientifically justified". Physics of Life Reviews. 11 (1): 101–103. Bibcode:2014PhLRv..11..101R. doi:10.1016/j.plrev.2013.11.003. PMID 24268490.
  39. ^ Villatoro, Francisco R. (June 17, 2015). "On the quantum theory of consciousness". Mapping Ignorance. University of the Basque Country. Retrieved August 18, 2018. Hameroff's ideas in the hands of Penrose have developed almost to absurdity.
  40. ^ Baars BJ, Edelman DB (2012). "Consciousness, biology and quantum hypotheses". Physics of Life Reviews. 9 (3): 285–294. Bibcode:2012PhLRv...9..285B. doi:10.1016/j.plrev.2012.07.001. PMID 22925839.
  41. ^ Georgiev, Danko D. (2017). Quantum Information and Consciousness: A Gentle Introduction. Boca Raton: CRC Press. p. 177. ISBN 9781138104488. OCLC 1003273264.
  42. ^ Litt A, Eliasmith C, Kroon FW, Weinstein S, Thagard P (2006). "Is the brain a quantum computer?". Cognitive Science. 30 (3): 593–603. doi:10.1207/s15516709cog0000_59. PMID 21702826.
  43. ^ Churchland, Patricia S. "Brainshy: Non-Neural Theories of Conscious Experience" (PDF). Retrieved 2021-03-03.
  44. ^ Hagan, S.; Hameroff, S. R.; Tuszyński, J. A. (2002). "Quantum computation in brain microtubules: Decoherence and biological feasibility". Physical Review E. 65 (6): 061901. arXiv:quant-ph/0005025. Bibcode:2002PhRvE..65f1901H. doi:10.1103/PhysRevE.65.061901. PMID 12188753. S2CID 11707566.
  45. ^ Hameroff, S. (2006). "Consciousness, Neurobiology and Quantum Mechanics". In Tuszynski, Jack (ed.). The Emerging Physics of Consciousness. The Emerging Physics of Consciousness. The Frontiers Collection. pp. 193–253. Bibcode:2006epc..book.....T. doi:10.1007/3-540-36723-3. ISBN 978-3-540-23890-4.
  46. ^ Jump up to: a b c Yu, W.; Baas, PW (1994). "Changes in microtubule number and length during axon differentiation". The Journal of Neuroscience. 14 (5): 2818–2829. doi:10.1523/jneurosci.14-05-02818.1994. S2CID 11922397.
  47. ^ Jump up to: a b Hameroff, S.R. (1998). "Quantum Computation In Brain Microtubules? The Penrose–Hameroff "Orch OR" model of consciousness". Philosophical Transactions of the Royal Society A. 356 (1743): 1869–1896. Bibcode:1998RSPTA.356.1869H. doi:10.1098/rsta.1998.0254. Archived from the original on 2010-05-31. Retrieved 2009-11-28.
  48. ^ Kikkawa, M. (1994). "Direct visualization of the microtubule lattice seam both in vitro and in vivo". The Journal of Cell Biology. 127 (6): 1965–1971. doi:10.1083/jcb.127.6.1965. PMC 2120284. PMID 7806574.
  49. ^ Kikkawa, M., Metlagel, Z. (2006). "A molecular "zipper" for microtubules". Cell. 127 (7): 1302–1304. doi:10.1016/j.cell.2006.12.009. PMID 17190594. S2CID 31980600.CS1 maint: multiple names: authors list (link)
  50. ^ F. J. Binmöller & C. M. Müller (1992). "Postnatal development of dye-coupling among astrocytes in rat visual cortex". Glia. 6 (2): 127–137. doi:10.1002/glia.440060207. PMID 1328051. S2CID 548862.
  51. ^ Jump up to: a b Froes, M. M.; Correia, A. H. P.; Garcia-Abreu, J.; Spray, D. C.; Campos De Carvalho, A. C.; Neto, V. M. (1999). "Gap-junctional coupling between neurons and astrocytes in primary central nervous system cultures". Proceedings of the National Academy of Sciences. 96 (13): 7541–46. Bibcode:1999PNAS...96.7541F. doi:10.1073/pnas.96.13.7541. PMC 22122. PMID 10377451.
  52. ^ Beck, F.; Eccles, J. C. (1992). "Quantum aspects of brain activity and the role of consciousness" (PDF). Proceedings of the National Academy of Sciences. 89 (23): 11357–11361. Bibcode:1992PNAS...8911357B. doi:10.1073/pnas.89.23.11357. PMC 50549. PMID 1333607.
  53. ^ Friedrich Beck (1996). "Can quantum processes control synaptic emission?". International Journal of Neural Systems. 7 (4): 343–353. Bibcode:1995IJNS....6..145A. doi:10.1142/S0129065796000300. PMID 8968823.
  54. ^ Friedrich Beck; John C. Eccles (1998). "Quantum processes in the brain: A scientific basis of consciousness". Cognitive Studies: Bulletin of the Japanese Cognitive Science Society. 5 (2): 95–109. doi:10.11225/jcss.5.2_95.

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