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Orchestrated objective reduction

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Orchestrated objective reduction (Orch-OR) is a theory of consciousness, which is the joint work of theoretical physicist, Sir Roger Penrose, and anesthesiologist Stuart Hameroff. Mainstream theories assume that consciousness emerges from the brain, and focus particularly on complex computation at synapses that allow communication between neurons.[citation needed] Orch-OR combines approaches to the problem of consciousness from the radically different angles of mathematics, physics and anesthesia.

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 gave him an interest in brain structures.

The mathematical and scientific basis of Orch-OR is universally rejected by mainstream mathematicians,[1][2][3] philosophers,[4][5][6][7][8][9] and scientists.[10][11][12][13][14]

The Penrose–Lucas argument

The Penrose-Lucas argument states that, since humans are capable of knowing the truth of Gödel-unprovable statements, human thought is necessarily non-computable.[15]

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.[16]

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.[15] 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 an 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[17]

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, computer scientists and philosophers,[5][4][6][7][2][3][1][8][9] and the consensus among experts in these fields is that the argument fails,[18][19][20] with different authors choosing different aspects of the argument to attack.[20][21]

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,[1] 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.[22]

Solomon Feferman, a professor of mathematics, logic and philosophy has made criticisms of Penrose's argument.[23] He faults detailed points in Penrose's second book, Shadows of the Mind, but says that he does not think that they undermine the main thrust of his argument. As a mathematician, he 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.[24]

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

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 an random eigenstate of the 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[citation needed] that isolated systems may still undergo a new form of wave function collapse, which he calls objective reduction (OR).

Penrose sought to reconcile general relativity and quantum theory using his own ideas about the possible structure of spacetime.[15][25] 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 threshold for Penrose OR is given by his indeterminacy principle t = ħ/E, where t is the time until OR occurs, E is the gravitational self-energy or the degree of spacetime separation given by the superpositioned mass, ħ 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.[26]

The creation of the Orch-OR model

When he wrote his first consciousness book, The Emperor's New Mind in 1989, Penrose 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.[27][28] 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).[25]

Hameroff's contribution to the theory derived from studying brain cells (neurons). His interest centered on the cytoskeleton, which provides an internal supportive structure for neurons, and particularly on the microtubules,[28] 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.[28]

Microtubule condensates

Hameroff proposed that microtubules were suitable candidates for quantum processing.[28] 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.[29] During entanglement, particles' states become inseparably correlated.

Hameroff originally suggested the tubulin-subunit electrons would form a Bose-Einstein condensate, but this was discredited.[30] He then proposed a Frohlich condensate, a hypothetical coherent oscillation of dipolar molecules. However, this too has been experimentally discredited.[31] 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.[32][33] 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 gamma waves. Here, Hameroff built upon[34] the much less controversial theory that gap junctions are related to the gamma oscillation.[35]

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. The Orch in Orch-OR stands for orchestrated, where orchestration refers to the hypothetical process by which connective proteins, known as microtubule-associated proteins (MAPs) influence or orchestrate the quantum processing of the microtubules.

Further to this, in 1998, Hameroff made 20 testable predictions related to his proposal.[36] However, most of these proposals have been falsified. The proposed predominance of 'A' lattice microtubules, more suitable for information processing, has been falsified by Kikkawa et al.,[11][12] who showed that all in vivo microtubules have a 'B' lattice and a seam. The suggestion of coherent photons has been falsified, as has the existence of gap junctions between neurons and glial cells,[37] and the proposal that photons do not decohere in the retina.[38]

Criticism

The main 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.[10] 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. Quantum decoherence in photosynthetic energy transfer has been recently observed to last for 660 fs[39] rather than the 25 milliseconds required by Orch-OR, and this is compatible with Tegmark's calculations. More recent papers involving Guerreshi, G., Cia, J., Popescu, S. and Briegel, H.[40][41] are looking to improve their model of entanglement in protein, a test which could falsify theories of non-trivial coherence or entanglement in protein.

In response to Tegmark, physicists Scott Hagan, Jack Tuszynski and Hameroff[42][43] 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, but still well short of the 25 ms required if the quantum processing in the theory was to be linked to the 40 Hz gamma synchrony, as Orch-OR suggested. To bridge this gap, the group made a series of proposals. It was supposed that the interiors of neurons could alternate between liquid and gel states. In the gel state, it was further hypothesized that the water electrical dipoles are oriented in the same direction, along the outer edge of the microtubule tubulin subunits.

Hameroff et al. proposed that this ordered water could screen any quantum coherence within the tubulin of the microtubules from the environment of the rest of the brain. Each tubulin also has a negatively charged tail, which attracts positively charged ions. It is suggested that this could provide further screening. Also, they suggest that microtubules could be pumped into a coherent state by biochemical energy. Finally, it is suggested that the configuration of the microtubule lattice might be suitable for quantum error correction, a means of resisting quantum decoherence. Others have suggested that microtubule coherence may reach the synapses via dendritic lamellar bodies, where it both influences synaptic firing, and is transmitted across the synaptic cleft to other neurons.[13][14]

Several other criticisms have come to the fore over the years. Papers by Georgiev, D.[13][14] 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, and mismodelling of dendritic lamellar bodies (DLBs) discovered by De Zeeuw et al.,[44] which showed that the DLBs are located micrometers away from gap junctions. Further Hameroff's hypothesis that cortical dendrites would be shown to contain mainly 'A' lattice microtubules was experimentally disproved by Kikkawa et al[11][12] which showed that all in vivo microtubules have a 'B' lattice and a seam.

Recently the debate has focused round papers by Reimers et al. [45] and McKemmish et al. [46] and Hameroff's replies to these,[30] 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

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  46. ^ 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)
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