 OrchOR

OrchOR (Orchestrated Objective Reduction) 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. OrchOR 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 OrchOR 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.
Contents
The PenroseLucas Theorem
Main article: Gödel's incompleteness theoremsIn 1931, the mathematician and logician Kurt Gödel proved that any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. Further to that, for any consistent formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory.
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.^{[1]} He argued that while a formal proof system cannot, because of the theorem, prove its own incompleteness, Godeltype 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 running an algorithm. He asserted that the brain could perform functions that no computer could perform, known as "noncomputable" functions.
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!"^{[2]}
Similar claims about the implications of Gödel's theorem 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,^{[3]}^{[4]}^{[5]}^{[6]}^{[7]}^{[8]}^{[9]}^{[10]}^{[11]} and the consensus among experts in these fields seems to be that the argument fails,^{[12]}^{[13]}^{[14]} though different authors may choose different aspects of the argument to attack.^{[14]}^{[15]}
Douglas Hofstadter, in his Pulitzer prize winning book Gödel, Escher, Bach: An Eternal Golden Braid, explains that these "Gödelstatements" always refer to the system itself, similar to the way the Epimenides paradox uses statements that refer to themselves, such as "this statement is false" or "I am lying".^{[16]} But, of course, the Epimenides paradox applies to anything that makes statements, whether they are machines or humans, even Lucas himself. Consider:
 Lucas can't assert the truth of this statement.^{[17]}
This statement is true but cannot be asserted by Lucas. This shows that Lucas himself is subject to the same limits that he describes for machines, as are all people, and so Lucas's argument is pointless.^{[18]}
The quantum level
If correct, the PenroseLucas argument creates a need to understand the physical basis of noncomputational behaviour in the brain. Penrose went on to consider what it was in the human brain that might not be driven by algorithms. Most physical laws are computable, and therefore described by algorithms. However, the nature of quantum collapse is not known (and it appears to have some unusual features, such as irreversibility) making it a candidate for a noncomputable process.
In quantum theory, the fundamental units, the quanta, are in some respects quite unlike objects that are encountered in the large scale world described by classical physics. When sufficiently isolated from the environment, they can be viewed as waves. However these are not the same as matter waves, such as waves in the sea. The quantum waves are essentially waves of probability, the varying probability of finding a particle at some specific position. The peak of the wave indicates the location with maximum probability of a particle being found there. The different possible positions of the particle are referred to as superpositions or quantum superpositions. When the quanta are the subject of measurements, the wave characteristic is lost, and a particle is found at a specific point. This change is commonly referred to as the collapse of the wave function.
According to most believers in collapse, when the collapse happens, the outcome is random. This is a drastic departure from classical physics. There is no causeandeffect process or system of algorithms that can describe the choice of position for the particle deterministically.
This provided Penrose with a candidate for the physical basis of the suggested noncomputable process that he proposed as possibly existing in the brain. However, this was not the end of his problems. He had identified something in physics that was not based on algorithms, but at the same time, randomness was not a promising basis for forming a mathematical understanding of the aspectofmind that Penrose particularly focused on.
According to Marvin Minsky, because people can construe false ideas to be factual, the process of thinking is not limited to formal logic. But, this is exactly Penrose's point—that human thinking and consciousness is not formal logic, not a Turing machine, as are today's computers. Further, AI programs can also conclude that false statements are true, so error is not unique to humans. Another dissenter, 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."
Solomon Feferman, a professor of mathematics, logic and philosophy has made more qualified criticisms.^{[19]} He faults detailed points in Penrose's reasoning in his 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 computerlike or mechanistic search through proofs, but by trialanderror 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 counterexample, 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.^{[20]} However, as an algorithm is defined in the Oxford American Dictionary as a set of rules to be followed in calculations or problemsolving operations, the assignment of LPN to VPNs is not a computation as such, merely a database in which every VPN has a corresponding LPN. Thus, Searle's counterexample does not describe a computational algorithm that is not mathematically describable.
Objective reduction
Main article: Penrose interpretationPenrose now proposed that existing ideas on wave function collapse might only apply to situations where the quanta are the subject of measurement. He considered the case of quanta that are not the subject of measurements or interactions, but remain isolated, and proposed that these quanta may be subject to a different form of wave function collapse.
In this area, Penrose draws on both Einstein's general theory of relativity, and on his own notions about the possible structure of spacetime.^{[1]}^{[21]} General relativity states that spacetime is curved by massive objects. Penrose, in seeking to reconcile relativity and quantum theory, has suggested that at the very small scale this curved spacetime is not continuous, but constitutes a form of network.
Penrose postulates that each quantum superposition has its own piece of spacetime curvature. According to his theory, these different bits of spacetime curvature are separated from one another, and constitute a form of blister in spacetime. Penrose further proposes a limit to the size of this spacetime blister. This is the tiny Planck scale of (10^{−35} m). Above this size, Penrose suggests that spacetime can be viewed as continuous, and that gravity starts to exert its force on the spacetime blister. This is suggested to become unstable above the Planck scale, and to collapse so as to choose just one of the possible locations for the particle. Penrose calls this event objective reduction (OR), reduction being another word for wave function collapse.
An important feature of Penrose's objective reduction is that the time to collapse is a function of the mass/energy of the object undergoing collapse. Thus the greater the superposition, the faster it will undergo OR, and vice versa. Tiny superpositions, e.g. an electron separated from itself, if isolated, would require 10 million years to reach OR threshold. An isolated one kilogram object (e.g. Schrödinger's cat) would reach OR threshold in only 10^{−37} seconds. However objects somewhere between the scale of an electron and the scale of a cat could collapse within a timescale that was relevant to neural processing.
The threshold for Penrose OR is given by the indeterminacy principle E = ħ/t, where E is the gravitational selfenergy or the degree of spacetime separation given by the superpositioned mass, ħ is the reduced Planck constant, and t is the time until OR occurs.
There is no existing evidence for Penrose's objective reduction, but the theory is considered to be testable, and plans are in hand to carry out a relevant experiment.^{[22]}
From the point of view of consciousness theory, an essential feature of Penrose's objective reduction is that the choice of states when objective reduction occurs is selected neither randomly, as are choices following measurement or decoherence, nor completely algorithmically. Rather, states are proposed to be selected by a "noncomputable" influence embedded in the fundamental level of spacetime geometry at the Planck scale.
Penrose claimed that such information is Platonic, representing pure mathematical truth, aesthetic and ethical values. More than two thousand years ago, the Greek philosopher Plato had proposed such pure values and forms, but in an abstract realm. Penrose placed the Platonic realm 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 physical world can be seen as the external reality, the mental world as information processing in the brain and the Platonic world as the encryption, measurement, or geometry of fundamental spacetime that is claimed to support noncomputational understanding.
The creation of the OrchOR 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.^{[23]}^{[24]} The OrchOR theory arose from the cooperation of these two scientists, and were developed in Penrose's second consciousness book Shadows of the Mind (1994).^{[21]}
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,^{[24]} which are the important component of the cytoskeleton. As neuroscience has progressed, the role of the cytoskeleton and microtubules has assumed greater importance. In addition to providing a supportive structure for the cell, the known functions of the microtubules include transport of molecules including neurotransmitter molecules bound for the synapses, and control of the cell's movement, growth and shape.^{[24]}
Hameroff proposed that microtubules were suitable candidates to support quantum processing.^{[24]} 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 nonpolar regions, for example 8 tryptophans per tubulin, which contain π electronrich 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.^{[25]} Quantum entanglement is a state in which quantum particles can alter one another's quantummechanical state instantaneously and at a distance, in a way which would not be possible if they were macroscopic objects obeying the laws of classical physics.
In the case of the electrons in the tubulin subunits of the microtubules, Hameroff has proposed that large numbers of these electrons can become involved in a state known as a BoseEinstein condensate. These occur when large numbers of quantum particles become locked in phase and exist as a single quantum object. These are quantum features at a macroscopic scale, and Hameroff suggests that through a feature of this kind, quantum activity, which is usually at a very tiny scale, could be boosted to be a large scale influence in the brain.
Hameroff has proposed that condensates in microtubules in one neuron can link with microtubule condensates in other neurons and glial cells via gap junctions.^{[26]}^{[27]} In addition to the synaptic connections between brain cells, gap junctions are a different category of connections, where the gap between the cells is sufficiently small for quantum objects to cross it by means of a process known as quantum tunneling. Hameroff proposes that this tunneling allows a quantum object, such as the BoseEinstein condensates mentioned above, to cross into other neurons, and thus extend across a large area of the brain as a single quantum object.
He further postulates that the action of this largescale quantum feature is the source of the gamma synchronization observed in the brain, and sometimes viewed as a neural correlate of consciousness.^{[28]} In support of the much more limited theory that gap junctions are related to the gamma oscillation, Hameroff quotes a number of studies from recent years.^{[29]}
The OrchOR theory combines Penrose's hypothesis with respect to the Gödel theorem with Hameroff's hypothesis with respect to microtubules. Together, Penrose and Hameroff have proposed that when condensates in the brain undergo an objective reduction of their wave function, that collapse connects to noncomputational decision taking/experience embedded in the geometry of fundamental 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 OrchOR stands for orchestrated to give the full name of the theory Orchestrated Objective Reduction. Orchestration refers to the hypothetical process by which connective proteins, known as microtubuleassociated proteins (MAPs) influence or orchestrate the quantum processing of the microtubules.
Criticism
The main objection to the Hameroff side of the theory is that any quantum feature in the environment of the brain would undergo wave function collapse (reduction), as a result of interaction with the environment, far too quickly for it to have any influence on neural processes. The wave or superposition form of the quanta is referred to as being quantum coherent. Interaction with the environment results in decoherence otherwise known as wave function collapse. It has been questioned as to how such quantum coherence could avoid rapid decoherence in the conditions of the brain. With reference to this question, a paper by the physicist, Max Tegmark, refuting the OrchOR model and published in the journal, Physical Review E is widely quoted.^{[30]} Tegmark developed a model for time to decoherence, and from this calculated that microtubule quantum states could exist, but would be sustained for only 100 femtoseconds (fs) at brain temperatures, far too brief to be relevant to neural processing. A recent paper by Engel et al. in Nature does indicate quantum coherent electrons as being functional in energy transfer within photosynthetic protein, but the quantum coherence described lasts for 660 fs^{[31]} rather than the 25 milliseconds required by OrchOR. This reinforces Tegmark's estimate for decoherence timescale of microtubules, which is comparable to the observed coherence time in the photosynthetic complex.
In their reply to Tegmark's paper, also published in Physical Review E, the physicists Scott Hagan, Jack Tuszynski and Hameroff^{[32]}^{[33]} claimed that Tegmark did not address the OrchOR 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 OrchOR. 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 OrchOR 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 tail extending out from the microtubules, which is negatively charged, and therefore attracts positively charged ions. It is suggested that this could provide further screening. Further to this, there was a suggestion that the 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 holding together quantum coherence in the face of environmental interaction. In the last decade, some researchers who are sympathetic to Penrose's ideas have proposed an alternative scheme for quantum processing in microtubules based on the interaction of tubulin tails with microtubuleassociated proteins, motor proteins and presynaptic scaffold proteins. These proposed alternative processes have the advantage of taking place within Tegmark's time to decoherence.
  Most of the above mentioned putative augmentations of the OrchOR model are not undisputed. "Cortical dendrites contain largely Alattice microtubules" is one of 20 testable predictions published by Hameroff in 1998^{[34]} and it was hypothesized that these Alattice microtubules could perform topological quantum error correction. The latter testable prediction had already been experimentally disproved in 1994 by Kikkawa et al., who showed that all in vivo microtubules have Blattice and a seam.^{[35]}^{[36]} Other peerreviewed critiques of OrchOR have been published in recent years. One of these is a paper published in PNAS by Reimers et al.,^{[37]} who argue that the condensates proposed in OrchOR would involve energies and temperatures that are not realistic in biological material. Further papers by Georgiev point to a number of problems with Hameroff's proposals, including the lack of explanation for the probabilistic firing of the axonal synapses,^{[38]} an error in the calculated number of tubulin dimers per cortical neuron,^{[39]} and mismodeling of dendritic lamellar bodies (DLBs) discovered by De Zeeuw et al.,^{[40]} who showed that despite the fact that DLBs are stained by antibody against gap junctions, they are located tens of micrometers away from actual gap junctions. Also it was shown that the proposed tubulinbound GTP pumping of quantum coherence cannot occur either in stable microtubules^{[41]} nor in dynamically unstable microtubules undergoing assembly/disassembly.^{[42]}
See also
 Electromagnetic theories of consciousness
 Holonomic brain theory
 Manyminds interpretation
 Penrose interpretation
 Quantum Aspects of Life (book)
 Quantum mind
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