Orch-OR
Encyclopedia
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 neuron
s. 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.
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. He argued that while a formal proof system cannot, because of the theorem, prove its own incompleteness, Godel-type 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 "non-computable" functions.
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, and the consensus among experts in these fields seems to be that the argument fails, though different authors may choose different aspects of the argument to attack.
Douglas Hofstadter
, in his Pulitzer prize
winning book Gödel, Escher, Bach: An Eternal Golden Braid, explains that these "Gödel-statements" 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". But, of course, the Epimenides paradox
applies to anything that makes statements, whether they are machines or humans, even Lucas himself. Consider:
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.
) making it a candidate for a non-computable 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 cause-and-effect 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 non-computable 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 aspect-of-mind 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. 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 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 number
s to specific vehicle identification number
s, 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. However, as an algorithm is defined in the Oxford American Dictionary as a set of rules to be followed in calculations or problem-solving 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 counter-example does not describe a computational algorithm that is not mathematically describable.
In this area, Penrose draws on both Einstein's general theory of relativity, and on his own notions about the possible structure of spacetime. 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 self-energy 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.
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 "non-computable" 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 non-computational understanding.
(1994).
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 microtubule
s, 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 synapse
s, and control of the cell's movement, growth and shape.
Hameroff proposed that microtubules were suitable candidates to support quantum processing. 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 tryptophan
s 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. Quantum entanglement is a state in which quantum particles can alter one another's quantum-mechanical 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 Bose-Einstein 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 cell
s via gap junctions. 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 Bose-Einstein 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 large-scale quantum feature is the source of the gamma synchronization
observed in the brain, and sometimes viewed as a neural correlate of consciousness. 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.
The Orch-OR 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 non-computational 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 Orch-OR 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 microtubule-associated proteins (MAPs) influence or orchestrate the quantum processing of the microtubules.
, refuting the Orch-OR model and published in the journal, Physical Review E is widely quoted. 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 rather than the 25 millisecond
s required by Orch-OR. 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 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 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 microtubule-associated 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 Orch-OR model are not undisputed. "Cortical dendrites contain largely A-lattice microtubules" is one of 20 testable predictions published by Hameroff in 1998 and it was hypothesized that these A-lattice 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 B-lattice and a seam. Other peer-reviewed critiques of Orch-OR have been published in recent years. One of these is a paper published in PNAS by Reimers et al., who argue that the condensates proposed in Orch-OR 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, an error in the calculated number of tubulin dimers per cortical neuron, and mismodeling of dendritic lamellar bodies (DLBs) discovered by De Zeeuw et al., 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 tubulin-bound GTP pumping of quantum coherence cannot occur either in stable microtubules nor in dynamically unstable microtubules undergoing assembly/disassembly.
Consciousness
Consciousness is a term that refers to the relationship between the mind and the world with which it interacts. It has been defined as: subjectivity, awareness, the ability to experience or to feel, wakefulness, having a sense of selfhood, and the executive control system of the mind...
, which is the joint work of theoretical physicist Sir Roger Penrose
Roger Penrose
Sir Roger Penrose OM FRS is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College...
and anesthesiologist Stuart Hameroff
Stuart Hameroff
Stuart Hameroff is an anesthesiologist and professor at the University of Arizona known for his scientific studies of consciousness.-Career:...
. Mainstream theories assume that consciousness emerges from the brain, and focus particularly on complex computation
Computation
Computation is defined as any type of calculation. Also defined as use of computer technology in Information processing.Computation is a process following a well-defined model understood and expressed in an algorithm, protocol, network topology, etc...
at synapses that allow communication between neuron
Neuron
A neuron is an electrically excitable cell that processes and transmits information by electrical and chemical signaling. Chemical signaling occurs via synapses, specialized connections with other cells. Neurons connect to each other to form networks. Neurons are the core components of the nervous...
s. Orch-OR combines approaches to the problem of consciousness
Consciousness
Consciousness is a term that refers to the relationship between the mind and the world with which it interacts. It has been defined as: subjectivity, awareness, the ability to experience or to feel, wakefulness, having a sense of selfhood, and the executive control system of the mind...
from the radically different angles of mathematics, physics and anesthesia.
Penrose
Roger Penrose
Sir Roger Penrose OM FRS is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College...
and Hameroff
Stuart Hameroff
Stuart Hameroff is an anesthesiologist and professor at the University of Arizona known for his scientific studies of consciousness.-Career:...
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
Gödel's theorem
Gödel's theorem may refer to:*Gödel's incompleteness theorems*Gödel's completeness theorem*Gödel's speedup theorem...
, while Hameroff approached it from a career in cancer research and anesthesia
Anesthesia
Anesthesia, or anaesthesia , traditionally meant the condition of having sensation blocked or temporarily taken away...
that gave him an interest in brain structures.
The Penrose-Lucas Theorem
In 1931, the mathematician and logician Kurt GödelKurt Gödel
Kurt Friedrich Gödel was an Austrian logician, mathematician and philosopher. Later in his life he emigrated to the United States to escape the effects of World War II. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the...
proved that any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent
Consistency
Consistency can refer to:* Consistency , the psychological need to be consistent with prior acts and statements* "Consistency", an 1887 speech by Mark Twain...
and complete
Complete theory
In mathematical logic, a theory is complete if it is a maximal consistent set of sentences, i.e., if it is consistent, and none of its proper extensions is consistent...
. 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
The Emperor's New Mind
The Emperor's New Mind: Concerning Computers, Minds and The Laws of Physics is a 1989 book by mathematical physicist Sir Roger Penrose.Penrose presents the argument that human consciousness is non-algorithmic, and thus is not capable of being modeled by a conventional Turing machine-type of digital...
(1989), Penrose made Gödel's theorem the basis of what quickly became an intensely controversial claim. He argued that while a formal proof system cannot, because of the theorem, prove its own incompleteness, Godel-type 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 "non-computable" 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!"
Similar claims about the implications of Gödel's theorem were originally espoused by the philosopher John Lucas
John Lucas (philosopher)
- Overview :John Lucas was educated at Winchester College and Balliol College, Oxford, where he studied first mathematics, then Greats , obtaining first class honors, and proceeding to an MA in Philosophy in 1954. He spent the 1957-58 academic year at Princeton University, deepening his...
of Merton College
Merton College, Oxford
Merton College is one of the constituent colleges of the University of Oxford in England. Its foundation can be traced back to the 1260s when Walter de Merton, chancellor to Henry III and later to Edward I, first drew up statutes for an independent academic community and established endowments to...
, Oxford
University of Oxford
The University of Oxford is a university located in Oxford, United Kingdom. It is the second-oldest surviving university in the world and the oldest in the English-speaking world. Although its exact date of foundation is unclear, there is evidence of teaching as far back as 1096...
. 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, and the consensus among experts in these fields seems to be that the argument fails, though different authors may choose different aspects of the argument to attack.
Douglas Hofstadter
Douglas Hofstadter
Douglas Richard Hofstadter is an American academic whose research focuses on consciousness, analogy-making, artistic creation, literary translation, and discovery in mathematics and physics...
, in his Pulitzer prize
Pulitzer Prize
The Pulitzer Prize is a U.S. award for achievements in newspaper and online journalism, literature and musical composition. It was established by American publisher Joseph Pulitzer and is administered by Columbia University in New York City...
winning book Gödel, Escher, Bach: An Eternal Golden Braid, explains that these "Gödel-statements" always refer to the system itself, similar to the way the Epimenides paradox
Epimenides paradox
The Epimenides paradox is a problem in logic. It is named after the Cretan philosopher Epimenides of Knossos , There is no single statement of the problem; a typical variation is given in the book Gödel, Escher, Bach, by Douglas Hofstadter:...
uses statements that refer to themselves, such as "this statement is false" or "I am lying". But, of course, the Epimenides paradox
Epimenides paradox
The Epimenides paradox is a problem in logic. It is named after the Cretan philosopher Epimenides of Knossos , There is no single statement of the problem; a typical variation is given in the book Gödel, Escher, Bach, by Douglas Hofstadter:...
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.
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
John Lucas (philosopher)
- Overview :John Lucas was educated at Winchester College and Balliol College, Oxford, where he studied first mathematics, then Greats , obtaining first class honors, and proceeding to an MA in Philosophy in 1954. He spent the 1957-58 academic year at Princeton University, deepening his...
's argument is pointless.
The quantum level
If correct, the Penrose-Lucas argument creates a need to understand the physical basis of non-computational 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 irreversibilityIrreversibility
In science, a process that is not reversible is called irreversible. This concept arises most frequently in thermodynamics, as applied to processes....
) making it a candidate for a non-computable process.
In quantum theory
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
, 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
Superposition principle
In physics and systems theory, the superposition principle , also known as superposition property, states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually...
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 cause-and-effect 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 non-computable 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 aspect-of-mind that Penrose particularly focused on.
According to Marvin Minsky
Marvin Minsky
Marvin Lee Minsky is an American cognitive scientist in the field of artificial intelligence , co-founder of Massachusetts Institute of Technology's AI laboratory, and author of several texts on AI and philosophy.-Biography:...
, 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
Artificial intelligence
Artificial intelligence is the intelligence of machines and the branch of computer science that aims to create it. AI textbooks define the field as "the study and design of intelligent agents" where an intelligent agent is a system that perceives its environment and takes actions that maximize its...
programs can also conclude that false statements are true, so error is not unique to humans. Another dissenter, Charles Seife
Charles Seife
Charles Seife is an American author, journalist and professor.His first published book was Zero: The Biography of a Dangerous Idea. He had written within the scientific community for years before this, having done freelance work for New Scientist, Scientific American, The Economist, Science, Wired...
, 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
Solomon Feferman
Solomon Feferman is an American philosopher and mathematician with major works in mathematical logic.He was born in New York City, New York, and received his Ph.D. in 1957 from the University of California, Berkeley under Alfred Tarski...
, a professor of mathematics, logic and philosophy has made more qualified criticisms. 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 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
John Searle
John Rogers Searle is an American philosopher and currently the Slusser Professor of Philosophy at the University of California, Berkeley.-Biography:...
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 number
Vehicle registration plate
A vehicle registration plate is a metal or plastic plate attached to a motor vehicle or trailer for official identification purposes. The registration identifier is a numeric or alphanumeric code that uniquely identifies the vehicle within the issuing region's database...
s to specific vehicle identification number
Vehicle identification number
A Vehicle Identification Number, commonly abbreviated to VIN, is a unique serial number used by the automotive industry to identify individual motor vehicles. VINs were first used in 1954...
s, 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. However, as an algorithm is defined in the Oxford American Dictionary as a set of rules to be followed in calculations or problem-solving 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 counter-example does not describe a computational algorithm that is not mathematically describable.
Objective reduction
Penrose 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. General relativity states that spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
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
Quantum superposition
Quantum superposition is a fundamental principle of quantum mechanics. It holds that a physical system exists in all its particular, theoretically possible states simultaneously; but, when measured, it gives a result corresponding to only one of the possible configurations.Mathematically, it...
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
Schrödinger's cat
Schrödinger's cat is a thought experiment, usually described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. The scenario presents a cat that might be...
) 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 self-energy 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.
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 "non-computable" influence embedded in the fundamental level of spacetime geometry at the Planck scale.
Penrose claimed that such information is Platonic
Platonism
Platonism is the philosophy of Plato or the name of other philosophical systems considered closely derived from it. In a narrower sense the term might indicate the doctrine of Platonic realism...
, representing pure mathematical truth, aesthetic and ethical values. More than two thousand years ago, the Greek philosopher Plato
Plato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...
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 non-computational understanding.
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. The Orch-OR theory arose from the cooperation of these two scientists, and were developed in Penrose's second consciousness book Shadows of the MindShadows of the Mind
Shadows of the Mind: A Search for the Missing Science of Consciousness is a 1994 book by mathematical physicist Roger Penrose, and serves as a followup to his 1989 book The Emperor's New Mind: Concerning Computers, Minds and The Laws of Physics....
(1994).
Hameroff's contribution to the theory derived from studying brain cells (neurons). His interest centered on the cytoskeleton
Cytoskeleton
The cytoskeleton is a cellular "scaffolding" or "skeleton" contained within a cell's cytoplasm and is made out of protein. The cytoskeleton is present in all cells; it was once thought to be unique to eukaryotes, but recent research has identified the prokaryotic cytoskeleton...
, which provides an internal supportive structure for neurons, and particularly on the microtubule
Microtubule
Microtubules are a component of the cytoskeleton. These rope-like polymers of tubulin can grow as long as 25 micrometers and are highly dynamic. The outer diameter of microtubule is about 25 nm. Microtubules are important for maintaining cell structure, providing platforms for intracellular...
s, 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 synapse
Synapse
In the nervous system, a synapse is a structure that permits a neuron to pass an electrical or chemical signal to another cell...
s, and control of the cell's movement, growth and shape.
Hameroff proposed that microtubules were suitable candidates to support quantum processing. Microtubules are made up of tubulin
Tubulin
Tubulin is one of several members of a small family of globular proteins. The most common members of the tubulin family are α-tubulin and β-tubulin, the proteins that make up microtubules. Each has a molecular weight of approximately 55 kiloDaltons. Microtubules are assembled from dimers of α- and...
protein
Protein
Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...
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 tryptophan
Tryptophan
Tryptophan is one of the 20 standard amino acids, as well as an essential amino acid in the human diet. It is encoded in the standard genetic code as the codon UGG...
s 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. Quantum entanglement is a state in which quantum particles can alter one another's quantum-mechanical 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 Bose-Einstein 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
Neuron
A neuron is an electrically excitable cell that processes and transmits information by electrical and chemical signaling. Chemical signaling occurs via synapses, specialized connections with other cells. Neurons connect to each other to form networks. Neurons are the core components of the nervous...
can link with microtubule condensates in other neurons and glial cell
Glial cell
Glial cells, sometimes called neuroglia or simply glia , are non-neuronal cells that maintain homeostasis, form myelin, and provide support and protection for neurons in the brain, and for neurons in other parts of the nervous system such as in the autonomous nervous system...
s via gap junctions. 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 Bose-Einstein 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 large-scale quantum feature is the source of the gamma synchronization
Gamma wave
A gamma wave is a pattern of neural oscillation in humans with a frequency between 25 to 100 Hz, though 40 Hz is prototypical.According to a popular theory, gamma waves may be implicated in creating the unity of conscious perception...
observed in the brain, and sometimes viewed as a neural correlate of consciousness. 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.
The Orch-OR 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 non-computational 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 Orch-OR 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 microtubule-associated 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 TegmarkMax Tegmark
Max Tegmark is a Swedish-American cosmologist. Tegmark is a professor at the Massachusetts Institute of Technology and belongs to the scientific directorate of the Foundational Questions Institute.-Early life:...
, refuting the Orch-OR model and published in the journal, Physical Review E is widely quoted. 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 rather than the 25 millisecond
Millisecond
A millisecond is a thousandth of a second.10 milliseconds are called a centisecond....
s required by Orch-OR. 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 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
Liquid
Liquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...
and gel
Gel
A gel is a solid, jelly-like material that can have properties ranging from soft and weak to hard and tough. Gels are defined as a substantially dilute cross-linked system, which exhibits no flow when in the steady-state...
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 microtubule-associated proteins, motor proteins and presynaptic scaffold proteins. These proposed alternative processes have the advantage of taking place within Tegmark's time to decoherence.
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Most of the above mentioned putative augmentations of the Orch-OR model are not undisputed. "Cortical dendrites contain largely A-lattice microtubules" is one of 20 testable predictions published by Hameroff in 1998 and it was hypothesized that these A-lattice microtubules could perform topological quantum error correction
Topological quantum computer
A topological quantum computer is a theoretical quantum computer that employs two-dimensional quasiparticles called anyons, whose world lines cross over one another to form braids in a three-dimensional spacetime . These braids form the logic gates that make up the computer...
. The latter testable prediction had already been experimentally disproved in 1994 by Kikkawa et al., who showed that all in vivo microtubules have B-lattice and a seam. Other peer-reviewed critiques of Orch-OR have been published in recent years. One of these is a paper published in PNAS by Reimers et al., who argue that the condensates proposed in Orch-OR 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, an error in the calculated number of tubulin dimers per cortical neuron, and mismodeling of dendritic lamellar bodies (DLBs) discovered by De Zeeuw et al., 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 tubulin-bound GTP pumping of quantum coherence cannot occur either in stable microtubules nor in dynamically unstable microtubules undergoing assembly/disassembly.
See also
- Electromagnetic theories of consciousnessElectromagnetic theories of consciousnessSeveral theorists have proposed that consciousness can be understood as an electromagnetic phenomenon. Their theories differ in how they relate consciousness to electromagnetism...
- Holonomic brain theoryHolonomic brain theoryThe holonomic brain theory, originated by psychologist Karl Pribram and initially developed in collaboration with physicist David Bohm, is a model for human cognition that is drastically different from conventionally accepted ideas: Pribram and Bohm posit a model of cognitive function as being...
- Many-minds interpretationMany-minds interpretationThe many-minds interpretation of quantum mechanics extends the many-worlds interpretation by proposing that the distinction between worlds should be made at the level of the mind of an individual observer. The concept was first introduced in 1970 by H...
- Penrose interpretation
- Quantum Aspects of Life (book)Quantum Aspects of LifeQuantum Aspects of Life is a 2008 science text, with a foreword by Sir Roger Penrose, which notably explores the open question of the role of quantum mechanics at molecular scales of relevance to biology. The book adopts a debate-like style and contains chapters written by various world-experts;...
- Quantum mindQuantum mindThe quantum mind or quantum consciousness hypothesis proposes that classical mechanics cannot explain consciousness, while quantum mechanical phenomena, such as quantum entanglement and superposition, may play an important part in the brain's function, and could form the basis of an explanation of...