Shadows of the Mind
Encyclopedia
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.
Penrose hypothesizes that:-
proved his incompleteness theorems, showing 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. The essence of Penrose's argument is 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, so that the computational theory of mind
is false, and computational approaches to artificial general intelligence are unfounded. (The argument was first given by Penrose in The Emperor's New Mind
(1989), and is developed further in Shadows of The Mind. An earlier version of the argument
was given by J. R. Lucas
in 1959. For this reason, the argument is sometimes called the Penrose-Lucas argument).
and general relativity
. Penrose proposes that a quantum state remains in superposition until the difference in space-time curvature reaches a significant level. This idea is inspired by quantum gravity
, because it uses both the physical constants
and 
. It is an alternative to the Copenhagen interpretation
, which posits that superposition fails under observation, and the many worlds hypothesis, which states that each alternative outcome of a superposition becomes real in a separate world.
Penrose's idea is type of objective collapse theory
. In these theories the wavefunction is a physical wave, which undergoes wave function collapse as a physical process, with observers playing no special role. Penrose theorises that the wave function cannot be sustained in superposition beyond a certain energy difference between the quantum states. He gives an approximate value for this difference: a Planck mass worth of matter, which he calls the "'one-graviton' level".
He then hypothesizes that this energy difference causes the wave function to collapse to a single state, with a probability based on its amplitude in the original wave function, a procedure taken from standard quantum mechanics
.
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.
process are not widely accepted in scientific circles (Drew McDermott
, David Chalmers
and others). 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."
In May 1995 Stanford mathematician
Solomon Feferman
attacked Penrose's approach on multiple grounds, including the mathematical validity of his Gödelian argument and theoretical background. In 1996 Penrose offered a consolidated reply to many of the criticisms of 'Shadows'.
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.
have constructed the Orch-OR
theory in which human consciousness is the result of quantum gravity effects in microtubules. But Max Tegmark
, in a paper in Physical Review E, calculated that the time scale of neuron firing and excitations in microtubules is slower than the decoherence
time by a factor of at least 1010. The Tegmark paper has been widely cited by critics of the Penrose-Hameroff proposal. The reception of the paper is summed up by this statement in his support: "Physicists outside the fray, such as IBM's John Smolin, say the calculations confirm what they had suspected all along. 'We're not working with a brain that's near absolute zero. It's reasonably unlikely that the brain evolved quantum behavior', he says."
Since this time, however, all arguments concerning the brain being "too warm and wet" have been dispelled, as multiple "warm and wet" quantum processes have been discovered.
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 serves as a followup to his 1989 book The Emperor's New Mind: Concerning Computers, Minds and The Laws of Physics.
Penrose hypothesizes that:-
- Human consciousnessConsciousnessConsciousness 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...
is non-algorithmic, and thus is not capable of being modeled by a conventional Turing machineTuring machineA Turing machine is a theoretical device that manipulates symbols on a strip of tape according to a table of rules. Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a CPU inside a...
-type of digital computer. - Quantum mechanicsQuantum mechanicsQuantum 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...
plays an essential role in the understanding of human consciousnessConsciousnessConsciousness 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...
, specifically, he believes that microtubules within neurons support quantum superpositions - The objective collapseObjective collapse theoryObjective collapse theories are an approach to the interpretational problems of quantum mechanics. They are realistic, indeterministic and reject hidden variables...
of the quantum wavefunctionWavefunctionNot to be confused with the related concept of the Wave equationA wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves. Typically, its values are complex numbers and, for a single particle, it is a function of...
of the microtubules is critical for consciousnessConsciousnessConsciousness 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... - The collapse in question is physical behaviour that is non algorithmic and transcends the limits of computability.
- The human mind has abilities that no Turing machineTuring machineA Turing machine is a theoretical device that manipulates symbols on a strip of tape according to a table of rules. Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a CPU inside a...
could possess because of this mechanism of non-computable physics.
Mathematical thought
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 his incompleteness theorems, showing 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. The essence of Penrose's argument is 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, so that the computational theory of mind
Computational theory of mind
In philosophy, the computational theory of mind is the view that the human mind is an information processing system and that thinking is a form of computing. The theory was proposed in its modern form by Hilary Putnam in 1961 and developed by Jerry Fodor in the 60s and 70s...
is false, and computational approaches to artificial general intelligence are unfounded. (The argument was first given by Penrose in 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), and is developed further in Shadows of The Mind. An earlier version of the argument
Minds, Machines and Gödel
Minds, Machines and Gödel is J. R. Lucas's 1959 philosophical paper in which he argues that a human mathematician cannot be accurately represented by an algorithmic automaton...
was given by J. R. 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...
in 1959. For this reason, the argument is sometimes called the Penrose-Lucas argument).
Objective reduction
Penrose's theory of Objective Reduction is a prediction of Sir Roger Penrose about the relationship between quantum mechanicsQuantum 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...
and general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
. Penrose proposes that a quantum state remains in superposition until the difference in space-time curvature reaches a significant level. This idea is inspired by quantum gravity
Quantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...
, because it uses both the physical constants
and Gravitational constant
The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...
. It is an alternative to the Copenhagen interpretation
Copenhagen interpretation
The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...
, which posits that superposition fails under observation, and the many worlds hypothesis, which states that each alternative outcome of a superposition becomes real in a separate world.
Penrose's idea is type of objective collapse theory
Objective collapse theory
Objective collapse theories are an approach to the interpretational problems of quantum mechanics. They are realistic, indeterministic and reject hidden variables...
. In these theories the wavefunction is a physical wave, which undergoes wave function collapse as a physical process, with observers playing no special role. Penrose theorises that the wave function cannot be sustained in superposition beyond a certain energy difference between the quantum states. He gives an approximate value for this difference: a Planck mass worth of matter, which he calls the "'one-graviton' level".
He then hypothesizes that this energy difference causes the wave function to collapse to a single state, with a probability based on its amplitude in the original wave function, a procedure taken from standard quantum mechanics
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...
.
Orchestrated Objective reduction
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 Mind (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.
Gödelian argument and nature of human thought
Penrose's views on the human thoughtThought
"Thought" generally refers to any mental or intellectual activity involving an individual's subjective consciousness. It can refer either to the act of thinking or the resulting ideas or arrangements of ideas. Similar concepts include cognition, sentience, consciousness, and imagination...
process are not widely accepted in scientific circles (Drew McDermott
Drew McDermott
Drew McDermott is a Professor of Computer Science at Yale University. He was born in 1949, and lived in the Midwestern United States , for four years, and in Brazil .-Education:...
, David Chalmers
David Chalmers
David John Chalmers is an Australian philosopher specializing in the area of philosophy of mind and philosophy of language, whose recent work concerns verbal disputes. He is Professor of Philosophy and Director of the Centre for Consciousness at the Australian National University...
and others). 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."
In May 1995 Stanford mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
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...
attacked Penrose's approach on multiple grounds, including the mathematical validity of his Gödelian argument and theoretical background. In 1996 Penrose offered a consolidated reply to many of the criticisms of 'Shadows'.
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.
Microtubule hypothesis
Penrose and Stuart HameroffStuart Hameroff
Stuart Hameroff is an anesthesiologist and professor at the University of Arizona known for his scientific studies of consciousness.-Career:...
have constructed the Orch-OR
Orch-OR
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...
theory in which human consciousness is the result of quantum gravity effects in microtubules. But Max Tegmark
Max 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:...
, in a paper in Physical Review E, calculated that the time scale of neuron firing and excitations in microtubules is slower than the decoherence
Quantum decoherence
In quantum mechanics, quantum decoherence is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition. A consequence of this dephasing leads to classical or probabilistically additive behavior...
time by a factor of at least 1010. The Tegmark paper has been widely cited by critics of the Penrose-Hameroff proposal. The reception of the paper is summed up by this statement in his support: "Physicists outside the fray, such as IBM's John Smolin, say the calculations confirm what they had suspected all along. 'We're not working with a brain that's near absolute zero. It's reasonably unlikely that the brain evolved quantum behavior', he says."
Since this time, however, all arguments concerning the brain being "too warm and wet" have been dispelled, as multiple "warm and wet" quantum processes have been discovered.
See also
- The Emperor's New MindThe Emperor's New MindThe 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...
- Computational theory of mindComputational theory of mindIn philosophy, the computational theory of mind is the view that the human mind is an information processing system and that thinking is a form of computing. The theory was proposed in its modern form by Hilary Putnam in 1961 and developed by Jerry Fodor in the 60s and 70s...
- 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...
- The Road to Reality: A Complete Guide to the Laws of the UniverseThe Road to Reality: A Complete Guide to the Laws of the UniverseThe Road to Reality: A Complete Guide to the Laws of the Universe is a book on modern physics by the British mathematical physicist Roger Penrose, published in 2004...
, a 2004 book by Penrose - Alan TuringAlan TuringAlan Mathison Turing, OBE, FRS , was an English mathematician, logician, cryptanalyst, and computer scientist. He was highly influential in the development of computer science, providing a formalisation of the concepts of "algorithm" and "computation" with the Turing machine, which played a...
, creator of the Turing testTuring testThe Turing test is a test of a machine's ability to exhibit intelligent behaviour. In Turing's original illustrative example, a human judge engages in a natural language conversation with a human and a machine designed to generate performance indistinguishable from that of a human being. All... - Orch-OROrch-OROrch-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...