In 1931, the mathematician and logician Kurt Gödel 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, Gödel-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.[1] For this reason, the argument is sometimes called the Penrose-Lucas argument).
Penrose's idea is a 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".[2] 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.
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, Stuart Hameroff read The Emperor's New Mind and suggested to Penrose that certain structures within brain cells (microtubules) were suitable candidate sites for quantum processing and ultimately for consciousness.[4][5] The Orch-OR theory arose from the co-operation of these two scientists and was developed in Penrose's second consciousness book Shadows of the Mind (1994).[6]
Hameroff's contribution to the theory derived from studying brain cells (neurons). His interest centred on the cytoskeleton, which provides an internal supportive structure for neurons, and particularly on the microtubules,[5] 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.[5]
Criticism
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Gödelian argument and nature of human thought
Penrose's views on the human thought process are not widely accepted in certain scientific circles (Drew McDermott,[7]David Chalmers[8] 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. 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.[9] In 1996, Penrose offered a consolidated reply to many of the criticisms of "Shadows".[10]
John Searle criticises Penrose's appeal to Gödel as resting on the fallacy that all computational algorithms must be capable of mathematical description. As a counter-example, Searle cites the assignment of license plate numbers (LPN) to specific vehicle identification numbers (VIN), 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.[11]
Microtubule hypothesis
Penrose and Stuart Hameroff have constructed the Orch-OR theory in which human consciousness is the result of quantum gravity effects in microtubules. However, in 2000, Max Tegmark calculated in an article he published in Physical Review E[12] that the time scale of neuron firing and excitations in microtubules is slower than the decoherence time by a factor of at least 1010. Tegmark's article has been widely cited by critics of the Penrose-Hameroff hypothesis. The reception of the article 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."[13] In other words, there is a missing link between physics and neuroscience,[14] and to date, it is too premature to claim that the Orch-OR hypothesis is right.
In response to Tegmark's claims, Hagan, Tuszynski and Hameroff[15][16] 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 24nm rather than the much smaller separations stipulated for Orch-OR. As a result, Hameroff's group claimed a decoherence time seven orders of magnitude greater than Tegmark's, although still far below 25ms. Hameroff's group also suggested that the Debye layer of counterions could screen thermal fluctuations, and that the surrounding actin gel might enhance the ordering of water, further screening noise. They also suggested that incoherent metabolic energy could further order water, and finally that the configuration of the microtubule lattice might be suitable for quantum error correction, a means of resisting quantum decoherence.
In 2007, Gregory S. Engel claimed that all arguments concerning the brain being "too warm and wet" have been dispelled, as multiple "warm and wet" quantum processes have been discovered.[17][18]
1 2 Penrose, Roger (1999) [1989], The Emperor's New Mind (New Preface (1999)ed.), Oxford, England: Oxford University Press, pp.475–481, ISBN978-0-19-286198-6
The Chinese Room Argument holds that a digital computer executing a program cannot have a "mind", "understanding", or "consciousness", regardless of how intelligently or human-like the program may make the computer behave. The argument was presented by philosopher John Searle in his paper, "Minds, Brains, and Programs", published in Behavioral and Brain Sciences in 1980. Similar arguments were presented by Gottfried Leibniz (1714), Anatoly Dneprov (1961), Lawrence Davis (1974) and Ned Block (1978). Searle's version has been widely discussed in the years since. The centerpiece of Searle's argument is a thought experiment known as the Chinese Room.
Sir Roger Penrose is a British mathematician, mathematical physicist, philosopher of science and Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics in the University of Oxford, an emeritus fellow of Wadham College, Oxford, and an honorary fellow of St John's College, Cambridge and University College London.
Max Erik Tegmark is a Swedish-American physicist, cosmologist and machine learning researcher. He is a professor at the Massachusetts Institute of Technology and the president of the Future of Life Institute. He is also a scientific director at the Foundational Questions Institute and a supporter of the effective altruism movement.
Stuart Hameroff is an American anesthesiologist and professor at the University of Arizona known for his studies of consciousness and his controversial contention that consciousness originates from quantum states in neural microtubules. He is the lead organizer of the Science of Consciousness conference.
"Computing Machinery and Intelligence" is a seminal paper written by Alan Turing on the topic of artificial intelligence. The paper, published in 1950 in Mind, was the first to introduce his concept of what is now known as the Turing test to the general public.
The Emperor's New Mind: Concerning Computers, Minds and The Laws of Physics is a 1989 book by the mathematical physicist Sir Roger Penrose.
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Orchestrated objective reduction is a theory which postulates that consciousness originates at the quantum level inside neurons, rather than the conventional view that it is a product of connections between neurons. The mechanism is held to be a quantum process called objective reduction that is orchestrated by cellular structures called microtubules. It is proposed that the theory may answer the hard problem of consciousness and provide a mechanism for free will. The hypothesis was first put forward in the early 1990s by Nobel laureate for physics, Roger Penrose, and anaesthesiologist and psychologist Stuart Hameroff. The hypothesis combines approaches from molecular biology, neuroscience, pharmacology, philosophy, quantum information theory, and quantum gravity.
The electromagnetic theories of consciousness propose that consciousness can be understood as an electromagnetic phenomenon.
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The philosophy of artificial intelligence is a branch of the philosophy of technology that explores artificial intelligence and its implications for knowledge and understanding of intelligence, ethics, consciousness, epistemology, and free will. Furthermore, the technology is concerned with the creation of artificial animals or artificial people so the discipline is of considerable interest to philosophers. These factors contributed to the emergence of the philosophy of artificial intelligence. Some scholars argue that the AI community's dismissal of philosophy is detrimental.
In philosophy of mind, the computational theory of mind (CTM), also known as computationalism, is a family of views that hold that the human mind is an information processing system and that cognition and consciousness together are a form of computation. Warren McCulloch and Walter Pitts (1943) were the first to suggest that neural activity is computational. They argued that neural computations explain cognition. The theory was proposed in its modern form by Hilary Putnam in 1967, and developed by his PhD student, philosopher, and cognitive scientist Jerry Fodor in the 1960s, 1970s, and 1980s. Despite being vigorously disputed in analytic philosophy in the 1990s due to work by Putnam himself, John Searle, and others, the view is common in modern cognitive psychology and is presumed by many theorists of evolutionary psychology. In the 2000s and 2010s the view has resurfaced in analytic philosophy.
The Penrose interpretation is a speculation by Roger Penrose about the relationship between quantum mechanics and general relativity. Penrose proposes that a quantum state remains in superposition until the difference of space-time curvature attains a significant level.
The quantum mind or quantum consciousness is a group of hypotheses proposing that classical mechanics alone cannot explain consciousness, positing instead that quantum-mechanical phenomena, such as entanglement and superposition, may play an important part in the brain's function and could explain critical aspects of consciousness. These scientific hypotheses are as yet untested, and can overlap with quantum mysticism.
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Jack Tuszyński is a Polish professor of oncology and physicist.
The Penrose–Lucas argument is a logical argument partially based on a theory developed by mathematician and logician Kurt Gödel. In 1931, he proved that every effectively generated theory capable of proving basic arithmetic either fails to be consistent or fails to be complete. Mathematician Roger Penrose modified the argument in his first book on consciousness, The Emperor's New Mind (1989), where he used it to provide the basis of the theory of orchestrated objective reduction.
Quantum Night is a 2016 science-fiction thriller novel written by Canadian novelist Robert J. Sawyer. Set in 2020, the book touches on themes of quantum physics, psychology, current politics and ethics.
Models of consciousness are used to illustrate and aid in understanding and explaining distinctive aspects of consciousness. Sometimes the models are labeled theories of consciousness. Anil Seth defines such models as those that relate brain phenomena such as fast irregular electrical activity and widespread brain activation to properties of consciousness such as qualia. Seth allows for different types of models including mathematical, logical, verbal and conceptual models.
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