Roger Penrose
Encyclopedia
Sir Roger Penrose OM FRS
(born 8 August 1931) 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. He has received a number of prizes and awards, including the 1988 Wolf Prize for physics which he shared with Stephen Hawking
for their contribution to our understanding of the universe. He is renowned for his work in mathematical physics, in particular his contributions to general relativity
and cosmology
. He is also a recreational mathematician
and philosopher.
, Essex
, England, Roger Penrose is a son of Lionel S. Penrose
and Margaret Leathes. Penrose is the brother of mathematician Oliver Penrose
and of chess Grandmaster Jonathan Penrose
. Penrose attended University College School
and University College, London, where he graduated with a first class degree in mathematics
. In 1955, while still a student, Penrose reintroduced the E. H. Moore
generalized matrix inverse (also known as Moore–Penrose inverse after it had been reinvented by Arne Bjerhammar
(1951). Penrose earned his Ph.D.
at Cambridge
(St John's College
) in 1958, writing a thesis on "tensor methods in algebraic geometry" under algebraist and geometer John A. Todd. He devised and popularised the Penrose triangle
in the 1950s, describing it as "impossibility in its purest form" and exchanged material with the artist M. C. Escher
, whose earlier depictions of impossible objects partly inspired it. Escher's Waterfall
, and Ascending and Descending
were in turn inspired by Penrose. As reviewer Manjit Kumar puts it:
In 1965, at Cambridge, Penrose proved that singularities
(such as black hole
s) could be formed from the gravitational collapse of immense, dying star
s.
In 1967, Penrose invented the twistor theory
which maps geometric objects in Minkowski space
into the 4-dimensional complex space with the metric signature (2,2). In 1969, he conjectured the cosmic censorship hypothesis
. This proposes (rather informally) that the universe protects us from the inherent unpredictability of singularities
(such as the one in the centre of a black hole) by hiding them from our view behind an event horizon
. This form is now known as the "weak censorship hypothesis"; in 1979, Penrose formulated a stronger version called the "strong censorship hypothesis". Together with the BKL conjecture and issues of nonlinear stability, settling the censorship conjectures is one of the most important outstanding problems in general relativity
. Also from 1979 dates Penrose's influential Weyl curvature hypothesis
on the initial conditions of the observable part of the Universe and the origin of the second law of thermodynamics
. Penrose and James Terrell independently realized that objects travelling near the speed of light will appear to undergo a peculiar skewing or rotation. This effect has come to be called the Terrell rotation
or Penrose–Terrell rotation.
Penrose is well known for his 1974 discovery of Penrose tiling
s, which are formed from two tiles that can only tile
the plane nonperiodically, and are the first tilings to exhibit fivefold rotational symmetry. Penrose developed these ideas based on the article Deux types fondamentaux de distribution statistique (1938; an English translation Two Basic Types of Statistical Distribution) by Czech geographer
, demographer and statistician
Jaromír Korčák. In 1984, such patterns were observed in the arrangement of atoms in quasicrystal
s. Another noteworthy contribution is his 1971 invention of spin network
s, which later came to form the geometry of spacetime
in loop quantum gravity
. He was influential in popularizing what are commonly known as Penrose diagram
s (causal diagrams). In 2004 Penrose released The Road to Reality: A Complete Guide to the Laws of the Universe
, a 1,099-page book aimed at giving a comprehensive guide to the laws of physics
. He has proposed a novel interpretation
of quantum mechanics
. In 2010, Penrose reported possible evidence, based on concentric circles found in WMAP data of the CMB
sky, of an earlier universe existing before the Big Bang
of our own present universe.
Penrose is the Francis and Helen Pentz Distinguished (visiting) Professor of Physics and Mathematics at Pennsylvania State University
. Penrose is married to Vanessa Thomas, head of mathematics at Abingdon School
, with whom he has one son. He has three sons from a previous marriage to American Joan Isabel Wedge, whom he married in 1959.
(1989), he argues that known laws of physics are inadequate to explain the phenomenon of consciousness. Penrose proposes the characteristics this new physics may have and specifies the requirements for a bridge between classical and quantum mechanics (what he calls correct quantum gravity). Penrose uses a variant of Turing's halting theorem to demonstrate that a system can be deterministic without being algorithmic. (E.g., imagine a system with only two states, ON and OFF. If the system's state is ON if a given Turing machine halts, and OFF if the Turing machine does not halt, then the system's state is completely determined by the Turing machine, however there is no algorithmic way to determine whether the Turing machine stops.) Penrose believes that such deterministic non-algorithmic processes may come in play in the quantum mechanical wave function reduction, and may be harnessed by the brain. He argues that the present computer is unable to have intelligence because it is an algorithmically deterministic system. He argues against the viewpoint that the rational processes of the mind are completely algorithm
ic and can thus be duplicated by a sufficiently complex computer. This contrasts with supporters of strong artificial intelligence, who contend that thought can be simulated algorithmically. He bases this on claims that consciousness transcends formal logic
because things such as the insolubility of the halting problem
and Gödel's incompleteness theorem prevent an algorithmically based system of logic from reproducing such traits of human intelligence as mathematical insight. These claims 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. Marvin Minsky
, a leading proponent of artificial intelligence, was particularly critical, stating that Penrose "tries to show, in chapter after chapter, that human thought cannot be based on any known scientific principle." Minsky's position is exactly the opposite - he believes that humans are, in fact, machines, whose functioning, although complex, is fully explainable by current physics. Minsky maintains that "one can carry that quest [for scientific explanation] too far by only seeking new basic principles instead of attacking the real detail. This is what I see in Penrose's quest for a new basic principle of physics that will account for consciousness."
Penrose responded to criticism of The Emperor's New Mind with his follow up 1994 book Shadows of the Mind
, and in 1997 with The Large, the Small and the Human Mind. In those works, he also combined his observations with that of anesthesiologist Stuart Hameroff
.
Penrose and Hameroff have argued that consciousness
is the result of quantum gravity effects in microtubule
s, which they dubbed Orch-OR
(orchestrated objective reduction). 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 10,000,000,000. The reception of the paper is summed up by this statement in Tegmark's support: "Physicists outside the fray, such as IBM's John A. 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'". Tegmark's paper has been widely cited by critics of the Penrose–Hameroff position.
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.
Hameroff, in a lecture in part of a Google Tech talks series exploring Quantum biology, gave an overview of current research in the area, and responded to subsequent criticisms of the Orch-OR model.
Phillip Tetlow, although himself supportive of Penrose's views, acknowledges that Penrose's ideas about the human thought process are at present a minority view in scientific circles, citing Minsky's criticisms and quoting science journalist Charles Seife
's description of Penrose as "one of a handful of scientists" who believe that the nature of consciousness suggests a quantum process.
, and refers to himself as an atheist. In the film A Brief History of Time
, he said, "I think I would say that the universe has a purpose, it's not somehow just there by chance ... some people, I think, take the view that the universe is just there and it runs along–it's a bit like it just sort of computes, and we happen somehow by accident to find ourselves in this thing. But I don't think that's a very fruitful or helpful way of looking at the universe, I think that there is something much deeper about it." Penrose is a Distinguished Supporter of the British Humanist Association
.
of the Royal Society of London
in 1972. In 1975, Stephen Hawking
and Penrose were jointly awarded the Eddington Medal
of the Royal Astronomical Society
. In 1985, he was awarded the Royal Society
Royal Medal
. Along with Stephen Hawking
, he was awarded the prestigious Wolf Foundation Prize for Physics
in 1988. In 1989 he was awarded the Dirac Medal and Prize
of the British Institute of Physics
. In 1990 Penrose was awarded the Albert Einstein Medal
for outstanding work related to the work of Albert Einstein
by the Albert Einstein Society
. In 1991, he was awarded the Naylor Prize of the London Mathematical Society
. From 1992 to 1995 he served as President of the International Society on General Relativity and Gravitation.
In 1994, Penrose was knighted
for services to science. In 1998, he was elected Foreign Associate of the United States National Academy of Sciences
. In 2000 he was appointed to the Order of Merit. In 2004 he was awarded the De Morgan Medal
for his wide and original contributions to mathematical physics. To quote the citation from the London Mathematical Society:
In 2005 Penrose was awarded an honorary doctorate (Honoris Causa) by Warsaw University and Katholieke Universiteit Leuven
(Belgium), and in 2006 by the University of York
. In 2008 Penrose was awarded the Copley Medal
. He is also a Distinguished Supporter of the British Humanist Association
and one of the patrons of the Oxford University Scientific Society
. In 2011, Penrose awarded the Fonseca prize, which is given by the University of Santiago de Compostela
.
Penrose also wrote forewords to Quantum Aspects of Life
and Zee
's book Fearful Symmetry.
The Forum
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
(born 8 August 1931) is an English
English people
The English are a nation and ethnic group native to England, who speak English. The English identity is of early mediaeval origin, when they were known in Old English as the Anglecynn. England is now a country of the United Kingdom, and the majority of English people in England are British Citizens...
mathematical physicist and Emeritus
Emeritus
Emeritus is a post-positive adjective that is used to designate a retired professor, bishop, or other professional or as a title. The female equivalent emerita is also sometimes used.-History:...
Rouse Ball Professor of Mathematics
Rouse Ball Professor of Mathematics
The Rouse Ball Professorship of Mathematics is one of the senior chairs in the Mathematics Departments at the University of Cambridge and the University of Oxford. The two positions were founded in 1927 by a bequest from the mathematician W. W. Rouse Ball...
at the Mathematical Institute, University of 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...
and Emeritus Fellow of Wadham College. He has received a number of prizes and awards, including the 1988 Wolf Prize for physics which he shared with Stephen Hawking
Stephen Hawking
Stephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...
for their contribution to our understanding of the universe. He is renowned for his work in mathematical physics, in particular his contributions to 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...
and cosmology
Physical cosmology
Physical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of the universe and is concerned with fundamental questions about its formation and evolution. For most of human history, it was a branch of metaphysics and religion...
. He is also a recreational mathematician
Recreational mathematics
Recreational mathematics is an umbrella term, referring to mathematical puzzles and mathematical games.Not all problems in this field require a knowledge of advanced mathematics, and thus, recreational mathematics often attracts the curiosity of non-mathematicians, and inspires their further study...
and philosopher.
Career
He was born in ColchesterColchester
Colchester is an historic town and the largest settlement within the borough of Colchester in Essex, England.At the time of the census in 2001, it had a population of 104,390. However, the population is rapidly increasing, and has been named as one of Britain's fastest growing towns. As the...
, Essex
Essex
Essex is a ceremonial and non-metropolitan county in the East region of England, and one of the home counties. It is located to the northeast of Greater London. It borders with Cambridgeshire and Suffolk to the north, Hertfordshire to the west, Kent to the South and London to the south west...
, England, Roger Penrose is a son of Lionel S. Penrose
Lionel Penrose
Lionel Sharples Penrose, FRS was a British psychiatrist, medical geneticist, mathematician and chess theorist, who carried out pioneering work on the genetics of mental retardation. He was educated at the Quaker Leighton Park School and St...
and Margaret Leathes. Penrose is the brother of mathematician Oliver Penrose
Oliver Penrose
Oliver Penrose FRS, FRSE is a British theoretical physicist.He is the son of the scientist Lionel Penrose, brother of the mathematical physicist Roger Penrose, and brother of chess master Jonathan Penrose...
and of chess Grandmaster Jonathan Penrose
Jonathan Penrose
Jonathan Penrose, OBE is an English chess player, emeritus Grandmaster, and International Correspondence Chess Grandmaster who won the British Chess Championship ten times between 1958 and 1969. He is the son of Lionel Penrose, a world famous professor of genetics, and brother of Roger Penrose...
. Penrose attended University College School
University College School
University College School, generally known as UCS, is an Independent school charity situated in Hampstead, north west London, England. The school was founded in 1830 by University College London and inherited many of that institution's progressive and secular views...
and University College, London, where he graduated with a first class degree in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
. In 1955, while still a student, Penrose reintroduced the E. H. Moore
E. H. Moore
Eliakim Hastings Moore was an American mathematician.-Life:Moore, the son of a Methodist minister and grandson of US Congressman Eliakim H. Moore, discovered mathematics through a summer job at the Cincinnati Observatory while in high school. He learned mathematics at Yale University, where he was...
generalized matrix inverse (also known as Moore–Penrose inverse after it had been reinvented by Arne Bjerhammar
Arne Bjerhammar
Arne Bjerhammar was a Swedish geodesist. He was professor at Royal Institute of Technology in Stockholm. He was born in Båstad, Scania in the south of Sweden.His research covered many fields of geodesy...
(1951). Penrose earned his Ph.D.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
at Cambridge
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
(St John's College
St John's College, Cambridge
St John's College is a constituent college of the University of Cambridge. The college's alumni include nine Nobel Prize winners, six Prime Ministers, three archbishops, at least two princes, and three Saints....
) in 1958, writing a thesis on "tensor methods in algebraic geometry" under algebraist and geometer John A. Todd. He devised and popularised the Penrose triangle
Penrose triangle
The Penrose triangle, also known as the Penrose tribar, is an impossible object. It was first created by the Swedish artist Oscar Reutersvärd in 1934. The mathematician Roger Penrose independently devised and popularised it in the 1950s, describing it as "impossibility in its purest form". It is...
in the 1950s, describing it as "impossibility in its purest form" and exchanged material with the artist M. C. Escher
M. C. Escher
Maurits Cornelis Escher , usually referred to as M. C. Escher , was a Dutch graphic artist. He is known for his often mathematically inspired woodcuts, lithographs, and mezzotints...
, whose earlier depictions of impossible objects partly inspired it. Escher's Waterfall
Waterfall (M. C. Escher)
Waterfall is a lithography print by the Dutch artist M. C. Escher which was first printed in October, 1961. It shows an apparent paradox where water from the base of a waterfall appears to run downhill before reaching the top of the waterfall....
, and Ascending and Descending
Ascending and Descending
Ascending and Descending is a lithograph print by the Dutch artist M. C. Escher which was first printed in March 1960.The original print measures 14" x 11 1/4”. The lithograph depicts a large building roofed by a never-ending staircase. Two lines of identically dressed men appear on the staircase,...
were in turn inspired by Penrose. As reviewer Manjit Kumar puts it:
As a student in 1954, Penrose was attending a conference in Amsterdam when by chance he came across an exhibition of Escher's work. Soon he was trying to conjure up impossible figures of his own and discovered the tri-bar – a triangle that looks like a real, solid three-dimensional object, but isn't. Together with his father, a physicist and mathematician, Penrose went on to design a staircase that simultaneously loops up and down. An article followed and a copy was sent to Escher. Completing a cyclical flow of creativity, the Dutch master of geometrical illusions was inspired to produce his two masterpieces.
In 1965, at Cambridge, Penrose proved that singularities
Singularity theory
-The notion of singularity:In mathematics, singularity theory is the study of the failure of manifold structure. A loop of string can serve as an example of a one-dimensional manifold, if one neglects its width. What is meant by a singularity can be seen by dropping it on the floor...
(such as black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
s) could be formed from the gravitational collapse of immense, dying star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...
s.
Twistor theory
In theoretical and mathematical physics, twistor theory maps the geometric objects of conventional 3+1 space-time into geometric objects in a 4 dimensional space with metric signature...
which maps geometric objects in Minkowski space
Minkowski space
In physics and mathematics, Minkowski space or Minkowski spacetime is the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated...
into the 4-dimensional complex space with the metric signature (2,2). In 1969, he conjectured the cosmic censorship hypothesis
Cosmic censorship hypothesis
The weak and the strong cosmic censorship hypotheses are two mathematical conjectures about the structure of singularities arising in general relativity....
. This proposes (rather informally) that the universe protects us from the inherent unpredictability of singularities
Singularity theory
-The notion of singularity:In mathematics, singularity theory is the study of the failure of manifold structure. A loop of string can serve as an example of a one-dimensional manifold, if one neglects its width. What is meant by a singularity can be seen by dropping it on the floor...
(such as the one in the centre of a black hole) by hiding them from our view behind an event horizon
Event horizon
In general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms it is defined as "the point of no return" i.e. the point at which the gravitational pull becomes so great as to make escape impossible. The most common case...
. This form is now known as the "weak censorship hypothesis"; in 1979, Penrose formulated a stronger version called the "strong censorship hypothesis". Together with the BKL conjecture and issues of nonlinear stability, settling the censorship conjectures is one of the most important outstanding problems in 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...
. Also from 1979 dates Penrose's influential Weyl curvature hypothesis
Weyl curvature hypothesis
The Weyl curvature hypothesis, which arises in the application of Albert Einstein's general theory of relativity to physical cosmology, was introduced by the British mathematician and theoretical physicist Sir Roger Penrose in an article in 1979 in an attempt to provide explanations for two of the...
on the initial conditions of the observable part of the Universe and the origin of the second law of thermodynamics
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...
. Penrose and James Terrell independently realized that objects travelling near the speed of light will appear to undergo a peculiar skewing or rotation. This effect has come to be called the Terrell rotation
Terrell rotation
Terrell rotation is the name of a mathematical and physical effect. Specifically, Terrell rotation is the distortion that a passing object would appear to undergo, according to the special theory of relativity if it were travelling a significant fraction of the speed of light...
or Penrose–Terrell rotation.
Penrose is well known for his 1974 discovery of Penrose tiling
Penrose tiling
A Penrose tiling is a non-periodic tiling generated by an aperiodic set of prototiles named after Sir Roger Penrose, who investigated these sets in the 1970s. The aperiodicity of the Penrose prototiles implies that a shifted copy of a Penrose tiling will never match the original...
s, which are formed from two tiles that can only tile
Tessellation
A tessellation or tiling of the plane is a pattern of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible. Tessellations frequently appeared in the art...
the plane nonperiodically, and are the first tilings to exhibit fivefold rotational symmetry. Penrose developed these ideas based on the article Deux types fondamentaux de distribution statistique (1938; an English translation Two Basic Types of Statistical Distribution) by Czech geographer
Geographer
A geographer is a scholar whose area of study is geography, the study of Earth's natural environment and human society.Although geographers are historically known as people who make maps, map making is actually the field of study of cartography, a subset of geography...
, demographer and statistician
Statistician
A statistician is someone who works with theoretical or applied statistics. The profession exists in both the private and public sectors. The core of that work is to measure, interpret, and describe the world and human activity patterns within it...
Jaromír Korčák. In 1984, such patterns were observed in the arrangement of atoms in quasicrystal
Quasicrystal
A quasiperiodic crystal, or, in short, quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry...
s. Another noteworthy contribution is his 1971 invention of spin network
Spin network
In physics, a spin network is a type of diagram which can be used to represent states and interactions between particles and fields in quantum mechanics. From a mathematical perspective, the diagrams are a concise way to represent multilinear functions and functions between representations of...
s, which later came to form the geometry of 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...
in loop quantum gravity
Loop quantum gravity
Loop quantum gravity , also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the theories of quantum mechanics and general relativity...
. He was influential in popularizing what are commonly known as Penrose diagram
Penrose diagram
In theoretical physics, a Penrose diagram is a two-dimensional diagram that captures the causal relations between different points in spacetime...
s (causal diagrams). In 2004 Penrose released The Road to Reality: A Complete Guide to the Laws of the Universe
The Road to Reality: A Complete Guide to the Laws of the Universe
The 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 1,099-page book aimed at giving a comprehensive guide to the laws of physics
Physical law
A physical law or scientific law is "a theoretical principle deduced from particular facts, applicable to a defined group or class of phenomena, and expressible by the statement that a particular phenomenon always occurs if certain conditions be present." Physical laws are typically conclusions...
. He has proposed a novel interpretation
Penrose interpretation
The Penrose interpretation is a prediction of Sir 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...
of 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...
. In 2010, Penrose reported possible evidence, based on concentric circles found in WMAP data of the CMB
CMB
CMB can mean:*The IATA airport code for Bandaranaike International Airport, Colombo – Sri Lanka's only international airport*C.M.B., the debut album of American R&B and pop group Color Me Badd...
sky, of an earlier universe existing before the Big Bang
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
of our own present universe.
Penrose is the Francis and Helen Pentz Distinguished (visiting) Professor of Physics and Mathematics at Pennsylvania State University
Pennsylvania State University
The Pennsylvania State University, commonly referred to as Penn State or PSU, is a public research university with campuses and facilities throughout the state of Pennsylvania, United States. Founded in 1855, the university has a threefold mission of teaching, research, and public service...
. Penrose is married to Vanessa Thomas, head of mathematics at Abingdon School
Abingdon School
Abingdon School is a British day and boarding independent school for boys situated in Abingdon, Oxfordshire , previously known as Roysse's School. In 1998 a formal merger took place between Abingdon School and Josca's, a preparatory school four miles to the west at Frilford...
, with whom he has one son. He has three sons from a previous marriage to American Joan Isabel Wedge, whom he married in 1959.
Physics and consciousness
Penrose has written controversial books on the connection between fundamental physics and human (or animal) consciousness. In The Emperor's New MindThe 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), he argues that known laws of physics are inadequate to explain the phenomenon of consciousness. Penrose proposes the characteristics this new physics may have and specifies the requirements for a bridge between classical and quantum mechanics (what he calls correct quantum gravity). Penrose uses a variant of Turing's halting theorem to demonstrate that a system can be deterministic without being algorithmic. (E.g., imagine a system with only two states, ON and OFF. If the system's state is ON if a given Turing machine halts, and OFF if the Turing machine does not halt, then the system's state is completely determined by the Turing machine, however there is no algorithmic way to determine whether the Turing machine stops.) Penrose believes that such deterministic non-algorithmic processes may come in play in the quantum mechanical wave function reduction, and may be harnessed by the brain. He argues that the present computer is unable to have intelligence because it is an algorithmically deterministic system. He argues against the viewpoint that the rational processes of the mind are completely algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
ic and can thus be duplicated by a sufficiently complex computer. This contrasts with supporters of strong artificial intelligence, who contend that thought can be simulated algorithmically. He bases this on claims that consciousness transcends formal logic
Formal logic
Classical or traditional system of determining the validity or invalidity of a conclusion deduced from two or more statements...
because things such as the insolubility of the halting problem
Halting problem
In computability theory, the halting problem can be stated as follows: Given a description of a computer program, decide whether the program finishes running or continues to run forever...
and Gödel's incompleteness theorem prevent an algorithmically based system of logic from reproducing such traits of human intelligence as mathematical insight. These claims 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. 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:...
, a leading proponent of artificial intelligence, was particularly critical, stating that Penrose "tries to show, in chapter after chapter, that human thought cannot be based on any known scientific principle." Minsky's position is exactly the opposite - he believes that humans are, in fact, machines, whose functioning, although complex, is fully explainable by current physics. Minsky maintains that "one can carry that quest [for scientific explanation] too far by only seeking new basic principles instead of attacking the real detail. This is what I see in Penrose's quest for a new basic principle of physics that will account for consciousness."
Penrose responded to criticism of The Emperor's New Mind with his follow up 1994 book Shadows of the Mind
Shadows 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....
, and in 1997 with The Large, the Small and the Human Mind. In those works, he also combined his observations with that of 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:...
.
Penrose and Hameroff have argued that 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...
is the result of quantum gravity effects in 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 they dubbed 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...
(orchestrated objective reduction). 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 10,000,000,000. The reception of the paper is summed up by this statement in Tegmark's support: "Physicists outside the fray, such as IBM's John A. Smolin
John A. Smolin
John A. Smolin is an American physicist at IBM's Thomas J. Watson Research Center.Smolin is best known for his work in quantum information theory, where, with collaborators, he introduced several important techniques, including entanglement distillation, for quantum error-correction and the...
, 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'". Tegmark's paper has been widely cited by critics of the Penrose–Hameroff position.
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.
Hameroff, in a lecture in part of a Google Tech talks series exploring Quantum biology, gave an overview of current research in the area, and responded to subsequent criticisms of the Orch-OR model.
Phillip Tetlow, although himself supportive of Penrose's views, acknowledges that Penrose's ideas about the human thought process are at present a minority view in scientific circles, citing Minsky's criticisms and quoting science journalist 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...
's description of Penrose as "one of a handful of scientists" who believe that the nature of consciousness suggests a quantum process.
Religious views
Penrose does not hold to any religious doctrineDoctrine
Doctrine is a codification of beliefs or a body of teachings or instructions, taught principles or positions, as the body of teachings in a branch of knowledge or belief system...
, and refers to himself as an atheist. In the film A Brief History of Time
A Brief History of Time (film)
A Brief History of Time is a 1991 American documentary film about the physicist Stephen Hawking, directed by Errol Morris. Its title derives from Hawking's bestselling book of the same name, but whereas the book is an explanation of cosmology, the film is a biography of Hawking's life, featuring...
, he said, "I think I would say that the universe has a purpose, it's not somehow just there by chance ... some people, I think, take the view that the universe is just there and it runs along–it's a bit like it just sort of computes, and we happen somehow by accident to find ourselves in this thing. But I don't think that's a very fruitful or helpful way of looking at the universe, I think that there is something much deeper about it." Penrose is a Distinguished Supporter of the British Humanist Association
British Humanist Association
The British Humanist Association is an organisation of the United Kingdom which promotes Humanism and represents "people who seek to live good lives without religious or superstitious beliefs." The BHA is committed to secularism, human rights, democracy, egalitarianism and mutual respect...
.
Awards and honours
Penrose has been awarded many prizes for his contributions to science. He was elected a FellowFellow
A fellow in the broadest sense is someone who is an equal or a comrade. The term fellow is also used to describe a person, particularly by those in the upper social classes. It is most often used in an academic context: a fellow is often part of an elite group of learned people who are awarded...
of the Royal Society of London
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
in 1972. In 1975, Stephen Hawking
Stephen Hawking
Stephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...
and Penrose were jointly awarded the Eddington Medal
Eddington Medal
The Eddington Medal, named after Sir Arthur Eddington, is awarded by the Royal Astronomical Society nominally once every two years for investigations of outstanding merit in theoretical astrophysics.- Recipients :* 1953 Georges Lemaître...
of the Royal Astronomical Society
Royal Astronomical Society
The Royal Astronomical Society is a learned society that began as the Astronomical Society of London in 1820 to support astronomical research . It became the Royal Astronomical Society in 1831 on receiving its Royal Charter from William IV...
. In 1985, he was awarded the Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
Royal Medal
Royal Medal
The Royal Medal, also known as The Queen's Medal, is a silver-gilt medal awarded each year by the Royal Society, two for "the most important contributions to the advancement of natural knowledge" and one for "distinguished contributions in the applied sciences" made within the Commonwealth of...
. Along with Stephen Hawking
Stephen Hawking
Stephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...
, he was awarded the prestigious Wolf Foundation Prize for Physics
Wolf Prize in Physics
The Wolf Prize in Physics is awarded once a year by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Mathematics, Medicine and Arts. The Prize is often considered the most prestigious...
in 1988. In 1989 he was awarded the Dirac Medal and Prize
Dirac Prize
The Dirac Prize is the name of four prominent awards in the field of theoretical physics, computational chemistry, and mathematics, awarded by different organizations, named in honour of Professor Paul Dirac, one of the great theoretical physicists of the 20th Century.- The Dirac Medal and Lecture...
of the British Institute of Physics
Institute of Physics
The Institute of Physics is a scientific charity devoted to increasing the practice, understanding and application of physics. It has a worldwide membership of around 40,000....
. In 1990 Penrose was awarded the Albert Einstein Medal
Albert Einstein Medal
The Albert Einstein Medal is an award presented by the Albert Einstein Society in Bern. First given in 1979, the award is presented to people who have "rendered outstanding services" in connection with Albert Einstein each year.- Recipients :...
for outstanding work related to the work of Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
by the Albert Einstein Society
Albert Einstein Society
The Albert Einstein Society was founded on 28 June 1977 by Dr Max Flückiger. It is located in Bern, Switzerland and is most noted for awarding the Einstein Medal. This medal is awarded to individuals who have made an outstanding contribution to science that is related to the work of Albert Einstein....
. In 1991, he was awarded the Naylor Prize of the London Mathematical Society
London Mathematical Society
-See also:* American Mathematical Society* Edinburgh Mathematical Society* European Mathematical Society* List of Mathematical Societies* Council for the Mathematical Sciences* BCS-FACS Specialist Group-External links:* * *...
. From 1992 to 1995 he served as President of the International Society on General Relativity and Gravitation.
In 1994, Penrose was knighted
Knight Bachelor
The rank of Knight Bachelor is a part of the British honours system. It is the most basic rank of a man who has been knighted by the monarch but not as a member of one of the organised Orders of Chivalry...
for services to science. In 1998, he was elected Foreign Associate of the United States National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
. In 2000 he was appointed to the Order of Merit. In 2004 he was awarded the De Morgan Medal
De Morgan Medal
The De Morgan Medal is a prize for outstanding contribution to mathematics, awarded by the London Mathematical Society. The Society's most prestigious award, it is given in memory of Augustus De Morgan, who was the first President of the society....
for his wide and original contributions to mathematical physics. To quote the citation from the London Mathematical Society:
- His deep work on General Relativity has been a major factor in our understanding of black holes. His development of Twistor TheoryTwistor theoryIn theoretical and mathematical physics, twistor theory maps the geometric objects of conventional 3+1 space-time into geometric objects in a 4 dimensional space with metric signature...
has produced a beautiful and productive approach to the classical equations of mathematical physics. His tilings of the plane underlie the newly discovered quasi-crystals.
In 2005 Penrose was awarded an honorary doctorate (Honoris Causa) by Warsaw University and Katholieke Universiteit Leuven
Katholieke Universiteit Leuven
The Katholieke Universiteit Leuven is a Dutch-speaking university in Flanders, Belgium.It is located at the centre of the historic town of Leuven, and is a prominent part of the city, home to the university since 1425...
(Belgium), and in 2006 by the University of York
University of York
The University of York , is an academic institution located in the city of York, England. Established in 1963, the campus university has expanded to more than thirty departments and centres, covering a wide range of subjects...
. In 2008 Penrose was awarded the Copley Medal
Copley Medal
The Copley Medal is an award given by the Royal Society of London for "outstanding achievements in research in any branch of science, and alternates between the physical sciences and the biological sciences"...
. He is also a Distinguished Supporter of the British Humanist Association
British Humanist Association
The British Humanist Association is an organisation of the United Kingdom which promotes Humanism and represents "people who seek to live good lives without religious or superstitious beliefs." The BHA is committed to secularism, human rights, democracy, egalitarianism and mutual respect...
and one of the patrons of the Oxford University Scientific Society
Oxford University Scientific Society
The Oxford University Scientific Society is a student scientific society at the University of Oxford. It was founded in 1882 as the Oxford University Junior Scientific Club. It is one of the oldest undergraduate science societies in the world. It organizes talks on scientific subjects on a weekly...
. In 2011, Penrose awarded the Fonseca prize, which is given by the University of Santiago de Compostela
University of Santiago de Compostela
The Royal University of Santiago de Compostela - USC is a public university located in the city of Santiago de Compostela, Galicia, Spain. A second campus is located in Lugo, Galicia....
.
Works
- Techniques of Differential Topology in Relativity (1972, ISBN 0-89871-005-7)
- Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic Fields (with Wolfgang Rindler, 1987) ISBN 0-521-33707-0 (paperback)
- Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time Geometry (with Wolfgang Rindler, 1988) (reprint), ISBN 0-521-34786-6 (paperback)
- The Emperor's New Mind: Concerning Computers, Minds, and The Laws of PhysicsThe 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...
(1989, ISBN 0-14-014534-6 (paperback); it received the Rhone-Poulenc science book prize in 1990) - Shadows of the Mind: A Search for the Missing Science of ConsciousnessShadows of the MindShadows 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, ISBN 0-19-853978-9 (hardback)) - The Nature of Space and Time (with Stephen HawkingStephen HawkingStephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...
, 1996, ISBN 0-691-03791-4 (hardback), ISBN 0-691-05084-8 (paperback)) - The Large, the Small, and the Human Mind (with Abner Shimony, Nancy Cartwright, and Stephen Hawking, 1997, ISBN 0-521-56330-5 (hardback), ISBN 0-521-65538-2 (paperback), Canto edition: ISBN 0-521-78572-3)
- White Mars or, The Mind Set Free (with Brian W. Aldiss, 1999, ISBN 978-0-316-85243-2 (hardback))
- 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...
(2004, ISBN 0-224-04447-8 (hardcover), ISBN 0-09-944068-7 (paperback)) - Cycles of Time: An Extraordinary New View of the UniverseCycles of Time (book)Cycles of Time: An Extraordinary New View of the Universe is a science book by mathematical physicist Roger Penrose published by The Bodley Head in 2010...
(Bodley Head (23 Sep 2010) ISBN 978-0-224-08036-1)
Penrose also wrote forewords to Quantum Aspects of Life
Quantum Aspects of Life
Quantum 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;...
and Zee
Anthony Zee
Anthony Zee is a Chinese American physicist, writer, and currently a professor at the Kavli Institute for Theoretical Physics and the physics department of the University of California, Santa Barbara.Zee obtained his Ph.D. from Harvard in 1970, supervised by Sidney Coleman...
's book Fearful Symmetry.
See also
- Conformal Cyclic CosmologyConformal Cyclic CosmologyThe Conformal Cyclic Cosmology is a cosmological model in the framework of general relativity, advanced by the theoretical physicist Sir Roger Penrose. In CCC, the universe iterates through infinite cycles, with the future timelike infinity of each previous iteration being identified with the Big...
- 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...
- MultiverseMultiverseThe multiverse is the hypothetical set of multiple possible universes that together comprise all of reality.Multiverse may also refer to:-In fiction:* Multiverse , the fictional multiverse used by DC Comics...
- 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;...
- Illumination problemIllumination problemThe illumination problem is a resolved mathematical problem first posed by Ernst Straus in the 1950s. Straus asked if a room with mirrored walls can always be illuminated by a single point light source, allowing for repeated reflection of light off the mirrored walls...
Further reading
- Ferguson, Kitty (1991). Stephen Hawking: Quest For A Theory of Everything. Franklin Watts. ISBN 0-553-29895-X.; see Box 34.2.
External links
- Dangerous Knowledge – Penrose was one of the principal interviewees in a BBC documentary about the mathematics of infinity directed by David MaloneDavid Malone (independent filmmaker)David Malone, author of The Debt Generation, is also director of acclaimed documentaries on philosophy, science and religion originally broadcast in the UK by the BBC and Channel 4.-Work:Malone's work includes...
- Penrose's new theory "Aeons Before the Big Bang?":
- Original 2005 lecture: "Before the Big Bang? A new perspective on the Weyl curvature hypothesis" (Isaac Newton Institute for Mathematical Sciences, Cambridge, Nov 11, 2005).
- Original publication: "Before the Big Bang: an outrageous new perspective and its implications for particle physics". Proceedings of EPAC 2006. Edinburgh. 2759–2762 (cf. also Hill, C.D. & Nurowski, P. (2007) "On Penrose's 'Before the Big Bang' ideas". Ithaca)
- Revised 2009 lecture: "Aeons Before the Big Bang?" (Georgia Institute of Technology, Center for Relativistic Astrophysics)
- BBC interview on the new theory
- Roger Penrose on The Forum
- Penrose on sidestepping reason
- Shaking Up Foundations of Math: Roger Penrose on Kurt Gödel's Groundbreaking Work
- Hilary Putnam's review of Penrose's 'Shadows of the Mind' claiming that Penrose's use of Godel's Incompleteness Theorem is fallacious
- Penrose Tiling found in Islamic Architecture
- Two theories for the formation of quasicrystals resembling Penrose tilings
- Tegmark, Max. 2000. "The importance of quantum decoherence in brain processes". Physical Review E. vol 61. pp. 4194–4206.
- "Biological feasibility of quantum states in the brain" – (a disputation of Tegmark's result by Hagan, Hameroff, and Tuszyński)
- "Toilet Paper Plagiarism" – D. Trull about Penrose's lawsuit concerning the use of his Penrose tilings on toilet paper
- Roger Penrose: A Knight on the tiles (Plus magazine)
- Penrose's Gifford Lecture biography
- Quantum-Mind
- Audio: Roger Penrose in conversation on the BBC World Service discussion show
The Forum
The Forum (BBC World Service)
The Forum is the BBC World Service's flagship discussion programme. It brings together prominent thinkers from different disciplines and different parts of the world to try and create stimulating discussion, informed by highly distinct academic, artistic and cultural backgrounds.-Format:Each...