Penrose , Sir Roger

(1931–) British mathematician and theoretical physicist

Penrose, the son of the geneticist Lionel Penrose, was born at Colchester in Essex. He graduated from University College, London, and obtained his PhD in 1957 from Cambridge University. After holding various lecturing and research posts in London, Cambridge, and in America at Princeton, Syracuse, and Texas, Penrose was appointed professor of applied mathematics at Birkbeck College, London, in 1966. In 1973 he was elected Rouse Ball Professor of Mathematics at Oxford.

Penrose has done much to elucidate the fundamental properties of black holes. These result from the total gravitational collapse of large stars that shrink to such a small volume that not even a light signal can escape from them. There is thus a boundary around a black hole inside which all information about the black hole is trapped; this is known as its ‘event horizon’. With Stephen Hawking, Penrose proved a theorem of Einstein's general relativity asserting that at the center of a black hole there must evolve a ‘space–time singularity’ of zero volume and infinite density where the present laws of physics break down. He went on to propose his hypothesis of ‘cosmic censorship’, that such singularities cannot be ‘naked’; they must possess an event horizon. The effect of this would be to conceal and isolate the singularity with its indifference to the laws of physics.

Despite this Penrose went on in 1969 to describe a mechanism for the extraction of energy from a Kerr black hole, an uncharged rotating body first described by Roy Kerr in 1963. Such bodies are surrounded by an ergosphere within which it is impossible for an object to be at rest. If, Penrose demonstrated, a body fell into this area it would split into two particles; one would fall into the hole and the other would escape with more mass-energy than the initial particle. In this way rotational energy of the black hole is transferred to the particle outside the hole.

From the mid-1960s Penrose has been working on the development of a new cosmology based on a complex geometry. Penrose began with ‘twistors’ – massless objects with both linear and angular momentum in twistor space. From these he attempted to reconstruct the main outlines of modern physics. The matter is pursued not only by Penrose but through a number of ‘twistor groups’ who communicate through a Twistor Newsletter. The fullest account of twistor theory is to be found in Spinors and Space-Time (2 vols., 1984–86) by Penrose and W.Windler.

In 1974 Penrose introduced a novel tiling of the affine plane (Penrose tiling). Periodic tilings in which a unit figure is endlessly repeated can be constructed from triangles, squares, and hexagons – figures with three-, four-, or six-fold symmetry. The plane cannot be tiled by pentagons, which have a five-fold symmetry; three pentagons fitted together always leave a crack, known to crystallographers as a ‘frustration’. It was also known that crystal structures could have two-, three-, four-, or six-fold rotational symmetries only. No crystal, that is, could have a five-fold rotational symmetry.

Penrose's method of tiling the plane involved constructing two rhombuses by dividing the diagonal of a regular parallelogram by a golden section. These could be combined according to simple rules so as to cover the plane, even though there was no simple repeated unit cell. The rhombuses can be assembled in such a way as to have an almost five-fold symmetry. As such they were seen as an interesting oddity, usually discussed in columns devoted to recreational mathematics. However, things changed dramatically in 1984 when Dany Schectman of the National Bureau of Standards and his colleagues found that a rapidly cooled sample of an aluminum–manganese alloy formed crystals that displayed a five-fold symmetry. ‘Quasicrystals’, as they soon became known, developed rapidly into a major new research field and became the subject of hundreds of papers.

In addition to continuing his work on twistor theory Penrose also published a widely read book, The Emperor's New Mind (1989). The book is an attack on aspects of artificial intelligence. In it he argues that there are aspects of mathematics that cannot be tied to a set of rules. We cannot allow “one universally formal system…equivalent to all the mathematicians' algorithms for judging mathematical truth.” Such a system would violate Gödel's theorem. Nor can we accept that algorithms used are so complicated and obscure that their validity can never be known. We do not in fact ascertain mathematical truth solely through the use of algorithms. “We must see the truth of a mathematical argument to be convinced of its validity,” Penrose has insisted. Consequently when we see the validity of a theorem, in seeing it “we reveal the very nonalgorithmic nature of the ‘seeing’ process itself.”

He further developed his arguments in Shadows of the Mind(1994), in which he also answered many of the objections raised against the earlier work. Penrose has also published (in collaboration with Stephen Hawking) The Nature of Space and Time (1996), in which they develop their own cosmological viewpoints. Thus while Penrose presents his own twistor view of the universe, Hawking concentrates on problems connected with quantum cosmology.