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	Penrose triangle
		In 1954, Roger Penrose, after attending a lecture by the artist M. Escher, rediscovered the impossible triangle and drew it in its most familiar form, which he published in a 1958 article in the British Journal of Psychology, coauthored with his father Lionel.
		Penrose was also unfamiliar with the work of Reutersvärd, Piranesi, and others who had created impossible figures previously.
		Penrose's impossible triangle, unlike Reutersvärd's earlier version, was drawn in perspective, which added an additional size paradox to the object.
	www.daviddarling.info /encyclopedia/P/Penrose_triangle.html (245 words)

	Encyclopedia: Roger Penrose (Site not responding. Last check: 2007-11-05)
		Sir Roger Penrose, OM, FRS (born 8 August 1931) is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the University of Oxford.
		Roger Penrose is the son of scientist Lionel S. Penrose and Margaret Leathes, and the brother of mathematician Oliver Penrose and chess grandmaster Jonathan Penrose.
		Penrose and Stuart Hameroff have constructed a theory in which human consciousness is the result of quantum gravity effects in microtubules.
	www.nationmaster.com /encyclopedia/Roger-Penrose (3311 words)

	Penrose (Site not responding. Last check: 2007-11-05)
		Penrose was awarded his Ph.D. for his work in algebra and geometry from the University of Cambridge in 1957 but by this time he had already become interested in physics.
		Penrose spent the academic year 1956-57 as an Assistant Lecturer in Pure Mathematics at Bedford College, London and was then appointed as a Research Fellow at St John's College, Cambridge.
		One of Penrose's major breakthroughs was his introduction of twistor theory in an attempt to unite relativity and quantum theory.
	www-gap.dcs.st-and.ac.uk /~history/Mathematicians/Penrose.html (2164 words)

	Roger Penrose
		Penrose and Hameroff have constructed a theory of human consciousness in which human consciousness is the result of quantum gravity effects in microtubules.
		And another quote, this one from Charles Seife: 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.
		Roger Penrose is the son of scientist Lionel S Penrose and the brother of mathemetician Prof Oliver Penrose and chess Grand Master Jonathan Penrose
	www.brainyencyclopedia.com /encyclopedia/r/ro/roger_penrose.html (693 words)

	ROGER PENROSE FACTS AND INFORMATION (Site not responding. Last check: 2007-11-05)
		Roger Penrose is the son of scientist Lionel S. Penrose and Margaret Leathes, and the brother of mathematician Oliver_Penrose and chess grandmaster Jonathan_Penrose.
		In 1965 at Cambridge, Penrose proved that singularities (such as fl_holes) could be formed from the gravitational collapse of dying immense stars.
		Roger Penrose is well-known for his 1974 discovery of Penrose_tilings, which are formed from two tiles that can only tile the plane aperiodically.
	www.igopay.com /Roger_Penrose (1169 words)

	Penrose Lionel Sharples - Search Results - MSN Encarta
		Penrose, Lionel Sharples (1898–1972), English physician and geneticist who carried out pioneering work on mental retardation and Down Syndrome.
		Penrose, Boies (1860-1921), American politician, born in Philadelphia, Pennsylvania.
		Penrose prepared for college with private tutors and also...
	ca.encarta.msn.com /Penrose_Lionel_Sharples.html (74 words)

	Roger Penrose (Site not responding. Last check: 2007-11-05)
		Penrose has worked closely with Stephen Hawking, often providing the mathematics necessary to underpin Hawking's brilliant and profound approach to physics and cosmology.
		Penrose's achievements in mathematics and physics - and I have touched on only a small fraction - spring from a lifelong sense of wonder towards the mystery and beauty of being.
		Penrose was on in the summer of 2000 on BBC Radio 4, interviewed by the lovely and perceptive
	clublet.com /c/c/why?RogerPenrose (667 words)

	Penrose biography
		Penrose was awarded his Ph.D. for his work in algebra and geometry from the University of Cambridge in 1957 but by this time he had already become interested in physics.
		Penrose spent the academic year 1956-57 as an Assistant Lecturer in Pure Mathematics at Bedford College, London and was then appointed as a Research Fellow at St John's College, Cambridge.
		One of Penrose's major breakthroughs was his introduction of twistor theory in an attempt to unite relativity and quantum theory.
	www-history.mcs.st-andrews.ac.uk /Biographies/Penrose.html (2278 words)

	3.3
		The first [680] in the Penrose family of replicators was a set of “A” and “B” type tilt-blocks, cut from plywood or vulcanite, and placed on a track where they could slide freely but not pass each other.
		Penrose [681-685] went on to devise an ingenious interlocking column design which allowed the replication of a multipart machine which is free to move about in a 2-dimensional agitation environment strewn with a random assortment of premanufactured constitutive columns.
		Explains Penrose [683]: “When the neutral unit at left joins the seed (b), it disengages one of the hooks holding the seed together and sets the blocking mechanism so that only one more neutral unit can be added.
	www.molecularassembler.com /KSRM/3.3.htm (602 words)

	Jonathan Penrose - Chesspedia, The Free Chess Encyclopedia Pushedpawn.org
		Jonathan Penrose (born 1933) is an English chess grandmaster who won the British Chess Championship ten times from 1958 to 1969.
		He is the son of Lionel Penrose and brother of Roger Penrose.
		Penrose was the leading British player for several years in the 1960s and early 70s, winning the British Championship a record number of times.
	pushedpawn.org /test6/Jonathan_Penrose.htm (163 words)

	Roger Penrose Summary
		Penrose suspects that a greater understanding of the functioning of the human brain may depend on a fundamentally new understanding of physics, to be sought in a radical new theory of quantum gravity.
		Penrose also developed the concept of what is now known of Penrose tiling (the complete covering without gaps or overlaps of a two-dimensional planar surface with two sizes of rhomboid or pentagon shaped tiles).
		Penrose and Stuart Hameroff have constructed a theory in which human consciousness is the result of quantum gravity effects in microtubules.
	www.bookrags.com /Roger_Penrose (5262 words)

	If an Electron Can Be in Two Places at Once, Why Can't You? \| Physics & Math \| DISCOVER Magazine (Site not responding. Last check: 2007-11-05)
		Penrose believes he has identified the secret that keeps the quantum genie tightly bottled up in the atomic world, a secret that was right in front of us all along: gravity.
		Penrose developed the idea of cosmic censorship, which holds that infor-mation about processes hap-pening within fl holes remains forever hidden from out-side observers.
		Penrose’s faith began to waver while he was a graduate student at Cambridge.
	discovermagazine.com /2005/jun/cover (1265 words)

	Roger Penrose Biography \| Encyclopedia of World Biography
		His father was the geneticist Lionel Penrose, an expert on mental defects, whose interest in geometry was communicated to his son.
		Penrose collaborated with his father on the creation of a visual illusion that was incorporated into lithographs by the Dutch artist M. Escher, whose work included many mathematical elements.
		Penrose's book includes that equation and hundreds of others as it ranges over computers, minds, and the laws of physics, to mention just the subjects explicitly named in the subtitle.
	www.bookrags.com /biography/roger-penrose (948 words)

	A Closer Look: Peter Penrose (Site not responding. Last check: 2007-11-05)
		Penrose grew up in Florida listening to his mother's extensive record collection which included everything from the bluesy pop sound of Charlie Rich and the gospel music of André Crouch to the silky smooth Carpenters and Lionel Richie.
		For listeners it has resulted in a topnotch first release with Penrose's tenor voice sliding easily from one rhythm to another, always clear and in sync with singable lyrics.
		Penrose has walked on the wild side a bit during the turbulent teenage years.
	www.acloserlook.com /9708acl/music/peterpenrose.html (299 words)

	Roger Penrose - South Africa (Site not responding. Last check: 2007-11-05)
		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.
		Penrose hints at the characteristics this new physics may have and specifies the requirements for a bridge between classical and quantum mechanics (what he terms correct quantum gravity, CQG).
		In 2005 Sir Roger Penrose was awarded an honorary doctorate (Honoris Causa) by Warsaw University and Katholieke Universiteit Leuven (Belgium), and in 2006 by the University of York.
	roger-penrose.zdnet.co.za /zdnet/Roger_Penrose (1518 words)

	Jonathan Penrose vs Mikhail Tal (1960) "Penrose to the Occasion"
		Sir Roger Penrose, OM, FRS (born 8 August 1931) is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the University of Oxford.
		Roger Penrose is the son of scientist Lionel S. Penrose and Margaret Leathes, and the brother of mathematician Oliver Penrose and chess grandmaster Jonathan Penrose.
		On the computer issue, ironically I belive Jonathan Penrose retired from correspondence chess because he didn't want to be playing people who were using computers to generate their moves.
	www.chessgames.com /perl/chessgame?gid=1105990 (1011 words)

	Roger Penrose Biography (Site not responding. Last check: 2007-11-05)
		Sir Roger Penrose is perhaps best known as the author of several books of popular science, including The Road to Reality.
		Roger Penrose's father, Lionel Penrose was a medical geneticist and Fellow of the Royal Society.
		In 1945 the Penroses returned to England and Roger's father was appointed Professor of Human Genetics at University College London; Roger attended University College School and later gained his B.Sc.
	www.321books.co.uk /biography/penrose-roger.htm (227 words)

	Penrose, Lionel Sharples (Site not responding. Last check: 2007-11-05)
		He was the first to demonstrate the significance of the mother's age.
		Penrose was born in London and educated at Cambridge.
		Early in his career, Penrose advanced the study of schizophrenia and developed a test for its diagnosis.
	www.cartage.org.lb /en/themes/Biographies/MainBiographies/P/Penrose/1.html (83 words)

	Roger Penrose (Site not responding. Last check: 2007-11-05)
		Sir Roger Penrose, is a member of the faculty of Oxford University
		Sir Roger Penrose OM (born August 8 1931) is an English scientist and academician.
		Roger Penrose is the son of scientist Lionel S. Penrose, and the brother of mathematician Oliver Penrose and chess grandmaster Jonathan Penrose.
	www.worldhistory.com /wiki/R/Roger-Penrose.htm (1016 words)

	Impossible triangle
		In 1954 physicist Roger Penrose, after attending a lecture by the Dutch graphic artist M. Escher, rediscovered the impossible triangle and drew it in its most familiar form, which he published and popularized in a 1958 article, co-authored with his father Lionel Penrose, that appeared in the British Journal of Psychology.
		Penrose, who was stimulated by Escher's work, wanted to create something that illustrated an impossibility in its purest form.
		Penrose's impossible triangle, unlike Reutersvärd's earlier version, was drawn in perspective, which added an additional size paradox to the triangle.
	www.noordnet.net /optical_illusion/triangle.html (782 words)

	Impossible world: Articles: Impossible triangle
		In 1980 Swedish goverment decided to place impossible triangle and two other his figures at postage stamps, which were printed about two years..
		In 1954 english mathematician Roger Penrose after the lection of holland artist M.C. Escher drew impossible triangle in it's common view.
		Penroses sent a copy of the article to Escher and in 1961 M.C. Escher created lithograph "Waterfall".
	im-possible.info /english/articles/triangle/triangle.html (314 words)

	Roger Penrose - Biography (Site not responding. Last check: 2007-11-05)
		At Oxford, Penrose has been working on 'twistor theory' in which the four dimensions of space-time are quantized by imaginary numbers as opposed to real numbers.
		Penrose was elected a Fellow of the Royal Society of London in 1972 and a Foreign Associate of the United States National Academy of Sciences in 1998.
		Penrose's hypothesis of 'cosmic censorship' states that, within an event horizon (the interface between a fl hole and space-time), little or no radiation or information can escape, so that some events remain hidden to observers outside the fl hole.
	us.imdb.com /name/nm0672295/bio (443 words)

	Rhonda Roland Shearer / Marcel Duchamp's Impossible Bed... (Site not responding. Last check: 2007-11-05)
		Given Lionel and Roger Penrose's shared interest (also held by Roland) in visual illusions (motive); their frequent meetings (opportunity); and Roland's apparent enthusiasm for Duchamp's work (means); it is likely that Roland Penrose showed Lionel and Roger the Apolinère Enameled work before or at the time of the 1958 publication of their discovery.
		Tony Penrose agrees with me that the second scenario seems more likely, and that his father probably discussed Duchamp's optical illusions with Lionel and Roger in the course of the brandy and chess conversations that often took place in his family home.
		Moreover, the year that the Penroses published their paper was the very same year that they probably had seen Duchamp's bed at Roland Penrose's house.
	www.marcelduchamp.org /ImpossibleBed/PartI/page2.html (582 words)

	Viruslist.com - The Beginning - A Little Archeology
		In 1959, the British mathematician Lionel Penrose presented his view on automated self-replication in his Scientific American article 'Self-Reproducing Machines'.
		Unlike Neumann, Penrose described a simple two dimensional model of this structure which could be activated, multiply, mutate and attack.
		Shortly after Penrose's article appeared, Frederick G. Stahl reproduced this model in machine code on an IBM 650.
	www.viruslist.com /en/viruses/encyclopedia?chapter=153310910 (372 words)

	Penrose stairway
		An impossible figure named after by the British geneticist Lionel Penrose (1898-1972), father of Roger Penrose.
		It served as an inspiration for the staircase in M. Escher's famous print "Ascending and Descending." Although the Penrose stairway cannot be realized in three dimensions, this impossibility is not immediately perceived and, in fact, the paradox is not even apparent to many people at a quick glance.
		Although Escher and the Penroses made the Stairway famous, it was, unbeknownst to them, independently discovered and refined years before by the Swedish artist Oscar Reutersvard.
	www.daviddarling.info /encyclopedia/P/Penrose_stairway.html (175 words)

	Computers and Consciousness - Charles Sheffield
		While still a graduate student at Cambridge, England, in the mid-1950s, he developed Penrose's Theorem, a general theorem on plane conics with double contact, from which hundreds of other well-known results fall out as special cases.
		In the same period he and his father, the well-known geneticist Lionel Penrose, developed the "impossible" three-dimensional figures that form the basis of several of the artist Maurits Escher's best-known drawings.
		In 1960 Penrose introduced the spinors of Elie Cartan into general relativity, where they have become a powerful and accepted analytic method; five years latter, with Ezra Newman, he found a new way to characterize space-time geometry through the Newman-Penrose constants.
	www.worldandi.com /specialreport/1990/december/Sa17123.htm (240 words)

	Encyclopedia article on Roger Penrose [EncycloZine] (Site not responding. Last check: 2007-11-05)
		He has written books such as The Emperor's New Mind where he argues that known laws of physics do not constitute a complete system, and that true artificial intelligence is impossible.
		In 2004 Penrose released The Road to Reality: A Complete Guide to the Laws of the Universe, a 1000 page book aimed at giving a comprehensive guide to the laws of physics.
		In the same year he was awarded the De Morgan Medal for his wide and original contributions to mathematical physics, to quote the citation from the LMS (http://www.lms.ac.uk/activities/prizes_com/citations04.html)
	encyclozine.com /Roger_Penrose (816 words)

	Penrose (Site not responding. Last check: 2007-11-05)
		Lionel Penrose (1898-1972), English geneticist, father of Roger and Jonathan Penrose
		Roger Penrose (born 1931), English mathematical physicist, son of Lionel Penrose
		Charles W. Penrose (1832–1925), a leader in The Church of Jesus Christ of Latter-day Saints.
	www.worldhistory.com /wiki/P/Penrose.htm (135 words)

	Science and Society Picture Library - Search
		This is the first model of the 'impossible triangle' one of a series of 'impossible figures' designed and constructed by English geneticist Lionel Penrose in the 1950s.
		Penrose's discovery of the 'impossible figure' laid the foundation for the scientific study of illusions and investigations into the psychology of human perception.
		The Dutch artist M C Escher (1898-1972) was heavily influenced by Penrose's discovery, and incorporated an 'impossible triangle' into his well known 'Waterfall' lithograph.
	www.scienceandsociety.co.uk /results.asp?image=10327210 (135 words)

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