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188:'s method of composition—described as "creative automatism"; that is, each creative idea written down inspired a new idea—Reutersvärd started to draw a series of impossible objects on a journey from Stockholm to Paris in 1950 in the same "unconscious, automatic" way. He did not realize that his figure was a continuous flight of stairs while drawing, but the process enabled him to trace his increasingly complex designs step by step. When M.C. Escher's
235:. This paradoxical illusion can only be realized in the dream worlds of the film. In the film, the hero descends the stairs fleeing from a guard. In the real world, the hero should always be in front of the villain throughout this chase. However, in the case of the Penrose stairs the hero descends another flight of stairs to catch up to the antagonist and catch him unawares.
158:
than the previous one. I discovered the principle in an article which was sent to me, and in which I myself was named as the maker of various 'impossible objects'. But I was not familiar with the continuous steps of which the author had included a clear, if perfunctory, sketch, although I was employing some of his other examples.
120:
166:
A few months ago, a friend of mine sent me a photocopy of your article... Your figures 3 and 4, the 'continuous flight of steps', were entirely new to me, and I was so taken by the idea that they recently inspired me to produce a new picture, which I would like to send to you as a token of my esteem.
157:
working on the design of a new picture, which featured a flight of stairs which only ever ascended or descended, depending on how you saw it. form a closed, circular construction, rather like a snake biting its own tail. And yet they can be drawn in correct perspective: each step higher (or lower)
215:
by
Michael Lacanilao, was edited to create a seemingly cyclic stairwell such that if someone walks in either direction, they will end up where they started. The video claims that the stairwell, whose name evokes M.C. Escher's impossible objects, was built in the 1960s by the fictitious architect
139:
in
Amsterdam in 1954. He was "absolutely spellbound" by Escher's work, and on his journey back to England he decided to produce something "impossible" on his own. After experimenting with various designs of bars overlying each other he finally arrived at the impossible triangle. Roger showed his
59:, it is a two-dimensional depiction of a staircase in which the stairs make four 90-degree turns as they ascend or descend yet form a continuous loop, so that a person could climb them forever and never get any higher. This is clearly impossible in three-dimensional
105:
In their original article the
Penroses noted that "each part of the structure is acceptable as representing a flight of steps but the connections are such that the picture, as a whole, is inconsistent: the steps continually descend in a clockwise direction."
140:
drawings to his father, who immediately produced several variants, including the impossible flight of stairs. They wanted to publish their findings but did not know in what field the subject belonged. Because Lionel
Penrose knew the editor of the
171:
At an Escher conference in Rome in 1985, Roger
Penrose said that he had been greatly inspired by Escher's work when he and his father discovered both the Penrose tribar structure (that is, the Penrose triangle) and the continuous steps.
196:). Throughout the 1960s, Reutersvärd sent several letters to Escher to express his admiration for his work, but the Dutch artist failed to respond. Roger Penrose only discovered Reutersvärd's work in 1984.
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167:
Should you have published other articles on impossible objects or related topics, or should you know of any such articles, I would be most grateful if you could send me further details.
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74:
The "continuous staircase" was first presented in an article that the
Penroses wrote in 1959, based on the so-called "triangle of Penrose" published by Roger Penrose in the
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135:
Escher, in the 1950s, had not yet drawn any impossible stairs and was not aware of their existence. Roger
Penrose had been introduced to Escher's work at the
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92:) in March 1960. Penrose and Escher were informed of each other's work that same year. Escher developed the theme further in his print
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While the
Penroses credited Escher in their article, Escher noted in a letter to his son in January 1960 that he was:
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subject. After the publication in 1958 the
Penroses sent a copy of the article to Escher as a token of their esteem.
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Escher was captivated by the endless stairs and subsequently wrote a letter to the
Penroses in April 1960:
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was sent to Reutersvärd in 1961, he was impressed but didn't like the irregularities of the stairs (
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Penrose, L.S.; Penrose, R. (1958). "Impossible objects: A special type of visual illusion".
220:, as individuals have travelled to Rochester Institute of Technology to view the staircase.
184:, but neither Penrose nor Escher was aware of his designs. Inspired by a radio programme on
146:
and convinced him to publish their short manuscript, the finding was finally presented as a
82:
then discovered the Penrose stairs in the following year and made his now famous lithograph
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The staircase design had been discovered previously by the Swedish artist
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In their 2015 single called "Greek Tragedy," English rock band
185:
47:
in 1937 and later independently discovered and made popular by
1250:
Fashion, Faith, and Fantasy in the New Physics of the Universe
211:
based on the Penrose stairs illusion. The video, filmed at
777:"Study of algorithmic generation of the Penrose-Staircase"
574:"The Never-Ending Stories: Inception's Penrose Staircase"
511:"The Escherian Stairwell (Penrose Steps) | How It Works"
216:
Rafael Nelson Aboganda. The video was revealed to be an
340:"Impossible Pictures: When Art Helps Math Education"
515:
Facility Executive - Creating Intelligent Buildings
671:
347:Impossible Pictures: When Art Helps Math Education
502:
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390:
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229:The Penrose stairs appeared twice in the movie
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1363:Penrose interpretation of quantum mechanics
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248:depicts a complex set of Penrose stairs.
137:International Congress of Mathematicians
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18:
1284:The Large, the Small and the Human Mind
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1383:Penrose–Hawking singularity theorems
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700:Metaphor and Analogy in the Sciences
555:"Escherian Stairwell Deconstruction"
175:
674:The Eye Beguiled: Optical Illusions
13:
760:10.1111/j.2044-8295.1958.tb00634.x
637:"The Paradox of Pitch Circularity"
14:
1545:
1201:
537:"FACT CHECK: Escherian Stairwell"
337:
213:Rochester Institute of Technology
1428:Orchestrated objective reduction
1301:White Mars or, The Mind Set Free
1069:
572:Harshbarger, Eric (2010-08-19).
598:
565:
535:Mikkelson, David (6 May 2013).
509:Schwartz, Heidi (17 May 2013).
490:
424:Ascending and Descending in Nil
114:
448:
436:
414:
360:
331:
293:
1:
1388:Riemannian Penrose inequality
748:British Journal of Psychology
627:
143:British Journal of Psychology
76:British Journal of Psychology
1295:and Stephen Hawking) (1997)
1270:The Nature of Space and Time
635:Deutsch, Diana (July 2010).
238:The cover of the 2011 album
7:
553:Melikdjanian, Alan (2018),
259:
255:mentions the Penrose steps.
102:), which appeared in 1961.
10:
1550:
1452:Conformal cyclic cosmology
1413:Penrose graphical notation
409:Penrose & Penrose 1958
305:. Benedikt Taschen. 1992.
1460:
1353:Weyl curvature hypothesis
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1260:
1209:
1133:
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838:
1373:Newman–Penrose formalism
1107:Ascending and Descending
775:Lehr, Ferdinand (2022).
697:Hallyn, Fernand (2000).
420:YouTube, ZenoTheRogue,
286:
190:Ascending and Descending
125:Ascending and Descending
89:Ascending and Descending
1333:Abstract index notation
205:The Escherian Stairwell
1492:John Beresford Leathes
1432:Penrose–Lucas argument
1423:Penrose–Terrell effect
1218:The Emperor's New Mind
727:"Impossible Staircase"
725:IllusionWorks (1997).
244:by American rock band
169:
160:
132:
65:non-Euclidean geometry
24:
1368:Moore–Penrose inverse
1343:Geometry of spacetime
670:Ernst, Bruno (1992).
164:
155:
122:
63:but possible in some
55:. A variation on the
22:
1498:Illumination problem
1358:Penrose inequalities
1141:Accidental viewpoint
110:History of discovery
37:impossible staircase
1234:The Road to Reality
1226:Shadows of the Mind
1046:Vertical–horizontal
561:– via YouTube
559:Captain Disillusion
368:"Endless staircase"
319:on 23 November 2022
266:Mathematics and art
200:Escherian Stairwell
1534:Impossible objects
1146:Auditory illusions
941:Impossible trident
395:IllusionWorks 1997
224:In popular culture
133:
61:Euclidean geometry
35:, also dubbed the
25:
1524:Optical illusions
1511:
1510:
1447:Andromeda paradox
1418:Penrose transform
1348:Cosmic censorship
1169:
1168:
1161:Temporal illusion
1156:Tactile illusions
1126:(2015 photograph)
827:Optical illusions
710:978-0-7923-6560-0
656:10.1121/1.3488670
487:, pp. 75, 78
182:Oscar Reutersvärd
176:Oscar Reutersvärd
45:Oscar Reutersvärd
41:impossible object
16:Impossible object
1541:
1480:Jonathan Penrose
1437:FELIX experiment
1403:Penrose triangle
1308:
1296:
1293:Nancy Cartwright
1278:
1261:Coauthored books
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1189:
1182:
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1026:Schroeder stairs
1001:Peripheral drift
996:Penrose triangle
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813:
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733:on June 30, 2013
729:. Archived from
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372:Impossible World
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315:. Archived from
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281:Infinite descent
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84:Klimmen en dalen
57:Penrose triangle
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1486:Shirley Hodgson
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1442:Trapped surface
1393:Penrose process
1378:Penrose diagram
1338:Black hole bomb
1311:
1305:Brian W. Aldiss
1299:
1281:
1275:Stephen Hawking
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1256:
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1079:Popular culture
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1036:Spinning dancer
856:Ambiguous image
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53:Roger Penrose
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33:Penrose steps
30:
21:
1503:Quantum mind
1407:
1328:Spin network
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1092:Trompe-l'Ĺ“il
1090:
990:
956:Lilac chaser
926:Gravity hill
786:February 26,
784:. Retrieved
780:
754:(1): 31–33.
751:
747:
735:. Retrieved
731:the original
714:. Retrieved
703:. Springer.
699:
673:
659:. Retrieved
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613:. Retrieved
609:
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589:. Retrieved
577:
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544:. Retrieved
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518:. Retrieved
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457:, p. 72
450:
438:
428:, retrieved
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375:. Retrieved
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350:. Retrieved
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321:. Retrieved
317:the original
301:
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276:Strange loop
271:Shepard tone
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161:
156:
152:
141:
134:
130:M. C. Escher
123:
115:The Penroses
104:
97:
93:
87:
83:
75:
73:
69:nil geometry
51:and his son
36:
32:
28:
26:
1102:(1864 book)
1006:Poggendorff
981:Oppel-Kundt
976:Necker cube
971:MĂĽller-Lyer
946:Irradiation
781:Archive.org
650:(3): 8–14.
443:Hallyn 2000
253:The Wombats
246:The Strokes
209:viral video
80:M.C. Escher
43:created by
1518:Categories
1099:Spectropia
1016:Rubin vase
966:McCollough
961:Mach bands
911:Ehrenstein
906:Ebbinghaus
871:Barberpole
846:Afterimage
628:References
615:25 October
591:2020-06-05
541:Snopes.com
497:Ernst 1992
485:Ernst 1992
470:Ernst 1992
455:Ernst 1992
430:2022-07-09
1529:Stairways
1482:(brother)
1476:(brother)
1307:) (1999)
1277:) (1996)
1151:Illusions
1123:The dress
1115:Waterfall
916:Flash lag
896:Cornsweet
881:Café wall
861:Ames room
839:Illusions
737:March 16,
716:March 16,
661:March 16,
586:1059-1028
377:9 October
352:9 October
323:9 October
232:Inception
99:Waterfall
78:in 1958.
1488:(sister)
1470:(father)
1316:Concepts
901:Delboeuf
851:Ambigram
768:13536303
546:18 April
520:18 April
260:See also
94:Waterval
67:like in
39:, is an
1461:Related
1134:Related
1061:Zöllner
1051:White's
986:Orbison
951:Jastrow
680:Taschen
1303:(with
1287:(with
1273:(with
1253:(2016)
1245:(2010)
1237:(2004)
1229:(1994)
1221:(1989)
1086:Op art
1041:Ternus
1021:Sander
936:Hering
876:Bezold
766:
707:
686:
610:Genius
584:
309:
241:Angles
186:Mozart
1210:Books
1056:Wundt
1011:Ponzo
891:Chubb
640:(PDF)
578:Wired
343:(PDF)
287:Notes
207:is a
931:Grid
831:list
788:2024
764:PMID
739:2011
718:2011
705:ISBN
684:ISBN
663:2011
617:2023
582:ISSN
548:2019
522:2019
379:2020
354:2020
325:2020
307:ISBN
27:The
756:doi
652:doi
128:by
31:or
1520::
1291:,
779:.
762:.
752:49
750:.
682:.
678:.
646:.
642:.
608:.
580:.
576:.
557:,
539:.
513:.
477:^
462:^
401:^
387:^
370:.
345:.
71:.
1430:/
1195:e
1188:t
1181:v
833:)
829:(
819:e
812:t
805:v
790:.
770:.
758::
741:.
720:.
692:.
665:.
654::
648:6
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550:.
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381:.
356:.
327:.
96:(
86:(
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