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<ul id="toc-Escherian_Stairwell-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_popular_culture" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#In_popular_culture"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>In popular culture</span> </div> </a> <ul id="toc-In_popular_culture-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Notes</span> </div> </a> <ul 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Available in 31 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-31" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">31 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AF%D8%B1%D8%AC_%D8%A8%D9%86%D8%B1%D9%88%D8%B2" title="درج بنروز – Arabic" lang="ar" hreflang="ar" data-title="درج بنروز" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Penrouz_pill%C9%99k%C9%99nl%C9%99ri" title="Penrouz pilləkənləri – Azerbaijani" lang="az" hreflang="az" data-title="Penrouz pilləkənləri" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A7%87%E0%A6%A8%E0%A6%B0%E0%A7%8B%E0%A6%9C_%E0%A6%B8%E0%A6%BF%E0%A6%81%E0%A6%A1%E0%A6%BC%E0%A6%BF" title="পেনরোজ সিঁড়ি – Bangla" lang="bn" hreflang="bn" data-title="পেনরোজ সিঁড়ি" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A1%D1%82%D1%8A%D0%BB%D0%B1%D0%B8_%D0%BD%D0%B0_%D0%9F%D0%B5%D0%BD%D1%80%D0%BE%D1%83%D0%B7" title="Стълби на Пенроуз – Bulgarian" lang="bg" hreflang="bg" data-title="Стълби на Пенроуз" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Escala_de_Penrose" title="Escala de Penrose – Catalan" lang="ca" hreflang="ca" data-title="Escala de Penrose" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Penrose-Treppe" title="Penrose-Treppe – German" lang="de" hreflang="de" data-title="Penrose-Treppe" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Escalera_de_Penrose" title="Escalera de Penrose – Spanish" lang="es" hreflang="es" data-title="Escalera de Penrose" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/%C5%9Ctuparo_de_Penrose" title="Ŝtuparo de Penrose – Esperanto" lang="eo" hreflang="eo" data-title="Ŝtuparo de Penrose" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%BE%D9%84%DA%A9%D8%A7%D9%86_%D9%BE%D9%86%D8%B1%D9%88%D8%B2" title="پلکان پنروز – Persian" lang="fa" hreflang="fa" data-title="پلکان پنروز" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Escalier_de_Penrose" title="Escalier de Penrose – French" lang="fr" hreflang="fr" data-title="Escalier de Penrose" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%8E%9C%EB%A1%9C%EC%A6%88%EC%9D%98_%EA%B3%84%EB%8B%A8" title="펜로즈의 계단 – Korean" lang="ko" hreflang="ko" data-title="펜로즈의 계단" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%93%D5%A5%D5%B6%D6%80%D5%B8%D5%B8%D6%82%D5%A6%D5%AB_%D5%A1%D5%BD%D5%BF%D5%AB%D5%B3%D5%A1%D5%B6" title="Փենրոուզի աստիճան – Armenian" lang="hy" hreflang="hy" data-title="Փենրոուզի աստիճան" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Scala_di_Penrose" title="Scala di Penrose – Italian" lang="it" hreflang="it" data-title="Scala di Penrose" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Tangga_Penrose" title="Tangga Penrose – Malay" lang="ms" hreflang="ms" data-title="Tangga Penrose" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%95%E1%80%B2%E1%80%94%E1%80%BA%E1%80%B8%E1%80%9B%E1%80%AD%E1%80%AF%E1%80%B7%E1%80%85%E1%80%BA_%E1%80%9C%E1%80%BE%E1%80%B1%E1%80%80%E1%80%AC%E1%80%B8" title="ပဲန်းရို့စ် လှေကား – Burmese" lang="my" hreflang="my" data-title="ပဲန်းရို့စ် လှေကား" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Penrose-trap" title="Penrose-trap – Dutch" lang="nl" hreflang="nl" data-title="Penrose-trap" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%9A%E3%83%B3%E3%83%AD%E3%83%BC%E3%82%BA%E3%81%AE%E9%9A%8E%E6%AE%B5" title="ペンローズの階段 – Japanese" lang="ja" hreflang="ja" data-title="ペンローズの階段" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Penrosetrapp" title="Penrosetrapp – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Penrosetrapp" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Penrose_zinapoyasi" title="Penrose zinapoyasi – Uzbek" lang="uz" hreflang="uz" data-title="Penrose zinapoyasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Schody_Penrose%E2%80%99a" title="Schody Penrose’a – Polish" lang="pl" hreflang="pl" data-title="Schody Penrose’a" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Escada_de_Penrose" title="Escada de Penrose – Portuguese" lang="pt" hreflang="pt" data-title="Escada de Penrose" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9B%D0%B5%D1%81%D1%82%D0%BD%D0%B8%D1%86%D0%B0_%D0%9F%D0%B5%D0%BD%D1%80%D0%BE%D1%83%D0%B7%D0%B0" title="Лестница Пенроуза – Russian" lang="ru" hreflang="ru" data-title="Лестница Пенроуза" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Penrosen_portaat" title="Penrosen portaat – Finnish" lang="fi" hreflang="fi" data-title="Penrosen portaat" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Penroses_trappa" title="Penroses trappa – Swedish" lang="sv" hreflang="sv" data-title="Penroses trappa" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AF%86%E0%AE%A9%E0%AF%8D%E0%AE%B0%E0%AF%8B%E0%AE%9A%E0%AF%81%E0%AE%AA%E0%AF%8D_%E0%AE%AA%E0%AE%9F%E0%AE%BF%E0%AE%95%E0%AE%B3%E0%AF%8D" title="பென்ரோசுப் படிகள் – Tamil" lang="ta" hreflang="ta" data-title="பென்ரோசுப் படிகள்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Penrose_merdiveni" title="Penrose merdiveni – Turkish" lang="tr" hreflang="tr" data-title="Penrose merdiveni" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A1%D1%85%D0%BE%D0%B4%D0%B8_%D0%9F%D0%B5%D0%BD%D1%80%D0%BE%D1%83%D0%B7%D0%B0" title="Сходи Пенроуза – Ukrainian" lang="uk" hreflang="uk" data-title="Сходи Пенроуза" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Penrouzan_pordhad" title="Penrouzan pordhad – Veps" lang="vep" hreflang="vep" data-title="Penrouzan pordhad" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/C%E1%BA%A7u_thang_Penrose" title="Cầu thang Penrose – Vietnamese" lang="vi" hreflang="vi" data-title="Cầu thang Penrose" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%BD%98%E6%B4%9B%E6%96%AF%E9%9A%8E%E6%A2%AF" title="潘洛斯階梯 – Cantonese" lang="yue" hreflang="yue" data-title="潘洛斯階梯" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%BD%AD%E7%BD%97%E6%96%AF%E9%98%B6%E6%A2%AF" title="彭罗斯阶梯 – Chinese" lang="zh" hreflang="zh" data-title="彭罗斯阶梯" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> 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<div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Impossible object</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Impossible_staircase.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/Impossible_staircase.svg/220px-Impossible_staircase.svg.png" decoding="async" width="220" height="167" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/Impossible_staircase.svg/330px-Impossible_staircase.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/34/Impossible_staircase.svg/440px-Impossible_staircase.svg.png 2x" data-file-width="372" data-file-height="283" /></a><figcaption>Penrose stairs</figcaption></figure> <p>The <b>Penrose stairs</b> or <b>Penrose steps</b>, also dubbed the <b>impossible staircase</b>, is an <a href="/wiki/Impossible_object" title="Impossible object">impossible object</a> created by <a href="/wiki/Oscar_Reutersv%C3%A4rd" title="Oscar Reutersvärd">Oscar Reutersvärd</a> in 1937<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-IllusionWorks_4-0" class="reference"><a href="#cite_note-IllusionWorks-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> and later independently discovered and made popular by <a href="/wiki/Lionel_Penrose" title="Lionel Penrose">Lionel Penrose</a> and his son <a href="/wiki/Roger_Penrose" title="Roger Penrose">Roger Penrose</a>.<sup id="cite_ref-Penrose_1958_5-0" class="reference"><a href="#cite_note-Penrose_1958-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> A variation on the <a href="/wiki/Penrose_triangle" title="Penrose triangle">Penrose triangle</a>, 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 <a href="/wiki/Euclidean_geometry" title="Euclidean geometry">Euclidean geometry</a> but possible in some <a href="/wiki/Non-Euclidean_geometry" title="Non-Euclidean geometry">non-Euclidean geometry</a> like in <a href="/wiki/Nil_geometry" class="mw-redirect" title="Nil geometry">nil geometry</a>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>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 <i>British Journal of Psychology</i> in 1958.<sup id="cite_ref-Penrose_1958_5-1" class="reference"><a href="#cite_note-Penrose_1958-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> <a href="/wiki/M.C._Escher" class="mw-redirect" title="M.C. Escher">M.C. Escher</a> then discovered the Penrose stairs in the following year and made his now famous lithograph <i>Klimmen en dalen</i> (<i><a href="/wiki/Ascending_and_Descending" title="Ascending and Descending">Ascending and Descending</a></i>) in March 1960. Penrose and Escher were informed of each other's work that same year.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Escher developed the theme further in his print <i>Waterval</i> (<i><a href="/wiki/Waterfall_(M._C._Escher)" title="Waterfall (M. C. Escher)">Waterfall</a></i>), which appeared in 1961. </p><p>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."<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History_of_discovery">History of discovery</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Penrose_stairs&action=edit&section=1" title="Edit section: History of discovery"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="The_Penroses">The Penroses</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Penrose_stairs&action=edit&section=2" title="Edit section: The Penroses"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Ascending_and_Descending.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/6/66/Ascending_and_Descending.jpg/220px-Ascending_and_Descending.jpg" decoding="async" width="220" height="290" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/6/66/Ascending_and_Descending.jpg 1.5x" data-file-width="275" data-file-height="363" /></a><figcaption><i><a href="/wiki/Ascending_and_Descending" title="Ascending and Descending">Ascending and Descending</a></i> by <a href="/wiki/M._C._Escher" title="M. C. Escher">M. C. Escher</a> </figcaption></figure> <p>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 <a href="/wiki/International_Congress_of_Mathematicians" title="International Congress of Mathematicians">International Congress of Mathematicians</a> 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 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 <i><a href="/wiki/British_Journal_of_Psychology" title="British Journal of Psychology">British Journal of Psychology</a></i> and convinced him to publish their short manuscript, the finding was finally presented as a <a href="/wiki/Psychology" title="Psychology">psychological</a> subject. After the publication in 1958 the Penroses sent a copy of the article to Escher as a token of their esteem.<sup id="cite_ref-Ernst-71_9-0" class="reference"><a href="#cite_note-Ernst-71-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>While the Penroses credited Escher in their article, Escher noted in a letter to his son in January 1960 that he was: </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>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. [The stairs] 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) 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.<sup id="cite_ref-Ernst-75-78_10-0" class="reference"><a href="#cite_note-Ernst-75-78-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></p></blockquote> <p>Escher was captivated by the endless stairs and subsequently wrote a letter to the Penroses in April 1960: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>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. 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.<sup id="cite_ref-Ernst-75-78_10-1" class="reference"><a href="#cite_note-Ernst-75-78-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></p></blockquote> <p>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. </p> <div class="mw-heading mw-heading3"><h3 id="Oscar_Reutersvärd"><span id="Oscar_Reutersv.C3.A4rd"></span>Oscar Reutersvärd</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Penrose_stairs&action=edit&section=3" title="Edit section: Oscar Reutersvärd"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The staircase design had been discovered previously by the Swedish artist <a href="/wiki/Oscar_Reutersv%C3%A4rd" title="Oscar Reutersvärd">Oscar Reutersvärd</a>, but neither Penrose nor Escher was aware of his designs.<sup id="cite_ref-IllusionWorks_4-1" class="reference"><a href="#cite_note-IllusionWorks-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Inspired by a radio programme on <a href="/wiki/Mozart" class="mw-redirect" title="Mozart">Mozart</a>'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 <i>Ascending and Descending</i> was sent to Reutersvärd in 1961, he was impressed but didn't like the irregularities of the stairs (<span class="nowrap">2 × 15 + 2 × 9</span>). Throughout the 1960s, Reutersvärd sent several letters to Escher to express his admiration for his work, but the Dutch artist failed to respond.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Roger Penrose only discovered Reutersvärd's work in 1984.<sup id="cite_ref-Ernst-71_9-1" class="reference"><a href="#cite_note-Ernst-71-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Escherian_Stairwell">Escherian Stairwell</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Penrose_stairs&action=edit&section=4" title="Edit section: Escherian Stairwell"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>The Escherian Stairwell</i> is a <a href="/wiki/Viral_video" title="Viral video">viral video</a> based on the Penrose stairs illusion. The video, filmed at <a href="/wiki/Rochester_Institute_of_Technology" title="Rochester Institute of Technology">Rochester Institute of Technology</a> 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.<sup id="cite_ref-FacilityExecutive_12-0" class="reference"><a href="#cite_note-FacilityExecutive-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> The video claims that the stairwell, whose name evokes M.C. Escher's impossible objects, was built in the 1960s by the fictitious architect Rafael Nelson Aboganda. The video was revealed to be an <a href="/wiki/Internet_hoax" class="mw-redirect" title="Internet hoax">Internet hoax</a>, as individuals have travelled to Rochester Institute of Technology to view the staircase.<sup id="cite_ref-Snopes_13-0" class="reference"><a href="#cite_note-Snopes-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="In_popular_culture">In popular culture</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Penrose_stairs&action=edit&section=5" title="Edit section: In popular culture"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>The Penrose stairs appeared twice in the movie <i><a href="/wiki/Inception" title="Inception">Inception</a></i>. 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 unaware.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup></li> <li>The cover of the 2011 album <i><a href="/wiki/Angles_(The_Strokes_album)" title="Angles (The Strokes album)">Angles</a></i> by American rock band <a href="/wiki/The_Strokes" title="The Strokes">The Strokes</a> depicts a complex set of Penrose stairs.</li> <li>In their 2015 single called "Greek Tragedy," English rock band <a href="/wiki/The_Wombats" title="The Wombats">The Wombats</a> mentions the Penrose steps.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Penrose_stairs&action=edit&section=6" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Penrose_figures" class="extiw" title="commons:Category:Penrose figures">Penrose figures</a></span>.</div></div> </div> <ul><li><a href="/wiki/Mathematics_and_art" title="Mathematics and art">Mathematics and art</a></li> <li><a href="/wiki/Shepard_tone" title="Shepard tone">Shepard tone</a></li> <li><a href="/wiki/Strange_loop" title="Strange loop">Strange loop</a></li> <li><a href="/wiki/Infinite_descent" class="mw-redirect" title="Infinite descent">Infinite descent</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Penrose_stairs&action=edit&section=7" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20221123211752/https://www.illusionsindex.org/i/penrose-stairs"><i>Penrose Stairs</i></a>. Benedikt Taschen. 1992. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9783822896372" title="Special:BookSources/9783822896372"><bdi>9783822896372</bdi></a>. Archived from <a rel="nofollow" class="external text" href="https://www.illusionsindex.org/i/penrose-stairs">the original</a> on 23 November 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">9 October</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Penrose+Stairs&rft.pub=Benedikt+Taschen&rft.date=1992&rft.isbn=9783822896372&rft_id=https%3A%2F%2Fwww.illusionsindex.org%2Fi%2Fpenrose-stairs&rfr_id=info%3Asid%2Fen.wikipedia.org%3APenrose+stairs" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTorre" class="citation journal cs1">Torre, Matteo. <a rel="nofollow" class="external text" href="http://archive.bridgesmathart.org/2019/bridges2019-327.pdf">"Impossible Pictures: When Art Helps Math Education"</a> <span class="cs1-format">(PDF)</span>. <i>Impossible Pictures: When Art Helps Math Education</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200320024249/http://archive.bridgesmathart.org/2019/bridges2019-327.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 20 March 2020<span class="reference-accessdate">. Retrieved <span class="nowrap">9 October</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Impossible+Pictures%3A+When+Art+Helps+Math+Education&rft.atitle=Impossible+Pictures%3A+When+Art+Helps+Math+Education&rft.aulast=Torre&rft.aufirst=Matteo&rft_id=http%3A%2F%2Farchive.bridgesmathart.org%2F2019%2Fbridges2019-327.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APenrose+stairs" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://im-possible.info/english/articles/staircase/staircase.html">"Endless staircase"</a>. <i>Impossible World</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200706083413/https://im-possible.info/english/articles/staircase/staircase.html">Archived</a> from the original on 6 July 2020<span class="reference-accessdate">. Retrieved <span class="nowrap">9 October</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Impossible+World&rft.atitle=Endless+staircase&rft_id=https%3A%2F%2Fim-possible.info%2Fenglish%2Farticles%2Fstaircase%2Fstaircase.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3APenrose+stairs" class="Z3988"></span></span> </li> <li id="cite_note-IllusionWorks-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-IllusionWorks_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-IllusionWorks_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFIllusionWorks1997">IllusionWorks 1997</a></span> </li> <li id="cite_note-Penrose_1958-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-Penrose_1958_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Penrose_1958_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFPenrosePenrose1958">Penrose & Penrose 1958</a>, pp. 31–33</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">YouTube, ZenoTheRogue, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=DurXAhFrmkE"><i>Ascending and Descending in Nil</i></a>, <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220709150938/https://www.youtube.com/watch?v=DurXAhFrmkE">archived</a> from the original on 2022-07-09<span class="reference-accessdate">, retrieved <span class="nowrap">2022-07-09</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Ascending+and+Descending+in+Nil&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DDurXAhFrmkE&rfr_id=info%3Asid%2Fen.wikipedia.org%3APenrose+stairs" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><a href="#CITEREFHallyn2000">Hallyn 2000</a>, p. 172</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><a href="#CITEREFErnst1992">Ernst 1992</a>, p. 72</span> </li> <li id="cite_note-Ernst-71-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-Ernst-71_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Ernst-71_9-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFErnst1992">Ernst 1992</a>, pp. 71–72</span> </li> <li id="cite_note-Ernst-75-78-10"><span class="mw-cite-backlink">^ <a href="#cite_ref-Ernst-75-78_10-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Ernst-75-78_10-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFErnst1992">Ernst 1992</a>, pp. 75, 78</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><a href="#CITEREFErnst1992">Ernst 1992</a>, pp. 70–71</span> </li> <li id="cite_note-FacilityExecutive-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-FacilityExecutive_12-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchwartz2013" class="citation web cs1">Schwartz, Heidi (17 May 2013). <a rel="nofollow" class="external text" href="https://facilityexecutive.com/2013/05/friday-funny-the-escherian-starwall-exists/">"The Escherian Stairwell (Penrose Steps) | How It Works"</a>. <i>Facility Executive - Creating Intelligent Buildings</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190418164342/https://facilityexecutive.com/2013/05/friday-funny-the-escherian-starwall-exists/">Archived</a> from the original on 18 April 2019<span class="reference-accessdate">. Retrieved <span class="nowrap">18 April</span> 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Facility+Executive+-+Creating+Intelligent+Buildings&rft.atitle=The+Escherian+Stairwell+%28Penrose+Steps%29+%7C+How+It+Works&rft.date=2013-05-17&rft.aulast=Schwartz&rft.aufirst=Heidi&rft_id=https%3A%2F%2Ffacilityexecutive.com%2F2013%2F05%2Ffriday-funny-the-escherian-starwall-exists%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3APenrose+stairs" class="Z3988"></span></span> </li> <li id="cite_note-Snopes-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-Snopes_13-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMikkelson2013" class="citation web cs1">Mikkelson, David (6 May 2013). <a rel="nofollow" class="external text" href="https://www.snopes.com/fact-check/escherian-stairwell/">"FACT CHECK: Escherian Stairwell"</a>. <i>Snopes.com</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220520174759/https://www.snopes.com/fact-check/escherian-stairwell/">Archived</a> from the original on 20 May 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">18 April</span> 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Snopes.com&rft.atitle=FACT+CHECK%3A+Escherian+Stairwell&rft.date=2013-05-06&rft.aulast=Mikkelson&rft.aufirst=David&rft_id=https%3A%2F%2Fwww.snopes.com%2Ffact-check%2Fescherian-stairwell%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3APenrose+stairs" class="Z3988"></span> <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMelikdjanian2018" class="citation cs2">Melikdjanian, Alan (2018), <a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=eLAwG7CjF_k">"Escherian Stairwell Deconstruction"</a>, <i>Captain Disillusion</i>, <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230505025002/https://www.youtube.com/watch?v=eLAwG7CjF_k">archived</a> from the original on 2023-05-05<span class="reference-accessdate">, retrieved <span class="nowrap">2023-05-05</span></span> – via YouTube</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Captain+Disillusion&rft.atitle=Escherian+Stairwell+Deconstruction&rft.date=2018&rft.aulast=Melikdjanian&rft.aufirst=Alan&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DeLAwG7CjF_k&rfr_id=info%3Asid%2Fen.wikipedia.org%3APenrose+stairs" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHarshbarger2010" class="citation magazine cs1">Harshbarger, Eric (2010-08-19). <a rel="nofollow" class="external text" href="https://www.wired.com/2010/08/the-never-ending-stories-inceptions-penrose-staircase/">"The Never-Ending Stories: Inception's Penrose Staircase"</a>. <i>Wired</i>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1059-1028">1059-1028</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20151022043641/http://www.wired.com/2010/08/the-never-ending-stories-inceptions-penrose-staircase">Archived</a> from the original on 2015-10-22<span class="reference-accessdate">. Retrieved <span class="nowrap">2020-06-05</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Wired&rft.atitle=The+Never-Ending+Stories%3A+Inception%27s+Penrose+Staircase&rft.date=2010-08-19&rft.issn=1059-1028&rft.aulast=Harshbarger&rft.aufirst=Eric&rft_id=https%3A%2F%2Fwww.wired.com%2F2010%2F08%2Fthe-never-ending-stories-inceptions-penrose-staircase%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3APenrose+stairs" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://genius.com/The-wombats-greek-tragedy-lyrics">"Greek Tragedy"</a>. <i>Genius</i><span class="reference-accessdate">. Retrieved <span class="nowrap">25 October</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Genius&rft.atitle=Greek+Tragedy&rft_id=https%3A%2F%2Fgenius.com%2FThe-wombats-greek-tragedy-lyrics&rfr_id=info%3Asid%2Fen.wikipedia.org%3APenrose+stairs" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Penrose_stairs&action=edit&section=8" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDeutsch2010" class="citation journal cs1">Deutsch, Diana (July 2010). <a rel="nofollow" class="external text" href="http://deutsch.ucsd.edu/pdf/Acoustics_Today_2010_Jul.pdf">"The Paradox of Pitch Circularity"</a> <span class="cs1-format">(PDF)</span>. <i>Acoustics Today</i>. <b>6</b> (3): 8–14. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1121%2F1.3488670">10.1121/1.3488670</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20161225052036/http://deutsch.ucsd.edu/pdf/Acoustics_Today_2010_Jul.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on December 25, 2016<span class="reference-accessdate">. Retrieved <span class="nowrap">March 16,</span> 2011</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Acoustics+Today&rft.atitle=The+Paradox+of+Pitch+Circularity&rft.volume=6&rft.issue=3&rft.pages=8-14&rft.date=2010-07&rft_id=info%3Adoi%2F10.1121%2F1.3488670&rft.aulast=Deutsch&rft.aufirst=Diana&rft_id=http%3A%2F%2Fdeutsch.ucsd.edu%2Fpdf%2FAcoustics_Today_2010_Jul.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APenrose+stairs" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFErnst1992" class="citation book cs1">Ernst, Bruno (1992). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/opticalillusions0000erns"><i>The Eye Beguiled: Optical Illusions</i></a></span>. <a href="/wiki/Taschen" title="Taschen">Taschen</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/3-8228-9637-3" title="Special:BookSources/3-8228-9637-3"><bdi>3-8228-9637-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Eye+Beguiled%3A+Optical+Illusions&rft.pub=Taschen&rft.date=1992&rft.isbn=3-8228-9637-3&rft.aulast=Ernst&rft.aufirst=Bruno&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fopticalillusions0000erns&rfr_id=info%3Asid%2Fen.wikipedia.org%3APenrose+stairs" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHallyn2000" class="citation book cs1">Hallyn, Fernand (2000). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=iKleTxffj5IC&pg=PA172"><i>Metaphor and Analogy in the Sciences</i></a>. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7923-6560-0" title="Special:BookSources/978-0-7923-6560-0"><bdi>978-0-7923-6560-0</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">March 16,</span> 2011</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Metaphor+and+Analogy+in+the+Sciences&rft.pub=Springer&rft.date=2000&rft.isbn=978-0-7923-6560-0&rft.aulast=Hallyn&rft.aufirst=Fernand&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DiKleTxffj5IC%26pg%3DPA172&rfr_id=info%3Asid%2Fen.wikipedia.org%3APenrose+stairs" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFIllusionWorks1997" class="citation web cs1">IllusionWorks (1997). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130630143000/http://psylux.psych.tu-dresden.de/i1/kaw/diverses%20Material/www.illusionworks.com/html/impossible_staircase.html">"Impossible Staircase"</a>. Archived from <a rel="nofollow" class="external text" href="http://psylux.psych.tu-dresden.de/i1/kaw/diverses%20Material/www.illusionworks.com/html/impossible_staircase.html">the original</a> on June 30, 2013<span class="reference-accessdate">. Retrieved <span class="nowrap">March 16,</span> 2011</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Impossible+Staircase&rft.date=1997&rft.au=IllusionWorks&rft_id=http%3A%2F%2Fpsylux.psych.tu-dresden.de%2Fi1%2Fkaw%2Fdiverses%2520Material%2Fwww.illusionworks.com%2Fhtml%2Fimpossible_staircase.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3APenrose+stairs" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPenrosePenrose1958" class="citation journal cs1">Penrose, L.S.; Penrose, R. (1958). "Impossible objects: A special type of visual illusion". <i>British Journal of Psychology</i>. <b>49</b> (1): 31–33. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.2044-8295.1958.tb00634.x">10.1111/j.2044-8295.1958.tb00634.x</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/13536303">13536303</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=British+Journal+of+Psychology&rft.atitle=Impossible+objects%3A+A+special+type+of+visual+illusion&rft.volume=49&rft.issue=1&rft.pages=31-33&rft.date=1958&rft_id=info%3Adoi%2F10.1111%2Fj.2044-8295.1958.tb00634.x&rft_id=info%3Apmid%2F13536303&rft.aulast=Penrose&rft.aufirst=L.S.&rft.au=Penrose%2C+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APenrose+stairs" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLehr2022" class="citation web cs1">Lehr, Ferdinand (2022). <a rel="nofollow" class="external text" href="https://archive.org/details/algorithm-penrose-stairs-flehr/">"Study of algorithmic generation of the Penrose-Staircase"</a>. <i>Archive.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">February 26,</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Archive.org&rft.atitle=Study+of+algorithmic+generation+of+the+Penrose-Staircase&rft.date=2022&rft.aulast=Lehr&rft.aufirst=Ferdinand&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Falgorithm-penrose-stairs-flehr%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3APenrose+stairs" class="Z3988"></span></li></ul> </div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output 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href="/wiki/Barberpole_illusion" title="Barberpole illusion">Barberpole</a></li> <li><a href="/wiki/Bezold_effect" title="Bezold effect">Bezold</a></li> <li><a href="/wiki/Caf%C3%A9_wall_illusion" title="Café wall illusion">Café wall</a></li> <li><a href="/wiki/Checker_shadow_illusion" title="Checker shadow illusion">Checker shadow</a></li> <li><a href="/wiki/Chubb_illusion" title="Chubb illusion">Chubb</a></li> <li><a href="/wiki/Cornsweet_illusion" title="Cornsweet illusion">Cornsweet</a></li> <li><a href="/wiki/Delboeuf_illusion" title="Delboeuf illusion">Delboeuf</a></li> <li><a href="/wiki/Ebbinghaus_illusion" title="Ebbinghaus illusion">Ebbinghaus</a></li> <li><a href="/wiki/Ehrenstein_illusion" title="Ehrenstein illusion">Ehrenstein</a></li> <li><a href="/wiki/Flash_lag_illusion" title="Flash lag illusion">Flash lag</a></li> <li><a href="/wiki/Fraser_spiral_illusion" title="Fraser spiral illusion">Fraser spiral</a></li> <li><a href="/wiki/Gravity_hill" title="Gravity hill">Gravity hill</a></li> <li><a href="/wiki/Grid_illusion" title="Grid illusion">Grid</a></li> <li><a href="/wiki/Hering_illusion" title="Hering illusion">Hering</a></li> <li><a href="/wiki/Impossible_trident" title="Impossible trident">Impossible trident</a></li> <li><a href="/wiki/Irradiation_illusion" title="Irradiation illusion">Irradiation</a></li> <li><a href="/wiki/Jastrow_illusion" title="Jastrow illusion">Jastrow</a></li> <li><a href="/wiki/Lilac_chaser" title="Lilac chaser">Lilac chaser</a></li> <li><a href="/wiki/Mach_bands" title="Mach bands">Mach bands</a></li> <li><a href="/wiki/McCollough_effect" title="McCollough effect">McCollough</a></li> <li><a href="/wiki/M%C3%BCller-Lyer_illusion" title="Müller-Lyer illusion">Müller-Lyer</a></li> <li><a href="/wiki/Necker_cube" title="Necker cube">Necker cube</a></li> <li><a href="/wiki/Oppel-Kundt_illusion" title="Oppel-Kundt illusion">Oppel-Kundt</a></li> <li><a href="/wiki/Orbison_illusion" title="Orbison illusion">Orbison</a></li> <li><a class="mw-selflink selflink">Penrose stairs</a></li> <li><a href="/wiki/Penrose_triangle" title="Penrose triangle">Penrose triangle</a></li> <li><a href="/wiki/Peripheral_drift_illusion" title="Peripheral drift illusion">Peripheral drift</a></li> <li><a href="/wiki/Poggendorff_illusion" title="Poggendorff illusion">Poggendorff</a></li> <li><a href="/wiki/Ponzo_illusion" title="Ponzo illusion">Ponzo</a></li> <li><a href="/wiki/Rubin_vase" title="Rubin vase">Rubin vase</a></li> <li><a href="/wiki/Sander_illusion" title="Sander illusion">Sander</a></li> <li><a href="/wiki/Schroeder_stairs" title="Schroeder stairs">Schroeder stairs</a></li> <li><a href="/wiki/Shepard_tables" title="Shepard tables">Shepard tables</a></li> <li><a href="/wiki/Spinning_dancer" title="Spinning dancer">Spinning dancer</a></li> <li><a href="/wiki/Ternus_illusion" title="Ternus illusion">Ternus</a></li> <li><a href="/wiki/Vertical%E2%80%93horizontal_illusion" title="Vertical–horizontal illusion">Vertical–horizontal</a></li> <li><a href="/wiki/White%27s_illusion" title="White's illusion">White's</a></li> <li><a href="/wiki/Wundt_illusion" title="Wundt illusion">Wundt</a></li> <li><a href="/wiki/Z%C3%B6llner_illusion" title="Zöllner illusion">Zöllner</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="3" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Optical_Illustion-Ambiguous_Patterns.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Optical_Illustion-Ambiguous_Patterns.svg/30px-Optical_Illustion-Ambiguous_Patterns.svg.png" decoding="async" width="30" height="112" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Optical_Illustion-Ambiguous_Patterns.svg/45px-Optical_Illustion-Ambiguous_Patterns.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Optical_Illustion-Ambiguous_Patterns.svg/60px-Optical_Illustion-Ambiguous_Patterns.svg.png 2x" data-file-width="117" data-file-height="438" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Popular culture</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Op_art" title="Op art">Op art</a></li> <li><i><a href="/wiki/Trompe-l%27%C5%93il" title="Trompe-l'œil">Trompe-l'œil</a></i></li> <li><i><a href="/wiki/Spectropia" title="Spectropia">Spectropia</a></i> (1864 book)</li> <li><i><a href="/wiki/Ascending_and_Descending" title="Ascending and Descending">Ascending and Descending</a></i> (1960 drawing)</li> <li><i><a href="/wiki/Waterfall_(M._C._Escher)" title="Waterfall (M. C. Escher)">Waterfall</a></i> (1961 drawing)</li> <li><i><a href="/wiki/The_dress" title="The dress">The dress</a></i> (2015 photograph)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Accidental_viewpoint" title="Accidental viewpoint">Accidental viewpoint</a></li> <li><a href="/wiki/Auditory_illusion" title="Auditory illusion">Auditory illusions</a></li> <li><a href="/wiki/Illusion" title="Illusion">Illusions</a></li> <li><a href="/wiki/Tactile_illusion" title="Tactile illusion">Tactile illusions</a></li> <li><a href="/wiki/Time_perception" title="Time perception">Temporal illusion</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Roger_Penrose" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Roger_Penrose" title="Template:Roger Penrose"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Roger_Penrose" title="Template talk:Roger Penrose"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Roger_Penrose" title="Special:EditPage/Template:Roger Penrose"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Roger_Penrose" style="font-size:114%;margin:0 4em"><a href="/wiki/Roger_Penrose" title="Roger Penrose">Roger Penrose</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Books</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/The_Emperor%27s_New_Mind" title="The Emperor's New Mind">The Emperor's New Mind</a></i> (1989)</li> <li><i><a href="/wiki/Shadows_of_the_Mind" title="Shadows of the Mind">Shadows of the Mind</a></i> (1994)</li> <li><i><a href="/wiki/The_Road_to_Reality" title="The Road to Reality">The Road to Reality</a></i> (2004)</li> <li><i><a href="/wiki/Cycles_of_Time" title="Cycles of Time">Cycles of Time</a></i> (2010)</li> <li><i><a href="/wiki/Fashion,_Faith,_and_Fantasy_in_the_New_Physics_of_the_Universe" title="Fashion, Faith, and Fantasy in the New Physics of the Universe">Fashion, Faith, and Fantasy in the New Physics of the Universe</a></i> (2016)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Coauthored books</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="wrap"> <i><a href="/wiki/The_Nature_of_Space_and_Time" title="The Nature of Space and Time">The Nature of Space and Time</a></i> (with <a href="/wiki/Stephen_Hawking" title="Stephen Hawking">Stephen Hawking</a>) (1996) </span></li> <li><span class="wrap"> <i><a href="/wiki/The_Large,_the_Small_and_the_Human_Mind" title="The Large, the Small and the Human Mind">The Large, the Small and the Human Mind</a></i> (with <a href="/wiki/Abner_Shimony" title="Abner Shimony">Abner Shimony</a>, <a href="/wiki/Nancy_Cartwright_(philosopher)" title="Nancy Cartwright (philosopher)">Nancy Cartwright</a> and Stephen Hawking) (1997) </span></li> <li><span class="wrap"> <i>White Mars or, The Mind Set Free</i> (with <a href="/wiki/Brian_W._Aldiss" class="mw-redirect" title="Brian W. Aldiss">Brian W. Aldiss</a>) (1999) </span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Twistor_theory" title="Twistor theory">Twistor theory</a></li> <li><a href="/wiki/Spin_network" title="Spin network">Spin network</a></li> <li><a href="/wiki/Abstract_index_notation" title="Abstract index notation">Abstract index notation</a></li> <li><a href="/wiki/Black_hole_bomb" title="Black hole bomb">Black hole bomb</a></li> <li><a href="/wiki/Spacetime" title="Spacetime">Geometry of spacetime</a></li> <li><a href="/wiki/Cosmic_censorship_hypothesis" title="Cosmic censorship hypothesis">Cosmic censorship</a></li> <li><a href="/wiki/Weyl_curvature_hypothesis" title="Weyl curvature hypothesis">Weyl curvature hypothesis</a></li> <li><a href="/wiki/Contributors_to_general_relativity#P" class="mw-redirect" title="Contributors to general relativity">Penrose inequalities</a></li> <li><a href="/wiki/Penrose_interpretation" title="Penrose interpretation">Penrose interpretation of quantum mechanics</a></li> <li><a href="/wiki/Moore%E2%80%93Penrose_inverse" title="Moore–Penrose inverse">Moore–Penrose inverse</a></li> <li><a href="/wiki/Newman%E2%80%93Penrose_formalism" title="Newman–Penrose formalism">Newman–Penrose formalism</a></li> <li><a href="/wiki/Penrose_diagram" title="Penrose diagram">Penrose diagram</a></li> <li><a href="/wiki/Penrose%E2%80%93Hawking_singularity_theorems" title="Penrose–Hawking singularity theorems">Penrose–Hawking singularity theorems</a></li> <li><a href="/wiki/Riemannian_Penrose_inequality" title="Riemannian Penrose inequality">Riemannian Penrose inequality</a></li> <li><a href="/wiki/Penrose_process" title="Penrose process">Penrose process</a></li> <li><a href="/wiki/Penrose_tiling" title="Penrose tiling">Penrose tiling</a></li> <li><a href="/wiki/Penrose_triangle" title="Penrose triangle">Penrose triangle</a></li> <li><a class="mw-selflink selflink">Penrose stairs</a></li> <li><a href="/wiki/Penrose_graphical_notation" title="Penrose graphical notation">Penrose graphical notation</a></li> <li><a href="/wiki/Penrose_transform" title="Penrose transform">Penrose transform</a></li> <li><a href="/wiki/Terrell_rotation" title="Terrell rotation">Penrose–Terrell effect</a></li> <li><a href="/wiki/Orchestrated_objective_reduction" title="Orchestrated objective reduction">Orchestrated objective reduction</a>/<a href="/wiki/Penrose%E2%80%93Lucas_argument" title="Penrose–Lucas argument">Penrose–Lucas argument</a></li> <li><a href="/wiki/Free-orbit_experiment_with_laser_interferometry_X-rays" title="Free-orbit experiment with laser interferometry X-rays">FELIX experiment</a></li> <li><a href="/wiki/Trapped_surface" title="Trapped surface">Trapped surface</a></li> <li><a href="/wiki/Andromeda_paradox" class="mw-redirect" title="Andromeda paradox">Andromeda paradox</a></li> <li><a href="/wiki/Conformal_cyclic_cosmology" title="Conformal cyclic cosmology">Conformal cyclic cosmology</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Lionel_Penrose" title="Lionel Penrose">Lionel Penrose</a> (father)</li> <li><a href="/wiki/Oliver_Penrose" title="Oliver Penrose">Oliver Penrose</a> (brother)</li> <li><a href="/wiki/Jonathan_Penrose" title="Jonathan Penrose">Jonathan Penrose</a> (brother)</li> <li><a href="/wiki/Shirley_Hodgson" title="Shirley Hodgson">Shirley Hodgson</a> (sister)</li> <li><a href="/wiki/John_Beresford_Leathes" title="John Beresford Leathes">John Beresford Leathes</a> (grandfather)</li> <li><a href="/wiki/Illumination_problem" title="Illumination problem">Illumination problem</a></li> <li><a href="/wiki/Quantum_mind" title="Quantum mind">Quantum mind</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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