Strange loop

Strange loop

A strange loop arises when, by moving up or down through a hierarchical system, one finds oneself back where one started. Strange loops may involve self-reference and paradox. The concept of a strange loop was proposed and extensively discussed by Douglas Hofstadter in "Gödel, Escher, Bach", and is further elaborated in Hofstadter's book "I Am a Strange Loop", which appeared in 2007.

A tangled hierarchy is a hierarchical system in which a strange loop appears.


A strange loop is a hierarchy of levels, each of which may consist of objects, processes, or virtually anything else (such is the generality of the notion). Each level is linked to at least one other by some type of relationship. A strange loop hierarchy, however, is "tangled" (what Hofstadter refers to as a "heterarchy"), in that there is no well defined highest or lowest level. The levels are organized such that moving through them eventually returns one to one's starting point, i.e., the original level. Examples of strange loops that Hofstadter offers include many of the works of M. C. Escher, the information flow network between DNA and enzymes through protein synthesis and DNA replication, and self-referential Gödelian statements in formal systems.

In "I Am a Strange Loop", Hofstadter defines strange loops as follows:


* Hofstadter points to Bach's "Canon per Tonos", M. C. Escher's drawings "Waterfall", "Drawing Hands", "Ascending and Descending", the liar paradox and the proof of Gödel's Incompleteness Theorem as examples of strange loops.

* A Shepard tone is another example of a strange loop. Named after Roger Shepard, it is a sound consisting of a superposition of sine waves separated by octaves. When played with the base pitch of the tone moving upwards or downwards, it is referred to as the "Shepard scale". This creates the auditory illusion of a tone that continually ascends or descends in pitch, yet which ultimately seems to get no higher or lower

* Quines in software programing- wherein a program produces a new version of itself without any input from the outside. Metamorphic code.

* The liar paradox and Russell's paradox also involve strange loops as does René Magritte's painting The Treachery of Images.

* The mathematical phenomenon of polysemy has been observed to be a strange loop. At the denotational level, the term refers to situations where a single entity can be seen to "mean" more than one mathematical object. See Tanenbaum (1999).

Strange Loops in Popular Culture

* The use of a Shepard tone as the sound effect for the Infinite Staircase in Super Mario 64.

*The use of a Shepard tone in the song "Echoes" by Pink Floyd, from the album Meddle.

* In one level of the game Psychonauts, Raz shrinks in size to walk around the surface of a board game which contains a building with a window through which the original room with the board game can be seen. The player cannot enter or exit the room through this window, however, so it may not be considered a true Strange Loop.

* The novelty song "I'm My Own Grandpa" (sometimes rendered as "I'm My Own Grandpaw") by Dwight Latham and Moe Jaffe, performed by Lonzo and Oscar in 1948. The song is sung by a man who, through an unlikely (but legal) combination of marriages, becomes stepfather to his own stepmother — and thus becomes his own (step- + step- (or step- squared)) grandfather.

* The myriad time-travel paradoxes of classic Science Fiction can be perceived as creative versions of Strange Loops that fail by self-cancelling feedback. The two base forms of this are the Predestination paradox and the Ontological paradox

:Usually, these stories are variations on a core trope: a time-traveler alters events in the past in a way that precludes the initiation of the whole process in the first place - either by rendering time-travel itself impossible, or by somehow rendering his own existence null and void. Archetypal examples would include almost any of the many “Shoot Your Grandfather” stories (cf, "The Men Who Murdered Mohammed" by Alfred Bester).

:A quintessential (and recognized classic) SF Time-Travel Strange Loop story is “All You Zombies—” by Robert A. Heinlein. In this short story, Heinlein creates an Anti-Paradox (a self-generating/self-supporting/self-dependent tautological sequence) that exactly meets Douglas Hofstadter's criteria for a Strange Loop as quoted in Definitions (above) - specifically in regard to the criteria ...::"... despite one's sense of departing ever further from one's origin, one winds up, to one's shock, exactly where one had started out. In short, a strange loop is a paradoxical level-crossing feedback loop.

:The recursive loop in “All You Zombies—” occurs by way of an alteration of the past that leads to the very future in which same alteration becomes both necessary and inevitable. Specifically: a young hermaphrodite in female mode (as surgically adjusted right after birth so as to render her female reproductive organs dominant and fertile) becomes her own mother (supplying the egg and the womb) after being impregnated by her older time-travelling male version (after giving birth she/he is surgically adjusted into fertile and active male mode). This time-looped self-encounter/courtship/impregnation is stage-managed by her/his/their much older, male self who brings the younger male version back in time to meet (and court, seduce and impregnate) the female iteration. This all to ensure his/her/their eternal, self-generating closed-loop existence.::nota bene: during the story, the song "I'm My Own Grandpa" cited in Examples (above) is played on the jukebox in the bar managed by the narrator - who is the "final edition" of the main character.


* P.J. Tanenbaum, "Simultaneous intersection representation of pairs of graphs," "Journal of Graph Theory" 32 (1999) 171-190. ISSN [ 1097-0118]

ee also

* Autopoiesis
* Euthyphro dilemma
* Feedback loop
* Irony
* Klein bottle
* Möbius strip
* Ontological paradox
* Optical feedback
* Paradox
* Predestination paradox
* quines
* Shepard tone

Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Strange loop — Eine seltsame Schleife ist ein Fall von Selbstbezüglichkeit, bei dem der Gegenstand, der den Ausgangspunkt bildet, betroffen ist oder sogar beschädigt wird. Dabei kann ein Paradoxon entstehen. Eingeführt und ausführlich diskutiert wurde der… …   Deutsch Wikipedia

  • I Am a Strange Loop — Infobox Book name = I Am A Strange Loop image caption = author = Douglas Hofstadter illustrator = cover artist = country = USA language = English series = subject = Consciousness, strange loops, intelligence publisher = Basic Books release date …   Wikipedia

  • Loop (graph theory) — In graph theory, a loop (also called a self loop) is an edge that connects a vertex to itself. A simple graph contains no loops.Depending on the context, a graph or a multigraph may be defined so as to either allow or disallow the presence of… …   Wikipedia

  • loop-legged — mod. alcohol intoxicated. □ He’s too loop legged to drive. □ She has this strange tendency to get a little loop legged when she has four or five drinks …   Dictionary of American slang and colloquial expressions

  • Time loop — A time loop or temporal loop is a common plot device in science fiction (especially in universes where time travel is commonplace) in which time runs normally for a set period (usually a day or a few hours) but then skips back like a broken… …   Wikipedia

  • Allen Strange — (* 26. Juni 1943 in Calexico/Kalifornien; † 20. Februar 2008 auf Bainbridge Island/Washington) war ein US amerikanischer Komponist, Musiktheoretiker und Musiker. Strange studierte bis 1967 an der California State University, Fullerton Komposition …   Deutsch Wikipedia

  • List of Strange Days at Blake Holsey High episodes — The following is a list of episodes of the Discovery Kids series Black Hole High which premiered on October 5, 2002 and ended on January 28, 2006. A total of 42 episodes were produced spanning 4 seasons. Contents 1 Series overview 2 Season 1:… …   Wikipedia

  • for a loop — adverb 1. : into a state of amazement, excitement, or confusion members of the cast were thrown for a loop when they caught sight of him Cornelia O. Skinner that strange poetic touch which knocks the Japanese for a loop Time 2. : into a usually… …   Useful english dictionary

  • Coordinated management of meaning — (CMM), is a practical theory[1] that sees communication as doing things fully as much as talking about them. Taking the communication perspective consists of looking at communication (rather than through it to what it is ostensibly about) and… …   Wikipedia

  • Douglas Hofstadter — Douglas R. Hofstadter Hofstadter in Bologna, Italy, in March 2002 Born February 15, 1945 (1945 02 15) (age 66) New York, New York Occupation …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”