A singularity in Mathematics is a point where a graphed equation veers off towards infinity and ceases to give physically useful or meaningful results: hence the singularity point predicted at the heart of a Black Hole by theoretical models which assume the total mass must be compressed by Gravity into an infinitesimal volume whose gravitational attraction at close range approaches infinity. The Singularity, or technological Singularity, is a hypothetical point in time at which human Technology – in particular Computers, AI super-Intelligence and human intelligence amplification via computer interfacing (see Upload) or perhaps Drugs – similarly accelerates "off the map" into unpredictable regions. The usually expected result is a kind of Transcendence stripped of mysticism – or, in the words of a character in Ken MacLeod's The Cassini Division (1998), "the Rapture for nerds".
The Singularity concept is outlined in some detail in Vernor Vinge's symposium paper "The Coming Technological Singularity: How to Survive in the Post-Human Era" (presented 1993; 1993 Whole Earth Review): see links below. Vinge's sf citations include Greg Bear's Blood Music (June 1983 Analog; 1985), in which Biological rather than computer technology triggers a very rapid change from human to Posthuman mode. Two book-length nonfiction treatments of the theme are Damien Broderick's The Spike: Accelerating into the Unimaginable Future (1997) and Ray Hammond's The World in 2030 (2007). Others have argued vigorously against the possibility of a Vingean Singularity; still others suggest that our present internet- and cellphone-linked, data-threaded, information-dense existence is itself beyond prediction by past versions of our own culture – that, in other words, some version of the Singularity has already happened.
If post-Singularity intelligence is regarded as incomprehensible by definition, its direct representation may be avoided by various storytelling strategies. One is to show the effect on animals, as with the cat and assorted rodents that emerge from intellectual Arrested Development in advance of human characters in James White's "The Conspirators" (June 1954 New Worlds), or the Uplifted and Computer-interfaced chimpanzee of Vernor Vinge's "Bookworm, Run!" (March 1966 Analog). A similar role is played by the mentally subnormal in Poul Anderson's Brain Wave (1954) and Daniel Keyes's Flowers for Algernon (April 1959 F&SF; exp 1966), and by people immune to the biological transformation in Greg Bear's already-cited Blood Music. Similarly, the Singularity events of Charles Stross's Accelerando (fixup 2005) – including the remaking of the Solar System as a Matrioshka Brain (see Dyson Sphere) – are witnessed from outside by characters who despite fluidities of Upload and Reincarnation retain their essential humanity. The same author's Singularity Sky (2003) places its AI Singularity and subsequent human space-diaspora well before the story action. Vernor Vinge's Marooned in Realtime (1986) uses Stasis-Field suspension to skip over the Time Abyss during which, it is implied, the human Singularity took place and vanished into Transcendence.
The Stross title Accelerando conveys the expected dizzying pre-Singularity sense that information technology is beginning to speed out of control, as anticipated in the future-shock theme of John Brunner's The Shockwave Rider (1975). To those experiencing it, this may seem highly undesirable. Vinge's paper includes a section headed "Can the Singularity be Avoided?"; the galactic society of Frank Herbert's Dune (fixup 1965) has banned AI following the back-story's "Butlerian Jihad" – alluding to Samuel Butler's remarkable prophecy of Machine ascendancy in Erewhon (1872) – and Herbert's Jorj McKie/Consentiency sequence amusingly posits an official Bureau of Sabotage created to oppose the accelerating tendency of computerized bureaucracy. The stress of approaching Singularity is felt in various sf works which (as a further strategy for avoiding the indescribable) do not proceed to the actual takeoff point: examples include Warwick Collins's Computer World (1993), Lawrence Goldstone's Off-Line (1998), David Marusek's Heads sequence opening with Counting Heads (2005), and Sue Lange's We, Robots (2007 chap).
A useful approach for authors of post-Singularity stories is to include one or more atypical (in the Posthuman context) central characters with whom today's readers can empathize, like the Far-Future Avatar of Ada Byron, Countess of Lovelace (1815-1852) in Ada (1994) by Masaki Yamada, or the gestalt of five teenagers in Singularity's Ring (fixup 2008) by Paul Melko. Fiction and nonfiction by several of the authors mentioned here, including Vinge's seminal essay, have been assembled as Digital Rapture: The Singularity Anthology (anth 2012) edited by James Patrick Kelly and John Kessel. [DRL]
see also: Continuum: Roleplaying in the Yet; Omega Point.
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