The only way of discovering the limits of the possible is to venture a little way past them into the impossible (Arthur C. Clarke's 2nd law)

Friday, 29 January 2016

The Technological Singularity: A Definition

Synopsis: Careful expositions of a technological singularity anticipated by the mid-21st century can be uniquely described using three common characteristics: superintelligence, acceleration, and discontinuity.
First draft, with excerpts from: A.H. Eden, "The Singularity Controversy, Part I: Lessons Learned and Open Questions". Technical Report STR 2016-1, Sapience Project, January 2016, DOI 10.13140 arXiv:1601.05977

Many philosophers have portrayed the cosmic process as an ascending curve of positivity towards some maximal point or an ideal limit point (an omega point) at infinity, often at the vertical asymptote of an accelerating trajectory or the point at which the slope of an accelerating curve passes beyond unity, such as Henry Adams (The Law of Acceleration 1904; The Rule of Phase 1909) and Teilhard de Chardin (The Phenomenon of Man 1955).

The term 'technological singularity' in its contemporary senses traces back to John von Neumann, popularized by Vernor Vinge and Ray Kurzweil (The Singularity is Near 2005), and elaborated by Eliezer Yudkowsky, Robin Henson, and David Chalmers (The Singularity: A Philosophical Analysis 2010). But the various accounts of the term vary considerably, covering conflicting sense. This incoherence has raised doubt whether the term is meaningful, let alone subject of scientific analysis.

In 2013, several essays defining hypotheses of technological singularity were published the volume Singularity Hypotheses: A Scientific and Philosophical Analysis (Springer). A definition of the term singularity was offered in the introductory chapter, Singularity Hypotheses: An Overview, and further elaborated in 2016 (The Singularity Controversy, Part I: Lessons Learned).

Analysis conducted since 2007 has led us to conclude that all careful expositions of a technological singularity anticipated by the mid-21st century can be uniquely described using three common characteristics: superintelligence, acceleration, and discontinuity.


Superintelligence, at least as it is measured by traditional IQ tests (such as Wechsler and Stanford-Binet), becoming meaningless for capturing the intellectual capabilities of minds that are orders of magnitude more intelligent than us. Alternatively, we may say a graph measuring average intelligence beyond the singularity in terms of IQ score may display some form of radical discontinuity if superintelligence emerges. This remains true whether a particular account describes artificial superintelligence or a posthuman one. For example, it is commonly argued that the arrival of human-level AI may soon be followed by artificial superintelligence. And accounts of a singularity from human amplification describe superhuman cognitive capabilities, including unbounded memory and accelerating recall times, and the eradication of common obstructions to intelligent behaviour such as limited resources, disease and age.


The discontinuity in accounts of the singularity take the term to stand for a turning-point in human history, as in Von Neumann’s canonical definition (“some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue.”) Whether it is taken to last a few hours (e.g. a ‘hard takeoff’ or ‘FOOM’ scenarios) or a period spread over decades (e.g., ‘wave’), the singularity term appears to originate not from mathematical singularities but from the discontinuities of gravitational singularities — better known as black holes. Seen as a central metaphor, a gravitational singularity is a (theoretical) point at the centre of black holes at which quantities that are otherwise meaningful (e.g., density and space-time curvature) become infinite, or rather meaningless. This metaphor is useful to express the idea that superintelligence stands for that level of intelligence in which traditional measures become ineffective or meaningless.

Discontinuity is best explained using the event horizon surrounding gravitational singularities: we cannot understand or foresee the events that may follow a singularity in the way we cannot peek into black holes before crossing the event horizon : a boundary in space-time (marked by the Schwarzschild radius around the gravitational singularity) beyond which events inside this area cannot be observed from outside, and a horizon beyond which gravitational pull becomes so strong that nothing can escape, even light (hence “black”) — a point of no return. The emergence of superintelligence marks a similar point, an event horizon, because even “a tiny increment in problem-solving ability and group coordination is why we left the other apes in the dust” (Sandberg 2014): a discontinuity in our ontological and epistemological account of our existence.


Acceleration refers to a rate of growth in some quantity such as intelligence, computations per second per fixed dollar, economic measures of growth rate, total output of goods and services, and energy rate density . Other accounts of acceleration describe quantitative measures of physical, biological, social, cultural, and technological processes of evolution: milestones or paradigm shifts whose timing demonstrates an accelerating pace of change. For example, Carl Sagan’s Cosmic Calendar names milestones in biological evolution such as the emergence of eukaryotes, vertebrates, amphibians, mammals, primates, hominidae, and Homo sapiens , which show an accelerating trend. Some authors attempt to unify the acceleration in these quantities under one law of nature: quantitatively or qualitatively measured, acceleration is commonly visualized as an upwards-curved mathematical graph which, if projected into the future, is said to be leading to a discontinuity (see above).

To be completed

For a longer historical overview term see: Singularity Hypotheses: An Overview

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Amnon H. Eden
Sapience Project