which information doubled was getting faster and faster. In modern times, exponential knowledge progressions therefore change at an ever-increasing rate. Depending on the progression, this tends to lead toward explosive growth at some point. A simple exponential curve that represents this accelerating change phenomenon could be modeled by a doubling function. This fast rate of knowledge doubling leads up to the basic proposed hypothesis of the technological singularity: the rate at which technology progression surpasses human biological evolution. Criticisms Both Theodore Modis and Jonathan Huebner have argued—each from different perspectives—that the rate of technological innovation has not only ceased to rise, but is actually now declining. Gallery Kurzweil created the following graphs to illustrate his beliefs concerning and his justification for his Law of Accelerating Returns. See also Notes References TechCast Article Series, Al Leedahl, Accelerating Change History & Mathematics: Historical Dynamics and Development of Complex Societies. Edited by Peter Turchin, Leonid Grinin, Andrey Korotayev, and Victor C. de Munck. Moscow: KomKniga, 2006. Kurzweil, Ray (2001), Essay: The Law of Accelerating Returns . Further reading Link, Stefan J. Forging Global Fordism: Nazi Germany, Soviet Russia, and the Contest over the Industrial Order (2020) excerpt External links Accelerating Change, TechCast Article Series, Al Leedahl. Kurzweil's official site The Law of Accelerating Returns by Ray Kurzweil Is History Converging? Again? by Juergen Schmidhuber: singularity predictions as a side-effect of memory compression? Secular Cycles and Millennial Trends The Royal Mail Coach: Metaphor for a Changing World Evolution Futures studies Social change History of technology Sociological theories Technological change Linear theories