In futures studies and the history of technology, accelerating change is a perceived increase in the rate of technological (and sometimes social and cultural) progress throughout history, which may suggest faster and more profound change in the future. While many have suggested accelerating change, the popularity of this theory in modern times is closely associated with various advocates of the technological singularity, such as Vernor Vinge and Ray Kurzweil.
Early theories 
In 1938, Buckminster Fuller introduced the word ephemeralization to describe the trends of "doing more with less" in chemistry, health and other areas of industrial development. In 1946, Fuller published a chart of the discoveries of the chemical elements over time to highlight the development of accelerating acceleration in human knowledge acquisition.
One conversation centered on the ever accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue.
In his book "Mindsteps to the Cosmos" (HarperCollins, August 1983), Gerald S. Hawkins elucidated his notion of 'mindsteps', dramatic and irreversible changes to paradigms or world views. He identified five distinct mindsteps in human history, and the technology that accompanied these "new world views": the invention of imagery, writing, mathematics, printing, the telescope, rocket, radio, TV, computer... "Each one takes the collective mind closer to reality, one stage further along in its understanding of the relation of humans to the cosmos." He noted: "The waiting period between the mindsteps is getting shorter. One can't help noticing the acceleration." Hawkins' empirical 'mindstep equation' quantified this, and gave dates for future mindsteps. The date of the next mindstep (5; the series begins at 0) is given as 2021, with two more successively closer mindsteps, until the limit of the series in 2053. His speculations ventured beyond the technological:
The mindsteps... appear to have certain things in common - a new and unfolding human perspective, related inventions in the area of memes and communications, and a long formulative waiting period before the next mindstep comes along. None of the mindsteps can be said to have been truly anticipated, and most were resisted at the early stages. In looking to the future we may equally be caught unawares. We may have to grapple with the presently inconceivable, with mind-stretching discoveries and concepts.
Since the late 1970s, others like Alvin Toffler (author of Future Shock), Daniel Bell and John Naisbitt have approached theories of postindustrial societies. They argue the industrial era is coming to an end, and services and information are supplanting industry and goods. Some more extreme visions of the postindustrial society, especially in fiction, envision the elimination of economic scarcity.
Many sociologists and anthropologists have created social theories dealing with social and cultural evolution. Some, like Lewis H. Morgan, Leslie White, and Gerhard Lenski, declare technological progress to be the primary factor driving the development of human civilization.
Morgan's concept of three major stages of social evolution (savagery, barbarism, and civilization) can be divided by technological milestones, like fire, the bow, and pottery in the savage era, domestication of animals, agriculture, and metalworking in the barbarian era and the alphabet and writing in the civilization era.
Instead of specific inventions, White decided that the measure by which to judge the evolution of culture was energy. For White, "the primary function of culture" is to "harness and control energy." White distinguishes five stages of human development: In the first, people use energy of their own muscles. In the second, they use energy of domesticated animals. In the third, they use the energy of plants. In the fourth, they learn to use the energy of natural resources: coal, oil, gas. In the fifth, they harness nuclear energy.
White introduced a formula P=ET, where E is a measure of energy consumed, and T is the measure of efficiency of technical factors utilizing the energy. In his own words, "culture evolves as the amount of energy harnessed per capita per year is increased, or as the efficiency of the instrumental means of putting the energy to work is increased." The Russian astronomer Nikolai Kardashev extrapolated this theory to create the Kardashev scale, which categorizes the energy use of advanced civilizations. A Dyson sphere is Type II on this scale, and humanity is currently at about 0.72.
Lenski takes a more modern approach and focuses on information. The more information and knowledge (especially allowing the shaping of natural environment) a given society has, the more advanced it is. He identifies four stages of human development, based on advances in the history of communication. In the first stage, information is passed by genes. In the second, when humans gain intelligence, they can learn and pass information by experience. In the third, the humans start using signs and develop logic. In the fourth, they can create symbols, develop language and writing. Advancements in the technology of communication translates into advancements in the economic system and political system, distribution of goods, social inequality and other spheres of social life. He also differentiates societies based on their level of technology, communication and economy: (1) hunters and gatherers, (2) simple agricultural, (3) advanced agricultural, (4) industrial (5) special (like fishing societies).
Vinge's exponentially accelerating change 
The mathematician Vernor Vinge popularized his ideas about exponentially accelerating technological change in the SF novel Marooned in Realtime (1986), set in a world of rapidly accelerating progress leading to the emergence of more and more sophisticated technologies separated by shorter and shorter time intervals, until a point beyond human comprehension is reached. His subsequent Hugo award-winning novel A Fire Upon the Deep (1992) starts with an imaginative description of the evolution of a superintelligence passing through exponentially accelerating developmental stages ending in a transcendent, almost omnipotent power unfathomable by mere humans. His already mentioned influential 1993 paper on the technological singularity compactly summarizes the basic ideas.
Moravec's Mind Children 
In his 1988 book Mind Children, computer scientist and futurist Hans Moravec generalizes Moore's law to make predictions about the future of artificial life. Moore's law describes an exponential growth pattern in the complexity of integrated semiconductor circuits. Moravec extends this to include technologies from long before the integrated circuit to future forms of technology. Moravec outlines a timeline and a scenario in which robots will evolve into a new series of artificial species, starting around 2030-2040. In Robot: Mere Machine to Transcendent Mind, published in 1998, Moravec further considers the implications of evolving robot intelligence, generalizing Moore's law to technologies predating the integrated circuit, and also plotting the exponentially increasing computational power of the brains of animals in evolutionary history. Extrapolating these trends, he speculates about a coming "mind fire" of rapidly expanding superintelligence similar to the explosion of intelligence predicted by Vinge.
Kurzweil's The Law of Accelerating Returns 
In his 1999 book The Age of Spiritual Machines Kurzweil proposed "The Law of Accelerating Returns", according to which the rate of change in a wide variety of evolutionary systems (including but not limited to the growth of technologies) tends to increase exponentially. He gave further focus to this issue in a 2001 essay entitled "The Law of Accelerating Returns" which argued for extending Moore's Law to describe exponential growth of diverse forms of technological progress. Whenever a technology approaches some kind of a barrier, according to Kurzweil, a new technology will be invented to allow us to cross that barrier. He cites numerous past examples of this to substantiate his assertions. He predicts that such paradigm shifts have and will continue to become increasingly common, leading to "technological change so rapid and profound it represents a rupture in the fabric of human history." He believes the Law of Accelerating Returns implies that a technological singularity will occur before the end of the 21st century, around 2045. The essay begins:
An analysis of the history of technology shows that technological change is exponential, contrary to the common-sense 'intuitive linear' view. So we won't experience 100 years of progress in the 21st century—it will be more like 20,000 years of progress (at today's rate). The 'returns,' such as chip speed and cost-effectiveness, also increase exponentially. There's even exponential growth in the rate of exponential growth. Within a few decades, machine intelligence will surpass human intelligence, leading to the Singularity—technological change so rapid and profound it represents a rupture in the fabric of human history. The implications include the merger of biological and nonbiological intelligence, immortal software-based humans, and ultra-high levels of intelligence that expand outward in the universe at the speed of light.
The Law of Accelerating Returns has in many ways altered public perception of Moore's law. It is a common (but mistaken) belief that Moore's law makes predictions regarding all forms of technology, when really it only concerns semiconductor circuits. Many futurists[who?] still use the term "Moore's law" to describe ideas like those put forth by Kurzweil and others.
According to Kurzweil, since the beginning of evolution, more complex life forms have been evolving exponentially faster, with shorter and shorter intervals between the emergence of radically new life forms, such as human beings, who have the capacity to engineer (intentionally to design with efficiency) a new trait which replaces relatively blind evolutionary mechanisms of selection for efficiency. By extension, the rate of technical progress amongst humans has also been exponentially increasing, as we discover more effective ways to do things, we also discover more effective ways to learn, i.e. language, numbers, written language, philosophy, scientific method, instruments of observation, tallying devices, mechanical calculators, computers, each of these major advances in our ability to account for information occur increasingly close together. Already within the past sixty years, life in the industrialized world has changed almost beyond recognition except for living memories from the first half of the 20th century. This pattern will culminate in unimaginable technological progress in the 21st century, leading to a singularity. Kurzweil elaborates on his views in his books The Age of Spiritual Machines and The Singularity Is Near.
Some claim the exponential growth of technological progress may become linear or inflected or may begin to flatten into a limited-growth curve. In this model, instead of an overall acceleration of progress, technological advance jumps forward whenever there is a human "buy in" and stalls whenever there is no benefit large enough to profit the technologists. As a result, the sequence of changes never gets steep enough to become a singularity.
Examples of large human "buy-ins" into technology include the computer revolution, as well as massive government projects like the Manhattan Project and the Human Genome Project. The foundation organizing the Methuselah Mouse Prize believes aging research could be the subject of such a massive project if substantial progress is made in slowing or reversing cellular aging in mice.
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. The validity of their conclusions has been criticized by John Smart.
Choosing technological "milestones", defining the meaning of technological "growth", and similar semantic exercises often include significant subjectivity, and are therefore easily criticized. For example, it can be claimed that inventions are generally created by a fixed population of human inventors at a constant rate, regardless of their current technological prowess, and therefore technological "progress" is actually a function of population growth, not past inventions.
The preceding argument that technological 'progress' is a function of population growth however, does not make sense. It does not take into account that even with a relatively fixed number of inventors/engineers producing technology at a constant rate, that each new technology allows the next 'technological jump' to be exponentially larger than the previous one. For example, if technology were to advance at a rate of 1 unit per year (linear), but each unit was e^x larger than the previous unit, technology would be advancing at an exponential rate.
In fact, "technological singularity" is just one of a few singularities detected through the analysis of a number of characteristics of the World System development, for example, with respect to the world population, world GDP, and some other economic indices. It has been shown that the hyperbolic pattern of the world demographic, economic, cultural, urbanistic, and technological growth (observed for many centuries, if not millennia prior to the 1970s) could be accounted for by a rather simple mechanism, the nonlinear second order positive feedback, that was shown long ago to generate precisely the hyperbolic growth, known also as the "blow-up regime" (implying just finite-time singularities). In our case this nonlinear second order positive feedback looks as follows: more people – more potential inventors – faster technological growth – the carrying capacity of the Earth grows faster – faster population growth – more people – more potential inventors – faster technological growth, and so on. On the other hand, this research has shown that since the 1970s the World System does not develop hyperbolically any more, its development diverges more and more from the blow-up regime, and at present it is moving "from singularity", rather than "toward singularity".
Juergen Schmidhuber calls the Singularity Omega, referring to Teilhard de Chardin's Omega Point (1916). For Omega = 2040, he says the series Omega - 2n human lifetimes (n < 10; one lifetime = 80 years) roughly matches the most important events in human history.
Kurzweil created the following graphs to illustrate his beliefs concerning and his justification for his Law of Accelerating Returns.
Exponential growth in supercomputer power
See also 
- R. Buckminster Fuller, Nine Chains to the Moon, Southern Illinois University Press  1963 pp. 276–79.
- R. Buckminster Fuller, Synergetics (Fuller), http://www.rwgrayprojects.com/synergetics/s04/figs/f1903.html
- Moravec, Hans (1998). "When will computer hardware match the human brain?". Journal of Evolution and Technology 1. Archived from the original on 15 June 2006. Retrieved 2006-06-23.
- Moravec, Hans (June 1993). "The Age of Robots". Archived from the original on 15 June 2006. Retrieved 2006-06-23.
- Moravec, Hans (April 2004). "Robot Predictions Evolution". Archived from the original on 16 June 2006. Retrieved 2006-06-23.
- Ray Kurzweil, The Age of Spiritual Machines, Viking, 1999, p. 30 and p. 32
- The Law of Accelerating Returns. Ray Kurzweil, March 7, 2001.
- e.g., Johansen, A., and D. Sornette. 2001. Finite-time Singularity in the Dynamics of the World Population and Economic Indices. Physica A 294(3–4): 465–502
- e.g., Korotayev A., Malkov A., Khaltourina D. Introduction to Social Macrodynamics: Secular Cycles and Millennial Trends. Moscow: URSS, 2006; Andrey Korotayev. The World System urbanization dynamics. 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. ISBN 5-484-01002-0. P. 44-62
- Korotayev A., Malkov A., Khaltourina D. Introduction to Social Macrodynamics: Secular Cycles and Millennial Trends. Moscow: URSS, 2006.
- 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. ISBN 5-484-01002-0
- Kurzweil, Ray (2001, Essay: The Law of Accelerating Returns
- Heylighen, Francis (2007). "Accelerating Socio-Technological Evolution: from ephemeralization and stigmergy to the global brain". In Modelski, G.; Devezas, T.; Thompson, W. Globalization as an Evolutionary Process: Modeling Global Change. London: Routledge. ISBN 978-0-415-77361-4
- TechCast Article Series, Al Leedahl, Accelerating Change
- 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