The 3 schools of the Singularity

In 1965, statistician I.J. Good described a concept similar to today's meaning of the singularity, in “Speculations Concerning the First Ultraintelligent Machine”:      Text from The Singularity Summit - 2006

Let an ultraintelligent machine be defined as a machine that can far surpass all the intellectual activities of any man however clever. Since the design of machines is one of these intellectual activities, an ultraintelligent machine could design even better machines; there would then unquestionably be an 'intelligence explosion,' and the intelligence of man would be left far behind. 

Intelligence Explosion - The first ultraintelligent machine is the last invention that man need ever make.

The concept was solidified by mathematician and computer scientist Vernor Vinge, who wrote about a rapidly approaching “technological singularity” in an article for Omni magazine in 1983 and in a science fiction novel, Marooned in Realtime, in 1986. Seven years later, Vinge presented a paper, "The Coming Technological Singularity," at a NASA-organized symposium. Vinge wrote:

What are the consequences of this event? When greater-than-human intelligence drives progress, that progress will be much more rapid. In fact, there seems no reason why progress itself would not involve the creation of still more intelligent entities – on a still-shorter time scale. The best analogy I see is to the evolutionary past: Animals can adapt to problems and make inventions, but often no faster than natural selection can do its work – the world acts as its own simulator in the case of natural selection. We humans have the ability to internalize the world and conduct what-if's in our heads; we can solve many problems thousands of times faster than natural selection could. Now, by creating the means to execute those simulations at much higher speeds, we are entering a regime as radically different from our human past as we humans are from the lower animals. From the human point of view, this change will be a throwing away of all the previous rules, perhaps in the blink of an eye.

 Event Horizon - The Singularity is an exponential runaway beyond any hope of control.

Most recently, in 2005, inventor and futurist Ray Kurzweil released The Singularity Is Near, where he presented the singularity as an overall exponential trend in technological development:  Read NY Times article

What, then, is the singularity? It's a future period during which the pace of technological change will be so rapid, its impact so deep, that human life will be irreversibly transformed. Although neither utopian or dystopian, this epoch will transform the concepts that we rely on to give meaning to our lives, from our business models to the cycle of human life, including death itself. Understanding the singularity will alter our perspective on the significance of our past and the ramifications for our future. 

Accelerating Change - To truly understand the Singularity inherently changes one's view of life in general and one's own particular life.

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